3-D Computer-Generated Movies Using a Varifocal Mirror Eric G. Rawson An application of varifocal mirror autostereoscopic imaging to 3-]) computer-generated movies is de- scribed. A high speed movie projector and oscillating varifocal mirror project moving autostereoscopic images at 5 volumetric images per second. In order lo distribute evenly the component images along the depth axis, linear time scans of the image volume are required. However, the image position is a nonlinear function of the mirror displacement, which, in turn, has a riolinear freqiiency response to the mirror driving voltage. Analytical and experimental investigations are reported in which approximately linear scans for duty cycles approaching 90% were attained. I. Introduction Recently, Traub' described a new method for gener- ating three-dimensional images using a rapidly vibrating varifocal mirror of the type described by Muirhead in 1961. Figure 1 illustrates the principle of varifocal three-dimensional imaging. A thin Mylar film, which has a mirrorlike aluminized surface, is stretched taut over a loudspeaker and driven sinusoidally at about 15 Hz or 30 Hz. When vibrating in its lowest order mode, and at small amplitudes, the mirror surface is essentially spherical. When an observer views some object by reflection in the mirror, this mirror oscillation causes a corresponding oscillation of the reflected image position whose amplitude is typically fifteen to thirty times larger than the mirror pole displacement ampli- tude. As an undesired side effect, the image magnifica- tion is also a function of the image position. As the mirror sweeps from its convex extreme to its concave extreme, the object screen displays a rapid sequence of images. These are reflected in the mirror so as to appear to originate from a set of image planes distributed along the depth axis. If this display cycle is repeated rapidly enough, persistence-of-vision effects give the impression of a three-dimensional image. In this paper, a technique is described for displaying three-dimensional, computer-generated movies, using the varifocal mirror principle, and two problems associ- ated with attaining a constant spacing between the images along the depth axis are discussed. Such constant spacing is desirable in most cases of interest. I. 3-D Computer-Generated Movie System Figure 2 schematically shows the movie projection system. A special, high speed projector, loaned to us The author is with Bell Telephone Laboratories, Murray Hill, New Jersey 07974. Received 5 February 1968. by Wollensak Optical Products, projects a sequence of fifteen 2-D images onto a rear projection screen. Synchronous displacement of the image plane disperses these fifteen images more or less evenly along the depth axis, creating what is technically described as an autostereoscopic phantom image. The next fifteen movie frames are opaque, and during this time the image position returns to its starting point, in prepara- tion for the next sequence of fifteen 2-D images. Thus, a single 3-D image volume is assembled from a spatially distributed sequence of fifteen planar images. To accomplish this, the movie projector runs at about 4.50 frames/sec. The 16-mm movie film was generated with a GE 645 computer and a Stromberg-Carlson 4020 microfilm recorder. I order to synchronize the mirror oscilla- tions to the movie film, the computer was programmed to draw sync marks, that is, small transparent areas, on appropriate movie frames. During projection, the resulting light pulses are photoelectrically detected and are used to generate the sinusoidal voltage waveforms required to drive the speaker. Figure 3 is an attempt to illustrate the autostereo- scopic nature of the movie image. The subject of this particular film was deliberately kept simple. It coI- sists of a line outline of a house with a front yard and two front doors, through which two figures, a boy and a girl, move hack and forth. The top two photographs are oblique views of the image from two different directions, and the third is a single movie frame, which is included to assist in visually interpreting the top photographs. The blurring in the top two photographs is due to image jitter, the motion of the figures during the exposure, an(l to the shallow depth of focus of the camera that took these photographs. However, the pictures clearly show the three-dimensionality and the wide range of possible viewing angles of the volumetric image. August 1968 / Vol. 7, No. 8 / APPLIED OPTICS 1505
Transcript
3-D Computer-Generated Movies Using a Varifocal Mirror
Eric G. Rawson
An application of varifocal mirror autostereoscopic imaging to 3-]) computer-generated movies is de-scribed. A high speed movie projector and oscillating varifocal mirror project moving autostereoscopicimages at 5 volumetric images per second. In order lo distribute evenly the component images alongthe depth axis, linear time scans of the image volume are required. However, the image position is anonlinear function of the mirror displacement, which, in turn, has a riolinear freqiiency response to themirror driving voltage. Analytical and experimental investigations are reported in which approximatelylinear scans for duty cycles approaching 90% were attained.
I. Introduction
Recently, Traub' described a new method for gener-ating three-dimensional images using a rapidly vibratingvarifocal mirror of the type described by Muirhead in1961. Figure 1 illustrates the principle of varifocalthree-dimensional imaging. A thin Mylar film, whichhas a mirrorlike aluminized surface, is stretched tautover a loudspeaker and driven sinusoidally at about15 Hz or 30 Hz. When vibrating in its lowest ordermode, and at small amplitudes, the mirror surface isessentially spherical. When an observer views someobject by reflection in the mirror, this mirror oscillationcauses a corresponding oscillation of the reflected imageposition whose amplitude is typically fifteen to thirtytimes larger than the mirror pole displacement ampli-tude. As an undesired side effect, the image magnifica-tion is also a function of the image position.
As the mirror sweeps from its convex extreme to itsconcave extreme, the object screen displays a rapidsequence of images. These are reflected in the mirrorso as to appear to originate from a set of image planesdistributed along the depth axis. If this display cycleis repeated rapidly enough, persistence-of-vision effectsgive the impression of a three-dimensional image.
In this paper, a technique is described for displayingthree-dimensional, computer-generated movies, usingthe varifocal mirror principle, and two problems associ-ated with attaining a constant spacing between theimages along the depth axis are discussed. Suchconstant spacing is desirable in most cases of interest.
I. 3-D Computer-Generated Movie System
Figure 2 schematically shows the movie projectionsystem. A special, high speed projector, loaned to us
The author is with Bell Telephone Laboratories, Murray Hill,New Jersey 07974.
Received 5 February 1968.
by Wollensak Optical Products, projects a sequence offifteen 2-D images onto a rear projection screen.Synchronous displacement of the image plane dispersesthese fifteen images more or less evenly along thedepth axis, creating what is technically described as anautostereoscopic phantom image. The next fifteenmovie frames are opaque, and during this time theimage position returns to its starting point, in prepara-tion for the next sequence of fifteen 2-D images. Thus,a single 3-D image volume is assembled from a spatiallydistributed sequence of fifteen planar images. Toaccomplish this, the movie projector runs at about 4.50frames/sec.
The 16-mm movie film was generated with a GE 645computer and a Stromberg-Carlson 4020 microfilmrecorder. I order to synchronize the mirror oscilla-tions to the movie film, the computer was programmedto draw sync marks, that is, small transparent areas, onappropriate movie frames. During projection, theresulting light pulses are photoelectrically detected andare used to generate the sinusoidal voltage waveformsrequired to drive the speaker.
Figure 3 is an attempt to illustrate the autostereo-scopic nature of the movie image. The subject of thisparticular film was deliberately kept simple. It coI-sists of a line outline of a house with a front yard andtwo front doors, through which two figures, a boy and agirl, move hack and forth. The top two photographsare oblique views of the image from two differentdirections, and the third is a single movie frame, whichis included to assist in visually interpreting the topphotographs. The blurring in the top two photographsis due to image jitter, the motion of the figures duringthe exposure, an(l to the shallow depth of focus of thecamera that took these photographs. However, thepictures clearly show the three-dimensionality and thewide range of possible viewing angles of the volumetricimage.
August 1968 / Vol. 7, No. 8 / APPLIED OPTICS 1505
ALUMINIZED MYLAR SHEETVARIFOCAL MIRROR"
ACOUSTICAL DRIVERC.R.T. (LOUDSPEAKER)
SEQUENCEOF
PLANAROBJECTS B
abc
OBSERVER
SEQUENCE OF IMAGES",FORMED IN THE
"VARIFOCAL MIRROR"
Fig. 1. Atostereoscopi( display using a vibrating varifocal1'0I'.
HIGH SPEED 16MM/ MOVIE PROJECTOR
III. Varifocal Imaging EquationsFigure 4 defines the required terms. A varifocal
mirror having a disk radius R is displaced so that itspole 0 moves a distance A along the optic axis away
c from its rest position O; the mirror is spherical with aradius . An expression is required for s', the imagedistance in the fixed coordinate system with origin atOf. The spherical mirror equation (1/s + 1' =2/2') applies to the moving coordinate system with originat 0. The sign convention adopted is that all distancesmeasured to the right of the origin are positive; thus,s and sf are always negative.
It is convenient to express curvature as a function ofA rather than of r. From Fig. 1, noting that r is
mir negative, we have r2 = R2 + (r + A)2 , or r = (R +A2)/-2A. With this equation, together with thetransform equations s = sf- A and s = s/ - A, we
-VARIFOCALMIRROR
Fig. 2. Schematic diagram of the system used to project auto-stereoscopic computer-generated movies.
Experience with the above apparatus indicated thattwo desirable improvements would be: (a) to arrangethat the planar images were evenly spaced along thedepth axis, and (b) to increase the projection duty cycle.(The duty cycle of the system described is 50%.)Since projector equipment limitations require that the2-D source images be projected at a constant rate(actually the maximum possible rate), it follows that, inorder to distribute images evenly along the depth axiswith a 100% duty cycle, a sawtooth-wave motion ofthe image position along the depth axis is required.
The remainder of this paper is concerned with twoproblems, one analytical and one mechanical, whicharose during our attempts to achieve such a sawtoothimage motion.
The analytical problem arises because, as is shown inSec. III, the image distance is a nonlinear function ofthe mirror pole displacement. Hence, a sawtoothimage motion requires a more complicated mirrordisplacement waveform. The problem is to determinewhat mirror displacement waveform will yield thedesired sawtooth image motion. The equations re-lating the image and mirror pole displacements arederived and then used to solve for the required mirrordisplacement waveform.
Fig. 3. The two top photographs show oblique views of the 3-Ddisplay from two different directions. The blurring is due bothto figure movement and image jitter during the exposure, and tothe shallow depth of focus of the camera. The bottom photo-graph shows a single movie frame that is included to assist in
visually interpreting the top photographs.
1506 APPLIED OPTICS / Vol. 7, No. 8 / August 1968
VARIFOCALMIRROR
OBJECT 'F
I _ °fI o,
IMAGE
'4
"
C-CENTER OF --Sf - -- 1CURVATURE SSi-5
I- Ii i so g /
Fig. 4. Optical diagram showing the terrts lised in the aalysis.
a2
-a
a2
1
C2r 47r
t
fication equation, rn = - s'/s. For symmetrical mirrorvibrations, m oscillates about unity. Thus, in orderthat the reflected images be of a constant scale, the sizeof the object must be inversely proportional to theinstantaneous magnification. Using the transformequations (see above) and substituting for se' with Eq.(la), and expressing the result in dimensionless form,the object size correction factor is found to be
m, = (1 4 - 382)/(l + 2). (3)
Neglecting second order terms in yields m- 1 = 1 +4o-3 -=1 - A, which implies that, to the extent thatthis first order approximation is valid, corrections foranomalous perspective are not uniquely associatedwith a particular display geometry, i.e., a particularvalue of a-. Thus, a set of images, corrected accordingto Eq. (3) for a particular object distance, can bedisplayed at a different object distance with littleresultant distortion, if the displacement amplitude isappropriately adjusted so that @(t) remains unchanged.
The linear scan problem can now be defined mathe-inatically. The image displacement is to be a saw-tooth wave:
(b)
Fig. 5. Diagrams of (a) the sawtooth waveform )(t), and (b) thesecond order correction term D'(t) used in deriving an improved
mirror displacement waveform.
eliminate r, s, and s' from the spherical mirror equation.Solving for Sf', yields
It is convenient to define dimensionless variablesa- = s/R, a-' = s'/R, and a = A/R. Substitution intoEq. (la), yields its dimensionless form,
(-a + )(i + 82)( + 4 32) +8. (lb)
A highly useful approximation to Eq. (lb) can beobtained by noting that << 1, i.e., A << R. Hence,second order terms in can be neglected. Futhermore,3 << a- and << a', so that (-a + ) -a- and (a-'- 3) ~a-'. Thus,
a' = -/(l + 4). (2a)For convenience in what follows, and also to emphasizethe simplicity of this relation, two new variables aredefined: 2-a'/(- -) is a normalized image distanceratio that is unity when the mirror is flat, and ) -- 4 ao- is a new displacement factor that varies linearlywith the displacement and is a function of the displaygeometry through a-. Thus, Eq. (2a) becomes
2 = / ( - ). (2b)
In the interest of completeness, anomalous perspec-tive' and its correction are now considered. As theimage moves along the depth axis toward the observer,the image size diminishes in accordance with the magni-
(4)
where D(t) is a sawtooth wave. Solving for 4(t), yields
(5a)
which can, if desired, be solved numerically. Alterna-tively, (t) can be expressed as an analytical functionusing Fourier expansions. To this end, attentionis restricted to cases of limited sawtooth image motionssuch that D(t) I < 1. Thus,
4,(t) = D(t) - D2(t) + D3(t)- .... (5b)
The Fourier expansion of -F(t) is thus obtained by col-lecting like coefficients from the expansions of theterms D(t), -D2 (t), D3(t), etc. The Fourier expansionof the sawtooth D(t) is well known; D(t) = (2a/7r) E
(--l) '- (sinmwt)/m, where a is the image displacementhalf-amplitude and is the angular frequency of thesawtooth wave, as illustrated in Fig. 5(a). Theexpansion of the second term -D 2 (t) was calculated;D2(t) is illustrated in Fig. 5(b). Using this result, thesecond order approximation to ¢(t) can be written
'I,(t) - D(t) - D2 (t) = A + (Am cosmwt + B sinwt),1
where
AO
Bm = (-l)m-l(2e/mr),
Am = (-l)m-l(4a2 /m27r2) = ( )m-B 2.
(6)
Recalling that @P(t) -4 a-3(t), Eq. (6) therefore yieldsthe second order approximation to the required mirrordisplacement waveform (t).
In order to test these analytical conclusions, it wasdecided to compare, by means of computer calculations,the effectiveness of the second order approximation
August 1968 / Vol. 7, No. 8 / APPLIED OPTICS 1507
v -
a-7
X(t = 1/[l - D(t)] = I D(t),
4,(t = D(t)l[l + D(t)],
- - -
(a )
IMAGE POSITION LITIME)
,400 I"I,A l. U0 ' 'A
.000 N
A
.800 -
.600 l l I0.400 0.600 0.800 1.000 1.200 1.400 1.600
TIME (PERIOCS)
MIRROR POLE DISPLACEMENT PHI(TIME)
0.800 1.000 1.200 1.400TIME (PERIODS)
1 .600
The purpose of the above calculations was to examinethe nature of the imaging process and to verify thevalidity of Eqs. (5b) and (6). Depending upon theapplication it may be preferable to evaluate (t)numerically using Eq. (5a) and then carry out a numer-ical Fourier analysis of the resulting waveform to obtainthe Fourier expansion of (t). In this connection, itshould he noted that D(t) in Eq. (.5a) need not representa sawtooth wave, but can, in fat, represent any imagemotion that is (lesired. In such a case, numericalFourier analysis may be manlatory; the only require-ment is that the image motion be periodic.
IV. Suppression of High Order Vibrations inthe Mylar Mirror
The second problem encountered in achieving a saw-tooth image motion is the imperfect response of themirror to electrical driving waveforms that are rich inhigher frequency Fourier harmonic components. Thisis mainlv due to the ease with which the Mvlar mirrorwill oscillate in undesired higher order modes. The re-sults of experiments are now presented in which thisproblem was circumvented by driving the mirror with afiltered sawtooth wave, from which all Fourier compo-nents but a few of the lowest frequency ones were re-moved with a low pass filter.
Fig. 6. Comparison of image motion 2(t) and mirror motion 'P(t)')ver one oscillation period for three differeni driving waveforms.Ideally, what is desired is a straight; line (sawloot;h) waveforin illthe image position graph (the top graph). It is apparent; that, thesecond order image motion (B, top) is more linear thai the first,order image motion (broken line, top). The sine wave case (A) is
shown for comparison.
b (t) with the effectiveness of the first order approxima-tion l(t) - D(t) (the sawtooth wave) in attaining asawtooth motion of the image position. Figure 6shows the image position 2(t) (upper graph) and thecorresponding mirror displacement ((t) (lower graph)as functions of time for one mirror oscillation cycle.Ideally, what is required is a straight line, i.e., a portionof a sawtooth wave, on the image position (upper)graph. Three different driving waveforms, and theresulting image position waveforms, are shown. Theseare a sinusoidal driving waveform, labeled A, the firstorder (sawtooth) waveform 'I1(t), indicated by thebroken line, and the second order approximation 2(t),labeled B. * The chosen displacement amplitude(DIma, = 40.32 is one that is suitable for 3-D displayssuch as have been discussed. It can be seen in the topgraph that the second order image motion (curve B) isconsiderably more linear than the first order imagemotion (broken line). Thus, the analytical conclusionsembodied in Eqs. (5b) and (6) have been verified.
FOCUSED LASER BEAMMAKES A BRIGHT SPOTON MIRROR SURFACE
* Since the de response of the actual mirror-speaker combina-tion is zero, this fact is simulated in Fig. 6 by setting the de termin the expansion of 'D2 (t), i.e., Ao, to zero.
(b)
Fig. 7. Experimental apparatus used to record (a) mirror dis-placement waveforms, and (b) swept line images of a pinhole point
light source.
1508 APPLIED OPTICS / Vol. 7, No. 8 / August 1968
0
H
-01
s fsnn
In the following experiments, a simple sawtoothdriving voltage was used; no attempt was made togenerate and use a corrected driving waveform suchas was described in Sec. III. Such a waveform is un-necessary in the context of the present experiment,which is concerned with the control of high order mirrorvibrations.
The diameter of the varifocal mirror used in theexperiments is 17 cm.
Figure 7 schematically shows the apparatus used torecord the mirror displacement waveforms [Fig. 7(a)],and the effect of high order mirror vibrations on re-flected images [Fig. 7(b)]. In Fig. 7(a), a suitablypositioned dust particle on the mirror surface was il-luminated by a focused laser beam to provide a brightpoint source of light on the mirror surface. This wasimaged onto a 35-mm film strip that moved at constantspeed orthogonally to the motion of the spot image.Thus, the film recorded the time dependence of thedisplacement of one particular spot on the mirror sur-face. Spectral filtering of the driving voltage wave-form, when desired, was achieved with a Krohn-Hiteultra-low frequency, variable band pass filter, model330-A. Since the low cutoff frequency was always setat 0.02 Hz, the instrument was, in effect, being used asa low pass filter with a 24-dB/octave cutoff.
For clarity, photographs taken with the apparatusof Fig. 7(b) were double exposures; a first exposure ofthe pinhole apparatus was taken with the mirror at rest,and then a second exposure was taken with the mirrorin motion and only the pinhole illuminated. Theresulting image motion caused the pinhole to trace outa line in image space, parallel to the depth axis, whichthe obliquely viewing camera recorded.
Figure 8 illustrates what happens in the absence ofany low pass filtering. The first column in Fig. 8shows the driving voltage waveforms, and the secondcolumn shows the observed mirror displacement wave-forms as recorded with the apparatus of Fig. 7(a).The photographs in the third column show the reflectedline image of the pinhole light source, as recorded withthe apparatus of Fig. 7(b). Looking across the toprow, it is apparent that a sinusoidal driving voltageyields a smooth, nearly sinusoidal mirror displacement,and the pinhole line image is smooth and straight.
Using a sawtooth driving voltage (as shown in thesecond row), the displacement waveform clearly showsringing in some higher order vibrational mode that wasexcited by the transient. This, in turn, causes severebreakup of the reflected image of the pinhole. Thereflected line image is no longer smooth and straight,but is tortuously twisted. The bottom row shows thesame measurements made on a mirror that was heattreated to increase its tautness. Considerable improve-ment is evident but it is still not good enough.
Figure 9 shows the results of removing high frequencycomponents from the driving waveform with the lowpass filter. The filter cutoff frequencies are indicatedat the extreme left. At low cutoff frequencies (up toand including 200 Hz) the displacement waveformfollows the driving voltage reasonably closely without
noticeable ringing, and the line image of the pointsource is smooth and straight. (The distortion of thedriving waveform, which is most severe at low cutofffrequencies, is due to unequal phase retardation of thevarious Fourier components in the low pass filter.)At cutoff frequencies of 300 Hz and higher, ringing isincreasingly apparent. Thus, for this mirror, a cutofffrequency of 200 Hz yields a smooth, ring-free, almostlinear image displacement sweep that lasts for almost90% of the oscillation period.
V. Conclusions
A 3-D movie projection system has been describedthat uses a vibrating Mylar varifocal mirror and projectsautostereoscopic movies from computer-generated16-mm film. If the scanning waveform is (nominally)sinusoidal, an irregular distribution of images along thedepth axis is obtained and the duty cycle is limited to50%/.
It has been experimentally demonstrated that, if themirror driving waveform is a filtered sawtooth thatcontains no Fourier components above 200 Hz, itwill not excite undesired high order vibrational modes,and smooth, moderately linear image sweeps havingduty cycles approaching 90% can be achieved.
The Fourier expansion of a corrected sawtoothdriving waveform was derived that causes the imageposition to move more linearly with time.
Taken together these three results suggest that aprojection system can be constructed in which a drivingvoltage waveform is generated that accomplishes bothof the latter two results simultaneously. To be specific,such a waveform could be computed using, say, Eq. (6),but with modified Fourier coefficients A* = KmAmand B* = KmBm, where K is an attenuation factorthat is unity at harmonic frequencies below the desiredcutoff frequency and which falls off at 24dB/octaveabove the cutoff frequency. It is reasonable to presumethat, with such driving waveform, a highly linear imagesweep could be achieved with duty cycles still approach-ing 90%.
This waveform could then be recorded in aalog formdirectly on the 16-mm movie film (for instance, in anunused region of the computer-controlled image field).Photoelectric detection would then yield the desiredvoltage waveform, fully synchronized with the moviefilm. Alternatively, in other applications, the wave-form could be recorded as a variable width slit near theouter circumference of a rotating disk. Such a slitpattern might be fashioned on a circular glass plateeither photographically or by photoetching techniques.Here again, photoelectric detection of light transmittedthrough the slit on the rotating disk would yield thedesired waveform.
It is intriguing to note the similarity in the shapes ofthe calculated, corrected displacement waveforms (seeFig. 6, lower graph, curve B) and the sawtooth voltagewaveforms shown in Fig. 8, column 1, rows 2 and 3.Both have negative second derivatives during thescanning portion of the wave. The sawtooth voltagewaveform is curved owing to the simple electronic
August 1968 / Vol. 7, No. 8 / APPLIED OPTICS 1509
SPEAKERDRIVING -VOLTAGE
WAVE FORM
OBSERVEDDISPLACEMENT
WAVEFORM
DOUBLE EXPOSURE SHOWINGLINE-IMAGES OF A POINT
SOURCE
+ .02
- .02
VI .3V P.P. 4V PP
"k; ~ 3V P.
5V PP
7V P.P
12V P.
Fig. . This figure illustrates the distorting effects of higher order modes that appear whet a sinusoidal waveform (top row) is re-placeti by a sawtooth waveform (second row). Some improvement is obtained by heat treating the Mylar mirror (third row). The
voltages indicated are peak to peak. The mirror diameter is 17 cm.
DRIVING VOLTAGEWAVEFORM
DISPLACEMENTWAVEFORM
LINE IMAGES OFPOINT SOURCE
+ .02
3.0- .02
500 -
Fig. 9. This figure shows the results of removing high frequency Fourier components from the driving waveform by low pass filter-ing. Tie filter cutoff frequencies tue indicated at the extreme left. At a cutoff frequency of 200 Hz, this mirror displays a smooth
ring-free, nearly linear mirror displacement waveform, which lasts almost 90% of the oscillation period.
1510 APPLIED OPTICS / Vol. 7, No. 8 / August 1968
40
N
0 200z
LLI
Q:us
technique by which it is generated; it is actually aportion of an exponential curve. Perhaps such anexponential sawtooth wave could be deliberately tailoredto serve as an approximation to the desired waveform,providing a significant degree of linearization of theimage motion in an extremely simple manner.
This paper is based on material presented at theDetroit Meeting of the Optical Society of America,October 1967.
References1. A. C. Traub, Appl. Opt. 6,1085 (1967).2. J. C. Muirhead, Rev. Sci. Instrum. 32, 210 (1961).
Meetings Calendar continued from page 1482
4-5 APS Mtg., Hanover W. W. Havens, Jr., 28 W.120th St., New York, N.Y. 10027
4-5 APS Symp. and Fall Mtg., Low Energy NuclearPhysics, Albany Jack Smith, Dept. Phys., SUNY,Albany, N.Y. 12203
6-9
7
7-11
Industrial Res. Inst. Fall Mtg., Los Angeles Sec.-Treas., 100 Park Ave., New York, N.Y. 10017
SPSE Mtg., Chicago Chap. K. T. Lassiter, EastmanKodak Co., Dept. 942, Rochester, N.Y. 14660
18th Ann. Research Equipment Exhibit and Instru-ment Symp., Bethesda J. B. Davis, SMB, NIH,Bldg. 12A, 4003, Bethesda, Md. 20014
7-11 Course in Photomicrography, Chicago M. L.Fallert, McCrone Res. Inst., 461 E. 31st St., Chicago,Ill. 60616
7-11 Course in Techniques of ir Spectroscopy, PhiladelphiaLynn Bass, Sadtler Res. Labs., Inc., 3316 SpringGarden St., Philadelphia, Pa. 19104
7-11 Course in uv Spectroscopy, Philadelphia LynnBass, Sadtler Res. Labs., Inc., 316 Spring GardenSt., Philadelphia, Pa. 19104
9 SPSE Mtg., Dayton Chap. K. T. Lassiter, EastmanKodak Co., Dept. 942, Rochester, N.Y. 14650
9 SPSE Mtg., Boston Chap. K. T. Lassiter, EastmanKodak Co., Dept. 942, Rochester, N. Y. 14650
9-12 Optical Society of America, 53rd Ann. Mtg., Pitts-burgh Hilton M. E. Warga, OSA, 2100 Pa. Ave.,N.W. Wash., D.C. 20037
9-15 Internatl. Congr. and Exhibition of Instrum. andAutomation, Dusseldorf John Buck (Trade FairAgencies), Ltd., 44 Newman St., London W,U.K.
10-11 Symp. on Applications of Ferroelectrics, Wash., D.C.C. F. Pulvari, The Catholic University of America,Wash., D.C.
11 SPSE Mtg., No. California Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N.Y.14660
13-19 19th Internatl. Astronautical Cong., New YorkM. Gerard, Am. Inst. Aeronautics & Astronautics,1290 6th Ave., New York, N. Y. 10019
14 SPSE Mtg., Washington Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N. Y.14660
14 SPSE Mtg., Connecticut Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N.Y.14660
14-17 Am. Soc. for Nondestructive Testing 28th Natl.Fall Conf., Detroit P. D. Johnson, 914 ChicagoAve., Evanston, Ill. 60202
14-18 Course in Fusion Methods, Chicago M. L. Fallert,McCrone Res. Inst., 451 E. 1st St., Chicago, Ill.60616
14-18 Course in ir Interpretation, Pt. I, PhiladelphiaLynn Bass, Sadtler Res. Labs., Inc., 16 SpringGarden St., Philadelphia, Pa. 19104
14-18 Thermoanalysis Workshop, Philadelphia Lynn Bass,Sadtler Res. Labs., Inc., 3316 Spring Garden St.,Philadelphia, Pa. 19104
15 SPSE Mtg., Binghamton Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N. Y.14660
15-18 Am. Assoc. of Textile Chemists & Colorists Internatl.Tech. Conf., Montreal G. P. Paine, Box 12215,Res. Triangle Park, N.C. 27709
20-25 SMPTE, 104th Semiann. Conf., Wash., D.C. L. A.Bernhard, 9 E. 41st St., New York, N.Y. 10017
21-25 Course in Gas Chromatography, Philadelphia LynnBass, Sadtler Res. Labs., Inc., 316 Spring GardenSt., Philadelphia, Pa. 19104
21-25 Course in Microscopy in the Crime Laboratory,Chicago M. L. Fallert, McCrone Res. Inst., 461E. 31st St., Chicago, Ill. 60616
21-25 Course in Nuclear Magnetic Resonance, PhiladelphiaLynn Bass, Sadtler Res. Labs., Inc., 3316 SpringGarden St., Philadelphia, Pa. 19104
21-25 Course in X-ray Spectrochemistry, MilwaukeeP. Halter, Jr., General Electric, 4866 Electric Ave.,Milwaukee, Wisc. 63201
23-25 IEEE Ann. Internatl. Electron Devices Mtg., Wash.,D.C. D. A. Chisholm, Bell Telephone Labs., Mur-ray Hill, N.J. 07974
24-25 SPIE Sem.-in-Depth on Image Information Recovery,Philadelphia H. F. Sander, SPIE Ex. Secy., 216Avenida del Norte, Redondo Beach, Calif. 90277
24-26 Assoc. for Res. in Ophthalmology Mtg., ChicagoH. E. Kaufman, Ophthalmology Dept. U. of Fla.,Gainesville, Fla. 32601
27-Nov. 1 Ann. Mtg. Am. Acad. Ophthalmology and Otolaryn-gology, Chicago W. L. Benedict, 16 Second St.S.W., Rochester, Minn. 66901
28 SPSE Mtg., So. California Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N.Y.14650
28-30 7th Rare Earth Res. Conf., Coronado J. F. Nach-man, Res. Labs., Solar Div. of Internatl. HarvesterCo., 2200 Pacific Hwy., San Diego, Calif. 92112
28-31 ISA Ann. Instrument-Automation Conf. and Exhibit,Coliseum, New York D. R. Steam, ISA, PennSheraton Hotel, Pittsburgh Pa. 16219
28-31 ISA 5th Natl. Metrology Instrumentation Symp.,New York 530 Wm. Penn Place, Pittsburgh, Pa.16219
28-Nov. 1 Course in Microscopy of Polymers, Chicago M. L.Fallert, McCrone Res. Inst., 461 E. 31st St., Chicago,Ill. 60616
30 SPSE Mtg., Twin Cities Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N. Y.14660
30-Nov. 1 5th Graphic Arts Conf., Chicago M. A. Burnston,360 Lexington Ave., New York, N.Y. 10017
30-Nov. 1 15th Ann. Symp., Am. Vacuum Soc., PittsburghJ. H. Singleton, Westinghouse Electric Corp., R&OCtr., Churchill Boro, Pittsburgh, Pa., 16234
31-Nov. 2 SPSE Ann. Symp., Photo-Electronic Imaging, Wash.,D.C. SPSE, Main P.O. Box 1609, Wash., D.C.
November4 SPSE Mtg., Chicago Chap. K. T. Lassiter, Eastman
Kodak Co., Dept. 942, Rochester, N.Y. 146604-8 Course in Instrumentation for Managers, Phila-
8-11 APS 9th Ann. Mta. Plasma Physics Div., AustinW. E. Drummond, Physics Bldg. 330, U. Tex.,Austin, Tex. 78712
10-15 SMPTE, 104th Semiann. Conv., Wash., D.C. Ex.Sec., 9 E. 41st St., New York, N.Y. 10017
11 SPSE Mtg., Connecticut Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N.Y.14650
11 SPSE Mtg., Washington Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N.Y.14650
11-15 Course in Gas Chromatography, Philadelphia LynnBass, Sadtler Res. Labs., Inc., 3816 Spring GardenSt., Philadelphia, Pa. 19104
11-15 Course in ir Interpretation, Pt. I, PhiladelphiaLynn Bass, Sadtler Res. Labs., Inc., 3316 SpringGarden St., Philadelphia, Pa. 19104
13 SPSE Mtg., Boston Chap. K. T. Lassiter, EastmanKodak Co., Dept. 942, Rochester, N.Y. 14650
13 SPSE Mtg., Dayton Chap. K. T. Lassiter, EastmanKodak Co., Dept. 942, Rochester, N.Y. 14650
13-15 10th Eastern Analytical Symp., ACS, SAS, Am.Microchem. Soc, New York H. J. Pazera, Ana-lytical Res. Dept. 417, Abbott Labs., N. Chicago, Ill.60616
13-16 APS Mtg., Plasma Physics Div., Miami W. W.Havens, Jr., 335 E. 45th St., New York, N.Y. 10017
15 SPSE Mtg., No. California Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N.Y.14650
18-21 14th Conf. on Magnetism and Magnetic MaterialsNew York D. T. Teaney, IBM Thomas J. WatsonRes. Ctr., Box 218, Yorktown Heights, N.Y. 10598
19 SPSE Mtg., Binghamton Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N.Y.14650
19-22 Acoustical Soc. of America Fall Mtg., Cleveland335 E. 45th St., New York, N.Y. 10017
21 SPSE Mtg., Monmouth Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N. Y.14650
25 SPSE Mtg., Monmouth Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N.Y.14650
25-27 APS Mtg., Miami TV. W. Havens, Jr., 335 E. 45thSt., New York, N.Y. 10017
25-29 Course in Computerized Chemical InformationSystems, Philadelphia Lynn Bass, Sadtler Res.Labs., Inc., 3316 Spring Garden St., Philadelphia,Pa.19104
25-29 Course in Mass Spectrometry, Philadelphia LynnBass, Sadtler Res. Labs., Inc., 3316 Spring GardenSt., Philadelphia, Pa. 19104
27 SPSE Mtg., Twin Cities Chap. K. T. Lassiter,Eastman Kodak Co., Dept. 942, Rochester, N.Y.14650
December
? 8th Conf. on Thermal Conductivity, West LafayetteD. R. Flynn, Natl. Bur. Stds., Wash., D.C. 20234
2 SPSE Mtg., Chicago Chap. K. T. Lassiter, EastmanKodak Co., Dept. 942, Rochester, N.Y. 14650
2-6 Course in Gas Chromatography, Philadelphia LynnBass, Sadtler Res. Labs., Inc., 3316 Spring GardenSt., Philadelphia, Pa. 19104
2-6 Course in ir Interpretation, Pt I, Philadelphia
January22-24 Symp. on Instrumentation for the Process Industries,
College Station R. G. Anthony, Chem. Eng. Dept.,Texas A & M U., College Station, Tex.
28-31 IEEE Internati. Symp. on Information Theory,Ellenville Jack Wolf, Dept. Electrical Eng., Poly-technic Inst. Brooklyn, 333 Jay St., Brooklyn, N.Y.11201
APS-AAPT Mtg., New York W. W. Havens, Jr., 355E. 45th St., New York, N.Y. 10017
APS Mtg., St. Louis W. W. Havens, Jr., 335 E. 45thSt., New York, N.Y. 10017
March6-7 2nd Internatl. Symp. on Acoustical Holography,
Huntington Beach Symp. Secy., Douglas Ad-vanced Res. Labs., McDonnell Douglas Corp., 5251Bolsa Ave., Huntington Beach, Calif. 92647
9-14 ASP-ACSM Ann. Conv., Washington Hilton G. L.Loelkes, Jr., 8608 Cherry Valley La., Alexandria,Va. 22309
11-15 Optical Society of America Spring Mtg., El CortezHotel, San Diego M. E. Warga, OSA, 2100 Pa.Ave., N.W., Wash. D.C. 20037
24-27 APS Mtg., Philadelphia W. W. Havens, Jr., 335 E.45th St., New York, N. Y. 10017
7 ISA 10th NatI. Chemical and Petroleum Instru-mentation Symp., Toronto W. C. Virbila, BristolCo., Box 1790, Waterbury, Conn. 06720
