TO · 2.6 - Factors Effecting Resolution and Definition of the Display-Image 33 2.7 - Effects of...

$Page 1: TO · 2.6 - Factors Effecting Resolution and Definition of the Display-Image 33 2.7 - Effects of Diffraction on the Display-Image 49 Chapter 3 The Point Source of Light b6 3.1 - Introduction$
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UNCLASIFII

TECHNICAL REPORT: NAVTRADEVCEN 1628-1

STUDY OF

POINT LIGHT SOURCE

NON PROJECTION SYSTEM COMPONENTS

AS T IA

MAY 5 1960

~ k U.S. NAVAL TRAINING DEVICE CENTER

PORT WASHINGTON, L.I., NEW YORK

Technical Report: NAVTRADEXVCEN 1628-1

STUDY OF

POINT LIGHT SOURCE PROJECTION SYSTEM COMPONENTS

Prepared byThe deFlorez Company, Inc.Englewood Cliffs New Jersey

Contract Nonr 1628(00)

DistributionsSpecial Distribution List

Approved by:

Edw. C. Callahan, Captain, UBNCommanding Officer and Director

U. S. NAVAL TRAINING DEVICE CENTER

PORT WASHTNGTONI NEW YORK

MARCH 1959

NAV''AL);VCEN W128-1

Abtract

'"his report describer; the results of a study to ovaluatethc characteristics of existing point light source projection syatemcomponents and to develop new components with improved attributes.The components studied are the basic ones involved, namely, thepoint source of light, the display-object and the screen. Variationsin syztern parameters were studied intensively to determine theirinter-relationships and their effects on the qualities of the visualdisplays obtained. Valuwe of system parameters which achieve optimumvisual display qualities were then related to the basic components of thesysten to establish desirable attributes of these components.

This investigation has advanced the state of the art signif-icantly. The study developed that desirable characteristics of a pointlight source are a minimum diameter with adequate inten.sity, a widehorizontal angle o- light output and a minimum envelope enclosing thesource. A point source of light has been developed with a diameterof. 0035 inches, an intensity of 18 candles, a coverage angle in excessof 2200 and an envelope .072 inches from the source. This is veryclose to the theoretical optimum for available lamps. The display-object,which may be Lransparent or reflective, must be made from a strong,durable material with a high degree of optical clarity and must be decor-ated to provide realistic content together wIlh sharpness of detail. Thebest available display-object materials have been determined and display-object decoration techniques have been advanced to permit employment ofscale ratios in excess of 2000:1 with satisfactory realism. However,great potential for improvement in point source visual displays lies inthe area of display-object decoration. Reflectivity and shaoe are theimportant screen factors. A survey of available screen materialsrevealed that although lenticular screens offer the greatest reflectivity,glass beaded screens are most practicable when complex curved screensare employed. A screen shape which combines a cylindrical surfaceabove the observer's eye level with a segment of a torus shaped surfacebelow eye level was found to minimize the rate of change of positiondistortion (velocity distortion).

E

NAVTADEVCEN 1628-2

FOREWORD

This report (NAVTRADEVCEN 1628-1) is the first in a series designedto indicate the usefulness of the point-light source in presentingthe visual displays required for various training devices. Thisreport presents the current state of the art of point light sourceprojection techniques and indicates areas where further developmentwould contribute most to the usefulness of this technique in train-ing devices. This report describes the major components of thepoint light source projection system and discusses the parametersinvolved in selecting these components. Technical considerationsin the design of devices using point light source teckmiques arediscussed. Derivation of important relationships as well as otheruseful technical information are furnished in appendices.

The series of reports consists ofs

(1) NAVTADEVCEN 1628-I Study of Point Light Source ProjectionSystem Components

(2) NAVTRADEVCEN 1628-2 Utilization of Point Light Source Tech-niques in a "Break-out" Landing Attach-ment to a Twin-Engine Instrument Trainer

. (3) NAVTRADEVCZN 1628-3 The Application of Point Sou.rce Projec-tion Techniques to Helicopter LowAltitude Navigation Training

(.) NAV'J9D'VCZH 1628-4e The Application of Point Source Proj ec-tion Techniques to Low Altitude HighSpeed Navigation Training

(5) HAVTRADEVCZN 1628-5 Methods of Pr.esentinf Moving Objects inPoint-Light Source Visual Displays

(6) NAVTRADEVCEN 1628-6 The Application of Point Source Projec-tion Techniques to Air-to-Air GunneryTraining

(7) NAVTRADEVCEN 1628-7 The Application of Point Source Projec-tion Techniques to Air-to-Surface AttackTraining

(8) NAVTRADEVCEN 1628-8 The Application of Point Source Projec-tion Techniques to Air-to-Surface Obser-vation Training

iii

NAVTRADEVCEN 1628-1

(9) NAVTi1AD!,VCE 1628-9 The Application of Point Source Projec-tion Techniques to Surface Vessel Opera-tion Training

(10) NAVTADVCEI 1628-10 The Application of Point Source Projec-tion Techniques to Ground OperationTraining

(11) 1AVTRADEVCEM 1628-11 Evaluation of Expetiental Light Sourcesand Transparencies for the HelicopterHovering Filght Simiulation Device 2-FH-2

Each of the reports, NAVTRADO'CEN 1628-2 through 1628-10, discussesthe applicability o1 the point light source systew tu a specifictraining problem. Insofar as the point light technique is applicableto that problem, a typical disign for a suitable trainer is presentedand evaluated, The last report of the series (NAVTRADEVCEN 1628-11)compares two light sources and two transparencies as used on aspecific training device. TA. relative mcrits of these componentsare discussed and the importance of various paraetera to this train-ing task are evaluated.

Research, experimantal work and preparation of the reports werecarried out by Edwin K. SuLth, Frank J. Anastaslo, Sigmund Haran,BerdJ C. Kalustyan, Roy B. Sn yder and C. Philip Strakosch for thedeFlorez Company.

r nard We lash, Proje~t Engineer

(Jol~ H. Achilich HeadAir Applications BranchU. S. Naval Training Device Center

iv

NAVl RAl'&)EVCIN 1 %H-1

TABLE OF CONTENTS

Page

Abstract ii

Lh;t of Plu"-trahunwi viii

Liut of Symbols and Mathematical Sign Conventions xvi

Chapter 1 - hitroduction to the Point Light SourceProjection System and Its Components 1

1. 1 - Introduction I1.2 - The Point Source Projection System 11.3 - Basic Components 41.4 - History 51. 5 - Advantages of the Point Source

Projection Technique 61.6 - Limitations of the Point Source

Projection Technique 7

Chapter 2 - The Principles of Point Source ProjectionTechniquies 9

2. 1 - The Point Source Projection Principle 92.2 - Arrangement of Components 92.3 - Determination of Scale Ratios 132.4 - Distortions Due to Displacement Between

the Eye and the Point Source 162.5 - Distortion Due to Screen Curvature,

Rear Projection System 312.6 - Factors Effecting Resolution and

Definition of the Display-Image 332.7 - Effects of Diffraction on the Display-Image 49

Chapter 3 The Point Source of Light b6

3.1 - Introduction 563.2 - Requirements of the Point Source of Light 563.3 - Types of Point Source Lamps 583.4 - Reduction of Source Diameter by

Optical Means 683.5 - Other Approaches to Obtain a Small

Source Diameter 72

v

NAV'I.1R.ADIWVC I,,N tlJ

C'1pt~ I Tlwi DIN"~PI,"ty 07I)Jk-.t

4. 1 it 82 ,, iHP4. 8 -iqui 'rrnoto for na ''atlofan.Lory

1'r I:f~rfLI Dhphly-Objrw't4. :3 -p,; of '1raiuwp;Lro :io4,. 4 M v:iii':ut. iriwj Tu oliilkjIo;; 141

4. G - utla lWfucts4. '7 -Aerial Pliotocjraph, i uus 'I'rarv:pa ronri

Dlop ly -oc L u 1004. 8 R Peflective Dloplay-Objuct 103

CkitpLor 15 T Ihu Sc reeri 100

U. In L xLoduc'!ttll 108b. 2 - Sorutni 13ightri'., 10715.3 - T1YPe), of scroor, Surfaces lc)'/b. 4 - Fatbrlcatlon of a Gla:;s [3uaded Scree-n

for Point Source Proji.-Aion 2Q

Chapte r 63 - Sy,.itomrn- Design 120

Gloosary 123

Appendix I - StudIkij of the Distortion,. of the Display-Imago 128oil Ba~Lc Screen Shapes Re.ultlng from Dis-placerni.tit of the Eye from the Point Source

I-1 - Pojition Diktortlon on a Flat VerticalSc reen I2

1-2 - Po.;Ition Dotortion on a Flat HorizontalSc reeri 131

1-3 - Posittn Distortion on a Ciroular k"Wroonwith Ceniter at the Point, sIource 133

1-4 - )Iizu Dhotortion onl All Soreen Shape.; 1371-5 - Powition Dljtortiori on a Ci rcular' 8 creori

with Its; Ceriter at Ulu Eye of Ob.;orv(!rlhoIrg R'ear J(creer Projec (tion Sy:;1'rri 3

NAV'1ikAD WC1:~ 'u

) ~A4)J)fl(ix IT Do.2r~Ivr:L~h I 'Ro ' lijli fEdli:HLi )I

Rl-I - Dor'ivation of un 0,'xprciumL1 fl' * ht tiO~f thu )h(i'y-ria WiVdtii i)Ij tu ULho [I:,(or an Extridud otI -(!t) o than a1(Thorriotric Point :')ur-o 13

11-2 -Io rivaLtlor of a.r ~pnin for tho Qualityof Rosclution vnid Dofinl Lion a:; AfforLcd b)yM-ajnfix!atlon ;uitd thit 2uurzo Lo Dkinpbn.y-Objct Lirio WVidli li,tlio

113 -3 Derivation or an Isxpru.;on for Di:ApLay-Iznagu Quality wan Affuo(tid by i 4,Xt0[id~dSourco Sizu and by Di.ntanuo from fSour'cuto 0 !.,play -0 bj ut 1.18

Appondix MI - Interaotiozi of Dlffraotion and lixtoridud Lor~mIEffeots a,3 Di-splay-Objou-t Lino Width arid ItoDistarico from tho Exturidod Souroo, vary b

Appendix IV - Tabulation of Point Sourcu Larnpoi 155

Appendix V - Negative Meniscus Lenson 1 9A

V-1. - Introdurotion Ub9V-2 - The Aplanatic Noqative Meniscus Lens 1630V-3 - Other Lens with a Large Angle of Light

Output 13 bV-4 - Design Considerations 199

Appendix VI - Tabulation of Plastic Materials 203

Appendix VII- Tabulations of Inks, Dyes and Lr,'quprs 207

vil

.LIST OF ILLUSiRATIONS

Page

Frontispiece - An Artist's Concept of a Typical

Point Source Projection System.

Figure 1 - 1 - Observer's View of Display-Inage. 2

Figure 1 - 2 - View of a Projection System. 3

Figure 2 - 1 - Schematic Showing Effects of Size, Distanceand Orientation of Objects in Space on theAngle Subtended at tha Eye of an Observer. 10

Figure 2 - 2 - Schematic Showirg Effects of Display-ObjectSize, Orientation and Distance Relative to aPoint Source on Display-Image and on AngleSubtended at the Point Source. 11

Figure 2 - 3 Schematics of Component Arrangements ofPoint Source Projection Systems. 12

Figure 2 - 4 - Schematic Diagrams of Point Source Pro-jection Systems using Transparent andReflective Display-Objects. 14

Figure 2 - 5 - Determination of Scale Ratio, P, and ofTheoretical Magnification, M, fromCondiions to be Simulated. 15

Figure 2 - 6 Position Distortion, I , on Basic ScreenShapes at V.ewlng Angle, 6, for SelectedSystem Parameters. 18

Figure 2 - 7 - Rate of Change of Position Distortion,dj/d6, with Viewing Angle, 6, for ThreeBasic Screen Types and for SelectedSystem Parameters. 20

Figure 2 - 8 - Position Distortion,q , on a Flat VerticalScreen at Viewing Angle, 6 , for SelectedSystem Parameters. 22

vill

NAVTRADEVCEN 1628 - I

PageFigure 2 - 9 - Position Distortion, Y1 , on a

Horizontal Screen at Viewing Angle, 6,for Selected System Parameters. 23

Figure 2 - 10 - Position Distortion, T) , on a CircularScreen at Viewing Angle, 6 , for SelectedSystem Parameters. 24

F igure 2 - 11 - Rate of Change of Position Distortion,d)/d6, on a Fiat Vertical Screen atViewing Angle, 6,for Selected SystemParameters. 25

Figure 2 - 12 - Rate of Change of Position Distortion,dn/d 6, on a Horizontal Screen atViewing Angle, 6 , for Selected SystemParameters. 26

Figure 2 - 13 - Rate of Change of Position Distortion,dT)/d6, on a Circular Screen at ViewingAngle, 6, for Selected System Parameters. 27

Figure 2 - 14 - Sizq Distortion, A, , of a 100 Oblect( A 0 - 100) with Vie-vtng Angle, p0, onThree Basic Screen Shapes with SeLectedSystem Parameters. 29

Figure 2 - 15 - Size Distortion,&AI, of a 100 Object(A - 1oo). 30

Figure 2 - 16 - Rate of Change of qIze Distortion, d&i/d 6,of a 00, Object (a - 100) with ViewingAngle, 6 , on Three Basic Screen Shapeswith Selected System Parameters. 32

Figure 2 - 17 - Position Distortion - Rear Screen Projection,Curved Screen. 34

Figure 2 - 18 - Schematic Showing Effect of Different SourceDiameters S and S1, on Display-ImageQuaUty. 38

ix

,NAVTRALEVCEN l62 - I

P'ageFigure 2 - )19 - Schematic Showing Effnct of Reducing

Display-Object Line Width, J, on theUmbra, U, of the I)Dip.ay-rmage, D. 37

Figure , - 20 Enlargement, P', of DLplay-Image Widthwith Magnification, M, due to Use of anExtende Source, S, (1 I > 0) Pither than aGeometric Point Source, S', (Pl = 0). 38

Figure 2 - 21 Quality of Resolution and Definition, P", auAffected by Magnification, M, and by SourceSize to Display-Object Line Width Ratio , P1. 40

Figure 2 - 22 Subjective Evaluations of Display-ImagesProduced by Projecting a Hand DecoratedDisplay-Object With a 25 Watt Hafnium Lamp. 41

Figure 2 - 23 Subjective Evaluations of Display-ImagesProduced by Projecting a PhotographicDisplay-Object with a 25 Watt Hafnium Lamp. 42

Figure 2 - 24 - Subjective Evaluations of Display-ImagesProduced by Projecting a Hand DecoratedDisplay-Object with a 2 Watt ZirconiumLamp. 43

Figure 2 - 25 - Subjective Evaluations of Display-ImagesProduced by Projecting a PhotographicDisplay-Object with a 2 Watt ZirconiumLamp. 44

Figure 2 - 20 - Schematic Showing Effect of Source toDisnlay-Ohect Distance on Display-

.e Q4"Lty. 47

Figure 2 - 2 !lation of Image Quality to Extended Source)iameter, S, and Source to Display-Object

!Dlstance, a, when the Viewing Distance Islairgo (greator than '12").4

X

NAV'TRADEVCEN 16,8- I

Page

Figure - 8- Schematic Diagram of DiffractionP

Pattern Formation When Opaque Lineof Finite Width 3 is Projected by aGeometric Point Source. 50

Figure 2 - 29 - Effect of Diffraction Angle, f , on Display-

inage Quality Compared with Effect ofExteUded Source Angle, m, on Display-linageQuality for Selected Display-Object LineWidths, 1. 51

Figure 2 - 30 - Effect of Source Diameter on Resolution. 54

Figure 2 - 31 - R&solution Patterns. 55

Figure 3 - 1 - Va-iations in Diameter, Luminous Intensityand Luminance with Changes in Current fora 25 Watt Hafnium Lamp. 61

Figure 3 - 2 - Light Distribution of the 25 Watt Hafnium

Lamp. 62

Figure 3 - 3 - Assorted Point Source Lamps. 65

Figure 3 - 4 - Variations in Diameter, Luminous Intensity,and Luminance with Changes in Pow.r forthe Osram HBO-109 Lamp. 66

Figure 3 - 5 - Light Distribution of e Osram HBO-109Lamp. 67

Figure 3 - 6 - The Effect of Source Diameter on LuminousIntens'Ly When Source Diameter is Reducedby OTticat ELements. 69

Figure 3 - 7 Schemtic Diagram of OpticaL Arrangement

of de F torez Point Light Source, Model III. 70

Figure 3 - 8 - de Florez Point Light Source, Model I. 73

Figure 3 - 9 - Optical Elements. 74

xt

NAVTRADEVCEN 1628 - 1

Page

Figure 3 - 10 Schematic Diagram of Optical Arrangement

for Formation of a Point Source by use ofan Acrylic rip. 78

Figure 3 - 11 Experimental Equipment for Testing LightConcentrating Powers of Acrylic Tips. 77

Figure 3 - 12 - Light Concentration by an Acrylic Tip. 78

Figure 3 - 13 - Assorted Acrylic Tips for Light Concen-tration Tests. 79

Figure 4 - 1 - Example of a Rigid Transparency. 84

Figure 4 - 2 - Illustration of a Flexible Transparency. 85

Figure 4 - 3 - Clearance Grooves in Rollers for ThreeDimensional Objects on a Transparency. 87

Figure 4 - 4 - OriginaL Layout of a Typical Area for aTransparency. 89

Figure 4 - 5 - SectionaLized OriginaL Art Work forReproduction to Another Scale Ratio. 91

Figure 4 - 6 - Layout of Guide Lines to Scale ofFinaL Transparency. 92

Figure 4 - 7 - Masking Cronaflex Original Prior toAlrbrusbing. 93

Figure 4 - 8 - Section of Airbrushed Original PositiveMade on Translucent Cronaflex. 94

Figure 4 - 9 - Dyeing Transparency by Dip DyeingTechniques.

Figure 4 - 10 - Photographic Transparemy. 96

Figure 4 - 11 - Light Losses Due to Surface Reflection fora Transparent Material with Index ofRefraction of 1. 523. 98

Figure 4 -12 - "Mountains" Made by Hand FormingFlexible Acetate. 101

xii

NAVTRADEVCEN 1828- 1

PageFigure 4 - 13 - "Mountains" Made by Vacuum Forming

Semi-Flexible W, nylite. 102

Figure 4 - 14 - Schematic Diagram Showing the DoubleImage Effect Encountered When a ThreeDimensional Object Mounted on ReflectiveDisplay-Object is Projected. 105

Figure 5 - 1 Screen Gain with Viewing Angle for aMatte Screen. 110

Figure 5 - 2 Screen Gain with Viewing Angle for aDa-Lite Glass Beaded Screen. 111

Figure 5 - 3 Screen Gain with Viewing Angle for aRadiant Diffuse Metallic Coated "Superama"Screen. 112

Figure 5 - 4 - Screen Gain with Viewing Angle for aNylco Lenticular Screen. 113

Figure 5 - 6 - Screen Gain Test Apparatus. 114

Figure 5 - 6 - Variation in Ligit Transmission with ViewingAngle for a Rear Projection Screen. 115

Figure 5 - 7 Variation in Light Ref lectivity with ViewingAngle for a -Rear Projection Screen. 116

Figure 5 - 8 - Screen Supporting Structure. 118

Figure 5 - 9 - A Typical Forming Tool for FiberglassReinforced Plastic Panels. 119

Figure I - 1 - Schematic Diagram Showing Position Dis-tortion on a Flat Vertical Screen Resultingfrom Displacement of the lye from thePoint Source. 129

Figure I - 2 Schematic Diagram ftow"ng Positlen Dis-tortion on a Flat Horizonal Semen Resultingfrom Displacement of the Zye from timPoint Bource. 132

xiii

NAVTRAI)EVCEN 168d3 - I

I 'ageFigure I - 3 - Schuematic Diagram Showirng Positlon

Distortion on Circular Screen Centered atthe Point Source Resulting from Displace-ment of the Eye from the Point Source. 134

Figure I - 4 - Schematic Diagram Showing Size Distortionon a Flat Vertical Screen Resulting fromDisplacement of the Eye from the PointSource. 138

Figure I - 6 Schematic Diagram Showing Position Dis-tortion on a Circular Screen Centered atthe Eye when Using the Rear Screen Pro-jection System. 141

Figure II - 1 - Schematic Diagram Showing Width of theImages Formed by Projection of OpaqueLine of Width, J, by Extended Source, 5,and by Geometric Point Source, S'. 144

Figure II - 2 Schematic Diagram Showing Characteristicsof the Images Formed by Projection ofOpaque Line of Width, J, by Extended Source,S, and by Geometric Point Source, S'. 146

Figure II - S - chematic Diagram Showing the Angle, o(,Subtended at a Line of Demarcation on aDisplay-Object by an Extended Source, S,and the Angle, A3 , Subtended at the Eye ofthe Observer by the Display-Image Formedby that Line and Extended Source, S. 149

Figure III - 1 - Schematic D'agram Showing the Effer'ts ofDiffraction ind of Extended Source on theDisplay-Lr,age. 153

Figure V - 1 - Ray Tracing Diagram of Aplanatic NegativeMeniscus Lens. 162

Figure V - 2 - Diagram of Image Formation by the Aplanai!-Negative Meniscus lem;. 16,8

Figure V - 3 Diagram o! Aolanatic Meniscus ln:m; Showingl~ight Input and Light Out put. 172

iv

.NAVT'RADEVCEN 10128 - 1

i'ageFigure V - 4 - Schematics of Various Optical Arrange-

ments for Reducing Source Diameter andIncreasing Angle of Coverage. 181

Figure V - 5 - Variation in Source Diameter and LuminousIntensity with Real Source to First LensDistance for Single and Double MeniscusLens Systems. 182

Figure V - 6 Effect of Source to Display-Object Distanceon RF~olution for Single and Double MeniscusLens Systems. 183

Figure V - 7 Ray Tracing Diagram of Piano-Concave Lens. 187

Figure V - 8 - Ray 'r:..cing Diagram of Non-AplanaticNegative Meniscus Lens. 14

Figure V - 9 - Design of a Non-Aplanatic NegativeMeniscus Lens. 198

Figure V - 10 - Drawing of de Florez Point Light Sarce,Model 111. 201

xv

List of Symbols and Mathematcal Sign Conventlons

List of Symbols

A - Altitude to be simulated, in feet.

A' - Minimum altitude to be simulated, in feet.

A" - Maximum altitude to be simulated, in feet.

AR - Range of altitude to be simulated, (A" -A'), in feet.

B - Luminance of the object of a lens, in candlesper square Inch.

B' - Luminance of the image formed by a lens whenthe luminance of the object is B, in candles persquare inch.

D - Display-image width produced by display-objectline width ; when projected on screen at distanceb by extended source S at distance a, in inches.

D- Display-image width produced by display-objectline width I when projected on screen at distanceb by geometric point source S' at distance a, ininches.

D- Display-image width produced by display-objectline width 3 when projected on screen at distanceb by extended source Slat distance a, in inches.

D- Display-image width produced by display-objectline width 3 when projected on screen at distanceb by extended source S at distance a1 , in inches.

DI - Display-image width produced by display-objectline width 3 when projected on screen at distanceb by geometric point source S' at distance a', ininches.

D2 Display-image width produced by display-objectline width 3' when projected on screen at distanceb by extended source S at distance a, in inches.

xvi

NAVFrRADEVCXN 162 -1

D- Display-image width produced by display-objectline width J when projected on screen at distance

b by geometric point source S' at distance a",in inches.

D3 Display-image width produced by display-objectline width J" when projected on screen at distanceb by extended source S at distance a, in inches.

F - Luminous flux incident on a lens, In luxaens.

F' - Luminous flux transmitted by a lens, in lumens.

G - Width of penumbra on either side of umbra U,(1/2 (D - U)), in inches.

G1 Width of penumbra on either side of umbra Ul, ininches.

G" Width of penumbra on either side of umbra U", ininches.

Luminous intensity on object side of lens or lenssystem, in candles (lumens per steradian).

I' Luminous intensity on image side of lens ur lenssystem, in candles (lumens per steradian).

I - Width. of a line on the display-object, in inches.

3' - Width of any line on the display-object less than3, in inches.

;" - Width of any line on the display-object wider than3, in inches.

M - Theoretical magnification of point s3virce display-object, (D'/Z), inches per inch.

M- Theoretical magnification of point source display-object, at minimum point source to display-objectdistance a', (DI/J), in inches per inch.

M- Theoretical magnification of point source display-object at maximum point source to display-objectdistance a", (D' /1), in inches per inch.

2

Xvii

NAVTRADEVCEN 1628-1

P Scale ratio, (A/a), in feet por foot.

P 1 Ratio of extended source diameter S to display-object line width J, (S/;), in inches per inch.

P1 Enlargement uf the display-image occasioned byuse of extended source S rather than a geometricpoint source S', (D/D'), in inches per inch.

P" Ratio of the width of umbra to the total display-image width projected by extended source S,(U/D), in inches per inch.

R Radlus of any refracting spherical surface, in

Inches.

RI Radius of the first surface of a lens, in inches.

R 2 - Radius of the second surface of a lens, in inches.

S - Extended "point source" diameter, in inches.

S' - Geometric point source of light (diameter of S' is 0).

S t Any extended "point source" diameter greater thanS, in inches.

U - Width of umbra of display-image D, in inches.

U1 - Width of umbra of display-image D, in inches.

U" - Width of umbra of display-image D", in inches.

U2 - Width of umbra of display-image D2 , in inches.

U3 - Width of umbr- of display-image D3 , in inches.

X. Y.Z - Arbitrary variables, introduced for mathematicalconvenience and defined to suit particular require-ments In each Instance.

xvlii

NAV'rRADEVCFN 1628-1

a - Distance from point source to display-objecL, in feet.

a' - Minimum distance from point source to display-object,in feet.

a" - Maximum distance from point source to display-object,in feet.

aR - Range of distances from point source to display-object(a" - a'), in feet.

a- Any distance from point source to display-object

greater than a, in feet.

b - Distance from display-object to display-image, in feet.

d - Distance from point source to screen, in feet.

h - Horizontal displacement of eye from point source,in feet.

I - Angle of incidence of light on a reflecting or refractingsurface, in degrees.

i - The angle at which a ray at slope angle 01, is incidenton the first surface of a lens, in degrees.

12 - The angle at which a ray refracted by the first surfaceof a lens at angle q., is incident on the second surface,n degrees.

m - Lateral magnification by refractive surfaces, in inchesper inch.

m1 - Lateral magnification due to the first surface of a lens,in inches per inch.

- Lateral magnification due to the second surface of a lens,in inches per inch.

mL Total lateral magnification of a lens, (mI. m2 ), in inchesper inch.

xlx

NAVTRADEVCEN 1628-1

n - Index of refraction of any medium.

n' Index of refraction of any other medium.

n, - Index of refraction of air (n1 - 1)

n2 - Index of refraction of glass.

r - Angle of refraction of light emerging from arefractive surface, in degrees.

r,- The angle at which a ray incident on the firstsurfaue of a lens at angle i, is refracted by thatsurface, in degrees.

r 2 The angle at which a ray incident on the secondsurface of a lens at angle i2 is refracted by thatsurface, in degrees.

s - The distance measured along t1 , optical axis fromthe object of a refracting surface to that surface, ininches.

' - The distance measured along the optical axis froma refracting surface to the imago formed by thatsurface, in inches.

si- The object distance of a lens; the distance measuredalong the optical axis from the object of the firstsurface to the tirst surface, In inches.

s- The distance measured alQng the optical axis from thefirst surface to the image formed by that surface when

the object is at distance a ,, in inches.

s 2 - The distance from the object of the second surface(this is the Image of the first surface) to the secondsurface, in inches.

s - The image distance of a lens; the distance measuredalong the optical axis from the second surface to theImage formed by that surface when the object Is atdistance s2 , in inches.

~XX

NAVTRADEVCEN 1628-1

t - Thickness of a Ions at the cptical axis, in Inches.

v - Vertical displacement of eye from point source,in feet.

- Extended source angle, in degrees.

(3 - The angle with Its vertex at the eye of the observersubtended by the edges of a detail on the display-imag(in degrees.

r - Diffraction angle, in degrees.

- Viewing angle, in degrees.

6, - The viewing angle toward the top of a detail on thedisplay-image, in degrees.

62 - The viewing angle toward the bottom of a detail onthe display-image when 6, is the viewing angle to thetop of that detail, in degrees.

.A - The angle at the eye subtended by the line of sightat v! 3wing angle 62 and the line of sight at viewingangle 6 , (6j- 6 ), in degrees.

- Projection angle, in degrees.

- The projection angle toward the top of the detail onthe display-image which is viewed at angle 6,in degrees.

a -The projection angle toward the bottom of the detailon the disp~ay-ixnage which is viewed at angle 62in degrees.

- Thu angle at the point source subtended by the line ofprojection at projection angle Sa and the line of projectionat projection aagle V , I C' - in degrees.

- Position distortion, ( - 6 ), in degrees.

Xxt!

NAVT'! AD1,VCEN 628-1

Tb, - Position di,,Lortion, ('; - d, ), in dogreeo.

T1 - Position distorton, ( - ), In degreeo.

A - Size distortlon, (A's- A6), in degrees.

- Slope angle of any ray on the object side of a lens, Indegrees.

04 8, - The slope angle of any ray Incident on the fist surfaceof a lens, in degrees.

- The slope angle of a ray incident on the second surfaceof a lens when the ray is incident at angle 9, on the firstsurface, In degrees.

E - The slope angle after refraction by a lens system of theray which has slope angle 6 before refraction, in degrees.

-) rne slope angle after refraction by the first surface ofa lens of the ray which has slope angle 0, before re-fraction, in degreLs.

e2 - Tho slope angle after refraction by the second surfaceof a lens of the ray which has slope angle 62 beforerefraction, In degroe.

X - The wavelength of light.

- The entrance half angle. This Is the limiting valueof 6 for a specified aperture, in degrees.

- The exit half angle when the entrance half angle is ,

In dogrees

Ci - The entranco solid angle when the entrance plane angleIs2V5, in ste .'lans.

- The ex it solid angle when the exit plane angle Is2 0,In steradians.

- Total longitudinal magnification of a lena, ( - (nL) 2 ),in Inches per inch.

xxhi

NAV'T'ADIVCEN lG,,,- 1

g3inCunventlons in thu Point Source SS _st

1. Vertical displacement or the eye from the point source -positive when the point source is above the lovel of theeye and negative when the point source is below the levelof the eye.

2. Horizontal displacement of t )(yo from the point source -positive when the point source h, behind tho observer andnegative when the point sourco Is In froat of the observeras the observer faces the screen.

3. Projection angle - posltive when the line of projection isdownward from the point source and negative when the lineof projection Is upward from the point source.

4. Viewing anale - positive when tho line of sight I downwardfrom the observer ts eye and negative whun the iin'., of sightis upward from the observerts eye.

5. Position distortion - positive when the projection angle isf- algebraically greater than the viewing angle. Since the

other distortions are derived from position distortion, theirsign convntions are similarly dorived.

Slun Conventions in Optics

1. All figures aro drawn with the light incident on the reflectngor refracting surface from the left.

2. The object distance is positive when the object is at the leftof the vortex of the surface in question. (the vertex of a re-fracting jurface is the point where the surface crosses theoptical axis).

3. The ima stance is positive when the image is at the rightof the ye, of the surface In question.

4. The radius of curvature is positive when the center of curva-ture lies at the right of the vertex of the surface In question.

b. The slope angles are poItive when the axis must be rotatedcounter clockwise through less that, W/2 to bring it into co-Incidom'e with the ray.

xxiii

NAVTRADEVCEN 1628-1

6. Tho angles of incidence and refraction are positive whenthe radius of curvature must be rotated counter-clockwisethrough less than W/2 to bring it Into coincidence with theray.

7. Dstances perpendicular to the optical axis are positivewhen measured upward from the axis.

8. Positive lateral maanification indicates that the image iserect while negative lateral agnification indicates thatthe imags is inverted.

xxiv

NN.

FrontIipiece - An Artist's Concept of a ITypical Point,"ouron Projection

Systemn (Device 2-FH-5)

13vi

CHAPTER I

Introduction to the Point Light Source ProjectionSystem and Its Components

1. 1 Introduction

.This report describes the results of a study of the com-ponents of the point light source projection system made by The deFlorez Company, Inc., under --ontract Nonr 1628(00), for the U. S.Naval Training Device Center. In order to broaden the ra .ge ofapplicability of the point source system as a solution to tra!ningproblems requiring visual displays, a thorough study of existingcomponents and investigation and development of promising newcomponents was undertaken to increase the versatility of the system.The coifponents studied are the basic ones involved: the point sourceof light, the display-object and the screen.

1, 1.2 When the study began, the size and brightness character-istics of the point light pource represented a major limitation to thesystem. As a result of this study, the qualities of the point lightsource have been advanced so extensively, that subject matter detailand manufacture of the display-object have become major limitationsto the system.

1.2 The Point Source Proiection System

1.2.1 The point source projection system produces a continual,moving, wide angle visual display (frontispiece, figures 1-1, 1-2) toan observer who is actually stationary in space. This display is pre-sented wI'F appropriate perspective, size ana position relative to theobserver, thus simulating the visual world as viewed from any desiredposition and viewing angle in space. By appropriate movement of thedisplay, the viewing position and angle are changed simulating a corres-ponding movement of the observer in space. this change in viewingposition and viewing angle is smooth and continuous just as it is for anobserver actually moving in the real world. In addition, as the observeractually turns his head from side to side or up and down, the wide cov-erage of the visual display will present a continuous world to eitherside as well as above and below him.

1.2.2 The simulated movement of the observer on and above the

world of the display is completely non-programmed in direction and

NAV 1FJ.ADEVCEN 1(OM I

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aw

JIU

cQ

NAV'11.Ai'E vCiEN 12

'in

P "4

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rIiC4 C. 4 It

NAV'PRADEVCEN 1628-I

i basically limited In extent only by the "ends of the display world."Thus by appropriately attaching the projection systxm controls to control devices slmulating those on a vehicle, aircraft or ship, the obser-vor by manipulation of these controls will have the visual sensation ofoperating actual controls of the vehicle, aircraft or ship. The world ofthe visual display will react to each control manipulation by the obser-ver in the same fashion as the actual visual world would react to thecorresponding control manipulation by a vehicle operator. The pointsource projection system then presents a means for the training, prac-tice and testing of control manipulative skills wherever a visual displayis mandatory or desirable in the development of such skills. Of coursewhere visual cues together with other sensory cues are necessary, thepoint source projection system can be combined with other sensationpresenting devices to provide a full range of cues to the senses.

1.3 Basic Components

1. 3.1 The point source projection system utilizes a very small in-tense light source to project a display-object onto a screen with appro-priate drives and controls to move the light source and display-objectrelative to one another and with an appropriate supporting structure.The supporting structure and the drives and controls present generalengineerIng problems and are not unique to the point source system.They have therefore been included in this study only to the extent ofhighlighting special requirements and limitations imposed on them bythe point source system. The study has been directed rather to thethree basic components of the system: the point source of light, thedisplay-object and the screen and to the inter-relationships of thesecomponents as they affect the net end product of the system, the visualdisplay-image as seen by the observer.

1.3.2 The effects of each system variable on display-image qualityare reviewed In Chapter 2. These variables include source size andintensity; the display-object line width; the transparency (or reflectivity)and shape of the display-object; screen shape and reflectivity; the prop-erties of light and the position variables: source to display-object distance,display-object to screen distance and the position of the observer relativeto the projector components.

1. 3. 3 Each of the next three chapters, Chapters 3, 4, and 5, is de-voted Lo one of the basic components. Characteristics of componentsavailable at the beginning of the study are evaluated in relation tosystem requirements. New or improvd components developed In the

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NAVTRADEVCEN 1628-1

course of the study are evaluated in relation to requirements andexpected improvements.

Ij 4 Histor-Y

I During World War 11 the point source was applied as a solu-tion to few problems. In particular, it was used to produce shadow-graph projections of solid objects, especially of aircraft models in teachingaircraft recognition.

1.2 It wasn't until much later that point source projection wasmore fully exploited to the extent that elaborate display-objects weresubstituted for simple objects. A few of the more important recentevents in the application of point source follow:

May 1952 - A contract was awarded to Bell Airciaft by the U. S.Navy Special Devices Center to produce a HelicopterHovering Trainer for the HTL-l helicopter. Bell as-signed the de Florez Company a subcontract to domost of the engineering development on this program.

August 1952 - The feasibility of Point Source Projection, as it ir'A P currently used, was demonstrated by the de Florez Co.

February 1953 - de Florez demonstrated a complete mock upincluding screen, 3' square transparency with 3-Dobjects, and manually operated projector withi sixdegrees of freedom.

May 1955 - Device 2-FH-2, the first Helicopter Hovering Trainerwith a visual attachment was "flown" at Bell Aircraft,Buffalo, N.Y., for the first time.

April 1955 - Device 2-FH-4 Prime Contract was awarded to deFlorez by Special Devices Center to develop basiccomponents furthur and investigate possible applica-tions to specific training problems. Under thisprogram the following items were accomplished:

- First Hafnium lamp made having four times thebrightness of existing Zirconium lamp with a givensource diameter.


- First light source made utilizing meniscus lens todirectly reduce an Osram lamp source diameter.

- Application of point source system to training inground controlled approach (GCA) landings demon-strated.

- Application to training in air-to-air gunnery demon-

strated.

- Investigation of all available components.

August 1956 - Device 2-FH-5 Prime contract was awarded toMelpar to develop first complete Helicopter Simulatorwith visual attachment. Melpar awarded subcontractto de Florez to develop and produce basic components:light source, transparency, and screen.

- Model 1 point source completed utilizing optical systemfor reduction of real source diameter.

- First photographic flexible transparency completed.

December 1957 - Mock up of 2-FH-5 program was completedutili zing flexible transparency.

1.5 Advantages of the Point Source ProJection Technique

1.5.1 The point source projection technique can be used to advantagein training problems requiring visual displays because of itsdesirable features:

(a.) Presentation of the visual display is non-pro-grammed. The trainee is free to maneuver atwill within the range of the trainer.

(N) The visual display covers a very wide angle, wellabove the peripheral vision of the human eye. f-the-shelf" projection lamps provide displays up to160 degrees in azimuth while more sophisticated pointsource projectors can provide displays up to 200 de-grees in azimuth. Full 360 degree displays arepossible.

! -6-

NAVTRADEVCEN 1628-1

(c.) The visual display is siufficient1y correct in per-spective to be convincing, regardless of the rela-tive viewing position of the observer.

(d.) The display can be presented in color which addsto realism and provides secondary cues to objectidentification.

(e.) The components utilized in the point source tech-nique are inexpensive particularly when comparedwith other visual display techniques.

(f.) When necessary, three dimensional objects can bepresented in the display in proper perspective con-tributing greatly to the realism of the illusion.

1.6 Limitations of the Point Source Projection Technigg

1.6.1 The point source projection system is subject to some limi-tations:

(a.) The maximum distance visible in any direction islimited due to the total reflection of light which oc-curs when rays are incident at acute angles on atransparent medium denser than air. With flat trans-parent display-objects of commonly available mat-erials the observers simulated visibility is iitedto a distance equal to approximately ten times hissimulated viewing altitude.

(b.) Clarity of the display-image varies inversely withsimulated altitude. This means that as the obser-ver approaches the ground, the display-image defin-ition deteriorates, a reversal of conditions exper-ienced in real life.

(c.) Perspective is distorted moderately because of thedisplacement between the observer's eye and theprojection source. Distortion of position, and itsderivatives, size, velocity and acceleration result.

(d.) Because of limitations on scale resulting from dif-fraction effects and extended source effects, large

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NAVI'RADEVCEN 1628- 1

,dsplay-objects are required to present extensivetraining areas. Large d1iplay-obJects are difficultto produ:e and require elaborate structures andmechanisms for handling.

CHAPTER 2

The Prictpo,i of Point Light S3ource Projootloii rochniiqueo

2.1 The Point Source Projection Princirle

2.1.1 The principle underlying the point source projection systemIs analogous to one of the principles by which the eye sees. The eyeutilizes the angle subtended by a detail to judge its size, distance andorientation, comparing this angle with angles subtended by details ofknown size, distance and orientation which are adjacent in the field ofview. Thus, in Figure 2-1, the eye cannot distinguish details al, a2, a3,and a4 from one another if viewed i.n space without familiar detals forcomparison. Under the same circualstances It can readily dlst'nguishdetails bl, b2, b3, and b4 from one another though it cannot determinethe factor involved (distance, size, orientatior) without binocular con-vergence, a property of the two eyes used together. Therefore, if thedisplay-image produces the proper angles subtended at the eye of theobserver so that relative size, orientation, and distance of details Inthe field cf vision are in the regularly seen relation to one another,the display-image will be registered by the eye as identical to the sameset of details in the real world.

!) 2.1.2 Figure 2-2 shows that, if the angle subtended at the pointsource by the display-o&'J2-t is varied by adjusting orientation, distanceand size of the display-object relative to the point source, the display-image change is analogous to the changes in Figure 2- .b, provided thatthe eye is held at the same point as the point source or at the corres-ponding position on the opposite side of the screen. It can be said thatif the eye is concurrent with the real image of thp point source (sameside of screen) or with the virtual image of the point source (oppositeside of screen) relative to the screen as an image-forming surface, theobserver will have the same point of view to the display-image as thepoint source has to the' display-object and the display-image will betrue to the display-object in relative size of details, in distance beLweendetails and in perspective.

2. 2 Arrangement of Components

2.2.1 For distortion free projection, the point source componentsmust be arranged as shown in Figures 2-3a and 2-3b. It is obviousfrom Figure 2-3a that the eye' cannot be placed concurrent with the

-9-


a. Objects Which Subtend b. Objects Which SubtendEqual Angles at Eye Different Angles at Eye

Eye EyeEys NO _.Object--

al. Reference bl. Reference

Object

Objet Eye --

a2. Orientation b2. Orientation differssame as al. from bl.

Object- -.- bj

aS. Dtance sme as al. bS. Distance dlffersfrom bl.

a4. Sise same s al. b4. Use differs from bl.

FWieM 2-1 BOhematic MoWing fects at utse, Distance andOrlen&atit Of Objects In Rpose on the Angle ftb-tended at the Eye of an Obemer.

-IU-


Display Objects Which Subtend DifferentAngles at the Point Source

PointSource 8o o -k l j _ ..... D- play Dip la y

% - ---.. Object iunav'e

a. Reference

PointSource

.*~-Dsplay Di-splayObject Image

b. Orientationdiffers from "a".

• - Point-- 80otrce

a. Distancediers from "a".

POt \ - Display Object

. a~lseders from "a".

Filme 22 S omatic ibswi Mects a Diplay Object BlsoOrisuation ad= lative to a Point gourceon Display bage and on Angle ubtended at thePoit source.


Screen

Concurrent - /- -Poin Source -,1.Alternte

on E e -Position of EyeTnd Eye " " -at Virtual Image

Tra"saret' .. ' Point Source RelativeDisplay Object "-.., , to Screen

a. Projection of Transparent Display ObjectReal Point Source _' Screen

Concurrent -Virtual Point tarate

Position of Eyeto Display Obje"' at Virtual Imageands bj- of Point Source Relativeand Eye - . oScreen

Reflective to Se

Display Objectb. Projection of Reflective Display Object

-Cured Screen for Wide AngleDistortion due to Differences Coverage,Between Projection Angle andViewing Angle--

EIye PointSource

c. Rear Screen Projectien oua Cved Doreen

Figure 1- Sohematies of Cemupent Armuaemets ad Pelt breProjectie Sntms.

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NAVTRADEVCEN 1628-1

point source, first, because both cannot occupy the same space and,second, because the eye would then see the display-object and not thedisplay-image. In figure 2-3b the eye cannot be placed concurrentwith the virtual image of the point source relative to the display-object because the reflective type display-object would conceal thescreen. Location of the eye at the alternate position, the virtual imagepoint of the point source relative to the screen is free from distortiononly when a flat screen is used. However, a flat screen provides only alimited angle of coverage. The angle of coverage can be increased bycurving the screen around the observer, but the viewing angle isdistorted as shown in figure 2-3c because the projection distanceincreases while the viewing distance remains constant.

2.2.2 The point source and display-object form an obstruction tothe observer's view which in most instances is best located in the blindarea above his head or behind him. At the same time the observer'shead and body form an obstruction to projection which is best located inone of the observer's blind areas, in most cases, directly below him.To achieve these conditions the point source is located directly above theobserver and the display-object is also above him. Schematic diagramsof some practicable arrangemonts of components are shown in figure 2-4.

.3 Determination of Scale Ratios

2.3.1 The ratio of the size of details on the display-object to thesize of these details in the real world is the scale or scale ratio ofthe projection system. The scale ratio must be the same in all threeaxes in space; i. e., if the scale ratio of length is 2: 1. the scale ratioof width and height must also be 2: 1. The determination of this ratiois of great importance ior its numerical value determines the size ofdisplay-object needed to provide the extent of rcal world desired. Thesize of the display-object so determined will, in turn, dictate the sizeand type of mechanical equipment needed to move it. Figure 2-5 illus-trates how the display-object scale ratio is determined. All termsmust be expressed in the same dimensional terms. The screen distanceand theoretical magnification are not considered in determiningscale ratios, for by placing the observer's eye as close as possibleto the point source the observer's viewing angle is essentially the sameas the point source projection angle and the subtended angles are essentiallyequal and true to size. These errors are discussed in detail in paragraph 2. 4.

&The effects of an extended source and of diffraction on display-image definition, discussed in paragraphs 2.6.3 and 2.7, are major

- 13 -

NAVTrRADEVCEN 102 - 1 ,.Point Source

TransparentDisplayObject

/ Limits of" Some Detail

S/" on Display/ Object

Aimits of same Obever

Detail on /Display

- Screen

"~~ b , la "O

- -- Point Source

Rflective

Display Object

Point source

Limits ot f"0Mone Detail onO bire

Dona Disjlat

Ftgue 2 -4 -schematic Diagrams of PoI* so=rc Proj ection systemsUsing Transparent and Reflective Dtaplay.Objcts.

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NAVTRADEVCEN 16'93 - 1

Geometric I IPoit Source 8' a- I al

I a'

Display-Object <-

b

Display-Image

By defl~tnP - A /a andM D- J

Ire. thse vin the diagramP -A/s' - AN/&* - AR/aR

ARM A-A 0 -1 P(a' 10.a')

K' - NO/ - (A, +10/91

M" - Dj/I - (AN +b)/s"

Nowe that whil the diagrm shown is for a trnpr~display-object, the same rlodshlps are develoed for a ralatlvs

F"gr 2 -5 DstWmltoa of Beat Ratio P and 49 Tb8oreticalMaqnta M from Ooaditous to be Uimulate.

NAVTRADEVCEN 1628-i

factors in determining scale ratio. These effects and the point sourceenvelope dimensions limit the minimum distance between the pointsource and the display-object. In turn, this minimum distance mustrepresent at least the minimum altitude to be simulated. The limita-tion imposed by the point source envelope, being physical, Is absolutewhile the limitation imposed by extended source effects and diffrac-tion effects affect display-image quality and can be adjusted to the ex-tent that display-image quality at the lower end of the simulated alti-tude range can be compromiged. The maximum distance permissiblebetween the point source and the display-object is limited by the extentto which the distortion of the display-image, caused by the correspondingincrease in the point source to eye displacement, can be tolerated. Be-cause of the retro-directive nature of beaded screens, as discussed inChapter 5, large distances between the point source and the eye resultin decreases in display-image brightness which can be serious. Athird limitation on scale ratio determination is the economic and technicalproblem of producing display-objects with very large scale ratios asdiscussed in Chapter 4.

2.3.3 Thepe limitations indicate that display-object scale ratiosmust often be determined through compromises. Determined solelyon the basis of picture definition, the display-object scale ratio may betoo low for a display-object of desired area coverage so that the disr.lay-object becomes too large and unwieldy. This may create a need for avery large and complex mechanical system for moving the display-objectwhich in turn will impose a severe handicap on the design and complexityof the servo drives.

2.3.4 Very high scale ratios present their own difficulties. Display-objects of very large ratios are difficult, sometimes impossible to pre-pare. In addition, servo jitter must be eliminated since velocity errorsand oscillati6ns are considerably magnified.

2.4 Distortions Due to Displacement Between the Eye andthe Point Source

21. Displacement between the observer's eye and the point sourceleads to several types of display-image distortions which result in anerroneous visual presentation with regard to scene perspective, and,when the scene moves relative to the observer, with regard to apparentvelocity and acceleration of an object. If these distortions are excessivethe realism of the visual display may be so far impaired as to destroyits value as a training device. Although it is not possible

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NAVIRAD'EVCEN I628-i

to completely eliminate these distortions, it is possible to reduce th-mto a minimum by proper selection of system geometry and screen shape.These distortions may be grouped in three classifications: position dis-tortion, size distortion, and velocity distortion. Size and vel.ocity dis-tortions are derived from position distortion.

2.4.2 For purposes of this discussion, the point source, the eye,aEd te display-image are considered in the same vertical plane. Sincethe screen is assumed to be symetrical about the point source in thehorizontal plane, the viewing angle and the projection angle will beidentical and no distortion will be introduced in this plane. Some addi-tional distortion is introduced when the eye is outside of the verticalpoint source - image plane, but this can be made insignificant by keep-ing the eye to plane distance small.

2.4.3 Position Distortion

2.4.4 Position distortion may be defined as the difference betweent angle of projection to a point on the display-image and the viewingangle from the eye to the same point on the display-image. (AppendixI, figures I-1, 1-2 and 1-3) Position distortion depends upon the pointsource to eye distance, the point source to screen distance, the geo-metric relationship of the eye to the point source and the screen, the

• " angle of viewing, and the shape of the screen. Expressious for post-tion distortion in terms of these variables have been derived in App*3n-dix I and are the basis for the following illustrations and discussion.Throughout this discussion, the viewing angle is positive below thehorizontal and negative above.

2.4.5 Recalling that a convenient geometric arrangement is onewFere the point source is located directly above the eye, the positiondistortion, * , is plotted in figure 2-6 as a function of viewing angle, b ,for three fundamental screen shapes: a flat vertical screen, a flat hor-L.ontal screen, and a circular screen centered at the point source.Three values of the ratio of point source to eye distance to pointsource to screen distance, v/d, (0. 05, 0. 20, 0. 35) were selected be-cause in the usual point source projection system the point source toeye distance is expected to vary from I to 3 feet and the point sourceto screen distance is expected to vary from 8 to 20 feet.

2.4.6 The meaning of these curves in terms of an observer's viewo e display- Image may best be illustrated with an example. B theobserver's eye Is located 3' directly below the point source and avertical screen is located 15' from the point source (v/d . . 20), a pointprojected on the screen so that it is observed at a viewing angle 5QObelow the horizontal (6 - 500) would be seen 540 below the horizontal ifviewed from the point source (' m 4o). Similarly at ground level an obser-ver would expect to see the horizon directly in front of him at or slightly

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'1 NAWURADEVCEN 1628 -1

I 0 4

P4 Q

NAWT: ,ADEVCEN 1628-1

below his eye level (0 1 00) whereas it will be projected on the screen sothat he sees this horizon point 11, 5o above his eye level (q - 11. 50). As aresult of position distortion the observer sees each projected point higherthan he should and he will consider each point to be more distant than itactually is. The over-all effect of this distortion in terms of a particularterrain display is the so-called "bowl effect"; that is the observer sees theentire horizon line somewhat higher than normal and he feels that the contourof the terrain is bowl shaped and that he is located at the low point in tAebowl. Another position distortion phenomenon which seems to contributeto "bowl effect" is the slight curvature in the observer's view of the display-image of any straight line on the display-object introduced by curvature ofthe screen. The phenomenon is quite readily explained by considering thatthe point source and a straight line on the display-object form a plane whichintersects the screen surface to form the display-image of the line. Fromconsideration of solid geometry it can be seen that the intersection of thispoint source - display-object-line plane with a flat screen (another plane) isa straight line in space regardless of viewing position but that the hutersectionof this plane with any curved screen is a curved line in space and will appearcurved from any viewing position in space which is not in the point source -display-object-line plane. In normal point source systems where the obser-ver is below the point source and the screen is partly cylindrical and partlytorus shaped, almost all projected straight lines appear to the observer tocurve upward at the ends. The curvature is caused directly by displacementof the observer from the projection source and by screen curvature.

2.4. 7 From the curves in figure 2-6 it is evident that the smaller thevalue of the ratio, v/d, the smaller the position distortion at all viewingangles and for all screen shapes considered. Furthermore, the horizontalscreen shows lower distortion than either of the other shapes. At v/d equalto 0.20, maximum distortion on the horizontal screen is 60 23' and occursat a viewing angle of 410 48' below the horizontal. The maximum distortionon the vertical screen is 110 26' at a viewing angle of 50 43' above the hori-zontal while maximum distortion on the circular screen is 110 32' at a hori-zontal viewing angle. When viewing directly ahead or at small angles aboveor below the horizontal, position distortion is maximum for vertical andcircular screens and minimum for horizontal screens. (Of course the hori-zontal screen cannot be viewed at an angle above the horizontal.) Positiondistortion directly above and below the observer is zero. Note that positiondistortion on the circular screen is greater than on the vertical screenparticularly at viewing angles below the horizontal.

2.4.8 R is of interest to note the rate at which position distortion changesbase viewing angle changes over the limits of visibility. Figure 2-7 showsthis rate of change, dl /d3, for v/d equal to 0. 20. Note that the circularscreen provides an almost uniform rate of change of position distortion overthe full range of viewing angles. The rate of change of position distortion pro-vided by the horizontal screen is also quite uniform in the area between 15below the horizontal and 750 below the horizontal. This represents a major

-19-

NAVTRADEVCEN 1628 1

944

020

NAVTRADEVCEN 1628-1

portion of the useful projection area on a horizontal screen. f;Ute ofchange of position distortion on the vertical screen is subject to consider-able variation.

2.4.9 Figures 2-8, 2-9, and 2-10 illustrate the effect of varying thehorzontal distance, h, between the obsorver's eye and the point source(v positive). In all cases the point source remains above the level of theobserver's eye. When h is positive the point source is behind the obser-ver and when h is negative the point source is forward from the observer.When the point source is moved bbck from the observer distortion atviewing angles below the horizontal is decreased and distortion at viewingangles above the horizontal is increased. The values of distortion thatare negative are completely theoretical because the observer's head willinterfere with projection and no image will be formed at these viewingangles. When the point source is moved forward from the observer'sposition, position distortion is increased for viewing angles below thehorizontal and is decreased for viewing angles above the horizontal. Herenegative distortion values are hypothetical because the point source willinterfere with the observer's view of the screen. From these curves itmay be concluded that when a display-image directly below the observeror at large angles below the horizontal is not required, position distortionon the remaining portion of the display-image below the horizontal can bereduced by moving the point source back from the observer. Location ofthe point source forward of the observer should be avoided except wherefeatures very close to or beneath the feet of the observer are absolutelyessontial to the display-image requirements of a problem.

2.4.10 The rate of change in position distortion with change in viewingangle dn /d6 , for the conditions where the point soumce is located for-ward or behind the observer is shown on figures 2-11, 2-12, and 2-13for v/d equal to . 20. When the point source is moved to a position forward

of the observer's eye (h negative) the rate of change of position distor-tion on both vertical and circular screen becomes more uniform at view-Ing angles below the horizontal but becomes more irregular at pointsimmediately above the horizontal. When projected on the horizontal screenthe rate of change of distortion becomes more irregular at viewing anglesjust below the horizontal. When the point source is moved to a locationbehind the observer's eye (h positive) the rate of change of positiondistortion is more uniform on a vertical screen at viewing anglesgreater than 400 below the horizontal but is more irregular between thehorizontal and a viewing angle 400 below it. On the horizontal screenthe rate of change of position distortion becomes more irregular over theentire range of viewing angles. On the circular screen the rate of changeof position distortion is also less uniform at viewing angles below the

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NAV1FRAD1EVCEN 1.628 -1

A.1

I 12I00

00

NAVTRADEVCEN 16;t~3 I

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-27-


horizontal.

2 Rate of change of position distortion is analogous to the dis-tortion of the velocity of a point on the display-image when the display-object is moved. The more uniform the rate of velocity distortion theless likely it is that the observer will detect it. Therefore, it can beseen that a uniform rate of change of position distortion is desirableparticularly when the display-image requirements include visual cuesto velocity.

2.4.12 Size distortion

2. 4. 13 Position distortion of the end points of an object lead to dis-tortion in its size, so that the object appears smaller or larger than itactually is. Size distortion is dependent upon the same variables asposition distortion and in addition is dependent upon the size of the ob-ject viewed. Size distortion in combination with position distortion re-sults in a distortion of perspective in the display-image.

2.4.14 The effect of size distortion was studied by considering anobject on the display-image subtending an angle, a6 -10o at the eyeof thu observer. As this object is viewed at different viewing angles,6, size distortion, al, assumes values as shown in figure 2-14 whenv/d is equal to .20 and h is equal to 0. Positive values of size distor-tion,ay, mean that the object is actually larger than it appears whilenegatve values mean that the object Is smaller. Thus an object viewedat 35 below the horizontal on a vertical screen appears to be 100 insize but is actually only 8.250 (ATI--1.750). An 8. 50 object viewed atan angle 200 below the horizontal and at 11. 50 object viewed at an angle250 above the horizontal on the same vertical screen will both appear tobe 100 in size.

2.4.16 The curves of figure 2-15 show the distortion in size,An, ofa 100 object over the range of viewing angles,6, as the point source ismoved forward (h negative) and back (h positive) relative to the observer.Note that a family of curves can be established for every size object(different values ofW). One of the effects of size distortion is to lead tofalse judgements of distances. Thus, an object which appears largerthan it actually is seems closer to the observer than It actually is.

2.4.1 6 The rate of change of the size of an object, dAVl/d6, as theviewing angle, 6, Is varied provides a cue to the velocity with which

-28 -

NAVTRADEVCEN t-1.02

NZ P1 -

~U o

0 '1i-2:-

NAVIIIALJMVUINJI~

h v

2

-80 -40408D- egrees

2-15&- Size Distortion, A~ 'I on a t Vertical Screen

GENERAL EXPRESSIN

where object siz6 in

PAAETR001 h -v

v/d -. 2 -point source

h - rvPoite - point soure

ft15 Negaive D pitounA~,o la oio

2-15c - Size Distortion, 0i', on a C Icuzlar ScreenFigure 2 -15 - Size Distortion, I&I of a 10 Object ( & 00

-30-

the object approaches, or departs from the viewer. If an object isviewed in the distance ( '-0) and it approaches the viewer (6-900),the size of the object should change uniformly in a specific mannerto give the proper illusion of speed. A departure from this rate ofchange In size gives the unrealistic impression that the object ismoving particularly slow or fast. Figure 2-16 shows the rate ofchange of size distortion with viewing angle for an object 100 Insize when v/d is equal to 20 and h is equal to 0.

2.4.17 Again an example will best illustrate the use of thespcurves. If an object traveling towards the observer ( 6 = 0 to 0 -- 900)is seen at a viewing angle of 600 below the horizontal on a flat verticalscreen, it appears to move. 03T slower than is actually the case(where T is the angular velocity d 6/dt defined by the speed of thedisplay-object and the dimensions of the system). Positive valuesof velocity distortion mean that the object appears to move slowerthan is actually the case, while negative values have the oppositeeffect.

,24.18 Since the curves in figures 2-11, 2-12, 2-13, and 2-16provide cues to velocity distortions, the slope of these curves providea measure of acceleration distortion. Regions where the slope of

- these curves is sharp, indicates areas when acceleration distortionis great and may be disturbing and distractive to the observer.

2.4.19 These studies indicate not only the magnitude and effect ofdistortion due to displacement of the eye from the point source butalso indicate that in a problem where the visibility angle is defined(for example, from 400 above to 400 below the horizontal) it is possibleto minimize distortion by adjusting the system geometry includingscreen shape. In this process, however, the ratio v/d should be heldas low as possible. The value of d is limited by the space limitationsimposed on the design of the projection system.

Distortion Due to Screen Curvature. Rear Projectio System

5.1 As previously pointed out, (paragraph 2.2. 1) if the screen usedwith a rear screen projection system is curved about the observer toachieve a wide angle of projection, distortions are introduced in thedisplay-image because the projection distance increases while the viewingdistance remains constant (figure 2-3c). This distortion is caused entirelyby curving the screen and is independent of the eye to screen distanceand of the point source to screen distance provided these twodistances are equal. Position distortion,n , due to curving the screen

31 -

r4-

c~a)

(at))

4 I4

rz~ I

CIDa

NAVT' RADEVCEN 10'r24 - I

about the eye of the observer is plotted in figure 2-17a for the fullrange of viewing angles, 6. This distortion occurs when the =creerlis curved from the observer's left to his right as well as when it iscurved from above the observer to his feet. When the curvature iscompounded (spherical screen) the distortions are compounded. Notethat the distortions are small with small viewing angles from the"straight forward" viewing angle but increase sharply when the view-ing angle is greater than 300 from the "straight forward" viewingangle. The rate of change of position distortion, dn/d6, with thisprojection system is illustrated in figure 2-17b. This rate furnishesa clue to velocity distortion. Note that the rate is. small where thedistortion is small and it Is large where the distortion Js large. Therate of change of this velocity, the slope of the curves in figure 2-17b,is a cue to acceleration. In the area where position distortion issnball acceleration distortion is small. When viewing angle exceeds15 to either side of the "straight forward" position the slope of thecurve is constant and acceleration distortion is constant.

2.6 Factors Effecting Resolution and Definition of theDisolav - emage

2.6.1 Good resolution and definition are important qualities of anyimage. An image with good definition is sharp and clear with distinctdemarcation between details, whereas one with poor definition is blurred.An image with good resolution presents fine details tis separate individualobjects, whereas one with poor resolution presents letails running intoone another and not separable into individual obje, . * In a projectionsystem, the degree to which the resolution and definition of the display-image approach the resolution and definition of the display-object maybe termed the resolving and defining power of the source and is an impor-tant criterion for evaluation of the system. Resolution and definitionare very closely allied. Indeed, the resolving power of a projectionsystem is usually limited because of deterioration in definition. As theedges of adjacent lines become more blurred, each individual lineloses its identity and merges into one blurred image.

2 2 In the point source projection system, definition of the display-image depends primarily on the source diameter to display-object line widthratio, Pl, on the point source to display-object distance, a, and on the effects

* Resolving power is often measured by the number of lines per unitwidth of a regular pattern of opaque lines on a transparent backgroundwhich can be individually distinguished. The greater the number of lines,the greater is the resolving power of the system.

33

NAVTRADEVCEN 1628-

30 General Expression

S20 i.tan1l CI 7S

10

- 20 40 60

0 4 0 b -D rees.- 1O

i -30

2-17a - Position Distortion, at Viewing Angle,

.80 -40 -20 20 40 80

SIII I I

.2 General Expressiond 2cosb -1

.1.0

2-17b - Rate al Change of Position Distortion, di/d b, at ViewingAngte,gb

Figure 2-17 - Position Distortion - Rear Projectio, Curved Boren

-34-


of diffraction, Resolution depends primarily on the source diameter todisplay object line width ratio, and on the effects of diffraction.

2.0.3 By far the most important factor affecting resolution and def-inition is the size of the extended source; that is, any source which de-parts from a geometric point source. The projection of an opaque lineof finite width by a geometric point source yields a well defined magni-fied image which is totally black on an illuminated background. Use ofan extended source results in deterioration in the sharpness of this image.Each element of the extended source acts as a geometric point source andthe over-all effect is to enlarge the image of the line, reduce the totallyblack area (the umbra) and cause a gray area (the penumbra) on bothsides of the umbra as shown in figure 2-18. The penumbra ' a grayarea graduating from totally black immediately adjacent to the umbra to tot-ally white immediately adjacent to the illuminated background. The lar-ger the source (assuming a constant display-objeet line width) the smalleris the ratio of umbra to penumbra-plus-umbra, P". As this ratio de-creases, image definition deteriorates until finally it becomes impossibleto differentiate between the umbra and the penumbra. At this point theprojected display-image is enlarged beyond the theoretical magnification(magnification with a geometric point source)and the display-image con-trast is considerably reduced from the possible mairium.

2.6.4 The display-object line width may accentuate the effects of theextended source. As the display-object line width decreases and ap-proaches the extended iource diameter, it is clear from figure 2-19 thatthe umbra becomes a smaller and smaller portion of the total imagewidth. When the display-object line width becomes less than the ex-tended source diameter the umbra gradually disappears and only a graydisplay-image remains. Figure 2-20 illustrates the *.xtent to which theuse of ani extdnded source enlarges the display-image line width overand above the theoretical magnification. It also shows that when theo-retical magnification exceeds 10, further increase in theoretical magni-fication has little effect on display-image definition. These curves areplotted for selected values of the ratio of the extended source diameterto the display-object width, Pl. The relative increase in the extendedsource projected image size over the geometric point source projectedimage size, P', with theoretical magnification is plotted in accordancewith equations derived in Appendix I1. Note that as the extended sourcediameter approaches and exceeds the display-obj ect line width (P1greater than 1), the display-image becomes greatly enlarged above thetheoretical magnification. Indeed, for a P1 value of 2, the image sizeis twice the theoretical for a magnification of 2.

-35-

NAVTIRADEVCEN 1628 - 1

S

a

b

-- ...... .... -0"D

By definition ki > S. I a, b and I are held constant It can be easily shownby similar triangles that

U"< U

D" > D

0>0

Figure 2- 18 - Schematic Showing Effect of Different Source Diameters,S and S1, on Display-Image Quality.

-36-

It NAVTRADEVICEN 10;18

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NAVTRADIEVCIEN 16283 1

04

'I

1 04

+. +

I La

c4i 4 -4 v4 .,,4

-38-

NAVTRADEVCEN 1628 -I1

2.6. b The extent to which the ratio of umbra to total display-imagearea, P", decreases with an extended source is Illustrated in Figure 2-l.Theso curves are plotted for selected values of P, and compare the be-havior of the ratio P" with changes in theoretical magnification from equa-tions derived in Appendix I. Note that as PI approaches and exceeds Ithe umbra decreases sharply so that when P1I equals 2 with a theoreticalmagnification of 2 there is no umbra. Here the image is entirely grayand is not easily recognized.

2.6.6 The above theoretical curves mean that details on the display-obje.t must be represented with wide lines relative to the source diam-eter even at the risk of ecaggeration in order to achieve satisfactorydefinition. It is important that the ratio Plbe minimized and certainlyshould not exceed unity. It is preferable not to use values of P.greaterthan 0. 5.

2.6.7 Experimental confirmation of this rule is presented in figures2-22, 2-23, 2-24 and 2-25. These curves represent the subjective im-pressions of three observers who viewed static scenes consisting of pro-jections of hand decorated display-objects or photographic display-objects.Two different light sources were used: the 25 watt hafnium concentrated

-. arc lamp (. 013" source diameter), and the 2 watt zirconium lamp (. 004"source diameter), Figure 2-22 illustrates the impressions of the obser-vers with the combination of the 2b watt hafnium lamp and several handdecorated transparent display-objects. These transparencies consistedof the same scene made to different scales: 500:1, 1000:1, and 2000:1.The source to display-object distance was varied and the observers wereasked to render an opinion of the static display-image quality by class-fying each as "good, satisfactory, marginal or poor'. While the curvesrepresent the average of the opinions, these did not differ appreciably.Note that the carves in Figure 2-22 appear to be in close agreement. Forsource to display-object distances greater than 2" the display-image isgood or saLisfactory. However, below the 2" distance the image tends todeteriorate. The curves are similar because the display-object line widthdid not differ appreciably in spite of the different scales of the objects.

2.6.8 The curves in Figure 2-23 were obtained in the same mannerexcept that photographic display-objects were used with the 25 watt haf-nium lamp. Here again the same scene was depicted at several differ-ent scales. In this instance a marked deterioration in display-imagequality occurred at lamp distances between two and four inches, depend-ing on the scale ratio of the photograph. Quality deteriorates more

-39-

NAVTRVADFEVCEN 12-

:4

I +4

- -%-

0

P4 -4 A Nc

Call pin4 ~ .4 -4

P4

P4 p-4

P4

-40-

NAVTRADEVCEN 1(28 - 1.

Source: 25W Hafnium Lamp - 1.25 Amps.10 (Source Diameter. 013 inches)

Display-Object: Hand Decorated (Transparent)Projection Room Condition: LighttightScreen Type: Rear ProjectionDistance From Display-Object to Screen: 72 inchesViewing Distance: 72 inchesNote: Display-Image :udged Under Static Conditions

8 0

.. .... . ...... ..... .

/ , ~- Good o . o

/ u,8 / UtSI fatory

Marginal

-. ~~ a7 natisfactory

I Display-Objectcale Ratio@:

x 2000:12 I 0 1000:1

*v 500:1BW

-1 , 5 t 7 8 9, 10 11 12,Source to Dlsplay-Object Distance - bnhes

Figure 2- 22 - Subjective Evaluations of Display-Image Produced byProjecting a Hand Decorated Display-Object With a25 Watt Hafnium Lamp.

-41-


10 Source: 25W Hanium Lamp - 1.25 Amps.(Source Diameter . 013 Inches)

Display-Object: Photographic (Transparent)Projectibn Room Condition: IlghttightScreen Type: Rear ProjectionDistance From Display-Object to Screen: 72 inchesViewing Distance: 72 inchesNote: Display-Image ;udged Under Static Conditions.

80

. Satiactory

j Marginal

0

Unsattactoz7

Dislay-objectScale Ratios

o4000:1x2000:1

2 0 1000:1S500:1

1 2 3 4 5O 6l i 0 1 2

Source to DispLay-Object Distance - Inches

F"gr 2 -23 - SobjeetlY. Evaluatlons of Display-Images Produced byProjecting a Photographic Display-Object With a25 Watt Haum Lamp.

-42-


Source: 2 W Zirconium Lamp (Source Diameter . 0045 in.)

10 Display-Object: Hand Decorated (Transparent)Projection Room Condition: UtghttightScreen Type: Rear ProjectionDistance From Display-Object to Screen: 72 inchesViewing Distance: 72 inchosNote: Display-Image ;udged Under Static Conditions

8

Satisfactory

18 ~~marginal-, -'

I/ Unsatisfactory

DIuMeaW-Obiect

ola* Ratios:

2 ~x 2000:1o 1000 : 1,, 500:1

i d 3 4 8 ,, 1o 11 12'

Source to Dlalay-Object Distance - Inches

Figure 2-24 - Sobjectlve Evaluations of Dlsplay-mages Producedby Projectin a Hand Decorated Display-Object Witha 2 Watt Zirconium lamp.

-43-

NAV'TF?.AEEVCEN 1628 - I

Source: 2 W Zirconium Lamp (Source Diameter .0045 in.)1C 'Display-Object: Photographic (Transparent)

Projection Room Condition: LighttightScreen Type: Rear ProjectionViewing Distance: 12 inchesDistance From Display-Object to Screen: '72 inchesNote: Display-Image Judged Under Static Conditions

o Satisfactory '

Marginal

4 o

Ia

Display.Object.Scale Ratios: v

2 4000 :12000 1

0 1000 :1S500 1

1 .,3 5 6 FI 8 0 11 12

Source to Display-Object Distance - Inches

Figure 2 -2b Subective Evaluations of Display-Inages fProduced byProjecting a Photographic Di.,;play-Object With a 2 WattZirconium Laamp.

-41-

NAVTRADEVCFA I2M- I

rapidly with larger scale ratlo primarily bocauw the PI value at highscale ratios is relatively large and thurefore the dlsplay-rnago deter-lorates rapidly at largo magnificationi. The large Pl ratio re:,ultsfrom the fie dstail re7ouded on photographic film.

2.6_9 The curves in figure 2-24 were obtained using a 2 watt zir-conium lamp as the light source and the sams hand decorated transpar-ent display-objects ased to obtain figure 2-22, Note that for large theo-retical magnifications, the quality of the display-image was consideredsuperior to that obtained with the 25 watt hafnium lamp. This is di-rectly attributable to the smaller source diameter and its effect on theratio P. ' The poor image quality at low magnifications was not a re-sult of poor Image definition, but primarily results from a low level ofscreen illumination. The low light output of thp 2 watt zirconium lampprojects the display-image at a screen Illumination below the thresholdlevel and, at low magniflcationn, the fine detail Is then not easily dis-tinguished. :-reen illumination seriously affect, impressions of display-image quality, especially if the illumination is near o- below the thresh-old level. To a lesser degee, the deterioration of p clure quality atlow magnifications can be attributed to dlffraction effecto a describedin paragraph 2.7.

2.0.10 The photographic display-objects used to obtai figure 2-23were projected with the 2 watt zirconium lamp to obtain the c'urves infigure 2 -2b. Here again th3 effect of the :imaller diameter ;ource Isevident In tho improved image quality. Indeed, witt: low scale ratios,the image quality is good at high magnifications since the photographicdisplay-oL, act appears more realistic than the hand d,',orated display-obje A. IHowever, with large scale ratio; varying between 2,000:1 and4, 000:1 the dhsplay-image deteriorates rapidly at high majinlfioation.;.This is explained by noting that the inhorerit nature of photography isto depict all details. At large scales, much detail Is present on thedisplay-object as fine line work a:id minute area. of ,olor. Any ofthese linoj or area; smaller than th, sour,.,. diameter I:; los;t when amagnification )f 10 i; reached. Ea!h remaining ,lAail on the display-image must rult from dotall.; on th, I. iplay-objeot larger than thepoint source diameter. Nevertheless ; the magnification lncre.aes, thetotal blurred are:a (f th .. ;,'r !o inc re!a:;e, becr:iu; the blurred ima'Je.3of no longer definod fino detail:; rnfo :.o oiiu anothir and d,' :;troy thedefinition or larger dtaih12. With rn,'h detail present, the .h0ole imagerapidly loses its ba ;io :iaraoto ristic., an, l 1)0,mo:S an in, il:;tngui:-1aiieiL' ure of colo" bl'ond ;. The tetorkoratioui at low magni ifioation L-, a-

gain the rosult )f po " .;.rc'm illunilnatioli and ,iffraotion.


2.6.1 A second important factor limiting resolution and definition ofthe display-image is the point source to display-object distance. Theimportance of this factor derives directly from the effects of an extendedsource on the display-image. It will be recalled that the use of an ex-tended source reduced the umbra of the display-image and causes a pen-umbra to be projected on both sides of the umbra. If the extended sourcediameter and display-image line width are held constant, the ratio of umbrato total display-image area decreases as the source to display-object dist-ance decreases. This phenomenon is illustrated in figure 2-26. Figure2-27 shows the effect of varying the source to display-object distance onthe image quality for selected values of source diameter. The curves inthis figure are plotted from expressions derived in Appendix II, usingangular definition as an objective measure of imrge quality. ThL ob-jective measure of image quality has been correlated with subjective eval-uations of image quality using the data available from figures 2-22, 2-23,2-24 and 2-25. Two assumptions underlie figure 2-27: (1) two adjoiningareas of different colors are projected by a source of finite diameter; (2)the observer is very close to the projection source. Upon projection, an"area of demarcation", separates the two color areas on the display-im-age rather than the distinct line of demarcation which separates the colorareas on the display-object. The "area of demarcation" increases withmagnification and is also a linear function of source diameter. As veenby the observer, tho area of demarcation subtends an angle in spacwhich may be termed angular definition.

2.6.12 The curves in figure 2-27 can be of value in determining theminimum source to display-object distance which will give an acceptabledisplay-image when using any particular diameter source. Converselywhen it is desired that the source approach the display-object withinsome particular minimum distance, the largest source diameter whichwill give acceptable display-image quality can be determined from thesecurves. When used in this manner it must be remembered that thesecurves are based on the following conditions: (a) The Pj ratio is lessthan I. for the majority of the details; (b) the display-image quality isjudged statically; (c) the projection is normal to the screen and is viewednormal to the screen; (d) the source to display-object distance is the min-imum distance measured normal to the display-object plane. It should benoted that when the angle of projection deviates from the normal to thedisplay-object plane, the source to display-object distance increases aathe secant of the angle between the normal and the angle of projection inquestion. Thus when a large display-object area is projected by a pointsource of light, details on the display-object remote from a point direct-ly beneath the point source may be projected with good definition even

-46-

NArRADEVCEN 1628 - 1

b

D DI

By definition "Le,~ 1 5, b and 3are held constant, it can easily beshown by elma~i trianqles that

" D1

F"gr 2 - 28 Schematic 3aowing Effect of Source to Display-objectDistanc, on Display-Image Quality

-47-

NAVTRAf)EVCiEN 1628 I

Figure 2-27 - R~elation of Image Quality to ExtendedSource Diamnetero 8, and Source to Display-Object£ Distance, a, When the Viewing Distance to U~rge

~ (greater than 72")2. C/7

S/

441600,/

S-.000O'

0'0 0

j6001 S 6

S&.007'

0 5 1.5 20

-48-

NAVTRADEVCEN 1628-1

though details immediately beneath the point source may be projected asa blur. When the display-object is a terrain presentation, this meansthat the near scenery will be blurred but that distant scenery will bepresented clearly, conditions which may be satisfactory for certaintraining problems. It must be appreciated, therefore, that informationobtained from Figure 2-27 should be modified to suit the type of display-object used, the projection conditions, and the display-image roquirementsof the problem.

2 Effects of Diffraction on the Display-Imace

2.7.1 A very subtle and usually troublesome consequence of the wavenature of light is diffraction, that is very slight spreading of a beam oflight as it passes over an o-aque object. The wavefront, on striking theedge of an opaque object, creates secondary wavelets which can be con-sidered as eminating from the edge of the opaque object and which spreadout in all directions. Indeed, the light appears to bend around the edgeof the opaque object. These wavelets interfere with or reinforce themajor wavofront and result in alternate dark and light bands in the vicin-ity of the projected umbra edge as in Figure 2-28. Within the umbra lightbands of diminishing intensity can be noticed while in the bright area darkbands appear. The over-all effect is to reduce the image definition becausethe alternate light and dark bands occurring along the edge of the projectedimage make it difficult to distinguish the edge.

2.7.2 Diffraction effects are not a function of size of the source butare influenced primarily by the source to the display-object distance, thedisplay-object line width, and the wave length of light. Diffraction wouldbe the factor limiting the resolution and definition of the. display-imageprojected by a geometric point source of light. Since both diffraction andextended-source effects result in loss of definition of the display-image,it may be of interest to inow which of these effects is most significantin a given instance. Equations defining the diffraction angle, ( , and theextended source angle, c , in terms of sourme to display-object distance,display-object line width, .and the wave length of light are given in AppendixMI. Them equations are derived by considering the display-object line Inthe same nature as a slit, and by assuming the point source to display-object distance to be very large in comparison with the display-objectline width.

S The curves in Figure 2-29 show the effects of source to display-object distance on diffraction angle, ' , and on extended source angle,

-49-

NAVTRADEVCE'N 1628-1

Geometric Point Source

a

opaque Line of WidthJon Dsplay-Object

'I'

I I

Screenon r

FhDiffraction Region

0

Plan View of Portion ofDiffraction Pattern

on Screen

Figure 2 - 28 -Schematic Diagram of Diffraction Pattern FormationWhen Opaque Line of Finite Width ; is Projected bya Geometric Point Source of Light

-50-


.028

.028 - ( (- .001)

.024

.022

S.020

I'

.014

.012(I (- .001)

.010 -- (,T .002),,J . .(;= .004) ("=.oo3) - -

.008

.008 f

/ ((V- .004)

*o4~--\r \

.004206

0 - -- - - - ,1K

0 1 2 3 4 5 6 7

a - Inches

Figure 2 - 29 - Effect of Diffraction Angle, y, on Display-Image QualityCompared with Effect of Extended Source Angle,cK, onDisplay-Image Quality for Selected Display-Object LineWidths, 3.

-5[t-


0cc, for selected values of display-object line width, J, when extendedsource diameter, S, equals ;. The subjective image quality evaluationsused in figure 2-27 have been super-imposed in figure 2-29. Thus forany combination of source to display-object distance and display-objectline width, the expected display-image quality as well as the majorcause of definition losses can be found from this figure.

2.7.4 The use of figure 2-29 is best explained by a few examples.If the source to display-object distance a, is held constant at 1V and thedisplay-object line width, ;, is allowed to assume different values, theintersection of the line, a-l", and the horizontal line representing thevalue of the diffraction angle, ( , at each value of Z will determine theimage quality. In addition, if the intersection falls above and to theright of the curve, a equals the wave-length of light, X , divided by thesquare of the diffraction angle, I , in radians, the major effect is dif-fraction; if it falls below and to the left of this curve the major effectis extended source. Thus, as T assumes values of 0.001, 0.002,0.004, 0.007, the image quality is respectively unsatisfa.tory, mar-ginal, satisfactory, and good. In the first three instances the majoreffect is diffraction; in the fourth, it is extended source.

2.7.A The following conclusions can be drawn from the curves:

Values of 3 .001 00Q15 .002

Image Quality Uhsat. Marg. Marg.Diffraction

Effect a >. 0376 a>. 084e a >. 1504Extended Source

Effect a<. 0376 a<. 0846 a<. 1504

V alues of 3 .003 .004 .006

Image Quality Sat. Sat. GoodDiffraction

Effect a >.3384 a>.6016 &>1.3536Extended Source

Effect a<.3384 a<.6016 wl.3538

For all values of a, the projected image is unsatisfactory for values of 3less than 0.0015, marginal for values of 3 between 0.0015 and 0.003, sat-isfactory for values of 3 between 0.003 and 0.006, and good for values of3 greater than 0.006.

-52-


9.7.6 The effect of source diameter on resolution with source to dis-play-object distance variatibn is illustrated in figure 2-30. Resolutionevaluations were made from a display-image obtained by projecting aresolution chart as display-object with different size sources. The res-olution chart, pictured in figure 2-31, is of the type used to test opticalobjectives. It consists of disthnut opaque lines of various widths andspacings etched on glass. The lines are placed n groups, each grouphaving very accurately held uniform line width and spacing. The groupsare made to vary in regular sequence from a very coarse width and spac-ing to a very fine pattern. The display-image is examinod to determinethe group with finest spacing and line width (lines per mim) that can beeasily distinguished.

2 The curves in figure 2-30 show the pronounced deterioration inresolution of the display-image as the source approaches the display-bb-ject when the source diameter is large (.017'). When the very smallsource diameter (.00450) of the 2 watt-zirconium lamp was used the lim-itation imposed on source to display-object distance by the lamp envelopewas reached before 'any display-image deterioration was noted. Using the.017" diameter source, a resolution peak was obtained at a source to dis-play-object distance of between 3 to 4 inches. This peak represents thepoint of best resolution where the effects of extended source and of dif-fraction are at a minimum. When the .0045 diameter source was used,no peak in the curve was obtained. At the smallest source to display-object distance physically obtainable the highest PI ratio measured wasequal to .. Presumbly, if the envelcpe restrietions were removed, andthe source could be made to approach the display-object more closely,the resolution would reach a peak and would fall off as with the largersource diameter lamp. Deterioration In resolution to the left of thepoint of best. resolution is caused by extended source effects and is veryrapid at small source to display-object distances. The deteriorationV' occurs at distances beyond 48 is caused by diffraction. It is very6. and appears to approach an asymptote well above minimum ac-ce%...ole resolution levels. Hence, diffraction effects are not usuallyconsidered critical. It should also be noted from this figure that theeffects of diffraction are independent of source diameter.

-53-

NAVTRADEVCSN 1628 - 1

L44

AoA

'iI4~Ii9

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Fi7ure 2-31 Reoloution Patt.orm,

CHAPTER 3

The Point Source of Light

3.1. Introduction

3.1. 1 In the previous chapters the reader was made aware of theimportance of the point source of light and its considerable influenceon display-image definition. In this chapter the characteristics in apoint light source which are desirable when used in the point lightsource projection system are discussed. The various types of sourceswhich are available and applicable to this system are described andevaluated with reference to these characteristics. Also included inthis chapter are approaches for producing a satisfactory source whichhave not met with success. These are included to acquaint the readerwith the pitfalls of these methods.

3.2 Requirements of the Point Source of Light

3.2.1. In order to qualify for point light source projection, a sourcemust meet the following requirements:

(a.) The source must have a very small diameter.The smaller the source diameter the better theimage definition possible and the finer the detailwhich can be projected successfully. A sourcewith a diameter of . 029" (Zirconium 26 watt) wasused in the development of Device 2-FH-2. In coop-eration with the de Florez study program, (2-FH-4),the Sylvania Company produced a concentrated arclamp with a diameter of . )13" (Hafnium). Thislamp was subsequently used on Device 2-FH-2rand produced the same light output as the Zir-conium source. Further work by the do FlorezCompany produced light sources with diametersas small as. 0035" having greater light outputthan their predecessors.

(b.) A source must have a high luminance to provideadequate screen illumination of the proje..cted display.Assuming that the radius, surface reflectivity ofthe screen and thj transparency of the display-

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INAVTRADEVCEN 1626- 1

object are established for a specific projection4ystem, the brightness of the display-image isdirectly proportional to the light output of thepoint light source. This output in turn is de-pendent on two factors: (1) the intrinsic bright-n. ss or luminance of the point light source and(2) its diameter. Since the diameter of the lightsource is usually dictated by certain standards ofdefinition required, it is apparent that the lumin-ance of the source largely controls the displaybrightness.

(c.) Light coverage in azimuth and elevation should beadequate, preferably greater than the peripheralvision of the human eye. Then a single sourcecan be used for the wide angle presentation.

(d.) The spectral distribution of the source in the vis-ible range should include all wave lengths so thatdisplay-object colors are faithfully projected.Source color temperatures between 3000 and 60000 Kappear to be satisfactory. Some adjustment of thelight quality can be made by the use of suitablefilters at the expense of light output. However,the color temperatures of the lamp can vary be-tween wide ranges because of the characteristicsof the eye. The eye can readily adjust itself toa gross color unbalance in the projected pictureif the projection is in a completely darkened room.In this event the general adaptation level of theeye, both for color and brightness, is not influ-enced by room. lighting and the effect is to makethe projected colors appear more nearly correctthan they actually are. However, if certain bandsof-color are completely absent from the spectraldistribution, as with certain qlowing vapor lamps,the projected colors can be noticeably distorted.

(e.) The envelope must be made as small as possibleto permit bringing the source very close to thedisplay-object, making possible high scale ratios andthereby increasing the operating range of the device.


(f) The glass envelope surrounding the source shouldbe free of striations which will project on to thescreen and adversely affect the display-image.These striations can be particularly harmful sincethe projected images of the striations do not movealong with the projected picture and therefore furn-ish the trainee with a cue that he is fixed in realspace.

(g.) The heat radiation of the source should be low sothat there is no danger to the display-object whichcan soften or burn under high temperature condi-tions. Dark areas within the transparencies, whichabsorb the major portion of heat energy, can beirreparably damaged. The introduction of a heatabsorbing glass, which is externally cooled, con-siderably relieves this condition; however, theglass may interfere with the source approachingthe display-object to within close limits. In addi-tion, cooling certain lamps will adversely affecttheir performance.

(h.) The operation of the source should not expose per-sonnel to dangor. Certain super high pressurelamps explode after aging sufficiently, and if properprecautions are not employed, serious accidents mayresult. In addition, high energy lamps emit largequantities of ultra-violet radiation which is harmfulto both s-*in and eyes in extreme cases.

(i.) On an average, the source should have a long lifeto minimize maintenance. Most lamps decrease inlight intensity as the lamp ages. This Is true ofboth the concentrated arc lanips and gaL ious dis-charge lamps. Aging effects can be overcome tosome extent. With the concentrated arc lampsthis Is done by increasing the current through thelamps. A super pressure lamp is best discardedfor safety reasons if there is an appreciable lossn light intetsity due to aging.

(.) The point light source should be of reasonable cost.

3.3 Tye of Point Source Lamps

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NAVTRADEVCEN 1628- £

3 There are many types of light emitting sources that existtoday and which are commercially available. Only a few of theselamps have the necessary prerequisites to be considered for use ina point source projection syi3tem. Only small diameter sources ofhigh photometric brightness will be described in the following paka-graphs. These lamps fall into two classifications:

(a.) Low pressure lamps which depend on a glowingmetallic substance for light radiation.

(b.) High pressure lamps which depend on a glowingvapor for light radiation.

The former category encompasses tungsten filament lamps and Sylvaniaconcentrated arc lamps. The latter category includes mercury andxenon arc lamps.

3.3. 2 Tungsten lamps were used successfully in Device 2-FH-2 asthe side lights to supplement the projection of the zirconium concen-trated arc lamp, which is only satisfactory for 1500of light coverage.Tungsten lamps can be made to operate close to the melting point oftungsten (3650 0K),but relatively speaking, the lamps are of 1ow photo-metric brightness (7000-8000 candles per square inch) and In order toobtain sufficient light output, the source diameter must be fairly large.WhAre definition can be compromised these lamps are sometimes ade-quate. They are particuarly useful because of the small envelope whichencloses the source.

3.3.3 A much more efficient light source is the Sylvania zirconiumconcentrated arc lamp which is made in the following wattaqe ratings:2, 10, 25, 40, 100, and 300. These lamps operate at a temperaturewhich is close to the boiling point of zirconium in a partial vacuum.The boiling point of zirconium at one atmosphere is approximately53000K. The brightness of these lamps is several times that of thetungsten family and is in the order of 23, 000 candles per square inch.The increased brightness is obtained because of the high operating tem-perature. The brightness increase follows the Stefan-Boltzmann lawwhich states that the total emissive power of a body is proportional tothe fourth power of its absolute temperature.

3.3.4 Basically, the concentrated arc lamp is an arc lamp providedwith permanent metallic anodes and a special refractory cathode. Thesetwo elements are sealed within a glass bulb in a partial vacuum of ar-gon, an inert gas. When the arc is established between the two elements

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NAVTRADEVCEN 1628-1

the cathodu lo raised to a temperaLure beyond the melting point.

3.3. 5 Early In the component otudy program Tho do Florez Companyinterested the Sylvania Corp. in making a superior light source with aHafnium cathode. This cathode replaced the Zirconium cathode in, theotandard 10 watt lamp. The Hafnium lamp, having a considerably higherboiling temperature than the Zirconium, can be operated at higher inputpower to emit substantially more light. These Hafnium lamps, whenused in lIle of the Zirconium lamps in 2-FH-2, gave considerably betterdefinition, especially noticeable in the "on-ground" position.

3. 3.6 The ,-ource diameter, light output, and brightness of the Hafniumlamp varies with tho power Input to the lamp as shown in Figure 3-1.The diameter is.013" at 25 watts input. For this diameter the measuredlight output is approximately 13 candles and the calculated brightness is80, 000 cd. per square inch. This value is almost 4 times that of theZirconium brightness and for this reason it is possible to obtain compar-able light outputs for about one-half the Zirconium diameter (.029"). Thecolor temperature of tht Hafnium lamp is about 3300 0K and the light dis-tribution is approximately that of the Lambert's Law emitter. The measuredlight distribution is shown in Figure 3-2. The lamp envelope permits thesource to approach the display-object to within 5/18". The lamp can beexternally cooled without affecting its operation so that it can touch the display-object without hsrmful effects. One minor undesirable feature about thelamp is the slight source "wander" within the refractory material. Thiscondition, which is more of a minor distraction than anything of consequence,can be relievwd by increasing the lamp currnnt.

3.3.7 Throughout the study, source diameters were measured byeither a micrometer microscope or by optical projection methods. Thelatter method involves projecting the source image on to a screen to makedirect measurements of the enlarged image and then determining themagnification ratio of the optical system so that the actual source diameter caneasily be calculated.

3.3.8 Variations in source diameter with current changes in this lampcan be used to advantage. It is possible to reduce the diameter when thislamp approaches the display-object to obtain better definition. The re-daction in light intensity will probably not be objectionable because theimages are enlarged and will therefore convey more information in spiteof the lower brightness. In addition, the eye will not easily notice gradualchanges in screen illumination because of its relative insensitivity to suchchanges.

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NAV'IRADEVCEN 1628 - 1

22.. Lamp Used: 25W Hafnium .22Measurement of Source Diameter: Optical ProjectionsProjection Hoom Condition: Lighttight /Note: Luminance Is Calculated From /

Luminous Itensity and Source /20

20 Diameter Assuming Source is /A Circle: I ,/

Source18 Diameter 18

.I0

'186

14-

Luminous Intensity12-

--- Rited Current .08.

10 / Luminance 10

.080-

/0

2 o 66 .6Power - Watts

.fl 1.0 1.4 1.8 2.2 2.8 3.6

Current - Amperes

Fiqure 3-1 - Variations in Diameter, Luminous Intensity and LuminanceWith Changes in Current for a 25 Watt Hafnium Lamp.

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NA\rraMADBVCEN 1628- 1

LAMP USED: 25 W Hafnium - 1.3 amps (Source Diameter -•0135")APPARATUS: Weston Lightmeter No. 1246PROIECTION ROOM CONDITION: Light tightDISTANCE BETWEEN LAMP & PHOTO CELL: 12"

14

IO ,

N 20/ / 30

4' ./ '70

I i"'. -,

2- : 80

0. 90

1 r'.41": CErjTF rLINF

Figure 3 -2 Light Distribution e the 25 Watt Hafnium Lamp.

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.3.3.9 Several attempts have been made to interest Sylvania in makinga hafnium lamp with a smaller envelope so that the numerical scale canbe increased for some applications. To date these attempts have notbeen successful. Sylvania believes that to do this it will be necessaryto reduce the anode area and as a result the lamp may operate at exces-sive temperatures. Moving the source closer to the envelope will havethe further harmful effect of causing the hafnium vapor to condense onthe glass surface, which will substantially reduce the light output of thelamp, and will cause the glass to abstYb more radiant heat. All of thesefactors would probably result in an extremely short life for the lamp. Itwill also be necessary to use a harder and more durable glass envelopewhich presents additional problems. Sylvania has indicated, however, thatit may be interested In undertaking this problem, at some future time.

3.3.10 Sylvania has also been approached on the possibility of placingmore than one cathode within the glass envelope with suitable light shieldsso that increased light coverage can be obtained. This, they feel, can bedone but it will be necessary to increase the Lnode size to obtain suffi-cient cooling and as a result the envelope will necessarily be increased.

3.3,11 The HBO-109 Osram mercury arc lamp Is a gaseous discharge

lamp wherein an electrical discharge causes the mercury to glow. Thisprocess takes place at a high vapor pressure ranging from 35-70 atmos-pheres. Because of these pressures an extremely high photometricbrightness is obtained rivaling the brightness of the sun. The radiationfrom this lamp Is characteristic of the mercury spectrum but also has afaint continuoua background of the incandescent electrodes. The chieflines in this spectrum of the mercury arc are as follows:

405 millimicrons (violet)436 millimicrons (violet)546 millilmicrons (green)577-579 millimicrons (yellow-gr, ,

Since the radiation in the visible range consists . imartly of well definedlines, a color temperature cannot be assigned t. this lamp.

3.3.1 2 The only red radiation derived from this lamp is from the In-candescent electrodes. The predominant violot radiation and lack of rodcauses the red areas in display-objects to appear wine colored. A sub-stantial quantity of ultraviolet light is also radiated, which can be detri-mental because it often causes crazing to occur in acrylic plastics dueto a photochomical proc':i. It will also affect the dyes In the display-obiect which are generally of an unstable nature under the best conditions.

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NAVTRADEVCEN 1628-1

3.3.13 Figure 3-3 Illu-tratoo the physical ch'tracteriuticc of the lamp.The operating electrodes, which are 1800 apart, are onclooed In a 1/2"diameter spherical quartz bulb. 'rho electrode at .right angles to the oper-ating electrodes is used exclusively for starting purpose., in the HBO-107lamp. However, Osram now manufactures a mercury arc lamp withoutthe starting electrode, the HBO-109.

'3. 14 When operated at its rating of 100 watts, the source diameteris . 014" ad emits approximately 250 candles. The photometric bright-ness is approximately 1 1/2 million candles per square Inch. This isabout 18 times that of the Hafnium lamp.

3.3.15 Variations in source diameter, light output and brightness withchanges in power input for this lamp are plotted in Figure 3-4. It isimportant to note that as the power is reduced the source diameter actuallyincrease and the brightness decreareo. This is a result of the reducedpressures within the lamp which accompany the reduced power inputs.The effect of increased diameter is the reverse of that found in the Hafniumlamp, where reduced power input resulted in decreased source diameter. Thecurve of light distribution is shown in Figure 3-5.

3.3. 18 Unfortunately, the Osram lamp emits a great deal of heat energy.For this reason it is difficult to use it directly as the projection source,particularly when the lamp must be operated very close to the display-object.Cooling the lamp, as is done with the Hafnium and Zirconium lamps is notadvisable because of the resulting Lcrease in source diameter and rAductionin light output. Another disadvantage of this lamp is the high pressure whichcreates a safety problem to personnel. Fortunately, in spite of continueduse, do Florez personncel have not experienced any Ill effects from this lamp,except for an occasional "sunburn". This problem can be solved satisfactoril)with ultraviolet absorbing filters or Plexiglas to make the transparency. Afact worthy of mention at this point Is that fingerprints must be removed withalcohol and distilled water from t). lamp before starting, so that the saltsfrom oily fingerprInts will not combine with and soften the quartz at highoperating temperatures which will promote shattering the lamp envelope.

3.3.17 Without question, this lamp produces the brightest source ofany lamp tested to (late. It has particular value in that the source can be"de-magnified" further even at the e.pense of considerable light loss.This lamp has made it possible to use some of the optical approaches,which will be described In the following paragraphs, for obtaining evensmaller source diamete-s.

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NAVTRAD)VCEN ILIB -I

96S! 2 3

U 7-

a

*, ---

I

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-1(30'

Scales shown are in inches

1. Sylvania 26 Watt Zirconium Arc Lamp2. Sylvania 2 Watt Zirconium Are Lamp3. Sylvania 25 Watt Hafnium Arc Lamp4. Osram 100 Watt Mercury Vapor Lamp -HB~o-107

Figure 3-3 Assorted Point Source Lamps

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NAV'' RADEVCIEN 16 28 - 1

1340Lamp Used: Osram HBO-109Measurement of Source Diameter: Optical ProjectionsProjection Room Condition: Lighttight /Note: Luminance is Calculated From /

Luminous Intensity and SourceDiameter Assuming Source Is / .028 300a Circle: /I /

t //

24Soc / .024 20|0

Source Diameter / /

~22 Luminous /Intensity ---- / v / 0

i!/ Luminanceg~o/ v A;

118 0 j0" / Rated

/ Power

16 , .008 100/ , o

/o/ /

14 / x x x .004 60x x x

Power - Watts

Figure 3- 4 - Variations in Diameter, Luminous lhtesity and LuminanceWith Changes in Power for Osram EBO- 109 Lamp

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NAV'11LA1)EVCEN 1(12B3 -I

LAMP USED: Osram HBO3 - 107 or Osram HBO - 109APPARATUS: Weston lightnieter No. 1246PROJECTION ROOM CONDIT'ION: Light tightDISTANCE BETWEEN LAMP &PHOTO CELL: 12"1

400 4

10 80-

0

Figure 3 - 5 -Light Distribution of the Osrarn HBO-109Lamp.

NAVTRADEVCEN l6M- 1

3. 3. 18 Representative point source lamps are shown in Figure 3-3.Appendix IV contains a list and pertinent data of the more promisingpoint source lamps whose source diametero measure less than .100".

3.4 Reduction of Source Diameter by Optical Means

3.4. 1 The method which has thus far produced the most satisfactorysource for point source projection makes use of an optical system toreduce, or "demagnify", a real source such as the Osram point lightsource. The extent of reduction, the type of image which is formed(real or virtual), and the position of the source image is dependent onthe character of and over-all focal length of the optical system, and theplacement of the real source with respect to this system. The intensity,or light output of the source, is dependent on the luminance of the realsource, the reduction ratio of the system and the efficiency of the opticalsystem. It should oe noted thol the luminance of the image source cannever exceed, and in all probability will be less than the luminance ofthe real source. As an approxii ,tion of the maximum intensity that canba obtained with an optical systom for the image of a real source, theluminance of the real source should be multiplied by the area of the Imagesource, A proof of this is given in Appendix V. Values of light intensityversus source diameter for a typical system are shown in Figure 3-6.

3.. The light coverage which will be obtained with an image sourcedepends on the numerical aperture of the optical system and the reductionratio. In accordance with the Abbe sine law, the ratio of the sine of theexit half angle to the sine of the entrance half angle is directly proportionalto the size redu tion of the image.

3.4.3 Figure 3-7 schematically represents a typical optical systemused to reduce a real source. It consists of a condenser lens or elements,an objective lens or elements, and a simple negative meniscus lens. Theredl source is placed at the focal point of the condenser system, therebyp.oducing a collimated beam of light as the output. The collimated beamis converged by the objective lens to produce a real image of the sourceat the focal point of the objective. The reduction in size of the image isequal to the ratio of the focal length of the objective to that of the con-denser.

3.4.4 The negative meniscus lens has a two-fold purpose. Its focallength and position are selected to obtain an additional reduction In thesize of the image and to further disrerse the light. Since the lens is :iug-

atlive, the image formed will be virtual and will appear to an observor to

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NAV'1rADEVCEN 1628 - I

Experimental Conditions

lRcsl Source: Osram HBO-10Y Lamp (11OW)with Luminous Intensity of 500Candles at Diameter , 016 in,

Apparatus: Weston Light Meter #1246

100 Projection Room Conditions: Lighttight

9O

80

o70 Theoretical xp e, Experimental

S50

3

20

10

Source Diameter - Thousandths of an Inch

Theoretical Relationship from the Inverse Square LAwI 1

where I 500 candles and S1 , . 016 Inches

Figure 3 - 6 - The Effect of Source Diameter on LuminousIntensity When Source Diameter In Reduced

By Optical Elements

NAvTFADLOVCEN 1628 - I

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1.4

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NAVTRADEVCEN 162H,-1

t)0 eminating from a point behind the meniscus lens, Appendix V fullyexplains the theory and application of the meniscus leni for demagnificatlonpurposes.

3.4.5 Utilizing an optical system typical of the one described, thede Ilorez Company has successfully produ-Iod light sources as smallas . 003b" having an intensity of approximately 18 candles along the opticalaxis. Light coverage is in excess of a complete hemisphere, althoughlight output falls off sharply at the extremities of the hemisphere. Out-put in a particular direction varies directly as the cosine of the anglefrom the optical axis to the direction in question. This source can ap-proach the display-object within .072 inches.

;. 4.6 Any high numerical aperture condenser lens can be utilized inthe optical system. However, the de Florez Company has been verysuccessful through the use of a single element quartz condenser lens,sinco this lens must be placed in close proximity to the Osram lamp andbe capable of withstanding the intense heat. To date spherical condensershave been u.-ed, although tests are now in progress utilizing two elements,one with parabolic surfaces, to eliminate th abberations accompanying9pherical surfaces.

3.4.7 High numerical aperture microscope objectives have been used: successfully as objective lenses. These are generally high quality lensescontaining fewer light absorbing elements than photographic objectives,since their field is not extensive. All glass to air surfaces are usuallycoated in the objective to increase the optical efficiency of the systemand to iliminate the possibility of ghost images due to reflections amongelements.

3.4.t8 Attempts have bern made to increase the optical efficiency by

placing a spherical mirror behind the Osram ,,ource, but it has beenfoun I that the source itself is fairly dense to the light rays which arereturned Lnd focused at the source. Consequently, efficiency is Increasedonly slightly. It is also essential that the mirror be aligned perfectlyor the final ima 3 will be larger than desired. It is generally true that,in the use of a mirror, any substantial increase in light output of thefinal image results from a misaligned mirror and an oversized image.

3.4.9 It Is obviously important to use good quality lenses throughoutthe optical system sin-e any abberations resulting from inferior lenses ordesign usually leads to an oversized image without an accompanyi, g in-crease in light. Most good quality microscope objectives aro sufficiently


suitable for the purpose since the only concern of the optical system is toform an image of a single point. Obviously, as it becomes desirable toreduce the diameter of the image further, aberrations become a greaterconcern.

3.4.10 A convenient location for the placement of filters to absorb heat,for color compensation, or for special effects, is that following the con-denser lens where the light is collimated. Special fog and haze effectscan be obtained utilizing graduated filters in this section in conjunctionwith auxiliary projection lights.

3.4.1i In order to obtain better definition for an "on ground" conditionit is possible to reduce the diameter of the source with accompanying re-ductions of apparent altitude. By varying the position of any of the ele-ments in the optical system a change n the reduction ratio is achieved.However, there is an accompanying decrease in the angle of light output.

3.4.12 Figure 3-8 illustrates a typical assembled optical system and

figure 3-9 shows typical optical elements.

3.5 Other Approaches to Obtain a Small Source Diameter

3.5.1 During the course of the study made by the de Florez Companyseveral unsuccessful attempts towards obtaining a small diameter sourceutilizing various approaches were made. These have been noted in theensuing paragraphs and are presented primarily to discourage any furtherwork along identical lines.

3.5.2 Producing Small Diameter Sources by "Piping" Light

3.5.3 An investigation was initiated early in the study phase of thisproject to determine the pos3ibility of taking advantage of the character-istics of acrylic plastics to "pipe" light to produce a small diametersource. It was believed that a plexiglas cone could be used to concen-trate the light by introducing a large quantity of light at the base of thecone, and after repeated internal reflections, the light would emerge fromthe point of the cone in concentrated form. This system makes use ofthe princip'q that if light in a dense medium strikes a surface of a rarermedium at an angle of incidence greater than the critical angle, the lightis totally reflected. For plexiglas, with a refractive index of approxi-mately 1. 5, the critical angle is about 420.

3.5.4 The system described appeared to have many advantages. Theconcentration of light at the tip could make it possible to approach the

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NAVTRADEVCEN 1628 -1

)4

nLn

.4

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NAV'1'RADEVCEN 1628 -1

Kto

-74-4


display-object very closely with the source. In addition, it is possible toseparate the infra-red radiation from the visible light radiation convenientlyby the use of suitable filters anywhere in the path of the light. Convectingair currents at high temperatures would pose no problem to the display-object, since the light source itself would be far removed from it. It wasbelieved that a great quantity of light could be "funnelled" into the coneeven at the expense of poor efficiency to obtain a bright source.

3.5.5 Figure 3-10 is a diagrammatic sketch of the test set up used toevaluate the principle. A ray of light, on striking the surface of the cone,is bent by an angle equal to the total corie angle after each reflection so Itis easy to ascertain the maximum number of reflections possible before theangle of incidence is reduced to a value below the t. .Itical angle and thelight ray is allowed to pass out of the cone after being refracted. The con-denser system was used to concentrate the light at the tip so that more lightwould emerge from the tip by avoiding unnecessary reflections. Figure 3-11is a photograph of the test model. Figure 3-12 is a photograph of the tipitself. Figure 3-13 illustrates the various shapes of tips tested.

3.5.6 The results of the tests made were not encouraging aAd this methodwas abandoned in favor of the meniscus lens system. The results can bedescribed briefly as follows:

(a.) Light transmission efficiency dropped markedly an thediameter of the cone tip was reduced. Efficicnciesof approximately 30% were obtainable for diametersof about 1/8" but were reduced to a few percent asthe tip diameter was decreased below 1/32". Mostof the light escaped from the plexiglas cone In thelast 1/4", and while it wal possible to recover aportion of this light by the addition of a reflectingaluminum foil cone around the tip, the total lightoutput was low for small diameter sources. Itwas definitely established experimentally that verylittle of the light was absorbed by the plexiglas andthat the greatest portion of light loss was a resultof the repeated reflections within the cone. Itshould be noted that a light ray on striking th,, jur-face of the cone at angles greater than th, -,rlticalangle is not totally reflected at an angle equal tothe incident angle but a small percentaga of thjlight is reflected back along the path of the orig-inal ray.

-7b-

NAVtlMDLVC1~N 102H

~I 'K\a j

a, -~p.

2

I IiiLL~~ Il

- -, 04~) a-IC"

-0 -C).4

00

-7(3-

NAVIR-IADIENCEN 1628~

-4,

0

4

N\AVTRADEVCIEN 1628 1

Figure 3-12 Light Concentration by an Acrylic Tip

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NAVIRADU4VCEN io2n -

0

1.4

0s4-

in

NAVTRAD]VCEN 1628-1

(b.) It is not pus bio to obtain a light covtwrr-Jo beyondLwlcoe tho critical anglo of Ploxigla;, (toLal angle 84)without employing other ineano for obtaining the uril-form dispersion of light. Ono such method would beto roughen the Plexiglas tip; but thin results in largeliaht losses.

(c.) It is extremely difficult to obtain a uniform lightdistribution because the small tip does not permitan accurate control of the light emitting surface.The reader will appreciate the difficulty of obtain-ing a uniform dispersing surface of extremely smalldiamenter.

(d.) Severe light dispersion, caused by the refractionof different wave lengths, resulted in many colorpatterns emitting from the tip.

3. 5.7 The possibility of u.=ing a highly reflective aluminum cone toconcentrate light In a similar fashion as the PlAxIglas cone also was studiedfor a brief period of time. This work did not show any promise and themethod was immediately discarded.

3. 5. Additional Attempts at Obtaining an Improved Point Source.

3.5.9 Other approaches which were pursued to obtain an improvedpoint soure but which did not lead to significant results will be mentionedhere. These approaches appear to be theoretically sound out have notbeen successful because of practical or manufacturing limitations:

(a.) The possibility of using a new material with a veryhigh boiling point as the cathode in the concentratedarc lamps was discussed with Sylvania. Under con-sideration was the use of tantalum carbide, whichSylvania has us.ed In the manufacture of some ofIts larger and more brilliant lamps. Sylvania at-tempted to make a lamp in the 25 watt size utilizingthis material, but after several failures, abandonedthe method. The tantalum carbide was extremelydifficult to grind In very small diameters (about.015") because of the brittle nature of the material.In addition, when this problem was resolved, it wasfound that the Impurities in the tantalum carbidewere quic-kly vaporized when an arc was established

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NAV'I1rADEVCEN 162H- i

and consequently tho cathodes Immediately woakenodand broke off.

(b.) The possibility of pressurizng the concentrated arclamp was also discussed with Sylvania so that theboiling point of the cathode material could be sub-stantially raised. Sylvania indicated that this wouldrequire more devalopment work than was ecoriom-ically feasible duo to the small demarfor concen-trated arc lamps.

(c.) The possibility of reducing the distance between theelectrodes of the Osram lamp was discussed withthe manufacturer. The indication from Osram wasthat this was not practical to do because of the dangerof shorting ,ut the electrodea after ,expansion as aresult of the wnerating temperatures.

(d.) The possibility of introducing a mechanical shleld,with a small diameter hole, (. 005" or less) withinthe envelope of the Osram lamp and very close tothe source so that the hole would establish thesource diameter was not considered practical.Osram did not feel they could properly supportsuch a shield within the envelope. They also feltthe arc would be shorted by the shield and that thehigh operating temperatures would pose a problemin locating a suitable shield material. The maximumtheoretical coverage that could be obtained with alamp of this kind would be 1800 but in all probabilitythe shield could not be placed close enough to approachthis value.

(e.) The possibility of using mirrors to reduce the sourcediameter of the Osram lamp was discussed with in-dividuals familiar with the design of optical mirrors.The indication received was that there is no easyand inexpensive method for obtaining this result andthat optical lenses appeared to be a better approach.

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CHAPTER 4

The Display-Objet t

4. 1. Introduction

4. 1.1 While, as previously mentionod, tho display-object may beeither transparent or reflective, the major portion of the work to datehas been devoted to development of the former. A very considerableamount of this work in the 2-FH-2, 2-FE-4 atid 2-FE-5 programs wasdevoted to development of suitable methods fo' pzoducing satisfactorytransparencies (a more convenient term for transparent display-object).Despite these efforts, this component still lags behind all others in thestate of the art since it requires considerable expendituresi of time, effortand money to produce a satisfactory transparency. This chapter dealsprimarily with the production of rigid and flexible transparencies, bothhand decorated and photographic. It also describes several special tran3-parency types, reflective display-objects, and the problems associatedwith the manufacture of each.

4. 2 Requirements for a Satisfactory Transparent Display-Object

4.2.1. A go6d transparency should possess the following qualities:

(a.) The transparency shoud be reasonablyrealistic, having jood aetail and colorcontrast to contribute to the realism.The details should be suffilietly accurateto present genuine visual cues to the ob-server.

(b.) The tram.parency should be free of striationsand imperfections which will detraut from arealistic presentat!on.

(c,) The transparency should have good lighttransmission characteristics.

(d.) The transparency should have good physicalcharacteristics, Including the strength tosupport its own weigat, good resistance to

NAV'L'RADiFVCDI,:N I(2G-1

tear, bending, and abrasion.

43 =ye, of Trans parencies

4.3.1 Transparencies fall into two physical types: rigid and flexible.It is unfortunate that rigid transparencies are limited to the smaller sizesfor they have considerable advantage over the flexible type. They areeasier to manufacture. Dyeing this type presents few serious problems,due to the nature of the transparency and dye materials. In addition thebase material is considerably clearer than the flexible type and there isless light absorption when compared to the flexible type. Generallyspeaking, a rigid transparency requires a less elaborate suspensionsystem and usually there is no need to get involved with troublesomeseams as with flexible types. The mounting of 3-D objects presentsfew difficulties. A good example of this type is shown in Figure 4-1.The base material for this transparency was Plexiglas II-A. Thistransparency was approximal.ely (5 square and was utilized on device 2-FH-2.

413.2 The single advantage of flexible transparencies is the factthat a more compact mechanical system can be designed to suppqrt themsince they can be readily rolled on to a drum, or they can be looped asmany tinres as is necessary and treated as an endless belt. It is thereforepossible to utilize a flexible transparency to simulate an extensive area.For example, a transparency for Device 2-FE-2, which was made of rigid

Plexilas, had an actual area of only 36 square feet. By comparison It isplanned to use a flexible transparency for Device 2-FH-5, which containsover 450 square feet.

4.3.3 The materials most commonly used in the manufacture of flexibletransparencies are acetates and duPont Cronar (a polyester base on whichis placed a photographic emulsion). The base material for Cronar isidentical to duPont Mylar, a very tough plastic possessing excellent strengthand tear characteristics. In addition its optical clarity is as good as, orbetter than any other flexible plastic materiRls; however, it is not as goodas some of the rigid plastic bases such as Plexiglas II-A.

4During the course of the 2-FH-4 investigation miuy transparencybases were tested to determine their applicability to the point light sourcetechnique. Appendix VI lists only the more promising materials tested andgives the pertinent information on each material. Following this data is alist of materials tested, but which proved unsatisfactory on at least one ofseveral accounts. Included in Appendix VI are both the rigid and the flex-ible types.

4.3. Figure 4-2 illustrates the use of a flexible transparency incombination mith a pulley conveying system. In order to keep the trans-

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parency perfectly flat and to reduce the amplitude of transparency vibrations,which are very troublesome in this type of display-object, the transparencyis subjected to considerable tension (approaching 100 lbs per linear foot).For this reason Cronar has found considerable use, since its tensile strengthis among the highest in plastics.

4.3.6 To facilitate proper tracking of the flexible transparency on theconveyor pulleys, special self-aligning rollers, licensed by the U. S. SteelCorp. under the name of "Lorg Aligner Rollers", are contemplated forDevice 2-FE-5. These rollers do not require any external control mecha.Ismto achieve proper tracking, but equalize lateral forces in the transparencyby self adjustment of the roller outside sections which are free to move.

4.3.7 The use of Cronar has presented a few serious difficulties. Thismaterial cannot be seamed easily. It requires a special coated tape (.001"thick) to form a lap joint under the action of substantial heat and pressurein order to obtain transparencies which are wider th.n 42", the limitingwidth of Cronar. The special tape is manufactured by the G. T. SchjeldahlCompany located in Northfield, Minnesota.

4.3.8 Another problem, associated with flexible transparencies, isthe mounting of 3-D objects. In order to allow for the passage of 3-Dobjects around a conveying pulley, the pulley must be grooved. This isshown in figure 4-3. The grooves necessitate the programming of the3-D objects to a considerable extent since they must appear within well-defined lines.

4.3.9 It has been considered possible to off-set the advantage of theflexible material by using sheet-feeders and repilers to maintain thecontinuous flow of rigid transparencies. Another possibility for main-taining a continuous flow may be by making a continuous belt of rigidtransparencies by hinging the various sections together and obtainingan action similar to a sliding overhead garage door. Obviously, eitherof these systems necessitates the use of a very complicated transparencyconveying system.

4.3.10 Generally speaking, rigid transparencies are more easily dyedby hand decorated techniques while the flexible type are usually manufacturedby a combination of hand decorated and photographic techniques. Althoughthe use of Mylar presents many great advantages, It possesses a few draw-backs. The material Is impervious to practically all dyes and, consequently,a photographic emulsion, which can be dyed readily, must be used tomanufacture the transparencies.

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4..4 Mantufcturinig Techniques

4.4.1 Manufacture of Transpartincies by Hand Decorated Techniques.

4.4.2 Several types of dyes are available which are capable of dyeing1Phixiglas either by the dip process or spraying. In addition, these dyescan be applied with brush or pen. Dip dyeing generally leads to the mostsatisfactory results insofar as light transmission Is concerned. However,it is the most time consuming since it requires special clay barriers tobe erected on the transparency, outlining the area to be dyed. Thistechnique is especially troublesome on curved surfaces.

4.4.3 Color L generally applied to large areas by spraying. Colorsaruration is usually controlled by the proportion of inks and solvents inthe spray solution. The dye solution should be sprayed by someone skilledin the art. Respraying a surface to obtain additional color density is notusually suciussful, and generally results In fogging the surface. Thisdrastically reduces light transmission. If respraying a surface becomesnecessary, the surface scum, which usually forms due to respraying,can be removud by applying wide inasking tape to the dried, foggy surfaceand then removing the tape, '['his usually carries the surface deposit withit and will generally improve light transmLssion with some dyes.

. 4. 4 For very fine line work the rigid base materials can be etchedwth scriber. Appendix VII is a listing of pertinent data for all of thematerials which have been used to appi; color to plastic materials. Thesedyes are rated according to the method of application.

4.4.5 The Manufacture of Hand Decorated TransparenciesUtilizing Photographic Techniques

4.4.6 As explained previously, the photographic technique has wideapplication in the making of transparencies on Cronar since the photographicemulsion will easily receive art work, whereas, the base material will not.Thet various steps in the producton of such a transparency are as follows:

(a.) Layout of the area to be depicted to a suitablescale. See Figure 4-4.

(b.) Sectkinalizlng the layout so that it can be repro-duced to some other scale, namely the

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scale selected for the final transparency,Figure 4-5.

(c.) Layout of th3 basic information to scale onC ronaflex utilizing guide lines to depict largeareas. See Figure 4-6.

(d.) Masking the Cronaflex overlay prior toairbrushing as shown in Figure 4-7.

(e.) Actual airbrushing of the Cronaflex (originalpositive transparency) to obtain the effect of acontinuous tone. Spraying is done with blackInks. Figure 4-8 shows a completed airbrushedsection.

(.) Vanufacture of a negative of the Cronaflexpositive by photographic techniques. Thisnegative can be retouched prior to printingthe Cronar positive if corrections are re-quired for any reason. Exposure of bothnegative and positives can be done in a vacuumframe in sections or with a continuous printer.'With the former technique extreme care mustbe exercised to obtain proper registration be-tween the sections.

(g.) Combining the various sections o the trans-parency by seaming them.

(h.) Dieing the combined transparency as shown inFigure 4-9. A completed transparency sectionis shown in Figure 4-10.

4.4.7 To simplify the manufacture of transparencies, an investigationis presintly being conducted to determine the possibility of producingpositives directly from positives, thus eliminating the negative step.This appears to be possible by using a duPont positive print materialwhich can be handled in ordinary subdued light conditions during exposureand development.

4.4.8 To obtain an effect similar to the continuous tone obtained

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Figure 4-b Sectionalized Original Art Work for Reproduction to AnotherScale Ratio

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with photographic transpareticios, a special technique was utilized inman factu ring a rigid transparoncy fur Device 2-FH-2 which combinedphotographic and hand decorated technIques. Briefly, the system con-sists of dyeing the plate by the standard methods and then applying aspecial photographic coating over the dyed areas to obtain the simulatedcontinuous tone effects. This was done by applying a renhii over the entireplate and coating the resin with a light sensitive material. Positives ofthe photographic image desired (continuous tone and line ..atail) were placedin proper registration over the dyod areas and exposed to light. The ex-posed areas then became impervious to certain solutions and the unexposedareas were washed away, leaving a photographic image consisting of aresin residuA, This method made possible the inclusion of fline detailotherwise impossible by hand decorated techniques. The photographicwork in this instance ,as sub-contracted to the Truline Corporation,Saint Louis, Missouri.

4.5 Light Transmission Qualities of Transparent Materials

4. 5. I. It is in order to discuss the light transmission characteristicsof plastic,; since this subject has a rather profound influence on the poijitsource projection technique, especially in applications where low simulatedaltitudes are involved or where there is a requirement for the projectionof distant scenery.

I4. b. 2 A limitation of the point source projection technique is itsinability to project distant s-enery, if the transparency is perfectly flat(which is a condition for good perspective if the area to be portrayed isflat). For all practical purposes, light transmission is reduced to asmall amount at angles of 8b° of incident light. 'Ihis means that all scenerybeyond ten times the apparent altitude is not projected. This condition isradically different from what is normally experienced in true life shcemost of the scenery an observer sees is subtended by the first few degreesmeasured from the horizontal. Contouring the transparency so that lightincident on the distant scenery will rever exceed this flat angle will helpto relieve this condition. This can easily be done with flexible materials.Rigid materials must be permanently formnd.

4.5.3 Most materials used for the transparency base have indices ofrefraction of about 1. 5. Very little light loss occurs in the materials dueto absorption. Practically all of the light loss is due to the reflection fromeither the first or secund surface. Figure 4-11 is a graph of the light lossoccurring from the first surface as a function of the angle ,of incidence.For angles of incidence less than 70 °the light loss is not appreciable. Forthe first 400 the light loss is about 4% and is approximately 18% at 700.

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Intensity Intensity

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NAVTRADEVCEN 1628-1

After 700 the light loss rises very sharply and is about 70% at 85 0 .The light that is not reflected from the first surface Is refrarted follow-ing Snll's Law. As tie angle of icidence becomes larger and larger,the light is increasingly refracted so that the angle of incidence to thesecond surface approaches the critical angle for total reflection. As theangle approaches the critical angle, more of the light is reflected andless is refracted so that finally, only a small percentage reaches thescreen. Figure 4-11 also indicates the light loss from the second surfaceand the combined light loss flue to reflection from two surfaces. A methodis now under study for possibly reducing the light loss due to reflectedlight from rigid flat Plexiglas by providing one or more surfaces resezrrblingthe surface of Fresnel lens (surface configuration very much reduced.)This technique may be applicable to certain projection problems. Fabrica-tion of the surface described will probably present a few manufacturing aswell as projection difficulties which will have to be solved.

4. 5. 4 The light reflections off the transparency surface can be asource of trouble. The reflections are directed to the sc-een and inter-fere with the proper transparency projection. The reflected light ispartially polarized in the plane of the reflecting surface, and its effecton the projection can be reduced by introducing a filter (plane polarizingmaterial oriented at right angles to the reflecting plane) in the path of thereflected light.

4.5.5 Several successful attempts were made to coat Plexiglas sur-faces with anti-reflectioni coatings, but this only improved the light trans-mission for small incident angles and had no measurable effect at thelarger angles.

4.6 Special Effects

4.6.1 The use of three-dimensional objects on the transparency nasgreatly enhanced the effectiveness of the point source projection technique.Changes in the perspective of the objects themselves and with other objestsappearing in the scene make for a very realistic and convincing presentation.These th.ee-D objects are generally made of transparent paastic materials,usually rigid, which can be dyed and which will transmit light; however,crrtain objects have been made frum opaque materials and have been con-sodered adequately realistic.

4. 9. 2 Some contouring of the bane material hao been attempted tofollow the contour of a particular area. This has been done by formingPlexiglas and otliu rigid types of plastic, but is not considered practical

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UX(-cpt furu the rost gentlo contours:;. Sharp Chalgjeu II coi litir arodifficult to obtain without the u souof forming i'aclilt.s WI whch Itivariablyresult In internal striatlons or .u rfaee "Irrark-off" (sou fac abberatiom.),which are practically Impossible to ellminate. Contouring the entiretransparency is primarily used Lo improve tijht transmission and rigidity,as previously described, rather than ltriulatini a specific torrai i.

.6.3 Special 3-D objecLo, such as nountaili, havo burnt o-ccess-fully made by hand forming thin acetal.e raturial followed by spryliqj witha transparent plastic spray. The sprayed material hardens preservingthe shape producing mountains as shown In Figure 4-12. This; m:hod isvery flexible and does not require any forming faciliLies. Another methodwhich has been used successfully to make satisfactory mountains isaccoumplishud by vacuum forming semi-flexible vinylite. Mountains madeby this method are shown in Figure 4-13.

4.6.4 After forming, these mountains must be colored by paintingor dyeing, A fair rieauuru of s;kill is required since the mountains musttransmit sufficient light to hidicate conLours, but cannot be so trawsparentthat the mountain does not. appea. in the dioplay-image. The color satur-ation must be suifficlent to allow transmnission of light through only oneside of the mountain. After dyeing, the mountains are cemented to thetransparency.

4 I Another special effect that can sonietin:.s be used to Indicatesurface deprev:sions or crevices is the use of "]nrvurld mountains" mountedupside-down on the lower sid, of the transparency. Considerable skill mustbe used to dye the "crevice" and surrounding area to obtain realistic effects.

L . Several attempts were made to ca;t three-dimensional mountainsfrom liquid Plexiglas material. The finished products were too dense totransmit light and were not considered 6uccessful.

4. 7 Aerial Photooraphs as Tranaparet t Di;L,.lay-Object-.

4. The ue of direct aerial jphotogjraphs a.- dis;play-objects forpoint light s;ource projectiou techinques has only met with mediocre ::uccessthus far. The primary reasons for this are as follow.::

(a.) Aerial plotographs cou;airn coIt-id,T'rableminit detail which Is not capable of beingresolved by the point liqht o,ure. Sulb-staitial improvements IIt h pr,:; lfr day pointlight ;ources will be required b-fore directaerial photoqrap h; .-ai be is0:d. k'101h inl-

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provements are not expected in Lho nearfuture.

(b.) Direct color transparencies are far toodense to be utilized by preuent day pointlight sources.

(c.) Dii .ct aerial photographs are never perfectplan views as are those manufactured by theusual methods. Consequently, perspectivedistortion results.

(d.) Aerial photographs are limited in size andtherefore, registration of smaller sectionsin the manufacture of a large transparencypresents difficult problems.

4..8 Reflective Displa-Object

4..8..1 During the study an effort was made to find other types oftransparencies which would permit the observer to see greater distances.The reader should recall that a limitation on visibility results from thefa-t that light Is reflected from the surface of the transparencies at acuteangles.

4 8 2 This limitation can be used to advantage in certain casesinvolving transparencies which do not require a large number of three-dimensional objects of well-defined shapes. It has been found thatsuitable projection plates can be made under these conditiot s by mirror-Izing a sheet of Plexiglas or acetate so that a highly reflective coatingis obtained, On this surface is painted, with tran.sparent inks, suitableterrain information. Projection is aconiplished with conventional pointsources, eAcept for the following changes. The projection plate is in-vrt-d Ind suspended over the observer so that it possesses the usualdgrees of freedom. However, the point source is between the observerand the plate. This is shown in Figure 2-4. The scenery Is applied tothe plate ao a mirror image of the normal presentation used in the decorationof transparent plates.

4.8.3 The particular advantage of this projection plate in a pointsource projection system is that visability is not limited at acute anglesof incident light, since the system depends on total reflection. Distantscenery, which would normally be "blacked-out" with conventional trans-parencie', can now be projected.

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sincey thie tdhoe o th-e frmkn te gnsralcy ito thaeno ileredsrance frou thegthuos e be ten obsresatisaded footinngbteaheso frate rifletives co atingea~a aIrnmn the Plj -Adpcura esciladinmhpreen oerthe dort .

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CHAPTER 5

The Screen

.Introduction

5.1.1 This chapter deals primarily with the brightness of thedlsplay-Image and the method in which brightness is affected by thetype of screen surface utilized. It describes the various types ofscreen surfaces generally aviilable, their characteristics, and ad-vantages and disadvantages for-oint source projection. A methodfor making a satisfactory screen with a glass beaded aflective sur-face is described. At the present time this method appears to bemost suitable for point source work.

5.1.2 The effect of the screen contour on distortions in the display-image will not be included in this chapter since it has been tL-ated inChapter 2. It is important to note, however, that the screen designusually requires that several compromises be made. On the one handthe screen should be large to minimize the distortion which results fromthe displacement between the observerts eye and the source. In addition,a large diameter screen reduces the effects of binocular convergenceand the rate of change in binocular convergence with changes in sceneryposition. A large sczeen also minimizes the apparentness of the screengrain. On the other hand, the screen should be made as small as possibleso that the screen brightness is adequate and to minimize the space re-quirements of the device.

. No data is available which indicates the minimum screenbrightness required for training purposes. However, it is subitantialyless than that required for motion p icture theaters which generally main -tain a minimum of b to 1b foot-lamberts in the highlight areas uf theprojected display. It has been generally believed by the de Florez Companythat anywhere between .2 and . 5 of a foot-lambert is sufficient for trainingpurposes, if the observer is dark adapted. The values stated presupposethe use of a low density display-object.. Contrast between the highlightsand the shadow areaq of the display-object should not be great to insureadequate brightness of the shadow areas. Because of this and the use ofpastel colors In the manufacture of a display-object, the over-all impression

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that an observer ceceiveo when viewing the display image is that thescene is illuminated by low contrast, low brightness daylight conditionsresembling a cloudy day.

5.2 Screen Brightness

5.2.1. Screen brightness is determined 1y several factors, amongthem the light output of the source, the absorption characteristics ofthe display-object, the reflective characteristics of the screen itselfand its distance from the source. The problem of screen brightness isrendered particularly acute by the fact that a logarithmic relationshipexists between variations in absolute brightness !i'vel and correspondingvariations in the observer's sensory perception. Thus a relatively largeincrease in the measured value of screen brightness appears to the observeras a small increase o! brightness in the display-image viewed. Effortsmade to improve the characteristics of the point source and display -objectshave been discussed in previous chapters. The reflectivity cha -acter-istics of the screen will be discussed in the following paragraphs.

5.3 Types of Screen Surfaces

6.3.1 Several types of screen surfaces are available for use withprojection systems. These include:

(a.) Matte, or diffusing type surfaces

(b.) Directional, or specular reflection typesurfaces

5.3.2 Matte surfaces will reflect light equally in all directions.Consequently, they are the least brilliant, but are most suitable forviewing from the widest angle. Large theaters make use of this typeof surface extenrively. The surfa:e is smooth and consequentlypictures appear sharp even at sho t viewing distances.

5.3.3 The specular reflection, or retro-directive type surfacesdo not reflect light equally in all directions but favor a particular direc-tion. Thus, an observer sitting within the limits of the most favorableviewing angle will observe a picture brightness which is substantiallyin excess of that obtained with a matte type surface. The measure ofbrig'itness increase over that of a matte surface is generally describedas the "gain" of the scteen material.

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6.3.4 Obviou.,ly, if an observer Is seated outside the limits of themost favorable viewing angle, picture brightness will be decidedly lessthan at the favorable angle. It will probably be less than the brightnessof the display when projerted on a matte surface. Consequently, its gainwill be less than one.

6,b For the point source projection system the retro-directive typescreen surfaces are to be preferred sinue the positional relationship be-tween light source, screen and observer is generally fixed and the techniqueof retro-directive reflection can be applied.

5, 3.6 The more common types of specular screen surfaces are theglass beaded type, the metallic type, and, more recently, the lenticulartype. The most favorable type for point source projection appears to bethe glass beaded type. This type of screen is made by coating the screunsurface with a white adhesive, and then pressing or spraying tiny sphericalglass beads Into it. In this sense It is the first lenticular screen, eachbead being a minute spherical lens which is made to return light along aparticular direction. A ray of light falling on a glass bead is returned,after sevural refractions and reflections internal to the glass bead, withina cone of light whose axis is the ray of light falling an the bead. The returncone angle is controlled largely by the index of refraction o the glass bead,being smaller for the larger indices. Within the cone, glass beaded screensgive gains of approximately two.

5.3.7 Glass beaded screens are particularly suitable when curvedscreen surfaces are employed. Curving the surrease has very little effecton the return cone since the performance of the spherical bead is unchanged,even with curved surfazes.

b. 3.8 The surface texture of the beaded surface Is quite coarse.Because of this pictures appear unsharp when viewed from short distances(le. than about 69). From further back, however, the texture is notnoticeable. In order to reducc binocular convergence and distortioneffects, a screen radius is seldom lesis than 10 in a point source projectionsystem.

5.3.9 Metallic screens have been tried and have only provided moderate

su~icess with the point light source technique. Under favorable conditionsscreen gains between 2 and 0 can be obtained, but the return cone angle Isgenerally very narrow, thus barring the use of this type of surface wherethare is a large displacement between light source and observer. In addition,

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gal,,' markedly reduced when ctdrved surfaces are employed, sincethe r-+urn angle is greatly affected by th3 orientation of the reflectingplanu at the point where the ray strikes the plane. Also, wide differ-ences occur In the characteristics of metallic screens. Some are simplymade by silver coating a smooth base and others employ a fine silverparticle suspended within a thin plastic layer. Size and distribution ofthe particles is a major factor in determining a silver screen's gain.Another factor is the treatment of the screen surface after the metalliccoating has been applied. Metallic screens are generally smooth andsharp detail can be re,.olved even from a close viewing distance.

5.3.10 Lenticular screen surfaces are the most recent developmentin the field of screen design. The screen surface is embossed with apattern of tiny lenses, many thousands of them, which are made to con-trol the light return angle within very close limits. These screens werefirst made by utilizing metallic screens having special reflective character-istics and then embossing a particular pattern which caused light to bereflected in the desired manner. Theoretically, screen gains as high as100 or more are possible with this type of screen, but they are generallyvery expensive to make, and even more important, are generally onlysuitable with spherical screen sections. Any other type of curvaturewould require a variable lenticular pattern to control the return path, thusmaking the cost prohibitively high for point source work.

5.3.11 Typical curves of screen gain versus viewing angle are shownin Figures 5-1 through 5-4 for matte, beaded, metallic, and lenticularscreens respectively. A test staid for measuring screen gains is shownin Figure 5-b.

5.3.12 A special matte type surface worthy of m.ntion is the flatrear projection typo of screen. The use of this screen is requiredwhere rear projection systems are used. This system can be used toadvantage to minimize distortion by making it possible to place theobserver's eye at a position which s the mirror image of the sourceposition relative to the screen. However, in addition to lower lighttransmission, which redudes the screen brightness, additional problemsmust be resolved, especially for the wide angle illusions. Figures 5-8and 5-7 show curves of light transmission and reflectivity respectivelyfor the rear projection screen.

5.4 Fabrication of a Glass Beaded Screen for Point SourceProjection

5.4. 1 As previously indicated, glass beaded screens are made by firstpreparing a smooth white surface with a special white binder and pressing

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Reflected Luminance of Screen Under TestScreen Gain Reflected Luminance of Standard Matte, Screen

12. Incident

Light F lux

Reflected10 Light Flux. Viewing Angle

-.ScreenSurface

8

,,,

4

Matte Screen/ Reflectivity - 100%

2 Eautman Kodak Sta idardGray Card (White Side)

Gain - 0. 9

0 5 10 15 20 26 30

Viewing Angle - Degrees

Figure 5- 1 - Screen Gain with Viewing Angle for a Matte Screen

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Reflected Luminance of Screen Under Test12 Screen Gain =eflected Luminance of Standard Matte Screen

IncidentLight Flux

10.

ReflectedLight FluxLih FViewing

Anqle

8 [-Screen, Surface

0 6

4

2

"k-Matte Screen Reflectivity - 100%(Screen Gain - 1)

0 5 10 15 20 25 .30


Figure 5- 2 - Screen Gain with Viewing Angle for a Da-Lite

Glass Beaded Screen

)

-Ill-

NAV"'1R.ALDEVCEN 1.628- I

12 Screen Gain fcted Lumince of Screen Under restReflected Luminar, e of Stand. d Matte Screen

Incident10 Light Flux

Ref lectedLight F ux Viewing Angle8

ScreenSurface

6

4

2

Matte Ocreen Gain - 100%(Scrom Gain - 1)

0 5 10 15 20 25 30Viewing Angle - Degrees

Figure 5- 3 - Screen Gain with Viewing Angle for a Radiatit DiffuseMetallic Coated "Superama" Screen

- 112-

NAV'1,EUVC1WEN 1628 - 1

Screen Gain Reflected Luminance of Screen Under TestReoflected Eurninance of Standard Ma'et Screen

IncidentLight Flux

Reflected

10 Light Flux Viewing Angle

Screenjj;'Surface

LenticlesV ertical

0a)

4

Lenticles

Horizontal

k-Matte Screen Reflectivity - 100%

(Screen Gain - 1)0 , i o 16 i"0 25 30


Flgttm 6 - 4 - Screen Gain with Viewing Angle for a NylcoLenticular Screen

-113-

NAVI'IA DEV~\C1'N iMX8 - I

r

!T)

Lij

4

NAVI'RADEVCEN 10'X8 - 1

Source: 2b W Hafnium Lamp - 1. 8 Amps.Screen Type: Rear ProjectionScreen Size: 4 inches DiameterLamp to Screen Distance: 9 inchesScreen to Photo Cell Distance: 9 inchesProjection Room Condition: LighttightApparatus: Weston Light Meter No. 1246Determination of Efficiency:,

Flux Density to Photo Cell100C Flux Density to Screen x Screen Area

80 t ncidont Flux

0Scruo Area

VIewing Arigle

a 60

'I'ra.rnritted Flux

40040 a

0

20.\

-- T-- - r " r -. " , '- ----- -- r-10 20 30 40 50 60


Figure 5 - 6 - Variation in Light Transmission With Viewing AngleFor a Rear Projection Screen.

- II b-

NAV'I AIEVCEN 10,,H - I

Source: 25 W Itafnium Lamp - 1. 8 Amps.Screen Type: Rear ProjectionScreen Size: 4 inches DiametorLamnp to Screen Distance: 9 inchesScreen to PhotoCell Distanco: 9 inchesProjection Room Condition: LighttightApparatus: Weston Light Motor No. 1246Determination of Efficiency:

Flux-Density to Photo Cell100. lux Dens'ity to Screen x Screentirea

80

Incident Flux

Reflected Flux i

00. Vewing Angle

.Screen Area

UM 40.

20 0

'0

10 20 30 40 50Viewing Angle - Degrees

Figure 5- 7 - Variation in Light Reflectivity With Viewing AngleFor a Rear Projection Screen

- lit;-

NAV'1IUArJWCIN 1028-l1

0 , :pruyintj thu gin.-; ;s Load., to 1' 0-ipoe iflh (1r31th 111!L) 0h10nd: rMrOnt-oLi.,Tho bas ic rigid itracttiro rol- Lho ,,cr.,on can bo muof u[ hi rgijDui., roin-force,,d plL'Lltic panoto joinod together and siupported from the roar by ,.light aliimlnrn frame. A schemnatic ropru(-mtatlorl of thir;. typo o)f dos1griIs sihown in BFigure b-83.

5. 4.2 Thu varlouu n,,.,otie panolu can bo mact., from a niol ptwtoror wood form, whivh Ws actually the niegative of W.', ocioo-n panul dirod.A typical forming tool is -,hown i1,Figure b-9. Afte:r a partinig agernt Isapplied to tho ourfaco of tho formirng toot, a thin reniri --oatirvg I, appliudto the oarfac-e of tho tool andl ribooqiuut layoro of fiog s~ houto aridrosin, In liquId forn'i, are al.,no applied. Stru ,tural rill. (curi ouanily beinicludeil u~illizlntg thin toc.h:.ilque. After caring, tho rigid paniel Is removadfrom the mold. SUh.,Ljquert parieli, eariW be Mado nir1nilarly. Tho volu,,tivosurface is applied to thu paniol and tht-- oron panoin, can then be join,_dtogether a71d ;iupported bhy the alumninum struo ,turk) to form a !o11tln11()u,-surfac.o. Care rnuA~ bo t ,,orc isnd to obtain a -ontlniot.5 surface at thoJointo. This may e'oqui rt j~aridiivj arnd fillihig tho -.roviros with se mfiller.,,. It ha:;- burmn fouiid poenn bIeI to roduoe the apparontriuss8 of thoJo~nt by placttig' a poesn.uro .;j.;nitive tape, whose Lsurr(e ha,; boon bead3din a fashion onilar to tho ,-roon surfa-e, directly over the joint.

1-/

NAV I UAJ 'V(CEN I~

F i tr !) ,,

p4AvII~Ai)L~:v(2LKN 1i4~8 -

p4

.5-4C)

U'

p4'rI4'e)$40

~2)

p

'+4C)

I)

II

HSI

(IIii* 4

nlC)

4:

tljI'.)I) I$5'1

H.[~i

ii:;

CHAPTER 6

syLtomnuJ DesigAi

6.1. A projecttion system capable of presenting a non-programmedvisaal display is invariably a complex device. Therefore, it is esseatialto limit Its versatility from the outset to prevent it from becoming aneconomic "white elephant" and to In.iure that the period required for de-velopment will not be unduly long. There is a strong tendency for per-soniel esablishlnq requirements for a device to produce a rigorousspecification, generally calling for exact simulation of an operationalprocedure and greatly complicating the problem. It is therefore importantto determine:

(a.) That which 's essential to include fortraining purposes, that which is desirable,and that which being non-essential can besafely excluded.

(b.) The degree of complexity, the cost and the

development time that iW warranted for thedevico In proportion to its potential utilityfor training.

(c.) An estimate of its probable success, that is,its ability to perform In accordance with aspec ification.

6. 2 A careful analysis of the above considerations will generallyInvoive a thoroujh ;,tu, y of the projection system varlablfcJ which areclosely inter r:lated. A successful device generally rep, esents the bestcoinproml- u of theie several variables.

(a.) The area to be covered by the display and theconfiguratton of the area.

(b.) The altitudu range required.

(-.) The pitch and roll angles to be .lmulated.

(d.) Th, dofiniti on required within the ,i hplay.

(':.) The bigiLz1..,: required for the dk;piay. 4

-1,,o-

NAVYPRJADNVEN 1,o

(f.) T'ho vuh-(le to be simulated, IncludIng u thchara,'teristics as the vslIbility from within,its general physical arrangument and config-uration.

(g.) The distortions tolerable in the dboplay.

(h.) The total size of the training device.

6.3 Some of the more important considerations which enter intothe selection of a scale factor for the transparency include the minimumaltitude to be depicted, the total area to be simulated and the minimumsize of objects to appear in the display. The scale factor, together withthe size of the simulated area, generally dictates whether the transparencyshall be of the flexible or rigid type, Rigid transpar'encies generally limitthe size of the simulated area while the flexible ones provide greater cov-erage but complicate the projector. When it becomes necessary to simulat.ean "on-ground" condition, it is advisable to establish a scalb factor of lessthan 2000:1. If excellent definition in the visual display or detail in the3-D objects is required for a specific problem, the scale selecLed generallymay not exceed 500:1 although a scale factor of 1000:1 Is sometimes pos-sible.

6.4 Th3 ratio of maximum altituda to be simulated to minimumaltitude must be no greater than 100:1. and preferably should be less than50:1. Greater values of this ratio usually result in considerablo verticaltravel of the pohit source thereby reducing the visual display brightnessand increasing distortions at the maximum altitudes becau;ie of the largepoint source to eye displacement. In the case of a rigid transparencyutilizing endplates, the horizon line is considerably raised with largevertical travels of the source. The actual source travel should riot exceed6 to 10 inches.

(1. b Due to the extensive size of the transparency, of the projectorsupport mechanism, and.of the associated drive systems for obtainingthe six degrees of freedom, pitch and roll angles should generally belimited to ±200. Values in excess of this u;sally place a tremendou.;burden on the power srvos required for the device and greatly complicatethe projector su.,pension and driv mechanisms. Hlgh' r 'values alsorstrict the visibility of tho pilut when the projector is in an inclinedpot Ition.

-121

NAVTRADEVCEN 1638- t

6.6 The cockpit, ,)afiguratlon also plays an important role inpilot visibility. Obviously visibility (,an be no better than in the actualaircraft if trus slmuil.tion is to be achieved. Generally, simulatedvisibility is poorer than actual conditions since it is not always po:isibleto obtain the total anlar coverame both horizontally and vertically,Direct shadows of the cockpit, which fall within the usual areas of vio-ibility, ofteo restrict (-overage. In the event the cockpit configurationpr-ovldes for an instrument panel directly over the pilot's head, it isImpossible to coW away any of the overhead strupture of the cockpit,thereby inreasing tho source to eye displacement and the accompanyingdistortions.

6.7 As Indicated in Chapter 5, selection of the screen radius isbased on the brightness that is required for the display, the distortionstolerable in the display and the total .'oom size that In, available for thetraining device. The various binocular e ffects, of which little Is known,also dictate that the screen radius be made as large as practlcable. Arange of 10 to 20 feet appears to be proper for the projection screon radiu.;for point source syotems. A minimum screen brightness for the importantareas of approximately . 2 of a foot-lambert is required, although It isdesirable to Increase this value to about .4 if it is practical to do so.

6. 8 Summarizing, unles the visual display that is required isextremely simple, It will usually be necessary to sacrifice one or moriof the available variables. The compromise which must be made willbo dictated by the nature of the training problem and otten will spellsuccess or failure for the device.

Glossary

ABERRATION - a deficiency in an optical system or element causedby convergence to different foci, by a lens or mirror, of rays of lighteminating from one and the same point.

ABSORPTION - loss of a portion of the luminouis flux incident on abody which is prevented from passing through It.

ANGLE OF INCIDENCE - the angle at the point of incidence, betweenthe direction of incident light and a normal to the surface on which itfalls.

ANGLE OF REFRACTION - the angle beeen the direction of lightemerging from a surface and a normal to that surface.

APERTURE - the effective opening for the passage of light rays In

an optical system.

APLANATIC - free from spherical aberration and coma.

BRIGHTNESS - see luminance

CANDLE - the photometric unit of luminous intensity. One candleequals one-sixtieth of the luminous intensity of one square centimeterof a hollow enclosure at the temperature of solidifying platinum(17550 C).

COMA - the failure of a lens to image paraxial rays and rays throughits outer zones at the same point when the rays originate from Dointsnot on the optical axis.

DEFINITION - the sharpness of gradation of the demarcation betweendistinct areas or between details. (see also resolution)

DEGREES OF FREEDOM - number of variables needed to defineposition of a body in space. The six degrees of freedom of movementin space are: linear motion along the x, y, and z axes and rotarymotion about each of these axes.

DEMAGNIFICATION - sec magnification.

-123-

NAV'R.ADIEVCEN l121- I

DIlFiFRAC11ION - the oproadinU uf a bearn of ig(ht at'ULLTW thO ed~iooif an ois truAloln.

DIFFRACTION ANGLE - the a'igie bei weeri a lined~rawn fromrr thu)liqlat sourco to the mdge of an ohstructlun and the path of the diffractedlight.

DISPLAY-IMAGE - tho Image formed en tho screen and presentodto tho obLtervjrt: view.

DISPLAY-owsECr - that des Ign, decoration, pattorn, etc., Imposedbetwoen the light source and the screen to alter the antformity of thelight. The display-ubject may be tranoparent or reflectivo.

ENTRANCE ANGLE - the angle at a point object of a lenos on itloptical, axi~s subtended by the aperture of the optical system In question.

ENVELOPE - wi appiled to iarnpo, the glass, qiartz or' other trans-parotnt bull) oricloo'i g tho light emitting parUo.

EXIT' ANGIE - the angle at a point Iiage on the optical axiO of aref ratl nq :;iurfaoe formed by the aperture of the refra~tInwJ ourface.

E~XTENDED "TPOINT" SOURCE - soo point oouroo.

EXTENDED WITIRCE ANGLEd - tho anglo with Its, vortox at a linn ontho di.;play-ojjo ~t subtended by tho eromu odje.; of an 'ixtutited

FOOT-CANDLE - theo phiotorfritri' atilt of 11turninuation. Ono foot-aw 1If,Is tho illuminatiou produl!Oa Whon the lurinou:; tIux from 'ino candle f,1111normall- on a ourface at a distau' t u iui foot. On.! foot-candle I.,; nivner-iceilly cquivalenL to on( arrin pot, jqtaru foWot.

FLUX DENSITlY - A moa.;uro of totaql q'iaritity of light or Illumination.

ILLUMINATION - the Illumnationl of a .;ur~a(-o is tho anioun'. of luminowflux It rec* Iv -; por unit aroa. Tho tilt of ilIlumflination i.- tho fuot-i2.anlle.

IMAGE - p iut!I .ro o- couriterpa.,t of an o'1je t p red-i-o~d ol roe -vt ionor refra!tLion, or by the pa.;i:.a'J of ray.; throughi a .;mail aperturo. Animage formeid by tho actual ir cLonof 1Igtit ray.; I; roal. An iynageformed 'q tii'., pparoe (but no'. actLual) mnt .r~Jwct101 of IIUj~it ray.; iUvirtu-al.

-124-

NAV'IHiAD)PIVCEN t(PN -1

INCIDENT LIGHT - that light whkch falb oa :i ,urfra.e.

INDEX OF REFMACTI)N - tho rat.io rif Lhn vf!h,:.Ity of light In a va,!uumto tho volocity of light of a particular wave length in any oub~tauico k-nalilod the lndelt of refraction of the substance for .light o that particularwave length. The velocity of light In air Is co nearly equwi to it, v-iocityIn free -pace, that for most calcutations the index of rufractliu of aircan he assumed unity without Introducing olgrlficant error.

LINE WIDTH - the width of lines which define details on the display-obje.:t. This Is a measure of the fineness of details on the display-object.

LUMEN - the fundamental photometric unit. Ono lumun equals theamount of luminous flux radiating by a point source of one candle through-out a solid angle of such size as to surround a unit area at a unit distancefrom the source. By experiment it has been determined that fo:, a normalobserver one lumen is equivalent to 0. 00161 watt of monochromatic greenlight of a wave length of 5b mllllmlrons, corresponding to the maximilmof the visibility ,.urve.

LUMINANCE - the amount of luminous flux radiated per unit of solidanglo pr unit of area of an extended Lurco. Luminance, also calledbrightness, is expressed In candles per u.,it area.

LUINOUS FLUX - the rate of transfer of vl,;ibl, radiant enorgy. Theunit of ilu, h; th, Lumen.

LUMINOUS INTENSITY - tho amount of lurninouu. flux radiated per unito! oolid anglo In a givon direction by a point source. 'Ph, ui't of in-tnnity is the '!andle.

MAGNIFICATION - thl inr!rea.-m (magnification greater than t) ord-rea:we (magnificatton less; than I) in the size of an Image ai com-parud Lu the atual objeit. Reie-t1'tion (magnification ', '3 than .) mayalso ho, termnd iernagnificutior. A., applied to the point source syjtern,magnification refero to the enlargarnnt of the dl..play-Image over thesizo of the di;play-obje.ot during projection. The theoretical manificattonof Lht ;;ytern i; the ,nlar'jemornt of th), 11-play-image ,voe the display-o'jc t :Aizo whloh would I)(- oxpct.d if a grne.tric point touroo or ilgetwere: u:ijed for projectloni. Asi applied to optical oorniporiontss jut asmag.tfl,'atlon rcfn; to Lh, r!tjirj;j. meet or r(eu.ction or the image .;zeO ;a'comnparod vlth the objot s at-ie. amanifivation i: h niargont

1

NAVTW ADEVCEN 1628-1

as applied to those dimensions in a plane perpendicalar to the opticalaxis. Longitudinal magnification refors to that enlargemort uC dtmen-sions in planes containing the optical axis.

MENISCUS LENS - a lens having the cenLers of curvature of both refract-ing surfacos on thu same s-ide.

NEGATIVE LENS - a lens wh'ose thickness at the optical axis is lessthan its thickness at the periphecry.

OPACITY - the reciprocal of transparency.

OPTICAL AXIS - the line connecting the centers of curvature of therefracting surfaces of a lens. The axis of an optical system is theline connecting the centers of curvature and the midpoints of thespherical refracting surfaces which make up the nystem.

PENUMBRA - the gray portion of a shadow surrounding the umbra;

it receives light from some, but not all, parts of the light source.

PHOTOMETRY - the sclence of measuring light.

POINT LIGHT SOURCE - a small source of light approaching in sizethe classic geometric definition of a point. A geometric point sourceis a point source of light conceived as having 0 dimeln ono. This Isa theoretical concept only and cannot be achieved physically. An ex-tended "point" source or simply an e:<tended source, is a point sourcewith finite dimewlion:;.

PROJECTION ANGLE - the angle in a vertical plane, with ts vertexat the point source which is subterided by a ho-izontal line and the lineof projection toward aay point on tho display-Image.

REFLECTANCE - the ratio of reflected luminous flux to the totalincident flux In pe runit.

REFLECTION - that portion of luminous flux incident on a body whichis deflectud by a surface of the body without passing through thatsurfa-e.

NAV1PRADEVCEN 1628-l

REFRACTION - thp change In direction of a wave which results whenit enters another medium obliquely and when the velocity of the wavein the second medium is different from Its velocity in the originalmeed!urn.

RESOLUTION - the distinguishing of fine details from one another.Resovlvna power is the ability to distinguish among fine dotails andis commonly evaluated by determining ability to distinguish fine pointsor lines set close together as individual items.

RETRU-DIRECTIVE - the characteristic of being able to returnsomething along the same path by which it came.

SLOPE ANGLE - the angle formed between the optical axis of aler.. syutem and any ray which crosses the optical axis.

SPHERICAL ABERRATION - A deficiency caused by the failure ofa lens or mirror to image paraxial rays and rays through outer zones atthe same point when the rays originate at a point on the optical axis.

TRANSMIS3ION - the portion of total luminous flux Incident on a bodywhich passes through It.

TRANSMITTANCE - the ratio of transr",'L ad light to incident light inpercent.

TRANSPARENCY - th, ratio of the intensity of the tran',mitted lightto the Intoinsity of the incident light In percent. Also, a transparentdisp!ay-object. (son display-object).

UMBRA - the totally black portion of a shadow which receives nolight from the light source.

VIEWIN(C" ANGLE - th, anglo, in a vortical plane, with its vertexat the eye of the obsorvar which is subtended by a horizontal line andline of sight toward any point on the display-image.

-127-

APPENDIX I

Studies of the DbItortiono of the Displuy-Imge on 3asicScreen Shapes 1usulting from -i:lac ,orLt of the

Eye from the Point Source

I - I Position Distortion on a Flat Vertical Screen

By definition, position distortion, n , is

- Hence when 6,r . 0 (1)

In figure I - 1, let

-tnl Y Ytan- or tan,- (2)

6- tan-1 j -v( ) or T -1 (3)

Solve (3) for Y and substitute in (2)

-tan 1 +v (1 h .)tan] (4)

Substitute (4) in (1)

n~ - tan [v~ + (1-kh tan6] -6 (5)

Let

-12t -

NAVTRiIDEWVEN (A-I

-I----4

/ I,

/0 Wil/ ' 0

V)d

cs/

/ rzfX

0/04/

NAVTRADPVCEN 1.628-

Substitute (6) in (6) and differentiate with respect to

dn dtanX' -dd d F

But

d tan'X' -1 dX'

and

dX' / 1 h, sec2

77 - 3,

Therefore

h. 2d n s e e , , -- -I 7d' iTse (7)

Position distortion is greatest when dr /d 6 . 0. (7) then becomes

( h) )sec 2 6 + i+v +(1 h)tan q 2

Substitute the trigonometric identity 1 + tan 2d - sec2 6 and simplify

(1 - h)tan2' - 2v (- h)tan6 . v + h ()

For the case where the point source is located directly above the eye,h - 0; (8) becomes

6 - tan'() 9

-130-

NAV'RADEVCEN 162,- I

Substituto (9) in (5)

tan -vi tn1 f-v)d tada + -an-

But

- tan tan 1 "V,

Therefore

n - 2 tan- (() (10)

I - 2 Position Distortion on a Flat Horizontal Scroen

Using figure I - 2, it can be shown by similar reasoning that, fora flat horizontal screen,

-1rh -

.cot L (i- )cot (U)

*n (I -v. csoI (I - 1 t26 -1 (12)

Position distortion is greatest when dn)/6 - 0. (12) then becomes

co h ( ot6 = t v (13)v ,. 1) coto - , ) . ,

-431-

NAV'II?A1)PIVCEN 111)2T - I

1P/

29

J5 cd

tX rX

C8I

9/

/12

NAVT'.RA VC'tIN 1628- I

For the case where the point uource is directly above the eye,h , 0; (13) becomes"

6 cot"1 i (14)

And (11) becomes

Y) . cot-1 (1I - v v (16)

I - 3 Position Distortion on a Circular Screen with itsCenter at the Point Source

By definition, position distortion,) , is

S-6 Hencewhen -t , 0 (1)

In figure T- S, let

Y - d sin (16)

X - d cos (17)

6 tan-( I Y v or tand 6 =..-f (18)

Substitute (16) and (17) in (18)

tan - dsint -v (19)d-ost; -h

-133-

NA'I"'RADEVCIEN 16M~ 1

4-,

wj

R' V~

/S/ >

w P4 Cd/

/4/>14 0

01 11

1'AVT'IA I )VCIN 162- I

From trigonometry

% sintan, - Cos,, (20)

S3ubstitute (20) in (19) and'simplify

sin c - c v cos(, - h sine (21)

From trigonometry

sin Co -cost sin - sin( -5) (22)

And from (1)

snn = sin ( -) (2,3)

Substitute (22) and (2:3) in (21)

11 sin- v~ cosb5 h sin3 (24)

Iet

v c0, hx . co:; 6 - sin3 (25)

Substitute (2b) in (24) and differentiate with respect to6

d _ d (sin-IX ')" - d6

NAV'lUAI)LVVCIN 16 8- 1

But

d 1 dx'd 1-X z d

AnddX' " v.

" v sin6) - (cos 6)

Therefore

- 7. sin6 + h

1 "('cos6 - a" sin6

d vsin6 + hcos(

d6 d- - (vcos' - hsin,)

l'orition distortion Ir a maximum when dy)/d - 0; (26) then becomes

V "in + h cos(6 " 0

id' - (vco d - h sJ )2

- n -h.oi 6 C)

--V Sifn( - hco0n

sin h -c h (0hv --T h ,)

coV-

NAVTPRADEVCEN 1628 - 1

For the case where the point oource is directly above the eye ofthe observer, h -0 ; (27) becomes

• tan', 0- 0

And (24) becomes

1 - 4 Size Distortion on All Screen Shapes

In figure I - 4, an object viewed from the point source (a viewing

position free from distortion) subtends an angle at the eye

.(28)

When viewed from a position distant v below the point source anddistant h in front of the point source, the same object subtends anangle at the eye

46 -62-6, (9

Size distortion, a , is defined as

-Aa 3 - 6 (30)


-137-

NAv'UNAADEVCEN 1628 - I1

'.4J

Pci

4 ~04

-44

00

NAVTRADEVCION 1628 - 1

But, by definition,

',- ,-$, (ib)

Therefore

ATm 'h-n, (31)

Differentiate (31) with respect to 6

.d .i .d(-n, -" ,

d6 d6

dAn d rT d ,d - - -- (32)

I - 5 Position Distortion on a Circular Screenwith its Center at the Eye of ObserverUsing Rear Screen Projection System

By definition

l -J - (S Hence when -b , '-0 (1)

-139-

NAV'I'IIAI )t1VCI!,'N I(321:F - I

In fiure i - 5, int

'Y 11 -in5(3 )

X dcoo3 (34)

I 'hen

Stan yta (35)

Substitute (33) and (34) In (35)

tan 1 'sin 6 J (36)


[ stn6 ], (7,q tan-[ 2 -coso (37)

Let

X sin (38)2 - cos6

Substitute (38) In (37) and diffe"etlate with respect toJ

d v) d (tan"- X') 1

-1i40-

NAVT]RADEVCEN HIMU I

:j0

0

i

rCf

NAV"I"RALEVCErN 1628" 1

But

d (tan- X,) 1 dx,d 6 1 + X,2 dc

And

dX . (2 -co )(cosd ) - (sin8 )(sn )

d (2 - cos, )2

Therefore

d (2 - cos6 ) 1 (:39)

Position distortion is a minimum when d /dc- 0; then (39) becomes

- I 1 0 (40)

And (37) becomes

11M o (41)

-142-

AP PENDIX TIf

19erivation of Reolution Equations

II - 1 Derivation of an Expression for Distortion of theDisplay-Iimage Width due to the Uve of an ExtendedSource Rather than a Geometric Point Source

In figure II - I, let

X = (D - I)/2 or D a D' +2X (42)

By definition

M (a+b)/a or b- a(M-1) (43)

M- D'/T or D', JM (44)

P'- D/D' (45)

P s/ (48)


P,- (D' + 2X) D' (47)

By similar triangles In figure II - 1

8/2 X Sba or X (48)

-143-

NAVTRADEVCEN 1628 -1I

.0

0

0

.00

-144-

NAV1"RADEVClEN 162,3-1

Subutitute (43), (44) and (48) In (47)

P, JM S(M- )JM

S M-(49)


P,-I+1> (50)

2Derivation of an Expression for the Qualityof Resolution and Deflnition as Affected byMagiiificatin and the Source Size to Display-Object Line Width Ratio

;-

In figure I[ - 2, let

X - (D-D')/ or D D'+2X (51)

By definition

M (a+b)/a or b a(M - 1) (52)

M - D'/J or D' =6 TM (53)

D U + 2G (4)

P" U/D (b)

Pu S/J (56)

-14!)-

NAV'FRADE\JCEN 1628 - 1'

o ~

(1) ri~

o(I) ~0

.0

IIIcJ~I

I I'rz4

-146-

NAVTRAD EVCEN 1 (VF4- 1

By similar triangles from figure 11 - 2

S/a . G/b or G- Sb/a (57)

Similarly

S/2 X or X Sb (b8)

Substitute (57) In (58)

X aG/2 (59)

Oubstitute (51) and (59) in (54)

D'Y+2X- U+4X or U- D'-2X (60)

Substitute (bi) and (60) in (55)

D' - 2x (61)

Substitute (53) and (58) In (61)

Sbp,,.. JM- T (62)

JM + Sba

-147-

NA\T'PADfEVCEN 1i02H - L


" JM 4- S(M-'

-

pit -7M + -7 (M- 1)

Substitute for S/J for (56)

p,, M - P (MM '+Pl (M -7

11- 3 Derivation of an Expression for Display-ImageQuality as Affected by Extended Source Sizeand by Distance from Source to Display-Object

Consider a line of demarcation between a red and a green area on display-object projected by an extended "point" source, S, distant, a, from thedistlay-object as showq in figure I-3. A display-image Is formed by thisprojection system on a screen distant, b, from the display-object. Thisdisplay-image will consist of a red area and a green area separated by anarea of demarcation which will be a combination of red and green of width,X. The edges of this area of demarcation will subtend an angle, K, in spacewith its vertex at the line of demarcation on 'he display-object and willsubtend an angle,@, in space with its vertex at the eye of thepbserver.The angle, cx, subtenced by X at the display-object is equal to the anglesubtended by the extended source, S, at the same point. If the eye of Lhe

-148-


pp.% 0

P44

149-'c

rI"\ !V'I'I AtiF:VJHIN 162P,,- I

observer I.r placed to coincide with the cent-r of the extend-d -'ource,fo the following relalonihIps. hold. (In practice, the eye i held ao

close to the point source av po.-slble, Y

From figure 11 - '3

tan -x (64)

X

tan -- = 2(a +b) (65)

If a Is small cornpare , to b

a +b b (66)

Then

x x.(a +b)(6'")

Bubstitute tnls in (6b) and then (64) and (6b) become

tan tan (68)

And

- 1bO-

NAVYI!AD)IEVCtHN 1W- 1

Then

tan (70)

From trigonometry

tan,~. 2 tan(71)

1 - tan2

But If 4/2 is very small then in (71)

1 -tan 2 . ----. 1 (72)

And (711) becomes

2 tan - tan(

Then from (68), ('70) and (73)

tan t tanC r - (74)a

It can earily be shown that for(5 . 10 (ando 10) these approx-Imations are very close. While the eye will readily distinguish an arpaof demarcation which subtends an angle 1 > 10, the ability of the eyeto dirt' Ingulsh an area of edemarcation falls off rapidly as the angle sub-tended, , falls below 1

-l.bl-

A [iN )AX III

tnteraction of Diffract ion and .xterndud Nfoourc e focI sa, [Tplay-Objcct LAnn Width and It; Di:ranc,

from Lhe Plxtended ,ourco Vary

From the laws of, diffraction

sin '( r " (75)

From figure lf[ - 1

tan O-C - (7)

Wheny is very small, sinf(=( in radians and (75) becomes

X (77)

Whenor is small, 2 tano/2 Q tan . - in radians and('16) becomer

a

If J - S this may be written

J(78)a

If oc , in radians then from (77/) and (78)

X, iJ a

-152-

N AkT'I[A I KV \Cl I f;'

0 m40

Cd0wr

NAVrIRA1')RVCHKN 1628

Or

a 15

Substitute In this the value of J from (77)

a X12(79)

-1[A4-

A] PPHINDIX TV

rABULATION OF ]POINT' 8OURCP, [AMF8)

Name Make i Power Watts

Osrarn HBO-10'1* Osram-Gorman MV 100 most eff.

Osram XBO-162 Osrani-Germun XV 160

Concentrated Arc Sylvania CA -25C-25W (Zirconium)

Concentrated Arc Sylvania CA 22W (Zirconium)

Concentrated Arc SylvauLa CA 300DC 900W(Zirconium)

A-25 Hafnium Sylvania CA 2510W Cathode

A- 10 Hafnium Sylvania CA 10

Pointolite 20 CP Biddle T 20-ballastpower

Potitollte 100 CI Biddle 'T 60-ballastpower

Polntolite 150 CP Biddle r 100

NOTE: XV xenon vaporMV mercury vaporCA concentrated arcT tungstenL lengthD diameter

* 'I'ho COram 1IB0- 09 is identical to the Osrarn IIBO-107 exceptthat 11130-107 has a starting electrode and HBO-109 does not.

- lhb-

NAV'FIADIEVC1,N 1G2,8- I

'TA[,A'IMON OF POLNT SOURCE LAMiPS (Cont'd)

Table ofBrightness Source Distance0

Name (cd/in,2 ) *from unvulope (in,) Tienp K

Osram HBO-107 620, 000 .225"

Osram XBO-162 58,000 .375

Concentrated Arc 15,000 .453 3200C-25W (Zirconium)

Concentrated Arc 46,000 .26 32002W (Zirconium)

Concentrated Arc 23,800 1-5/8 3200DC 300W (Zirconium)

A-25 Hafnium 81, 000 Exp. . 453 in. max. 3300IOW Cathode

A-10 Hafnium .453 in. max. 3300

Pointolite 30 CP 4,450 .63 2700

Pointolite 1.00 CP 8,600 1.26 2700

Pointolite 150 CP 8,700 1.45 2700

* Candles per square Inch

NAV'ITAI)EVCEN 1Gt8 - I

'IABT1 4A'IION CF POtNI' SO!UJRCE IAMPIS (Cont'd)

'T'ablu ValuesOvcr-atl Int(ntty- rabl Arc

NSze (in.) Candioe Olynonn (in.

Osrarri HBO-107 L 3. 0:3 150 .0118 x .0118D .473

Osram XBO-162 L 5-7/8 260 L .069D .7b W .035

Concentrated Arc L 3-11/16 10.5 D .0287C-25W (Zirconium) D 1-1/8

Concentrated Arc L 2-1/16 .33 D .0032W (Zirconium) D 9/16

Concentrated Arc L .- 712 250 D .115DC 300W(Zirconum) D 3-1/4

A-25 Hafnium L 3-11/16 9.6 .014)2 lampslOW D 1-1/8 .008)

A-10 Hafnium L 3-11/16 3.3 .007)D 1-1/8 009)2 lamps

PoIntolite 30 CP 1T 2 30 .076D 1.25

Pointolite 100 CP L 3 100 .1

Pointolite 150 CP L 3 150 095

-1b7-

NAV'FIRADEVCEN 16Y8 - I

TABUI.,A''ION OF POINT SOURCE LAMPS (Cont.'d)

App. Coverage Temp. of Lamp PrssureName Angle of Light I -rnp .." Atmospheres"

Osram HBO-107 240+ Bulb 400 (app.) :35-70

Osram XBO- 162 360

Connwortrated Arc 1500 Bulb 179 .166-C-2bW (Zirconium) Base 62. 7

Concentr@ted Arc 900 BuIb 00 .003-2W (Zirconium) Base 37.7

Concentrated Arc 150+ Bulb 271 .43-DC 300W (Zirconium) Base 82. 2

A-25 .Hafnium 150°l+ Bulb 179 .166- .10W Cathode Base 62.7

A-10 Hafnium 1500+ Bulb 179 .166-Base 62. 7

Pointolite 30 CP 240+ up to 160 .333-

Pointolite 100 Cr' 240+ 160 .333-

Pointolite 150 CP 240 ° 160 .333-

-158-

APPENDDX V

Negative Meniscus Lenses

V-1 Introduction

V-i. I This appendix presents studies of the effects of the variablesinvolved in the design of a lens system utilizing the negative meniscuslens on the requirements of the ideal point source. These requirementsdiscussed in Chapter 3 (paragraph 3. 2) of this report may be summarizedas follows:

a) Minimum diameter

b) Maximum luminous intensity

c) Maximum angle of light output

d) Satisfactory Spectral Distribution

e) Minimum envelope

f ) Envelope free from striations

g) Envelope at or near room temperature

h) Safety

I) Maximum life

j) Reasonable cost

V-1. 2 A lens having the centers of curvature of both refracting surfaceson th same side is called a meniscus lens. When, in addition, a meniscuslens is thicker at the periphery than at the center, it is termed negative.

V-i. 3 A negative meniscus lens collects diverging rays of light emittedby a finite "point", source such as the Osram HBO-100 lamp. If thedistances between the center of the lamp and the centers of curvature ofthe lens are made to obey requirements derived in this Appendix, effectivesize reduction and a further divergence of the light is achieved. Being anegative lens, it creates a virtual image of the point source (object).Using this Virtual image as the object of a second lens, further sizereduction can be obtained. However, each successive lens, receives onlya small cone of the luminous flux emitted by the previous lens and the

-159-

NAV'I' AL VCEN 1,0M- I

turrnriouo flux Lransmitted by the lono ry.tern L1:.. thereby reduced,

V-I. 4 Tho variablos Involved in thu d, .;ign of otuch a Leno, systerraro: the optical glass (Including its Index of refraction), the radius ofthe lens surfaces, the minimurn lens thhokness and the positlon of the"point" source (object) with respect to the lens.

V-2 The Aplanatic Negalivu Muriicus lens,

V-2. 1 Introduction to Theory

V-2. 2 In sections V-?,. 0 and V-2. 7, it Is shown that if a point sourceof ligt serving as the object of a negatlvo muniscus lens is Located ata distance R1 + n2 RI from the first surface of the lens when the firstsurface has a radius of curvature, RI, and the lens has an index ofrefractio.. n2, then the lens will form a virtual image of the pointsource at . distance R1 + (RI/n2) + L from the second surface of thelens wheu the second surface has a radius of curvature, R2 - R1 + (Rln2) + t(equations 83, 88, 90, Y2 and 4). It is further shown that this virtualimage i smaller than the real point s6urce object by a factor of 1/n 2(equation RO).

V-2. 3 In sections V-2. 8 and V-2 9, it Ii shown that the maximum-angle of light output, 0', is sin-f (n2 ? n2 + 1 ) (equation 104). In

addition, it iL shown that, neglecting light losses in the lens due toreflection and absorption, the brightness of this Image, B', is equal tothe brightness of the object, B, (equation 107) and the luminous intensity

tf-+ ia.nage, I.a..ss than that of the object, I, by a factor offn2 + /in2 -+ I - n2 (equation 111).

V-2. 4 Ifi section V-2. 10, aberratons of this lens are discussed andIl' s hown that this lens is aplanatic (by definition, free from sphericalaberration and coma).

V-2. 5 In section V-,. 29, the parameters of a specific aplanaticniqative meniscus lens are calculated and, in section V-2. 34, thetheoretical and experimental characteristics of this lens are examinedwith particular attention to their relationship to requirements for thepoint source system.

-160-

NAVTU'RA1,,'.: (tN I6B - I

V-4. D UoveLwloprtnrit, of oxpressions for .,: object dlstance arid theI mago dstance

Consider that rays from a point source of light are incidenton a negative meniscus lens having an index of refraction, n2, and aradlus of curvature of the first surface, R1 , located in air n'j - 1)au shown in figure V-i. Then Snell's Law may be written

sin i1 = ri sin r, (80)

Consider triangle ACD in figure V-I; by the law of sines

sin 01 sin i l

R . '- (81)

Recalling that, by convention, G9 and s are positive and i1 and R,

are negative, make this explicit for the first surface:

sin &i . sin(- ii) - sin ii (81a)+ R S1 + R1

Substitute '80), where il - -1i and r I - -rl, in (8la)

sin -n2 sin r 1-R (82)

Let

sI + R 1 - -Kln 2

then

-(R1 4 Rjn 2 ) (83)

-161

['A W R ICIt.'L E N~.S' 102H.l .

n2

-1621

/R

A g, B /9 , / -

r --

Figure V - 1 - Ray Tracing Diagram of Apaauttic Negative MenscusLens.

-162-

.NAVrRADEVCEN iObTh, - I

Substitute this In (82)

sin , . -n2 sin ri

-RI -Rjn2

sin - sin r1

t9-- rI (84)

Consider triangle ABD in figure V-I; the sum of the angles equalsrrradians:

Gj+ il - rl +,r - T (8b)

Recalling that, by convention, 0, and E0, are positive and I, and rl arenegative, make this explicit for the first surface and simplify:

l ii + rl -E, 0 (85a)

Substitute (84) in this

sinO, -sin it (86)

Consider triangle BCD in figure V-i; by the law of odnes

sin 0,' sin ri- -1( I)

-13

NAV'TRAL)UVCEN 1628 - 1

1Luct]Ing that, by cony.Lion, §; is positive and r I , s I ' and R, arenegative, riako tfhl; explicit for the firot surface:

sin ()', - sin r I

I + rH (87a)

Substitute (86) in this:

-sin iI -sin r,-Rj -s I + R,

Substitute (80) in this and simplify

n-1

--R -sI'+ R

Solve for sl'

G R1 + LI (88)n2

Consider that the second surface of this lens has a radius, R2 . Thenrecalling thai, by convention, ) 2 and s) are positive and I and R2are negative, make (81) explicit for the second surface:

,in H 2 - sin in

3otving for 02

-164-

NAVI'RADEVCEN 128 tl-

Rin 12

Select the radius of the second surface so that the angle of incidence,12, of rays incident on this surface from the point image formed byt first surface is normal to the surface:

- (o:' + t)W S2 (90)

12i 0 (91)

sin 19 = 0

Substitute this In (89)

2 - - (92 )

Recalling that, by convention,(9 is positive and r 2 , s2' and R2are negative, make (87) explicit-or the second surfac..:"

int-2 ' - sin r 2--zI- "sp.' + R2

Solving for S2'

sin ros2 , . R2 - R2 sn(93)) 'I2' €

For the second surface Snell's Law nay be written

n2 sin 12 - sin r 2 (80a)

-165-

NAV]RADE VCE N 162b - I

But from (91.), sln 1 - 0, therefore

sin r 2 - 0

Substitute this in (93):

s2' R2 (94)

V-2.7 Development of expressions for magnification.

From Abbe's Sine Condition, the magnification of the objectby the first surface, mI1 , is

,I sine1 (95)n2 's nL 1 --


-, sin ri-n 2 sin i 1

Substitute (80) in this:

ml = (96)

From Abbe's Sine Condition, tho magnification of the object of thesecond surface, n2 , is

M2(07)

- 16f3-

NAVT'RADEVCEN 1028 - 1

Make (8b) explknit for the second surface where 12 0 and r 2 0:

&2 +1TE 2'

t:2- 62'

Substitute this in (97)

m 2 n2 (98)

The lateral magnification of a lens, m , is the product of themagnifications of the surfaces:

m1mL - m I m2 1,_L m m2 n2 (99)

By definition, the longitudinal magnification, RL, is

2 n

r L -. (m L) -n 2 2,(100)

V-2. 8 Development of expressions comparing the luminance of the-- image with that of the object

Under optimufn conditions (no light losses in the lens fromreflection and absorption), the luminous flux incident on the lens, F,is all transmitted by the lens. Then the luminous flux transmitted,F', is equal to F. When 0 is the limiting value of the slope angle, C),for a radius of aperture, Rl, as shown in figure V-2, Lambert'sCosine Law may be written

-167-

NAV'1'R LA)DEVCEN l(,B - 1

Ri Rn

ni

Figure V - 2 Diagram of Image Formation by the Apianatic NegativeMeniscus Lens.

- If h-

NATFRADlEVCEN l6*?B I.

F 2'rrB Y1jiv o-d (101)

Inteqrate this

F- T B Ylsl

Similarly on the image side

Flu fT B'YI' sin 2'

Where Y1 and Y ' are the area of the object and the image respectively,and s ' the limiting value of -' when V. is the limiting value of 6E

Since F - F', then

1 BY, sin2 V " B"Yi'sin2 /'

B Yl' sin2 0'- = - ~- (102)B' Y, sin2

From figure V-X,

R1 (10)

S n n +f +j W n,

I

NAV'I'J\LEVCEON 1t28- 1

Divide sin & by sine

S2I ± n2 (lob)

n22

Also from figure V-2, the area of the object of radius Y/2 is

Yl. IT ( Y/2)1

Similarly the area of the image of radius Y'/2 is

Y- (Y'/2)2

Therefore

Y Y

But, by definition, ana (99)

Y' 1

mL" ' n2 (106)

Substitute (106) and (I Ob) in (102):

B n22S n(10)

n#12

- t{ ~

NAV"I'AL)EVCN 1628 - 1

V-2. 9 Developmrient of exprc;"son, comparing the luminous Intensityof the image with that of the object.

By definition, the luminous intensity, I, is total luminous fluxwithin a small solid angle, w, when the total flux radiated is F. Sincethe flux radiated by the Osram IIBO-109 lamp is uniform through avery wide angle, when this lamp is properly oriented relative to thenegative ineniscus lens,

S(107)

wherew is the solid angle of flux in steradians incident on'the lens asshown in figure V-3. ci equals the area of the spherical surfacedivided by the square of its radius AT:

2ITXY 2IT Y

where

X a - IR, 2 + (Rln2 )

Y -X-R1 n2

Similarly tYe luminous intensity, 1', of the lens output is

F' - 'O '

where W ' Is the ;olid angle of flux in steradians transmitted by the lensas shown In figure V-3. (o ' equals the area of the spherical surface

r divided by the Nquare of Its radius I:

217 X'Y' 2 flYOX, = (1)

,4

-I'l -

NAVTRADEVCEN 1(1 -

/

< Bg I\ R2

1/

-- Rl \ \\n

Figure V- 3 - Diagram of Aplanatic Meniscus Lens Showing LightInput and Light Output.

-172-

NA VTPa, DEVCI 1021, - t

where

TM -R 2

y, R2 I-R cos¢'

and

1

COS - 2 2 + n22

Since F - F', then

Ij V 'W' (110)

Substitute (108) and (109) in this and simplify

in2. + 1 n2

V-2. 10 Evaluation of aberrations

V-2. 11 Spherical Aberration

V-2. 12 From a geometric point source on the optical axis consider-. that some ray travels alonq a path extremely close to the

optical axis (paraxial) and that some other ray travels along a path at

-173-

,NAVTiRADF,\VC1 lix I I:,S

a consIderably largcr angle, , to tho oplIcal ay)-s. After beingrefracted, these raysr, should cross the optical al:- at, the sarri point.Howevor, becau.,e of spherical aberration, 1he ray traveling along thepath at angle - will cro,s:: the optical axis before or after the paraxiatray crosses, Spherical aberration is a departure from the ideal lormrcondition wherein all rays from a geom.tric polnt object on the opticalaxis recombine to form a point image on the optical axis. Sphericalaberration present in a given lens is. the distancue measured along theoptical axis between the intercept of a ray through the lens zone Inquustion and the intercvpt of tho paraxial rays, and is usually expressedin terms of plus or minus percent of the focal length.

V-2. iS Uqually sphnrical aberration cannot be eliminatod from asingle lens. However, by combining two lenses having

spherical aberrations equal ia amount but opposite in sign, it Is possibleto eliminate spherical aber-atlon from a lens syot.emr,

V-2. 14 Note that for the negative menlvcus lens under discussion, theobject distance and the image di stance (equations 83, 88, 92

and 94) are independent of (-. This verifies that this negative meniscuslens is free from spherical aberration when the object distance isestablished according to (83) and the radius of the second surface isestablished according to (85) and (86).

V-2. 15 Coma

V-2..16 The aberration known as coma affects rays from points not onth- optical ax.s of ri lens. It is similar to spherical aberration

in that both arise from the failure of a lens t image paraxiaL rays andrays through outer zones at the same point. Coma differs from sphericalaberration, however, in that a point object is imayea uot as a circle buta- a comet-shaped figure.

V-2. 17 Consider again the rays discussed in paragraph V-2. 12. The- condition for ab:sence of coma is that the ratio sine 1/ sin@ 2'

remain constant. Not,, that thil; ratio for the negative meniscus Lensunh(!r discus;-ion iv i/n. (equation (105), a con-tant. Therefore, thisnegative rrni-lcus len;his fre,: from coma. Indeed, it is aplanatic as,defined.

V-2. 18 Chromatic aberration

V-2. 19 The refractive index of all optical material.. increases withthe frequency of light. The displacemnt of an image along the

-174-

NAVTRA)EVCEN 168- I

axis due to change in wavelength, Is catlod axial or longitudinalchromatism. The variation in the size of the image Is called Lateralor oblique chromatism. When any lens is corrected for axialchromatic aberration, generally all that can be done is to make thelens have the same axial intercepts for two wavelengths, usually thoseof the C and F lines of hydrogen. In this case the other wavelengthswill still focus in other planes, giving rise to a residual aberrationknown as secondary spectrum. One way to determine chromaticaberration is to obtain focal lengths of different wavelengths and usecertain theoretical relationships. The rrethod is very tedious andrequires ray tracing.

V-2. Chromatic aberrations of a single lens can never be eliminated;however, they can be compensated for with the proper combin-

ation of different lens elements.

V-2. 21 For the negative meniscus lens under di ursion all theaberrations, with the exception of chromatic, are negligible

since the object, as well as the image, are essentially point size (thesmaller the object the less is the amount of aberrations). Chromaticaberrations of this lens is the limiting factor on the size of the virtualpoint source, assuming perfect lens curvatures. Diminishing the

{. virtual point source further than . 002"1 can affect the projected imageby resulting in projections from two extremes of the color spectrum,thus creating a double image.

V-2.22 Astigmatism

V-2. 23 A pencil of rays that fails to unite at a single image point- after refraction is said to be astigmatic! and the system is

said to be affected with astigmatism. Although :-spherical aberrationand coma are forms of astigmatism, the teirn Is usually rest.ricted tothe aberration peculiar to the rays from point objects lying at aconsiderable distance from the axis.

V-2. 24 Astigmatism and the subsequent curvature of field effect are- negligible since the object and image under consideration are

e'ssentially point size and lie on or close to the optical axis.

V-2. 25 Distortion

- 'Vt,-

NAV1HAUVE WEN IG"Th

V-"U 2 Deformation of tho imagej(, whli ; itlkown- by HT .de'I )I v-Iterm, l'distort Ion''l Ir mouse-d by a va riatlon In the mragnifi-

cat~ori with the distancu from thu optical axhis . If tHi magnifIcatlot)'Icesswith t~his, 61i1tatince, tho distAortion I.., Cos Ide.-red pouliv(' ,Ifmagnif~atodcruasos as,, thir dlt anwcncras, dis-tortion Is

negative. From tho -,hape of the Inliage of a -.quare objoct, thw twotypes., of distortion are somrotirrnes" cafiled pin cus 'hion dLstortion (poslitive)and barrel distortion (negative).

V-2, 2 " 'The conditions for distortionless imnagery are:

a) the ratio tanG2 ' / tan- t must be constant for allvalues ofp

b) the systern must be Corrected for sphericL'laberrations.

V-2. 28 In paragraph V-2. 17 1t. was, ustablished thatC1 for thlo ncgat1Ve-rricnLscu.s lens sin 4 I/ sJn~ 6> ' equo lo I/ripV a Constant

(equation 105). It Iv easily ,,een then that unless ' equals,- )'I theratio of their tangents is not constnt. Hence, this leIns, Is not I preefrom distortion. llowever, s.ie' tOe objoct (tho point. mource) Is verysmall and is located on the optlc';.1I I!!xl, the distnce from the opticalaxi-s to the mojt rirnrotec element, of tho object 1, very small and theeffect., of dIl sorti am, nt cj uhIjIbI,

11 .9 'Fhooret ical cttlcuhttlotis i'r un e!xperimental lens.

V-,. '10 Slnue reductioni of the :,our(*,., di ariote r by an aplatiatic t' 3gatiNomrilcii.,n lens- I., Inve rs idy proportionatl to Owe Index of

ref raction of the tens1 mnatrial (e-quation 1,9), u rrmuteriv.l with an index of1. 838 was, ;;olectued (for dirscur.lon of Hti:, mrni'l :-i*e parugraph V1-4. 1).In order to obtain a sml nvelope abot I li' -':I rini I 'source formed bythe len,-, small loas radii muit bo u''w eti A ooiv.'nilt nt. firt ,.urfacoradius of .12b" was! veectcd.

V-2. 31 The param(eters of such a lIuns ;:.re calculated a.,- follow.-:

Given:

R . 125

n2 1.8

-1701-

I\AVTRAI)EVCEN 10'11,.) - 1

'T10 obN (itlI( rri O (lULt i'.i1 (H:3) h,

S1 (R1 + R~~)-.:360

Tic, irnago (IL-tricc of thn fir:.; -,urraco from equation (88) is

R.,~ + 1R4/ti 2 1

If a convordont nililtriurn lc'no thc~~mn, iLs-. 0625, then fromoquatioai . (100) and (~htho radlu,- of the tortond tnurfacu Is

02- -(81' + t) - - 2 0

Tifmin:age (ir~t aner' of the :'ord ourface (arid of the lens), fromo'qwidion (m~), it,

'lie iii;lUn~fication fromr eqluation (109) .;

m L /n 2 lb

TfIf? e!xi. half -angle from equation (101) io

ViTi2j 0

212Thori Owtotal agle of ightoupu i

NAVIIRAI)IV(PIN 1601 - I

V- . 3,,, The total luminou-: lntun:lty, 1, of an Ooram 11130-100 latampIs 350 tumew, per -.teradiuan (total lurninouw flux ciquubs bO

lumens per steradian x 4'r steradians - 4, 400 lurn ons) witha osourcediameter of . 015". Consider that this sourcve i placed to serve arobject of this lens; then the solid angle of flux,w , incident on the firstsurface of the lens, from equation (108) is

2 r XY 2 r !X 2 X A uteradinsx2 x

where

X + n .266

Y - X - I n2 .0:31

'he total flux input at the Lent ai; S. ,, - 2bHP h rnzt,:

A-sumingt no lo:'.-,eo In the lens the total flux output of Ow( Itn-m. L':

P'' F - 2b8 lumen,

The ,olld ;t,.'. of output of the 1,,n-, from (109), is

2'r X'Y' .fY'to,- - , 3. :i, Leradians

where

x, R? - .254

N A\'VI'NHPDEVCEN I i,"A 8 - t

Y, R'V - R-) cos' Mb

The luminous Intensity of output is

,, F'-- ,1 77. 3 candles

This can be verifiud with equation (1ii).

The diameter of the virtual source formed by the lens is

(.015)(. 53) 008,

V-2.:3 Actual measurements made with a lens of this design agreewell with the calculated values, except that luminous intensity

was approximately 20-25% lower than actual because of losses in thelotw, sy.t em by reflection and absorption.

V-2.. 34 Evaluation of the aplanatic negative meniscus lens relativeto ideal point source requirements.

V-2. il5 TheoreticaL calculations and experiments both prove that asthe -,izo of the source is optically reduced, the luminous

intensity is also reduced. Hence, it can be seen that two major require-ment- of the ideal point source, minimum diameter with maximumluinmiou- Intmslty, are inherently contradictory. In any particularIn-tance, it i-; necess.ary to compromise these characteristics to achievea atb'fartory result. The si'ze reduction achieved by the aplanaticngalive menilscus lew; is inversely proporticnal to the index of refractionof the ten.: material (equation U99). Therefore, in order to achieve a largesize reduction, the lens material selected must have a high index ofrefraction. The luminance of the virtual Image formed by the aplanaticnugative meniscus lens is, under optimum conditions, equal to the luminanceof the object (point source lamp) of the lir (equation 107). Since, bydefinition, luminriune i., th-,, luminous intensity pL.r unit of projected area,It can he --en th~l wh, -n th, ,I e of 'he point source object of th, lon.', I,reduced the turninou, nit,n:lity is" also reduced.

ago,

NAVTR'lAI)LEV(9N 16! -I

-~ 1LW~) L~~w'r urn itow 1,1 1.)O1t~y aLnd ; -ourc. dlariwl~or ure ptott~odlin fhjure 111-0) Iri Chapter 3. 'The expurirrintal data wa.Ii, obtainedu:sing the Osratn 11130-I0Oc lamp as, a sourcue and a tri triln corlistitUqof shorlcal cdnera rnicroorope object~lve, anid the! Qxperimeintalaplanatic no~ativo irrilse"us" mnl dttut (,-sd abOVe (Pua~ruhV-.9to V-2. -8:1). Data for tho theoretical curve wast computed fromt themraximnumn light. available fromr the Osorairr BC13- tOU tainp. Note that thethe..oretical luminous Intensity of a given sourco diameter U; alway.;higher (by approximateily 'X0%) than the luminous, Intens Ity actuallyproduced by tho lens train. This is oxplained by tho fact, that, there Intapproximately 20-269% los8 in the optical system by reflection and

aborption in thke lense ,s.

V-?,. T/ fly using two iduntloel mnrcus lenses it Is pos~lble to furtherrteduce the olme of tho actual point source, (figu-e V-4).

However, this technique decreaoes the light output efficiency 40-60%.Thu virtual imrage of the first lens serves as tho otflect of the secondlens. For technical reasons as m~l I as for economy the samne lensmaterial and desigjn was, usod for both lenses. iigure V-b shiows thevariation In lurrilnou.- intensity and In source diameter for single anddouble monnis-civs lens system- when distance betweeni the real sourcelamp anid Owu fir:.st lesir varied. In the event that the use, of differentyJiu!seo anfd differenit Internal radii is desired whon compounding mniscuslenoses, ciiarigous In thu performrance of the Ions system must be anticipated.

V-2.388 Th*v double rnentscus- lens systrnn hii:t a dis7tinct effect on theres-olution of the display-image. Figure V-6 .4hows the

improvemeont obtained by compoandiqu there Iorises. Tow( ver, ItiImprortant to note that this improvoement occur.,- at point source todisplay -obj oot distances less than 1. 4". At point s.ource to display-objectdistances; grvair than 1. 4", diffrart Ion effects,, come into play and thedouble muriseu:.-, t-un --yotorri is Inferior In resolution to the single lenssysteml.

V 4),. 3 0 Aiqie:; of ligh output on th, ordor ofr IR00 to 2000 are deoired.For I UIi'0 04anatic :LIV, ri i uiv n it scu lens: th- angle of light

output. h.. a f~uilon of 1 I w it it :f of ro frcauton of thw lens' mraterial (equo t ori10On), 'I'le form of t1hk. r-'1 lIcil tthI.- is uvh that for arn inul'x of refractionrof 2,, thle ani' of 11.11 i 0tit l i i:7 1120. 'inr'r exist;Hnj len rnt 'ti havejjIOd X"; [sIn:':: th " , f I)( tniqie * u,(f jIttjtt oit pul aictualily :Lidhivt, 'd is ie;r thanI X"Oo. Tlweiul of I itlut nuIIt 0V 1W P in' r ;u.-eI by deviatinj frorm tOw

aptna I ii'ii: n: I-m 'it o'nt'it inn :w: in2tI 5'' Ivi a.rtp V-3!

I-P-

NAVT~kAI)VCEi N -

9~oC

a) '0)

u) 0o 0)

NAV'1' AI-EV('UN -

38

36-- ,,--Aplanatic Object Distance

of Lenses Used

34 ..

32 I Real Source: Osramn HBO-109 Lamp (110 W)

Apparatus: Weston LIAght Meter No, 124630 Projection Roorn Condition: Lighttight

30'

282

26.

924, 10

P'22 9

'1 'S18'

16.Source Diameter - I

14 i Single Lens 5~~Diameter -" H

121 Double Lens -.

-0 -- K1..Luminous Intensity - Double Lens 2

Luminous Intensity - Single lens

1 2 3 4 6 6 7 8 9

Distance From Source to First Lens - Inches

Figure V - 5 - Variation in Source Diameter and LuminousIntensity With Real Source to First Lens DistanceFor Single and Double Meniscus Lens Systems,-.1 '-

NAVTIRADLEVCKJN I

7 -Source: Ouram HBO-10 LampExperimental Lens Specfical ions:

R , 1.25 inchest ,0625 incheisR2 R1 + Rl/n 2 + t

,n2 -1.88Two Lenses Required

Arrangement With Double Lenses:Second Lens Touching First

Resolution Chart: Curley PrecisionHigh Contrast Resolution ChartNo. 8006-P

Evaluation Method : Visual-recocdingthe Clarity Between Opaque Lines

Screen Distance: 60 inches

5la

4 "Ingle Lens

"~, 7 Double Lens

3

Source to Display-Object Distance - Inches

Figure V 6 - Effect of Source to Display-Object Distanceon Resolution for Single and Double MeniscusLen; Systems,

-Ici

1'IAVI I{AI )lV'CEN I

Anoljer 1.lufiilquo [or I ricr(!acirig the angle of ligjht output of tlio Uplanutir,W'QIiVe frri'nLcU~;t' I-rI. to apply a rrflective coaftlq to the baok pILunleof theo len:: (fIgure V/-4). lhi-, tuchnique roliec, on the fact that whr-nproporty drl-Ignod a reflective back ourfaCe of a moniscuO leno will cre!:iti,a Viltual irnage of the object (thoe actual point -,ource) which will bo ve rynear the virtual Image crnated through refraction by the leno, 'Thoref lr,'-hd rayo then appear to originate from the caine point aC thorefracted rayti. In addition, by properly crowning the back plane of themneniscus lons, It Iv pos,,ibte to join the roflected rays,_ at the pe(riphieryof the refracted rays. '[he final light output fromn such a lensioI. ,anuninterrupted portiooi of a -phere exceeding 180. Of couroe tho virtualsource of the reflocted r'ays Lis not (ierfwnlifted as Is the virtnal sourceof the refracted rays. rherefore, tho ditiplay-iniigo produce(,d by th-,reflected rays will be Inferior in quality to that, produc-d by the rofractedrays. In some training tasks thiu condition is acceptable and the absen ,coof peripheral vislon Is more harmful. IBrightnooss of the reflected ray

r will equal the brightness of the refracted rays If the are.-a of the refloctodring equals the area calculated from tho Internal radius of the inncuvlens. Where the areas are not equal Illumination on tho screen will varysharply between the reflective and refracted light rayo. Sincv, as heradii of the lens is made smaller the area of the r(?flec-tive surface doctiresfaster than the area calculated from the internal radius of the Imenriscw;"lens, there is a practical limit as to how small the monisc'us lens may be3made when using this technique.

V/-2. 40 The point source envelope Is IrnportatA to the extent that It Urrdlts,the cloveness to which the source may approach the display-

object. With the aplanatic negative meniscus lens Vystemn, the projectionsource is the virtual image of the Osrarri HBO- 109 lamrp produced by thelens. The point source envelope is then the Image distancv of the lenrarnd the iage distanco of tin lens Is equal to the radius of Its o'condourface (equation 92). '1h; turn is limited only by the Internal radiusof the mentscut- lons, the inimum praet.1cablv Ion.:: thickness, and t~heability of very smnall. lenses to tranomit sufficient, light.

V -2. 4 1 'romperaturo, of the menie'cus lens, the effeclive poirt sourc'envelope of this system, can be controlled and field to room

tempexrature provided the point sourco lamnp can be kept :suffic-iently farfrom tNe len., to prevent. exce~ssive heat tran.-fer.

NAV'III6AD)EVCE'N IW,,, - I

-Othlcr i,€.,.8e,,with a l ,arcj Anqjto of Light, Output

V-. 1 Introdurtion to theory

V-:. 2 In the previous sections of this appendix, it was- o-hown thatto achieve aplanatic conditions with a negative tnieniscus lens,

a specific relationship between the objct distance and the radius of thefir-st surface must be maintained, in particular, the object distanco1m1u1Ls b(,: equal to the radius of the first surface multiplied by the sumof on(! plus, the index of refraction of the Ions material. In addition,tho curvature of the -econd surfac, mus;t beb centered at the Image formedby the first tnurfac ,. In the following :;ectlonsu two lens type s-, a plano-concave and a non-aplanatic negative mreniscu, Lens, are evaluated. Inparagraph., V-3. 14 and V-3. 23, tlh capabilii,,,s of these letses as-related to point source ruquirerntnt are discus ed,

V-11. 8___ The plano-concave Ion-

V-:3. 4 One weaknons of the aplanatic negative rneniscur lm ins i its,10 1W.limited angle of output. Analysis of this lons reveals: that.

the angle of light output will be increased if the ucon- d o surface of th,,lens is designed to further diverge the output of the firot surface. fthe second surface Is a plane of nufficient extent to re'ceive the output

FW of the flr:st ,urfac,5 untl the angle of incidence of the rays striking these.i,-cond ourface equal or exceed the critical anglo (total reflection), theangl of output will be 1800. In addition, through the uso of a planeourface, economy of manufacture is obtained.

5 A theoretical analysis of such a plano-concave ltn:; i madeIn paragraph V-3. 8. 'Lhls analysis reveal:: that If ;t point

olourc,, of light sorving as the object of a piano-concave! lte: i.- locatedat a dioftanco R # n2 RI from the concave first ,urfac wi tlhIl:: surfacehas a radlus, of curvature, RI , and the len.,; has an ind(ex of refractlon,

' n2, then the len:, will form a virtual imago of the point sourc,, for eachinfinli:Irmal area of the second .urface. 'The virtual Irnra, ;e,,rvliwj a::a source for rays emrrij.fg~l.k l-ns at. angile 2 ' will he dis t.n." ("2 cos, 2') / CnO-.",in (i from the plane -.urfaco. (equation

1 0) It. 1urther --hown that these virtual i a: ry iattr thwn 1hreal point ,.ou re object by a factor of I/n: 2 (equal.ion 11 l).

-1 ¢!-

N AVTRA DE VC E N 132 8 - I

V4,(11 fn par.UJrapliVh .10 fl i1 :,, -,,owni that thlo lenL-,i aplaiiatICand Lh tr;tI:de fromr vhrorm3lJ-,.ri ol.h,,r aborratiou:, tffocto

V-2. IIn pavragruplir V-:3.114 and V-:!. 141 tho tlv orpticat anid r'xperimrintal- c'arac~nri.,Ati of thlo, lon. ar , d-Vuor. od.

V-. 81 Devloprritn of expro-s:1un.- for obj-ct di,-lancou nd irmagedivLanco and for lateral niagn~firatiori

Con~rider In figure V-i that rays from a point ourcu) of I Ight, are Incidenton a piano-conoave lons having arn lflde.x of refraction, n2 , and a1 radlu.",of curvature of Ur! flrt tiurface, R , loc'atfi In air (n, - 1). If thopoint zoource ohject I. locate(d at a d'int!anvo of R,4 Rin 2 fromr the flrot,,urfavo then t following equatloi: lhveood in paragraph:, V-2. 6 andV-2. 7 apply to the fir.-t ourface:

Ol+ RPn2) (83)

suRj n l' (88)

n22 (96)

11 the wucond surface is a plane located to obtain a cr-ven(onL minimumlono thlcknost, L., then the Imago formed by thi' r~.s. .rf;L('Q OerVes aSthe ob1 -1-t of the vecozid :rurfacn:

+ (: 't)(1)

onell'::- Law may be written for thr, 'econd ,urface:

Ty :-In 1, ,In r2 (80a)

NAVTRADEVChxJ 1(~

--.----. si __ _

spr

Figure V -7 - ky Tracing IAiagram of Pbiario-Concave L~ens.

NAVTRAI'I IEV(.I U'N I;',}f- I

F rom Abb '- S erie Condition, Lhir ImgrIirdfication of U h, obj(eL of .h,, econd ,tirface, M ,f ios

n2 sin 5 2

From the geometry of figure V-7, spocifIc for the tsucond surfacu

G2 "1i2 (11)

w- r2( )

Therefore (80a) may be written

n2 sin&2

sin9 2t

Substitute this in (97) above

n2 sine2112 - (lib)

''hie lateral magnification of this lens, mL, is the product of the rriagn-fications of the surfaces:

L m 1 2 (16)np?

NAV"I'AI)EVCEN I - 1

Froi l urn V-7, ,poe ftc for th,, socond -u rfa c

L x

Solvo this for X

sp, sin,-. 2.2if. (117)

x- - sinV

SubstiLutc in thik the value of sin&2 from (11b)

so sin 2'(1)12

Also from figure V-7, specific for the second surface

~x

Solve this for X

s2' sin E 2 (fl - sln I TO

SubtItute In tho tho value of X from (118)

L2 :;nn9 2 ' -s p I sin 0)2 '

in2 -siny-2

a

NAVI ADE[VCEN IC5,..- I

So[vw this for s2 ' and subsLitute the tr-jonorriwLr11c Identity

COS 2 -sn 2 2

s rn2 2 - (120)

If the value for X from (117) is substituted in (119)

s2 sinE) 2 S5 sin e 2 '

sin , s sin 2

and if this is solved for s2'

S2s - . (in 2 ) (121)

Remembering the trigonometric identities

1-sin2 y- cos 2 Y

sin Y/cos Y - tan Y

(121) becontet

tan H,,

,190-

- 190-

NAV1I'RADEVC EN 10C2N - t

\T'-3. 9 Note in (120) that a , & ' approacheo. 0, 2' approachesS -s/n2 and that as -7 ' approaches 900 s ' approaches 0.

Now express 1on (122) means that for each value of tle slope angle ofthe Incident rays 6 2 theru Is a corresponding aid unique value of theslope angle of the refracted rays --2 These refracted rays willappear to originate from a point source at a unique point distant s,from Lh., second :urfacu, when the object of the second surface is t1evirtual image of the point source formed by the first surface at distancec2 from the second surface. Expression (120) shows that distance a2'Is Indoed unique for each value of "J. Phystcally, this means that EherAy,- eriorging tro, this lens at eac value of ' originate from adifferent virtual point source and the lamlnou intensity of any one ofthese virtual point sources will be detarmined by the luminous fluxincident on that portion of the second surface which forms it.

V-3. 10 Evaluation of aberrations for the plano-concave lens

V-3. 11 Recalling from V-2.12 the requirements for freedom from- spherical aberration, it can be seen that the first surface of

the plano-concave lens is free from spherical aberration. Because the

second surface is a plane, it too is free from spherical aberration.

V-3.12 It can easily be shown from equations (95), (96) and (115)that the condition for freedom from coma, namely,

sin &-j/sin 6,' constant for all values of 6 i.-; also maintained.Therefore this lens is also aplanatic.

V-:3. 13 Chromnatism is similar to that discussed in paragraph V-2. 18above. The effects of other aberrations are negligible since

the object of the lens in this problem is essentially a point and lies on orvery near the optical axis.

V-a. 14 Experimental evaluations of a plano-concave lens.

V-3.15 Experimental evaluation of a piano-concave lens like that- discussed above shows that the light output in any direction&2

follows closely the cosine of E2". Hence, though a 1800 angle of output

-191-

NAV'TRAt-.EVC.EN 10", - 1

i.s theoretically po58lbie, thu liht output near th e .d(jo, or thil; h,)rriiphur:is extremely low.

V -3. 1 6 As explained in paragraph V-3. 0, this lens dorio not, form thevirtual image of the point source at one particular point for

the entire output cone of light; on the contrary, rayso at each Individualslope angle ' form a virtual source of the Initial object. However, eachof these sources radiate in only one direction, the direction -' corres,-ponding to 2 In (122). Therefore, the effective point source uh.sed forprojection consists of a unique ,jource for e ach direction of projection '"

V-3.17 The non-aplanatic negative men!ieus lcn;

V-3.18 As noted, the anglo of light output of an aplanatic negativemeniscus lens is a function of the index of refraction of the

lens material and is independent of the lens dimenslons (equation 104).This is also the case with magnification (equation 99). However, theangle of light output and the magnification can be changed It the pointsource object of the lens is; shifted from the aplarialic point wicresi a - ( nz).

V-3. 19 In paragraph V-3.22 it is shown that the image distance s'pvarles with the object distance ol In accordance with the

following expressions:

R1 I i tan sin - (ni,, X (126)n~ 1777)" RJ

02 -(s' + t) (90)

s2 ' -0 (4a)

in (126) as s, incr.a, ..... increAWe. but at a slower rate. hus a.-, Ilhpoint s:ource obj,,ct is' shll'~w;Ly ifrorn the apIlanat-i object, point., the

p -r)I --

NAVT'IIADEVCE 4 1(28- 1

llnrlap i;- 'AlhfLed away from the Lplatiatl' Irriage point in the oam, direction.

V-: i '0 i parajraph V-,, 22 It it ohown that the magn ication by thic.-- lr hi, n2,(I - i') / R 1 , (equation 129). From this it is

-vld-.nt that m, cI rIncre ,e the, maiwication decrease., and thoruforothe:: arrount of reduction increac.,

V-3, 1 Irn paragaph V-3. 23 the theoretical and experimental character-ictioc of thh lnrs are discusned,

V -. .. 1 D2evoltopment of expressions for object distance, iniage distanceani magnification for the non-aplanatic negative mnclscx , lens.

Con'idar In figure V-8 the ray AV from the point object to the extremeedg of th, first t;urfuco of a negative meniscus leno. If the lens is in airand ha.,, an Irdex of refraction, n2 , Snel].'s Law may be written

,-,In 11 - n? sin r (80)

From figure V-8 for ray AM

I (Sl -RK)2 + R1 '

Recalling that, by corventlon, R1 and i, are negative, make thI- explicitfor the ftr.1. :,urfaco

s I + Rl(123)

S 1 1 R

I A 3-

NAVTiRADEVCEN .162H t

mN

S1,r

Figure V - 8 -Ray racing Diagrani of Non-Aplanatic Negative

-t94-


Substituto this in (80)

.~~ ~ s nl , sl + Rl

+ R +n (124)

From figure V-8

sl ' - R1tanr I - I

&~ecalling that, by convention, rl,, s2 ' and Ri are negative, make thisexplicit for the first surface:

-tan r I -"4 + (125)

Solve for sl

st " R1 1 -tan r (125a)

Substitute (124) in this

-w R1 1+ tan sin- i l+R (126)

"elect the radius of the second surface, R2 , in the same manner as isdone for the aplanatic negative meniscus lens:

s 2 -(s ' +t) -R2 (90)(92)

spm (94)

- 1,95-

NAVTl{Al)K"jCiN 1 ENK - I

F~romi Abbe':.; Sine Conilion, the rm:tgnfication of the b~je-Ct by thefirst ,;urface, tin1 , L.

oin 1 ()

s in

R~ecall that (Bla) anid (87a~) apply to any negative munilncus lons3:

sI Mi( n I(B lb)

1i ~ ist' sin r, (87lb)

Divido (81,b) by (87b)

SubstituLt., t;In ll,/ sin r1 from (80) In t1ll:

Su~ltuu h~In :;I!3

inn1 (122

-In 01 1. -

''RA DEVC'EN 1623- I

Por the , ecornd :urf:ui , (1,M) rppiius

'Y2 - n2 (!

Therefore the lateral magnification of tillons, ml.,, ,"

rnL - mIrlr 1 n (129)

Remember that tr' t 2 2 substitute (127Y) in (129)

sin 1m Lsine '2' 12

V-3. 2:3 Experimental evaluation of the non-aplanatic negative

rneniscuL. lenuz.

'Y, A non-aplanatic negative meniscu.3 lens wao fabricatel in accordance withthe design shown in figurre V-U. Experiments with thh; lens included themeasurenient of virtual -,ource diameter, angular output and luminousilntetioity with this lens. Projection using the virtual source formed bythis lens proved satiofactory despite the slight increase in aborrations.One minor difficulty was encountered, The intensity of light declinesfrom a maxlmum at the optical axis to a minimum at the fringe of thecone o! output approximatply proportionally with the cosine of the angle.Experiments with the aplanatic negative meniscu; Ions indicated thatintensity with this tons wans quite constant over the entire cone of tightoutput.

4'v

-4,9/

N~AVTRA IEhVC1HIN l(l) -

r.2734__3126 Dia.

B5Rr

- .0625R

Figure! V - 9 -Design of a Non-APIltldic Nc'jative o~~ m;

NAVTILADEVCEN 1628 - 1.

V- D, :eIg i Com-idratlons

V-4, 1 The material for these experimental lenses is a rare earthelement glass manufacturcd by the Eastman Kodak Company

(EK-448). In the investigaton of existing high refractive index glassesthe following characteristics were consldured; clarity, absence of colortints and capability to withstand high temperatures and severe temperaturegradients, In addition, the lens material should not favor chromaticaberrations. EK-448 was chosen primarily for its high refractive index(1. .. 04) n iarl y. It h-s the disadvantage of being a "heat free" glass(not capable of withstanding high temperatures). Slight chromaticaberrations are inherent within the material; however, the effect isnegligible due to the small separation between the two extreme visiblewavelengths which are the 0. 00004 cm. wave and the ,00007 cm. wave.The separation involved is approximately. 002" w.Juh is smaller thanthe anticipated source diameter. Tests have not re )aled deleteriousaberra'ion effect to the naked eye. Rare earth ele,,r nt materials arenormally non-absorbent to the visual rays from 400 microns to 200 micronswith visual ray absorption not exceeding 2% per cm. of thickness.

V-1. 2 High refractive index is a necessary requirement because theA higher the refractive index, the smaller the R1 /n 2 value, that

is, the distance that the center of the output cone is disptaced from theback plane of the meniscus lens. The smaller ths R1/n 2 value, thegreater the angle of light output.

V-4.:3 The axial alignment of any lens system s t''ry 'kmportant. tassures more uniform flux distribution and a greater reduction

of the source. Care must be taken to avoid a temperature gradient in thechosen glass mater al (EK-448). Cooling the glass and lamp combinationis harmful to the latter since the cooling effect lowers the light output aswell as increases the source diameter of 'Uh HBO-t09.

V-4. 44 Experimentally many by-products of tho Inltial negative nielseu:lens have been evaluated. A single meniscus lens war designed

(see figure V-9) and experiments conducted. One of the experiments wasto place the negative menidcus lens at the pre-determined distance andevaluate the effectivenes s of the equations. Other tL.A;Ls on this lns evaluatedlight efficiency, effect of aberration, effect of extreme heat, and theres-olving power of the final point. source.

199-

NATPAI'.AWIVHNr 10)('l2 - 1

V -4. 1b Point Sori rr' A:;,mie nbly

v -4,0 Tio olriiluLo Lotfidowi (;onit1tlor ,)rr a )uec~ic 11i(AklpLi~f' ucornlo~. poinut -,ou rnn uo.,rib]y wat. dur ;gried rid 'i brI .,ah,,ii

'Pho. fol lowiruq wrt! the :eifLai for. 1111: cnr:

a) u poiri I. no 'edovice to irnriaetouchdownr coniiJLloin:wheuru the dRtutric betWeni Lire tlut' , yr arid thoearth ho 121.

b) the final lent; elementi touchinq the transpa ruurcy to beat roorn te.rnpcerature.

0) capable of projecting over P1301.d) the final point source to be approxiurisety .00411 In dia.c,) tight output. to bei in the viotity or 3O (-w idien.f) capable of oiriulatting udn blunt i. 10 huracteriutlcu.

V-4.7' To simnulate, touchdown at, a distance of 12' with in armnunedtratiop~aruncy ocale ratio of 24,000 :1, point source LO oute!r

giaoa envelope dintance mtit be .072"; conSoquently a very urinouative mneniSoua leo had to be utiliyxed as tho final Ion,, e Imneri. To

achi~vuLho .p led angular co\, 2raqo It wa-s ntecesary toc. wce a non1-aplanatic nieniocus Ions.: Rt wan further nocessary to cut the bottomisoctiori of the lens to assure the . 072"1 requirod for touchdown fliiur ltoni.T1his cutting away of the lens doo:, not. affect tOw projection :;ince ray::.emnitting U~oin that s;ct] on are blocked fromr tir ocreeni by th: e limpicop rouCkpit . The uritiro poi nt ,;ou rvo a.,ser bly was angliec 2150 from t liihori''otal In order to iii.] Ii the centrral portion of tire r eqjative mnirireilenai to project, onr a :;peelfic part, of tho ocreen mno.,t viewed by tLre p1 Jut..

VT-4. 8 1.1lqu r' V -10 t.hows the poinut source aw-.orbi y d' slqrod Losatisf.y Lhe above opocificatiori3. 'The deovico coirsi sis of thew

i 130- 101) io t'ou ry vapor DumprI 1)0:11tlorid hor'izontal ly In rr 't-. L rtoii i iii itho he i(.Iht of tire device. Thf in phluical conidenser Ohown iii the afl wr'arrr I.,,rabricated out. of' quartv hr orde r to withstalnd the high turnpe rato r(oneorunte red Ini th .;y:Atein. No hl filtr 10 I i r;ec t Lw '-ri tho('(rtratnd the oi id 'riser tier a.L I aval labie hn ir': tfiter tra)ri:tI riak;u--()on tc: tire Osr-trr ttintrip ronuho'l nj 'ratiirt bt'riprr''atu ro ' hi irrJfof tirjj cu it i : :( ' r 1,-. ti ink t ci! * pjri of I hi I liqi ii ft ix rtAidiInj r oi nr t1w( . rat ir I ano :r );it I -c It I i itri, i ii' : r iyr f()r 111 -,se r ii( )i i ii I(e 11 t ir nIcr :t -()I)(o[ij( ii-, IV( . Ihi I Ij1i. fluox -d IC hiir d p rior hi ) iii ii i n(.1 it Ow i i v t

NA VTR'~A DE V C'( -,N I( C8?- I

r., rx

.40.4

NAVTRADEIVCEN 1626- 1

because it has been found desirable to tnsert filters within this c:ollirnatedpath rathei, than in any other section of the device.

j-.9 The purpose of the heat filter is to protect ambient light filtersand the microscope objective since heat can only damage those

items rather than the condenser. The objective used ia this design iscapable of withstanding approximately 125(.. Higher temperatures tendto soften and distort the bonding material used between lenses. The solepurpose of the microscope objective is to reconverge the collimated beaminput; this, of course, is a necessary condition for the meniscus lens.All lenses and filters with the exception of the condenser have been coatedto minimize the light losses due to the optical elements, since 12 air toglass surfaces exist at which light losses can take place.

V-4. 10 This experimental point source assembly was ested for tur-ability, light efficiency, resolution and angular output. It

has been found satisfactory on all accounts. The resolution of this unithas been measured at approximately 6 lines per mm. It produces apoint source approximately .0045" in diameter with a light output ofabout 30 candles.

-202-

ApFTlEt1)111, viTABULATION OF PLAMIC MA'IER'TA LS

Name Manufacturer Chemical .amil Size - Max.

Lumirth Celanese Cellulose Acetate 41. 6" x 3.7511

L. 828flexible 20" x 50"

26" x 40"

Kodapak I Eastman Kodak Cellulose Acetate 40" wideF - 122flexible 20" x 50"

25" x 40"

Kodapak II Eastman Kodak Cellulose Acetate 40" wideF - 290 Butyrateflexible 20" x 50"

25" x 40"

Kodak IV Eastman Kodak Cellulose Triacetate 40" wide401

flexible 20" x 50"25" x 40"

Plexiglas II Rohme & Haas Acrylic; 100" x 120"V UVA

MIL -P -5425BrigidEnduron Pioneer Aliyl Base 48" x 48"

CR - 39 Scientific Corp Co-pollyrnerrigid

Mylar Du Pont Polyethylene 52" wide300 Terephthalate500'750flexible

Plastecele Du Pont Cellulose Acetate 20" x 60"sem i-flexible

-203-

NAVTIAI)EVCEN 128 ITABU LATION 01." tIAS'FIC IV,,, ,.A R L./ I,

'Thickneso PackakjLtItu Method ofName N --. , M ax. R77-a - ts Lr-ducing

Liumirth .003" ,,,n" x CastL. 828f lexible x

Kodapak I . 005" .020" x Ca stF - 122f lexible x

Kodapak 11 .001" .002" x CastF - 290flexible x

Kodapak IV .003" ,015", Cast401.

flexible x

Plexiglas II .080" 1. 0" X Cast S' UVA

MIL -P -54,"

Enduron . 031" 1. 0" x CastCR - 39rigid

Mylar . 003" .0075" X300500 x750flexible

PlasLeote . 020" 1. 01" x Compressionsere -fl cxbk molding

-, 1)1 -

NA VIRA rM:Vc3I, h:i!.;i-

TAIJUI,ATIIOI\J OF' N~I AM [C MATE~ PUAUS (ConLd)

of White U~ghL Avrage ModulutNarno Retacve ndoxND)~ ao~ of Ehuicity x 100

Lumirth 1. 490 86-9.3 60%, RHd - 2.7

flexible

Kodapak 1 1.29 Id 3 - 4 r

flexible

Kodapak Il 1.19 02 -2. Tr.- 290flexible

Koda.k V 1.29 90 3. 5- 4. 5T

Plexiglai.; 11 1.119 12 4. 25UVAMIL - P544rigid

Enduron 1. 503 go-P 2CR -39

Mylar 1.64 l

5001150floxible

NOTE:i All hml maidera: 1 are v 'ry c 1r.a r, froo ofdye mark,; arid :1 ritilotw..

W W IdelI' Twii:

( m l 1-(: fItm


PTAS TJC MATERIALS TESTED AND FOUND UNSATISFACTO.RY*

Pliofirn

Clopane

Cellulose nitrate

Polyflex I & II

Methaflex

Vinylite

Krene

Visqueen

* {' .- materials wore found wanting in one or more of the followingproperties:

a. Optical clariLyb. Tensile strengthc. Shear strengthd. Tearabilitye. Modulus of Elasticityf. Creep strength.

-206-

NAVTRADEVCEN 1,628-1

U) tp w ID 2t

-4 C4

b.. 0~ -0

5b

k FL4-4o PE-40A1 2 V

00Qc

Q) Cd vco w-4c

4-tS

'r- *C1C

e la cc.s aIQ

W4 [,2H El

-201 -

NAVI1.,RDYV\C'1IN I

4.

0,C

ri 0

4g C) dC0-1 0

(j) 1-

3/) C*

C.--

CL)~f L)~ I

CNil:>~

~ rL~i u~ 6 6~'Y

r.iP~ 'f' 'I A DIK V CJ j:;~~ -

0CI) (1) Cl)

-*1 .- t,0

Cl) (Al -4 14~ I~' a)CI) 0 0 C) C) Y Uz z

I ICI) .44 N N

a o s.~iLi Li I~4 ~4 ~ ~1

C)

Li 0

V ~

Lii-~ (I)

6 6 6 644

~rI)~) *ri

n .4 6 6 6 6,~

~6 6 6 6 6 6A 2

,C.2 .~,

CCI 0*)

2

.~ f~4CI, (I) ii) a)

.4

C)

C)CC C)

II (I U ~ ('~ 0I '.' C)*1 H H H ~' Iii H

j CIC (IC (C

~'1 ''d (~'r~(I~ r~ * C)C C1~4).~ ~ C) r*I,.~j IC ~ CCC C * , I

I C, ('C Ii)~)* g ' 'I (Cr I ('C 14 ~

rr'~1 ICI -CCC I ~ ' (I)II ~ ~ C I :1.

NAVT~RADEVCEN 1628 -1

000 z t4.

404

Ow0o Cu 0

'0 0 .to -W

0* ~0

-4 C4S 4 C

p 01

NAVTRADEVCEN 1628-1

Government's Rights In Data

in

Technical Report: NAVTRADSV%,'EN 1628-1

The Contractor agrees to and does hereby grait to the Govern-ment, to the full extent of the Contra,.tor's right to do so with-out payment of compensation to others, the ri ht to reproduce,use, and disclose for governmental purposes (including theright to give to foreign governments for their use %s the nation-al interest of the United States may demand) all or Pny part a(the reports, drawings, blueprints, data, and technil'al informa-tion specified to be delivered by the Contractor to thA Govern-...ent. un.r h.I.. contract; provided, however, that nothing con-tainel in this paragraph shall be deemed, directly or Ly impl-cation, to grant any license under any patent now or hereafterissued or to grant any right to reproduce anything ,lse calledfor by this contract.

II

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