Threshold Modulation Curves for Photographic Films

Threshold Modulation Curves for Photographic Films

T. J. Lauroesch, G. G. Fulmer, J. R. Edinger, G. T. Keene, and T. F. Kerwick

This paper describes studies of the threshold modulation curve for photographic film. The thresholdmodulation curve is an empirically derived relation showing the need at any spatial frequency for modula-tion in the aerial image of a tribar for resolution to be achieved. The paper deals with the history,raison d'6tre, theory, method of measurement, and accuracy and precision of the threshold modulationcurve. The statistical aspects of the threshold modulation curve are emphasized, and the influence offactors that cause variations in the curve are examined. Examples are given of current and potentialapplications of the threshold modulation curve.

1. Introduction

The modulation transfer function' (MTF) is onemethod of describing the image quality of an imagingsystem as a function of spatial frequency. Selwyn'suggested a threshold modulation (TM) curve forphotographic film as a description of ability to recordspatial frequencies and as a means of predicting for thehuman observer the limiting resolving power of a lens-film combination. The TM curve has been the subjectof much study and experimentation at Eastman KodakCompany and elsewhere2' 3 for several years.

The MTF-TM approach provides a graphical methodfor a systems approach to prediction of the subjectiveresolving power of a lens-film combination including theeffects of smear, focus, lens aberrations, or other defects.This kind of analysis points out the weakest element ina photooptical system and can be used for study prior tophysical fabrication and testing of a lens. It hasaugmented the approach of cascading MTF's whichfailed by itself to provide sufficient insight into thepictorial or interpretative significance of variations inthe components of a system. The MTF-TM approachfurnishes a single value indicator of system performancethat is often sought for comparative analyses. Specifi-cally, TM curves will enable one to predict the tribar'sresolving power, a frequently used measure of imagingcapability. While MTF has been used to describeimage quality, it relates to the strength of the signalwith little recognition of the noise component of the film.MTF has been used to make predictions of performancelimits by use of arbitrary threshold criteria, ignoring theinfluence of the human observer, a factor that can beintroduced by the TM curve.

The authors are with the Eastman Kodak Company, Ap-paratus Division, Research and Engineering, Rochester, NewYork 14650.

Received 11 August 1969.

The TM curve is hybrid in nature, as it is derivedfrom MTF information based on sine waves and fromsubjective observation of tribar images. It is theempirical nature of its origin which justifies its applica-tion.

The TM concept presupposes the acceptance of re-solving power as a useful index of system performance.Because of this assumption, the TM approach has theadvantages and the handicaps associated with resolvingpower.

"Resolving power became understandably popularfor evaluating the image-forming properties of photo-graphic materials, partly because it seems reasonablethat the ability to resolve minute details is an importantfeature of image quality, partly because the results areexpressible in comprehensible terms, and partly becauseresolving power appears to be an easy quantity to mea-sure (although in reality it requires much skill and pains-taking attention to apparently trivial matters of de-tail). But within recent years it has been increasinglyrealized that the advantages of resolving power as a cri-terion of quality are illusory. In the first place, it isnot a fundamental property of the photographic mate-rial; it depends upon many more factors than the turbid-ity characteristics of the emulsion. In the secondplace, the criterion of resolution is uncertain." 4

In spite of the disadvantages of resolving power andits failure to be the ultimate index of performance,5 ithas retained its position by default of other qualitydescriptors. Threats to its survival reached a peakabout 1955,67 and the situation appears to have re-verted since then.8 The resolving power limit remainsa convenient description of the performance of manyphotooptical systems, the capabilities of which are nototherwise readily described.

The major feature of resolving power which is carriedover to the measurement of the TM curve is the subjec-

April 1970 / Vol. 9, No. 4 / APPLIED OPTICS 875

tive nature of evaluation. The involvement of thehuman observer reduces the precision of the measure-ment and forces the application of a statistical approachto the use of data. In addition, certain theoreticallimitations apply to the collection and application ofTM/i data. These subjects are covered in this paper.

I. Measurement of a TM Curve

This section gives a broad description of the proce-dure used to measure the TXI curve of a photographicfilm. Later sections are used to describe restrictionsplaced on the gathering and application of TM data.

A single point on a TM curve is obtained by a rela-tively straightforward procedure. A resolving powertest target of known contrast is photographed in an ex-posure series by a lens of known MTF onto a photo-graphic film. This film is given a specific developmentand is observed visually to obtain a numerical value forthis limiting resolving power for optimum exposure.The modulation in the aerial image (ALNI) is calculatedby the product of the modulation (I) of the target andthe M\lITF of the image-forming lens for the spatial fre-quency of this particular measurement. The targetmodulation is calculated from the maximum and mini-mum luminances, B, in the target by the formula: Mll= (Bmax - Bmin)/(Bmax + Bmin). Since this product

describes the image modulation presented to the film atthe resolving power threshold, it is called the thresholdmodulation. Other TMV values are obtained by chang-ing the lens aperture and/or target contrast to obtaindifferent modulations. These TI values are plottedvs limiting resolving power; the line drawn through thepoints is called the TM\l curve for this particular film andprocessing.

Thus, the TMai curve of a photographic film processcombination presents as a function of spatial frequencythe minimum aerial image modulation required forlimiting resolving power, measured subjectively byhuman observers viewing images of optimum exposure.For a given resolving power pattern, it is presumably afunction only of the film and processing and is not re-stricted to a particular imaging system or target con-trast.

The basic resolving power test target for TM mea-surements and use is taken to have the generally ac-cepted tribar pattern, 9 although the concept could beequally applicable to other (but not all) periodic pat-terns.

The value of the limiting resolving power for optimumexposure is not clearly defined because of the scatter ofdata points and because the maximum may lie betweenmeasured points. The maximum value may be chosenfrom the data, or it may be obtained graphically using acurve drawn by hand or fitted using numerical curve-fitting techniques on the computer. The data generallycan be satisfactorily fitted with a parabola using a leastsquares technique, although a parabola may not beappropriate for data heavily influenced by adjacencyeffects. This graphical procedure is used at the East-man Kodak Company.

Similarly, the TM curve through the series of indi-vidual TMI points (each for optimum exposure) can bedrawn by hand or computer-fitted. Again, at EastmanKodak Company the procedure has been to use a leastsquares technique to fit a parabola to the data, althoughthe equation form may be a function of processing whereadjacency effects are large. This curve fitting proce-dure removes the factor of human judgment and pro-duces an equation which carries the TM information ina convenient form.

A conceptual argument for the use of a parabola witha constant term, TI = a + av2 as a mathematicalmodel for the TM curve is shown in Fig. 1, where ao anda, are constants and v is spatial frequency. The con-stant term ao represents the notion that a certain mod-ulation is required to resolve a tribar image even at lowfrequencies when the image is nt significantly influ-enced by the film MTF or grain noise. This constantis calculated from the measured TM data; it is not anassumed value based on theoretical consideration of themodulation required by the eye or the contrast of thefilm. The TM curve describing incident modulationwould have to vary with spatial frequency by the recip-rocal of the film MTF just to maintain a constant out-put modulation. Furthermore, as the spatial fre-quencies are increased, presumably the effect of grainnoise would increase requiring greater incident modula-tion in order to maintain a sufficient signal-to-noiseratio. The relationship between the signal and noise isprobably very complex as it is a function of the physicalaspects of the grain and image and the correspondingpsychophysical effect on the observer. The psycho-physical effects are greatly influenced by the viewingequipment and the conditions and restraints put on theobserver. The effects of the degradation by the filmVITF and the grain are combined in the frequency-squared term. A theoretical analysis is currently beingperformed at Eastman Kodak Company to give greaterinsight into the form of the TM curve. However, goodresults over a reasonable range of spatial frequencieshave been obtained by using the parabola with a con-stant term for fitting TM data for a variety of films andprocesses.

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Fig. 1. Conceptual form of the threshold modulation curve.

EFFECT OF NOISE-AND INCREASEDIMAGE SCATTERIN THE FILM /

876 APPLIED OPTICS / Vol. 9, No. 4 / April 1970

FREQUENCY BANDS:MEANLEVEL FUNDAMENTAL HARMONICS

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11111. Basic Assumptions Behind TMCurves-Validation Tests

The following assumptions are made in the prepara-tion and use of a TM curve as described in this paper.Assumptions:

(1) There is a constant ratio between the tribar re-sponse and the sine wave response of a lens.

(2) The scattering characteristics of the emulsion donot vary with the cone angle of the lens forming theimage, thereby varying the film MTF.

(3) Readers are influenced only by the modulation ofa tribar image and not by the waveform.

(4) The target quality (frequency content) is essen-tially the same for making and using the TM curve.

(5) The image characteristics of the tribar are de-termined by the lens MTF in one direction only, i.e.,there are essentially no symmetry requirements. Thisrequirement does not preclude diff erences between hori-zontal and vertical MTF's as is the case for image smearand for many aberrated lenses, but requires the ap-propriate MTF curve for the target orientation.

Testing the validity of these assumptions has beenthe object of five individual studies at Eastman KodakCompany. The results of these studies show the limitsof deviations from the nominal TM conditions within

which it is possible to retain reasonable correlation be-tween predicted and observed resolving power.

A. Relationship Between the Tribar and SineWave Response of a Lens

The sine wave response of a lens is involved in prep-aration and subsequent use of a TM curve. There-fore, there is a requirement for a constant relationshipbetween the tribar and the sine wave response for boththe TM lens and the lenses with which the TM curve isused. The amplitude spectrum of a tribar object, un-like that for an infinite sine wave object, is a continuumwith values at all frequencies. Therefore, the modula-tion of the tribar image will be affected by the full MTFof the lens and not only by the response at the funda-mental frequency as for a pure sine wave object.

Figure 2 shows the modulus of the tribar spectrumfor a target of 100 lines/mm. Also shown in Fig. 2 isthe modulus for this tribar pattern after imaging by adiffraction-limited lens with an MTF cutoff of 150lines/mm. There are essentially three bands of fre-quencies which describe the image of the tribar pattern:the mean level, the fundamental, and the harmonicfrequency bands. The modulation and waveform ofthe tribar image are influenced by each of these fre-quency bands. The counterparts of these frequencybands in the space domain are shown schematically inFig. 3.

Since the tribar pattern is finite in extent, a definitionof the modulation of a tribar image is somewhat arbi-trary. In a typical tribar target, the background den-sity is higher than the density of the bars. When sucha tribar pattern is altered by imaging, the central barhas greater illuminance than the outer bars and thespaces between the bars have greater illuminance thanthe background. The extent of this alteration is afunction of target contrast and lens MTF curve, beingleast for a low contrast target and an aberrated lens.

For this discussion the average modulation of thetribar will be defined as:

1(B -B2 + B3-B2 + B3-B4 B-B 4)M = -I ++ I4 B, + B2 B3 + B2 B3 + B 4 B5 + B4 /

The portions of the tribar image represented by valuesof B are shown in Fig. 3. Note that the backgroundilluminance is not accounted for in calculation of theimage modulation. The effect of the background illu-minance will be discussed in Sec. III.C.

Using this definition of modulation of a tribar image,the relationship between the tribar response and thesine wave response for a diffraction-limited lens wasinvestigated (see Fig. 4). The tribar pattern was con-sidered to be a three-bar pattern of infinite bar lengthin order to use a one-dimensional analysis. A plot ofthe ratio R of the tribar response to the sine wave re-sponse for a diffraction-limited lens is shown in Fig. 5.Note that for a diffraction-limited lens, the value of R isabout 1.3 over a frequency range of 0.3-0.8 of the sinewave cutoff. Outside the 0.3-0.8 region, R is variableand different from 1.3.


DISTANCE -

(b)

Fig. 3. Representation of tribar patterns in spatial domain:(a) perfect tribar pattern of 100 lines/mm; (b) schematic diagram

of a perfect tribar pattern degraded by a lens.

A computer analysis was made of the images ob-tained with two lenses which had hypothetical imper-fect surfaces and two diffraction-limited lenses with dif-ferent f numbers. The MTF curves for the four lensesare shown in Fig. 6(a). A series of plots of R vs relativespatial frequency for thefour lenses forseveraltarget con-trasts are shown in Fig. (6b), (c), and (d). The deviationsbetween R decrease at lower target contrast. For targetcontrasts less than about 2:1, R is essentially the samefor all four MTF curves tested. If limiting resolvingpower falls between 0.3 and 0.8 of XITF cutoff for boththe lens used to make the TMXI curve and the lens usedwith the TM curve, the tribar response will have a con-stant relation to the sine wave response. The values ofR for A1TF curves from obstructed and aberrated lenseshave been calculated with similar results. The MTF

curves C and D in Fig. 6(a) were selected as examples ofextreme deviation between the tribar and sine waveresponses.

Therefore, to have a TM curve which can be usedwith knowledge only of a lens sine wave response, thefrequency range where limiting resolving power occursshould fall between 0.3 and 0.8 of the MTF cutoff andthe target contrast should be no higher than 2:1.

B. Effect of Cone Angle of the Illuminating LensTI curves measured using target contrasts less than

2:1 and restricted to frequencies from 0.3 to 0.8 of lensMTF cutoff still show anomalous trends in the data.

Figure 7 uses the average data from eighteen TMcurves for 3404 film* made since 1966 using only theseprescribed conditions for target contrast and frequencyrange. Three curves are plotted separately based ondata obtained from target contrasts of 1.4, 1.7, and 2:1.For a given image modulation, the resolving power ob-tained with a high contrast target and small lens aper-ture is consistently higher than that obtained with a

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(b) sine wave response (MTF).

* Kodak High Definition Aerial Film 3404 (Estar Thin Base).


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Fig. 5. Ratio R of tribar response (modulus) to sine waveresponse (modulus) for a diffraction-limited lens.

target of lower contrast and a larger aperture lens. Ifthese data were normally distributed about a meancurve, the curves for different contrasts should lie ontop of each other because of the large sample size of thedata (approximately 218 resolving power readings ineach data point).

These trends in the TM data might arise from either adifference in the light diffusion in the emulsion with dif-ferent cone angles of illumination or a difference in theway readers see small variations in images from tar-gets of different contrasts. Or, the differences betweenTM curves made with the different target contrasts lessthan 2: 1 could be caused by the readers being influencedby the difference in the background level in the images.This effect is discussed in detail in Sec. III. C.

Threshold modulation could be affected by the inci-dent cone angle of the image-forming light which variesas a function of lens aperture. Larger relative aper-tures and cone angles could increase halation and diffu-sion in the emulsion. This increased scattering couldcause a different film spread function and therefore afilm MTF which varies with the numerical aperture ofthe lens. This effect is illustrated in exaggerated fash-ion in Fig. 8. The effect of cone angle would not be re-moved in allowing for the lens MITF, since lens 1/ITF is afunction of only diffraction and aberrations.

The variation of effective film MTF with the f num-ber of the illumination lens has been studied byothers.'"" Most reported work has been done withrelatively thick emulsion films not suited to high per-formance photooptical systems. Our work studied theeffect on 3404 film which has a very thin, fine grainemulsion.

The effect of lens cone angle on film MTF was studiedby measuring the MTF of 3404 film six times using lensapertures of f/3.7 to f/22.0 on a lens of known MTF's.Variable transmission sine wave targets were photo-graphed at each aperture. The inherent difficulties inmeasuring a film MTF with variable transmission sine

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S FOR 3404 FILM images. This program enables the user to follow aAND SEPT. 1968 given input (in this case a tribar object of selected con-

trast and frequency) through a photooptical system andCONTRAST :I examine the image frequency spectrum and contour in

CONTRAS/2:1 the output.4:1/ // Starting with typical TM data points, the image con-

tours and frequency spectra were examined to learn whycertain combinations of lens aperture and target con-trast produced higher or lower resolving power than ispredicted by TM curves. In addition, the image con-tours from obstructed lenses were compared with imagesmade using unobstructed lenses.

Figure 11 compares tribar image contours made withI | different combinations of lens aperture and target con-

150 200 trast. Note that for a given TM value, a small lens)WER (LINES/MM) aperture and high contrast target produces tribar im-

iction of target contrast. ages with an average illuminance level of the three barsprocess.) and two spaces that is considerably above the back-

ground level. A change in target contrast results in achange in this average level, whereas a change in lensaperture has much less influence on this average level.

wave targets (i.e., edge effects, nonlinear transfer char-acteristics) decreased the confidence in determiningany f number (cone angle) effect.

Figure 9 shows the apparent effect of lens aperture(cone angle) on film i\'ITF as a function of frequency.This plot shows that at low frequencies the larger aper-tures produce higher film i/ITFs. At higher frequen-cies, the smaller apertures produce a better film MTF.If there were no f number effect, the calculated filmMTF's for each aperture would be identical since theeffects of diffraction and aberrations in the lens wereremoved. These effects may be caused by the geom-etry of the illumination at the film plane, i.e., the coneangle of the light incident on the film.

Figure 8 gives sketches of the spread functions fortwo different apertures that would be necessary to pro-duce these results. The shapes of these spread func-tions have not been measured but only have been in-ferred on the basis of the results in Fig. 9.

Figure 10 shows the TM data for eighteen 3404 TMcurves plotted for sixf numbers. Table I compares thefnumber which is predicted to produce a better TM curve(based on a better film MITF) with the f number thatgave the better TM curve in actual measurements.Generally, the predicted and measured f numbers donot agree.

The differences in film MXTF shown in Fig. 9 cannotaccount for the differences in TIVI curves for variouslens f numbers shown in Fig. 10. The effect of the coneangle of the illuminating lens on the scattering charac-teristics of the emulsion (and therefore the film MTF)should be a function of that particular emulsion. Thetests described were made using 3404 film; it is possiblethat for other emulsions the cone angle of the lens couldsignificantly change the effective film i\ITF, making theTM curve a function of the lens f number.

C. Tribar Images for Different Target Contrasts

The IBM computer program IMSIM was used toevaluate the contours and frequency spectra of tribar

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(b) apparent film MTF's for two lens apertures.


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Fig. 9. Film MTF

and threshold modulation, one formed by a diffraction-limited, full aperture lens and the second made by anaberrated lens with an 18% elliptical obstruction. Themodulation at the fundamental frequency is the samefor both lenses as shown in Fig. 14 by the intersection ofthe two frequency spectra at 140 lines/mm. The imagecontours demonstrate that only a slight change inaverage intensity level occurs with the obstructed lens.This change will not greatly influence the readability ofthe images.

Therefore, conventional TM curves (measured withunobstructed, diffraction-limited lenses) may properlybe used to predict the performance of typical obstructedlenses. Experimental data shown in Fig. 15 demon-strate the conclusion that a TM curve is valid for usewith normally obstructed lenses (i.e., high-performancelenses with symmetrical, centered obstructions).

This data represents thirteen lens configurations ob-tained with one basic diffraction-limited lens modifiedwith circular and elliptical apertures and obstructionsfor the tests. Fourteen of the data points shown are

The frequency spectra of these image contours areshown in Fig. 12. It can be seen from this figure thathigher contrast targets and a slower lens produce ahigher modulus for the mean level. However, themodulus of the mean level remains nearly constantwith changes in aperture when the target contrast isheld constant. This difference of the tribar patternfrom the background intensity helps the observer todefine the target and probably accounts for the slightlybetter resolving power obtained with higher contrasttargets and slower lenses. The lens MTF multipliedby the target modulation does not fully describe theaerial image, but only describes the modulus of thethree-bar pattern with no reference to background illu-minance. Consequently, for a given TM value the ob-server will read higher resolving power for images madewith the higher contrast target and slower lens.

Resolution readers often remark that the imagesmade with higher contrast targets are easier to read.According to the reader the higher contrast images areeasier to find and they cut off more abruptly. Thisclaim of a more abrupt cutoff implies a smaller readererror when using the higher target contrasts and maybe one explanation for the higher resolving power read-ings with these targets and a slow f number lens. Also,if the mean level of the target makes the images easier tofind, it also means that the outer edges of the two out-side bars are well defined. When viewing high contrasttargets, the reader must decide only whether modulationexists between the outside bars and the middle bars,while with lower contrast targets a judgment must bemade for all three bars, thereby giving lower resolvingpower and less precision.

Obstructed lenses have a lower MTF at lower fre-quencies which does not affect the mean level modula-tion as much as does a change in target contrast. Fig-ures 13 and 14 compare the tribar image contours andfrequency spectra for two images of the same frequency

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Table I. Predicted and Observed f Number for BestTM Curve

Frequencyat which f number

f numbers f number at whichare predicteda to the better

compared, f numbers give the better TM curvelines/mm compared TM curve was obtained

90 11 with 8 8 11136 8 with 6 6 8136 6 with 3.7 3.7 3.7136 8 with 3.7 3.7 8.0190 6 with 3.7 3.7 6.0

a Based on differences in film MTF shown in Fig. 9.


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Fig. 12. Tribar image modulus spectra for two combinations oflens MTF and target modulation that produce identical incident

modulation at 75 lines/mm.

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averages of eighteen observations (six images, each readby three readers); eight of the data points each repre-sent three images, each read by three readers.

D. The Effect of Target QualityA resolving power test target should be specified by

its contrast and waveform or frequency content. Gen-erally the targets are made by optically reducing an art-work master onto photographic film. The processedfilm is traced with a microdensitometer and the targetcalibrated by its contrast which is calculated from thedensity difference between the bar and its adjacentspace. Usually there is no measurement made of thetarget waveform. In most cases the targets are used insystems with large reduction factors so the frequenciesof the target elements are relatively coarse and notsignificantly degraded by the photooptical system usedto make them. However, when testing high qualitysystems by autocollimation, high frequency resolvingpower test targets are required.

These high frequency targets are generally degradedsignificantly in the preparation process. When thetest target is degraded from the nominal tribar pattern,resolving power measurement made with that degradedtarget will be different (usually poorer) than measure-ments made with a high quality target. The magni-tude of the difference in resolving power obtained with anominal and a degraded target is a function of the MTFof the system used to make the degraded target and theXITF of the lens for which the target is a test object.

A computer simulation was made comparing theaerial image formed by a diffraction-limited lens of anominal and degraded target. The degraded targetwas simulated by imaging a perfect 100 lines/mmtribar object with a contrast of 2.33:1 through a dif-fraction-limited lens with an IVITF cutoff of 400 lines/mm. The degraded image was assumed to be recordedon a hypothetical film which did not distort the tone orwaveform of the image. The contrast of the degradedtarget was 2:1. Figure 16 compares the degradedtarget with a nominal 2:1 contrast target. The aerialimages at 100 lines/mm are shown in Fig. 17 for boththe nominal and the degraded target after passingthrough a diffraction-limited lens with a cutoff of 150lines/mm. While the modulation of both of the testobjects was the same, the modulation of the aerial imagemade from the degraded target is 0.070 and from thenominal target, 0.095. This difference is approximatelya 20% difference in aerial image modulation causing adifference in the measured resolving power of the lens.The effect of the target quality is more significant whenusing aberrated or obstructed lenses which have flat-ter MVITF curves than it is with the diffraction-limitedlenses used in the illustration.

I I I I I I I I - E. The Effect of Nonrotationally-0.016 -OQ DIB 0 0.008 0.016

DISTANCE (MM ) Symmetric MTFFig. 13 Tribar image contours of two 140 lines/mm images with

the same TM.Predictions made using only the MTF in the direction

of the tribar image have had good correlation with ob-


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Fig. 14. Tribar modulus spectra of two images with the sameTM.

served resolving power, regardless of the MTF in theother directions. A TM curve was made with a lenshaving an elliptical obstruction and aperture. Thistest verified that the dissimilar MTF in the two direc-tions and the flat MTF curve did not appreciablychange the measured TM curve. The TM curves forthe major and minor lens axes and the curve mea-sured with a circular, unobstructed lens are shown inFig. 18. The agreement is within the error boundsassociated with measurement of a TM curve (discussedin Sec. IV). Subsequent tests with a lens having alarge amount of astigmatism also had good agreementbetween predicted and observed resolution.

IV. Statistical Aspect of TM Curves

The measurement and application of a TM curve areproblems in statistics. The empirical origin of thecurve introduces errors in measurement from bothcalibration and application of the measuring device, inthis case the human observer. The graininess of thephotographic image produces statistical variations inthe noise component in the information transfer.Errors in knowledge of the original target contrast andthe MTF of the test lens become errors in the knowledgeof the signal component. Finally, when lens MTFcurves are used for prediction of performance, inexactknowledge of the lens MTF further reduces the accuracyof the predicted resolution.

PERFECTTRIBAR TARGET---

'DGRDEC / C~~~TRBA

C ' C /~~~~~~AR E

DDISTANCE

Fig. 16. Density profiles of a perfect tribar target and one madeusing a diffraction-limited lens with 400 lines/mm MTF cutoff.

0.9

InzU)

a.-:X

I0CD

0a.C,0L-

150 _ 0 ~ ~ ~ ~ 0

U) U.J100 _ t 0> X

co~~~~~~~~~~n~~s

0 50_

O ) 50 100 150 200PREDICTED RESOLVING POWER

(LINES / MM)

Fig. 15. Demonstration of predicted and measured limitingresolving power for obstructed lenses.

An error ellipse can be drawn about a single point inthe data used to prepare the TM curve. On the graphof threshold modulation vs spatial frequency, one axisof the error ellipse is set by the errors in measurement ofthe original target contrast and the MTF of the testlens, the latter being the dominant factor. Along thespatial frequency coordinate the error attributed to thehuman observer gives the length of the major axis of theerror ellipse.

The error in subjective reading of resolving power hasbeen measured by others. New measurements ofthis error at Eastman Kodak have agreed quite wellwith the earlier results. These new measurements weremade to assure the suitability of Kodak viewing equip-ment, a new test target format with (2)Hl 2 frequencyincrement and the criterion used by our readers. Theresults of this study using four readers are shown inFig. 19 and illustrate the applicability of gaussian sta-tistics to these studies.

The error in an individual TM datum point is domi-nated by the reader error and the error in test lensMTF. However, this error ellipse does not give anestimate of the error in a full TM curve drawn througha series of such points.

Two recent tests have been made at Eastman Kodak


l

Ivz0.J

.

IMAGE OF / IMAGE OFPERFECT , \xi DEGRADEDTARGET , TRIBAR

I TARGET ,-,

I I

/, \/ V C I

II I

I I I

I

Ci 'IC ~~~~~~~~~~I I

I I

DISTANCE -

exposure profiles of images of perfect and degradedof Fig. 16 formed by diffraction-limited lens with

MTF cutoff at 150 lines/mm.

UNOBSTRUCTEDDIFFRACTION -

MAJOR AXIS; LIMITED LENSABERRATED LENS, , iELLIPTICAL I , OBSTRUCTION 8 -

,_ -MINMINOR AXIS;-- '~.. ABERRATED LENS,

ELLIPTICALOBSTRUCTION

IlI I I I0 < > 40 80 120 160 200

RESOLVING POWER (LINES/MM)

Fig. 18. Replicated TM curves to demonstrate independence ofTM on asymmetric lens MTF.

100

-NORMAL DISTRIBUTIONRESOLVING POWEROBSERVATIONS

. 8 0< SAMPLE SIZE:

a/ 288 OBSERVATIONS

0 STANDARD DEVIATION:o60 7.6%

C,

Z 40

20

80 90 100 110 120RELATIVE RESOLVING POWER

(LINES / MM)

Fig. 19. Frequency histogram of resolving power readings aboutthe mean level.

to get an estimate of error in the TM curve. One testconsisted of evaluating three times the resolving powerimages used in the measurement of a TM curve. Theresults are shown in Fig. 20. The TM data used foreach curve consist of points at twenty different spatialfrequencies with three sets of images at each frequency.Each image was read by two readers. These pointsinclude images obtained by variation of both targetcontrast and test lens f number. Figure 20 shows thelarge influence of reader error on the resultant TMcurve.

The second test consisted of making five replicatedeterminations of a nominally identical TM curve.Each curve was obtained by the same procedure usingat least eighteen points along the spatial frequencyscale, three sets of images at each frequency and havingeach image read by two readers. The results areshown in Fig. 21. The top curve in Fig. 21 is the middlecurve in Fig. 20.

An estimate of TM curve error was obtained by cal-culating the standard deviation on the mean from thefive replicate curves shown in Fig. 21. This estimate ofthe standard deviation is shown in Fig. 22. The value,which is a function of sample size, varies with frequencyand in this case ranges from +5% at low frequencies(e.g., 60 lines/mm) to 10% at high frequencies (e.g.,200 lines/mm). A larger sample size would give abetter estimate of the mean, resulting in a smaller stan-dard deviation.

These two tests assume perfect knowledge of test ob-ject contrast and test lens MTF, factors which are bothovershadowed by reader error. The range in readervariation moves the datum point in a direction along thespatial frequency coordinate, but if image modulationis assumed to be constant, reader error moves the TMcurve in a vertical direction more than do errors in testlens \/ITF and target contrast.

No attempt has been made to sort out the variationin resolving power caused by the photographic film it-self and deleterious or fortuitous clumping of grains.It is assumed that this factor is small compared toreader error.

The one-standard deviation bands shown in Fig. 22give a measure of the dispersion of the TM curve for aspecific film-process combination, based on five replica-tions. Note from Fig. 21 that a replicate TM curvemay be expected to shift in level, i.e., to be generallyhigh or generally low rather than high at one end andlow at the other.

When a TM curve is crossed with an MTF curve for alens to make a prediction of limiting resolving power,the knowledge of the lens MTF curve must be con-sidered. The MITF of the test lens in this case is knownto about 0.03 unit of modulation (i.e., 3% of full


0.11-

U1)0a.

00-J

-JIt

Fig. 17. Logtribar targets

0.121-

B _

2:0

-J' 0.08

C0

2

Id 0.040

13

. . . . .

0.0

0.12

z.08LI-

o4 -

-J0

3RD

l I I I I40 80 120

RESOLVING POWER(LINES / MM)

160 200

Fig. 20. Three TM curves derived from replicate readings of TMimages for a single measurement (3404 films, D-19/D-76 process).

0.121-z2:0

C-

z-J0Z5 0.042:

C I I I I I0 4C

Fig. 21. Five replicate

80 120 160RESOLVING POWER (LINES / MM)

TM measurements for 3404 film, D-19/D-76 process.

scale), where this value is estimated to represent thestandard deviation. Figure 23 shows the combinationof TM and MTF curves with appropriate one-standarddeviation bands.

The intersection (point A) of the MTF and TMcurves in Fig. 23 gives the prediction of the most prob-able limiting resolving power to be expected with thislens-film combination. Since the standard deviationbands on the MTF and TM curves describe the disper-sion in each curve, and the curves are independent ofeach other, the intersections (points B and C) of thesebands give the standard deviation on the prediction.

The standard deviation on the prediction does not,however, give the standard deviation to be expected inthe observed data. The standard deviation on the pre-diction is derived only from the lack of knowledge of theTM and MTF curves themselves. The dispersion in thelens MTF gives no indication of the dispersion to be ex-pected in the observed resolving power data since theMTF measurement is independent of the resolvingpower readers. The dispersion in the TM curve, al-though predominantly influenced by resolving powerreader variability, will not give the standard deviationto be expected in the observed data because the TMcurve standard deviation band is calculated from fiveindependent curves and not individual datum points.The process of drawing a curve has an averaging effecton the individual resolving power readings and masksthe dispersion in the data. Consequently, the standarddeviation on the resolving power prediction is not ameasure of the dispersion anticipated in the observeddata.

The distribution of the observed data will not be un-like that illustrated in Fig. 19. The mean of the mea-sured resolving power values may or may not coincidewith the prediction. The prediction was made withcurves representing best estimates of the TM and MTF.The true TM or MTF levels may differ from these esti-mates. Assuming the MTF and TM curves used tomake the prediction are the true curves, the larger the

0.12

0.081-

0.12

2:0

4° 0.040

2

2 0.042:0.04K

0I I I

U0 40 80 120 160

RESOLVING POWER (LINES / MM)200

Fig. 22. Average of five replicated TM curves with standarddeviation of the mean TM (3404 film, D-19/D-76 process).

MTF CURVEWITH I.r-

40 80 120 160 200RESOLVING POWER (LINES/MM)

Fig. 23. Limiting resolving power to be expected from optimumTM and MTF curves (3404 film, D-19/D-76 Process; Kodak

25-mm Cine Ektar Lens at f/8.0).


n l l a l s s

2

5

I

.1

I

Il

number of observations, the higher the probability thatthe observed mean will occur at the predicted value.For the example shown in Fig. 23, the predicted resolv-ing power is 144 lines/mm with a standard deviationof approximately 9 lines/mm. If a sufficiently largesample size were obtained, and if the mean occurred atthe predicted value, the observed data would have astandard deviation of about 11 lines/mm according tothe distribution shown in Fig. 19. These standarddeviations on both the predicted and mean observeddata are indicated in Fig. 23. This illustration showsthe resolving power to be expected from optimum TMand MTF curves, i.e., to be expected at proper expo-sure using an in-focus lens without smear. Thesecurves ideally apply only to making a prediction wherethe result will not be influenced by use of differentreaders, different reading equipment, and different tar-gets.

The effect of changes in spatial frequency incrementin the target has been briefly examined at EastmanKodak. Targets with intervals of (2) M2 and (2) If havebeen compared with some gain in precision obtainedwith (2) 2 targets. The magnitude of the effect ofquantizing the target with smaller intervals depends onthe location of the statistical mean relative to the targetfrequencies. The effect decreases as the size of the in-terval is made smaller because the effect becomes hiddenin reader error.

The equipment used by resolving power readers canbe important, particularly if changes are made in modeof illumination. Readings are generally the highestwhen the source is specular. A good range in viewerluminance is desired, especially when evaluating anexposure series. Readers must also be given a broadrange of magnifying power in the microscope, but somecare should be made to monitor the magnifying powerused. Results are most consistent when about 2 lines/mm are presented to the eye, although this value varieswith subject luminance which depends on photographicdensity and illuminator luminance.

Reader error is by far the dominant factor in resolvingpower measurements and hence in measurement andverification of TM curves. The error to be expectedfrom a group of readers was indicated in Fig. 19 whenthe readers are collectively trained to use a specificcriterion for resolving power. In this case the criterionwas that the reader be able to identify the images ofthe three bars, fully separated along their entire length.This criterion is conservative compared to another re-quiring identification only of the number of bars andtheir orientation. In either case, an additional re-striction is usually imposed prohibiting the absence oftwo or more consecutive charts. A carefully definedset of criteria for establishing limiting resolving poweris one of the most important factors in this work.

Reader monitoring is an important aspect of resolvingpower measurements. Without monitoring, readerscan easily drift to a degree that is extremely serious.Although it is difficult to prepare a platinum bar or touse a standard wavelength to replace the king's foot inresolving power measurement, we have demonstrated

the value of using standard sample images to period-ically test readers for consistency. Nearly 100 imagescalibrated by ten consistently trained readers areused to periodically check the drift and variance ofreaders. An individual reader shows a scatter in hisreadings at one sitting or over a short period of time.These magnitudes of variability remain essentially un-changed over a long period of time but may followgeneral drift of level. Monitoring procedures can beused to control this long term drift. The immediateand short term variability of readers can be controlledpartially by use of a number of readers (five appears tobe an appropriate number). This short term erroraffects the precision of TM curves. The long term driftmust be controlled by use of standards and affects theaccuracy of TM curves.

V. Applications of TM CurvesTM curves provide resolving power information

about the film component of a system for a specific de-velopment. In systems analysis this information isvaluable to make predictions of performance both dur-ing and before manufacture. The technique permitsisolation of the effects of factors bearing on performance,e.g., the theoretical static performance of the lens, modi-fication of lens performance by introduction of aberra-tions, apertures, and obstructions, variation in lens per-formance due to mechanical and optical manufacturingtolerances, and limitations caused by image smear.TM curves can be used with other information to assessperformance of existing systems in the laboratory, inthe factory and in the field for those cases in whichpostoperational analysis can be carried out.

30-

2C

C-2

4JrInU)M

U-

0ir

m1

2

0.oI l iI

0.80 1.00(PREDICTED\OBSERVEDI

324 OBSERVATIONSMEAN: 0.986STANDARD DEVIATION: 0.116

L I I I I1.20 1.40

Fig. 24. Frequency histogram of observations of limitingresolving power normalized to predicted resolving power.


i - l f l -ll l . ....llrxl ,] .|l .11 . |

i

1I

TM curves can be used to make comparisons be-tween photographic development processes for a givenfilm or between different experimental emulsions in thesame product line. In this work certain precautionsare required to avoid covering up the real differenceswith apparent differences. Since significant differencesbetween TM curves are often very small, maximumcontrol must be exercised to reduce random and system-atic errors, namely, making photographic images witha common setup to minimize equipment and calibrationerrors, reading images concurrently to reduce readerdrift, etc.

An example will show the capability of a TM curvefor making a prediction of limiting resolving power.The example could be chosen to show with limited dataa very distorted picture, proving either that TM pre-dictions are excellent or very poor. The examplechosen, however, is one for which a relatively largeamount of data are available, and it serves to demon-strate the statistical nature of TM predictions.

The data used to make the correlation plot shown inFig. 15 were analyzed statistically after normalizationto obtain the results shown in Fig. 24. It is interestingto note that a large volume of data is needed to eliminatethe quantizing effect of test targets. The mean valueof the 324 observations is within 1 % of the prediction,and the standard deviation of the 324 observations is12%. This value is larger than the standard deviationof 71 % on reader variability shown in Fig. 19, a dif-ference attributed to the fact that a very high percent-age of these data as related to resolving power predictedand obtained with obstructed lenses. An obstructedlens has a relatively flat MTF curve which causes a lesswell-defined crossing with a TM curve than does an un-obstructed lens, giving a less sharply identified predic-tion. Readers viewing images photographed with anobstructed lens often comment on the difficulty in eval-uating limiting resolving power.

VI. Conclusions

The threshold modulation of a photographic film is auseful engineering tool for systems analysis when usedwith proper regard for the limitations of this technique.When careful attention is given to the statistical aspectof the measurement and use of TM curves, this ap-proach gives valuable insight into the random nature ofphotooptical imaging and the human observer. TheTM curve is empirically derived, bringing together thescience of the modulation transfer function and the sub-jectivity of resolving power. TM is based on the use oftribar resolving power as a useful indicator of photo-optical performance. A TM curve could be preparedand used for test object patterns other than the tribar,since the TM concept is applicable wherever correlationcan be established with sine wave response.

TM curves can be used in design, testing, and post-operational analysis of photooptical system perfor-mance, and can be used to examine the effects of para-metric variations in film, process, optics (including ob-

struction and aperture shape) and system optimization(including focus, exposure, and image motion compen-sation).

Because of the complexity of this subject and thelength of time over which it has been treated, many in-dividuals have been involved in these studies. Thewriters must acknowledge contributions of many co-workers at Eastman Kodak: L. P. Albertson, E. M.Granger, C. R. Hale, J. E. Hunt, W. Marquardt, S. A.Mason, C. J. Sickler, and C. P. Spoelhof, all of whomhave made significant contributions to TM studies.

This paper is for information only; the performanceof photographic films implied by data and graphs pre-sented is not intended to be binding on the EastmanKodak Company.

T. J. Lauroesch attended The Institute of Optics,University of Rochester, from 1949 to 1951 in theGraduate School program.

References

1. E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc. 58, 33(1946).

2. G. C. Brock et al., Interim Eng. Rept. No. 1, Itek Corp.9048-1, 14 (1962).

3. F. Scott, Phot. Sci. Eng. 10, 49 (1966).

4. F. Perrin, J. Soc. Motion Picture Television Engrs. 69, 151(1960).

5. G. C. Higgins and F. H. Perrin, Photo. Sci. Eng. 2, 66(1958).

6. National Bureau of Standards Circular 526, Optical ImageEvaluation, U. S. Dept. of Commerce (1954).

7. T. Suzuki and'S. Yonezawa, J. Opt. Soc. Amer. 46, 677(1956).

8. J. H. Altman, presentation at SPSE meeting (1967).

9. MIL-STD-150A.

10. L. 0. Hendeberg, J. Opt. Soc. Amer. 53, 1114 (1963).

11. V. A. Korndorf and I. A. Chernyi, Zh. Nauch. Prikl. Fotogr.Kinematogr. 9, 448 (1964).


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Threshold Modulation Curves for Photographic Films

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