JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Effect of Striated Fields on Critical Flicker FrequencyELAINE H. GRAHAM AND CARNEY LANDIS

New York State Psychiatric Institute, New York, New York(Received August 1, 1958)

Critical flicker frequency measurements were obtained as a function of retinal illuminance for a squarecentrally regarded field (8.5 degrees on a side) containing various numbers of vertical stripes. The visual fieldcontained under the different experimental conditions 0, 10, 30, 90, and 250 black lines per inch, corre-sponding to an angular subtense at the eye of 0.63, 0.21, 0.07, and 0.025 degree, respectively. Results indicatethat CFF decreases with increases in the number of stripes reaching a minimum at approximately 30 stripesper inch, and then may increase with further increases in the number of stripes. Except at the highestilluminances where the curve for the field containing the largest number of stripes (250 per inch) overtakesthat of an unpatterned field, all of the striped fields result in lowered CFF vs log retinal illuminance curveswhen compared with an unstriped field of the same size.

THE rate in cycles per second at which inter-T mittent light is perceived to change from flickerto fusion or vice versa, the so-called critical flickerfrequency (CFF), has been shown to depend uponmany variables. Some of the more important are theluminance,' wavelength,2 area,' retinal location,' light-dark ratio,4 and duration' of the stimulus. Certainconditions of the organism, e.g., age, effects due todrugs, anoxia, etc., also have been shown to be parame-ters of CFF. (See Landis 6 for a summary of thesefindings.)

One determinant which is of interest and has beenlittle investigated is the effect of subdivided or figuredfields. Vernon7 has indicated that the introduction of afigure into a flickering field, monocularly observed, mayreduce the CFF. Crozier and WolfI have reportedresults of studies with striated fields in which variouschanges were induced in the CFF vs logI (i.e., logluminance) relationship. Their findings, however, arecomplex and possibly inconclusive. In any case, suchexperiments merit further consideration and will beconsidered in greater detail in our discussion. Thepresent experiment is an attempt to study in a moresystematic way the effect of striated fields upon thecritical flicker frequency.

APPARATUS

A Maxwellian view optical system, a flicker apparatusand calibration devices, and four gratings comprised theessential parts of the equipment.

The optical system provided a square test patchwhich could be varied over a wide range of luminance.Light from a tungsten lamp passed through a small,

I S. Hecht and C. D. Verrijp, J. Gen. Physiol. 17, 251-268(1933-34).

2 S. Hecht and S. Shlaer, J. Gen. Physiol. 19, 965-977 (1936).3 S. Hecht and E. L. Smith, J. Gen. Physiol. 19, 979-988 (1936).4 See, for summary, S. H. Bartley, Vision (D. Van Nostrand

Company, Inc., Princeton, Ncw Jersey, 1941).6 R. Granit and E. L. Hammond, Am. J. Physiol. 98, 654-663

(1931).' C. Landis, Physiol. Rev. 34, 259-286 (1954).7 M. D. Vernon, Brit. J. Psychol. 24, 351-374 (1934).8 W. J. Crozier and E. Wolf, J. Gen. Physiol. 27,401-432 (1944).

circular aperture in a lamp-house and through a lenswhich brought it to a focus just beyond the plane ofrotation of the disk of the flicker apparatus. The light,at its focal point, entered an opening, 1.17 mm indiameter, in the end of a tube. The tube contained acollimating lens at focal distance from the opening. Theparallel rays passed through a filter box containingspaces for neutral tint filters and a holder for thegratings which were used to provide vertical lines in thefield of view. The field size was limited by a squareaperture, 17 mm on a side. The square aperture wasabout 1 cm closer than focal distance to the final lens inthe system, which lens brought the rays to a focus inthe position of the subject's pupil. Since the focaldistance of this lens was 11.5 cm, the square visualfield subtended a visual angle of 8.5 degrees on a side.Under the conditions described, accommodation by thesubject was about 1.3 diopters.

The flicker apparatus consisted of a metal disk withfour sectors cut out at regular intervals on the diskcircumference, the open and closed sectors being equalin angular subtense. The disk was attached to the axleof a Bodine dc motor (Type NSH-34) whose speed ofrotation could be varied by means of a General Radiospeed control (Type 170/AK), essentially a Variacin an ac output that is rectified before being supplied tothe motor. The axle of the motor at the end oppositethe rotating disk was attached by means of a universaljoint to a Weston tachometer, the output of which fedinto a voltmeter. The voltage reading was directlyproportional to the speed of rotation of the disk.Calibration by a Strobotac indicated that f=11.2Ewhere f is flashes per second and E, volts. This appara-tus produced a low-level noise, the amount of which wasnever great since high speeds were unnecessary for a4-sector disk; however, we performed a control experi-ment in which the hum was masked by the sound of anelectric fan.

The four gratings in this experiment are the onesdescribed by Shlaer' in his work on acuity. Looking intothe Maxwellian view system, the subject saw a square

9 S. Shlaer, J. Gen. Physiol. 21, 165-188 (1937).

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CRITICAL FLICKER FREQUENCY

field containing a number of equally wide verticalstriations, alternately illuminated and opaque. Thegratings employed provided 10, 30, 90, and 250 linesper inch, corresponding to an angular subtense at theeye per black (or light) line of 0.63, 0.21, 0.07, and 0.025degree, respectively.

The following method was used in calibrating thelight source.* A square of opal glass was placed in theposition of the grating. The luminance of the diffuselyilluminated area could then be measured by means of aMacbeth illuminometer. (Measurements could be madeeither at the final lens before the eye or with the lensremoved and the illuminometer placed close enough tothe opal glass so that its entire field was filled with light.Both procedures gave essentially the same results.)Once the luminance of the diffusely illuminated field wasknown, the subject regarded it through an artificialpupil, 2.50 mm in diameter, with the lens at focaldistance from the pupil. After the luminance wasreduced somewhat by the insertion of neutral filters,CFF determinations were made at 2 or 3 levels oneither side of an arbitrary but convenient figure of30 cps. (The actual density required for fusion at 30 cpswas found by interpolation.) Thereafter, the artificialpupil was removed and an opening of about 6-mmdiameter substituted. This opening, which was usedunder the conditions of the experiment, was not anartificial pupil but simply served as a device to aid thesubject to center his pupil on the image in the planeof the opening. The subject adjusted his eye until heobtained an appropriate view with maximum brightnessof the square visual field. At this point the opal glassscreen was removed, and the luminance available tothe Maxwellian view system was presented and reducedby a combination of filters. The diameter of the imageof the opening in the end of the tube was, due to thecharacteristics of the Maxwellian view system, reducedto 0.82 mm. Under appropriate conditions of viewing,as described in the foregoing, the image of the tubeopening was centered in the subject's pupil. A luminancewas set that would give a CFF value just above therequired 30 cps; then, a value was set that would give alower CFF. The exact density value for a criticalfrequency of 30 cps (to match that obtained with theopal glass) was obtained by interpolation. Such a valueof retinal illuminance for the Maxwellian view isequivalent to the calibrated troland value of the diffusescreen. (Equal luminances give equal critical flickerfrequencies for the same color, size, and retinal positionof light stimuli.) A critical flicker frequency of 30 cpswas chosen for use in calibrating as it is in the steeplyrising part of the flicker-log luminance curve and is wellabove the level of rod contribution. The total availableretinal illuminance of the Maxwellian view systemcould then be calculated from the value required to

* The authors wish to express their appreciation to ProfessorC. H. Graham for suggesting this calibration procedure.

produce fusion at 30 cps with due consideration of thefilters in the beam. It turned out by this calibration thatthe maximum illuminance available in Maxwellian viewwas 105 400 trolands. Retinal illuminance in trolands Ewas computed from the known pupil area in squaremillimeters, A and B, the candles per square meter,thus1 0: E= AB. The lamp was operated on a dcgenerator powered by a synchronous motor. When thelight output was applied to a sensitive photocell andcathode-ray oscilloscope, no ripple could be observed.

PROCEDURE

Through the tube in the darkroom wall, the subject,with his head stabilized by a Bausch & Lomb chinrest and head support, regarded monocularly the squaretest patch of illumination which was seen as flickering.The experimenter slowly increased the flicker frequencyuntil the subject reported the disappearance of flickerby means of a key and buzzer signal. The rate was thenfurther increased and then slowly decreased until thesubject signaled that flicker had reappeared. Six thresh-olds were thus obtained at each luminance level, threeascending alternating with three descending. In eachexperimental session, flicker thresholds were obtainedover a range of 6 log units of luminance in steps ofapproximately 0.3 log unit by use of appropriate filters.In general, determinations were begun at the highestluminance level and progressed down the scale. Thisdescending procedure was deemed the more suitablesince it was desired that light adaptation be relativelyconstant and complete at any given luminance level.

In sessions with gratings the subject was asked tosignal when he no longer saw the field as clearly striped.Sessions were terminated at about 10 cps since at thislevel the curves already had clearly exhibited therod-cone break. A complete rod curve was not obtainedbecause on the basis of preliminary experimentation itwas found that overlap between rod curves was verygreat.

A complete series consisted of five sessions: one with-out a grating, condition I; and four employing thepreviously described gratings in order of increasingnumbers of lines, condition II (grating A with 10 blacklines per in.), condition III (grating B, 30 lines per in.),condition IV (grating C, 90 lines per in.), and conditionV (grating D, 250 lines per in.). Each of two subjects(male graduate students) contributed two completeseries. Two additional experiments were performed.One involved the presence of a noise to mask the soundof the motor. This consisted of running one subjectunder condition I (no grating) and the second undercondition V (grating D) with an electric fan operating inthe darkroom. Another experiment was performedwhich enabled us to compare with our results the effectof reducing the test area (unstriated) by half. Such an

10 D. B. Judd, Handbook of Experimental Psychology, edited byS. S. Stevens (John Wiley & Sons, Inc., New York, 1951), p. 817.

581June 1959

E. H. GRAHAM AND C. LANDIS

arrangement allowed us to compare effects on CFF ofequal total light flux in gratings with those in an areawithout a grating. To accomplish this, the square fieldstop, 17 mm on a side, was replaced by one which was17X8.5 mm. A small notch for fixation was cut in thecenter of each long horizontal side. Each subject wasasked to fixate in alternate determinations during agiven session the upper and lower notches. This wasdone so that two alternate observations would provideregional retinal sensitivity conditions that existed forany one observation under condition I.

RESULTS

The results are presented in Table I and Figs. 1 and 2.Each tabular value for our two subjects is a mean oftwo sessions involving twelve determinations. In viewof the similarity between subjects, their combined dataare presented in the graphs. Data for each of the experi-mental conditions were obtained over a range of almostsix log trolands. The lower limit represents a pointchosen arbitrarily after the function exhibited a break.The part of the curve below the break is probablymainly the contribution of rods; in any case these data,under all conditions of the experiments, overlap to suchan extent that analysis is meaningless. The discussion,therefore, will be confined to the rising, presumably conepart, of the curves.

The general nature of the relationships obtained maybe seen in Figs. 1 and 2. Condition I (no grating)represented by vertical rectangles in Fig. 1 shows theusual sigmoid relationship between CFF and retinal

TABLE I. Critical flicker frequency (in cycles per second) as a function of square fields (8.5' on a side). Central regard. Dark and light

illuminance and is in line with data of earlier experi-ments with similar-sized areas.3

The results for condition II (grating A; 10 stripes perin.), indicated by circles in Fig. 1, while similar in shapeto those of the unstriated area, show a downward dis-placement along the ordinate axis. Otherwise stated, thepresence of a few stripes in the field lowers CFF, thelowering being somewhat greater at high retinal illumi-nances than at low. Critical frequencies are decreasedfurther by the introduction of a larger number ofstripes (grating B; 30 per in.) as indicated in the curvefor condition III (horizontal rectangles). It should benoted here that the decrease in CFF at the top of thecurve is less marked than it is for the steeply risingportion, but this apparent effect is due primarily to thedata of subject GH which do not reach a maximum forthis condition as early as the data of subject GY.

The results for condition IV (triangles with apexdown) appear to reverse the trend that has beenobserved under conditions II and III, i.e., a decrease inCFF with increase in number of lines. Except for thelowest portion of the curve (below about 20 cps), thedata fall above those for condition III and for a fewvalues of log trolands even above condition II. Inother words, an increase in the number of stripes in thiscase (grating C; 90 lines per in.) tends to raise the CFFabove the level induced by a less finely striated field, atleast over the range of higher illuminances.

This trend becomes more marked in the results forcondition V (grating D; 250 stripes per in.). Here thecurve (triangles with apex up) is raised still further on

retinal illuminance for vertically striatedstripes are equal in width.

Critical flicker frequencyNumber of black stripes per inch

logtrolands 0 0G 10 30 90 250 250b 0 0. Ob 10 30 90 250

Subject GH Subject GY

5.02 48.9 48.5 43.6 44.8 44.8 47.2 45.6 48.7 47.8 48.6 44.3 43.6 43.6 50.04.72 49.6 48.2 42.7 43.3 43.3 50.1 51.3 51.5 47.0 50.7 46.6 42.9 45.2 54.04.42 50.0 45.9 43.8 42.2 41.1 52.1 52.1 51.0 47.7 52.3 46.0 43.4 45.6 55.34.12 49.5 46.3 43.4 40.7 41.1 52.2 53.1 52.0 49.7 52.3 46.3 42.9 45.0 54.83.82 49.3 45.7 43.6 39.8 43.3 50.8 51.9 51.2 47.9 51.3 46.1 42.2 45.7 51.83.52 50.2 45.0 43.1 39.2 42.9 49.1 48.9 51.4 48.9 50.2 43.7 41.6 44.6 47.63.22 49.1 45.8 40.7 37.8 39.9 45.7 46.0 49.8 47.7 49.8 42.3 39.4 43.4 47.02.92 46.5 43.5 39.3 35.1 37.5 41.2 42.7 46.0 42.9 46.1 40.3 37.5 39.0 43.5a2.62 42.1 41.3 35.6 32.5 35.0 37.7 38.1 43.6 40.7 43.3 37.7 34.7 36.4 41.02.32 39.4 36.2 33.0 29.3 30.7 33.5 33.8 40.6 37.7 40.1 33.9 32.6 33.9 38.02.02 33.9 33.0 27.4 24.1 23.2 28.7 27.2 35.6 34.6 37.0 29.4 25.8 28.6 33.21.72 30.0 27.1 24.3 20.6 21.2 24.8 23.2 31.8 31.9 34.0 26.2 23.2 23.6 28.81.42 26.5 24.9 21.7 17.8 18.4 21.5 19.9 28.7 25.6 29.7 22.9 21.0 20.0 23.41.12 22.2 19.9 19.1 16.6 16.0 17.6 15.6 24.5 23.3 25.2 20.2 18.8 16.8 19.60.82 17.9 17.0 15.9 14.1 13.3 13.70 12.3 21.2 19.9 21.3 17.2 15.7 13.0 16.70.42 15.2 14.2 13.1 12.1 10.8 10.1 10.2 17.2 17.8 12.8 15.0 13.0 11.0 13.40.12 12.3 12.3 11.1 10.1 9.Oc 10.0 10.4 12.5 13.8 15.1 12.3 11.3 9.90 12.7

-0.18 9.ld 9.9 10.7 8.9 9.8 10.3 10.4 13.2d 12.1 12.7 10.4 10.3c 10.5 12.3-0.48 9.4d 9.5 10.5 9.7 10.6 10.4 10.5 ll.9 d 12.7 12.2 10.6 10.4 11.0 11.8

5 Area of stimulus field was reduced by one-half.b Masking noise was employed.0 Threshold for resolution of stripes.d Point based on one session only.

582 Vol. 49

CRITICAL FLICKER FREQUENCY

o 50

-I 0 1 2 0

U'CY 303

.. j220

U

I I0

-; 0 I 2 3 4 5LOG TROLANDS

FIG. 1. Critical flicker frequency as a function of log trolands for 5conditions of field striations. N=number of lines per inch.

the ordinate axis and finally at the highest illuminancesovertakes the curve for condition I.t

Figure 2 shows perhaps more clearly the effect of thegratings on CFF in this experiment. The data of Fig. 1have been replotted to show, for various constant logtroland values, the relationship between CFF and thenumber of stripes per inch. (The abscissa values wereplotted on a logarithmic scale because of the widerange employed.) It may be observed that the functionsfor the four highest retinal illuminances selected passthrough a minimum at 30 lines per in. (angular widthof line=0.210). For the lowest retinal illuminance, theminimum appears to shift to 90 lines per in. (angularwidth= 0.070). In general then, it may be said that at alllevels of retinal illuminance critical flicker frequency ishighest when no grating is present except for the caseof highest level where the highest CFF occurs with thefinest lines. Critical flicker frequency decreases betweenthe two extremes of no grating and the finest gratingreaching a minimum over most of the range of trolandswith a grating of 30 stripes per in.

The subjects' reports on when they ceased to see thefield as striped are relevant in this analysis. Grating Awas clearly resolvable throughout the sessions for bothsubjects. Grating B remained so for one subject, butfor our second subject, GY, was not clearly seen asstriped in one of his two sessions at a log troland valueof -0.18. Both subjects reported grating C justbarely striped at log trolands=0.12, and no stripesever observed at log trolands= -0.48. In all of these

t In analyzing our data for statistical significance we testedthem against the hypothesis that our five curves were randompermutations of the same basic function. The method involvedsetting up a 5X5 contingency table in which one variable was thenumber of stripes and the other the rank of the CFF values. Sincethere were 19 luminance levels, the number in each of the 25 cellscould vary between 19 and 0, the expected frequency in each cellon the basis of chance being 3.8. A chi square of 124, which for 16degrees of freedom, gives a value p<10-6 indicates that ourcurves are not random permutations of the same function. We areindebted to Professor W. J. McGill of the Psychology Depart-ment, Columbia University, for this analysis.

o 50za.1

Y40a:UL

"30

Ac

U

-J

10FcU

0-

0 10 100LINES PER INCH

FIG. 2. Critical flicker frequency as a function of number of linesper inch at five different levels of retinal illuminance as indicatedby log troland values attached to the curves. Abscissa axisrepresents logarithmic spacing.

cases, it should be noted that the acuity thresholds forthe stripes are below the break in the curves and thusdo not affect the results we have been considering. Withour finest grating (grating D), however, this is no longertrue. Subject GY failed to see stripes at log trolands=2.02 and 2.92; subject GH at log troland=0.82. Inthis situation where the stripes cannot be resolved, thegrating may be presumed to act as a filter which cuts theluminance in half and thus might be expected to producea shift of 0.3 log unit in the function. Since our twosubjects differ with respect to this point, and sinceexact acuity determinations were not made, what wecan say about the curve for condition V (triangles withapex up) in Fig. 1 is that a large part of it, from logtroland values of 0.82 to 2.92, is a transition zone inwhich the stripes were seen in some cases, not clearlyseen, or not seen at all in others. Above the upper limitof this zone, however, we feel safe in attributing theshape of the curve to the effect of the stripes.

The sessions employing a noise to mask the sound ofthe motor indicate that our subjects were not respond-ing on the basis of an auditory cue. Both sets of data(see Table I) obtained under these conditions weresimilar to the comparable curves of the experimentproper.

The results for the experiment in which an area one-half that of the original was used may be seen in Table I.CFF values for the half-area are, except for the very lowtroland values, lower than values for the large area asother investigators have found.8 The result that is ofparticular interest in connection with these experimentsis that the curve for the small area is different from thecurves for the gratings, CFF for the gratings beinglower in all cases except for grating D at the highestretinal illuminances. It seems clear that we are dealingwith a real effect of the stripes which goes beyond thatwhich could be expected on the basis of the reduction influx produced by the use of the grating.

It may be of interest to comment on some observa-tions that were made with steady light. Several ob-

l i

583June 1959

E. H. GRAHAM AND C. LANDIS

servers (including one of the authors) on viewinggrating D with the flicker apparatus off reported seeingflicker as well as other kinds of apparent movementphenomena, i.e., a widening and contracting of thestripes and a running of the stripes across the field.(There was some tendency for this kind of effect to existwith grating C as well, but not to such a marked extent.)Observation of the two coarser gratings did not producethese effects. Our observers did not report thesephenomena with steady light, but on one occasion, in anexperimental session with flickering light and withgrating D at a high illuminance level, GY had difficultyfusing even at very high frequencies. After lookingaway from the field for one minute, he was able toresume the experiment with no further difficulty. It isbelieved likely that the interference of effects such asthose described with steady light for some observersmay have accounted for GY's difficulty.1

DISCUSSION

The present experiment indicates that, within thelimits set by our procedure, CFF is a function of thenumber of lines in the visual field. The gratings usedcontained alternating opaque and illuminated lines ofequal width, the width varying from grating to grating.Our results show that for gratings with relatively fewstripes CFF decreases (in relation to an unpatternedfield of the same area) as stripes increase. Thereafter,the function passes through a minimum for a grating of30 stripes per in. (except for low troland values where itshifts to 90 stripes per in.), then it tends to increasewith further increases in the number of stripes.

It would be impossible at present to give a detailedexplanation of these effects; clearly more data andanalyses are required. For the moment it seems to be ofvalue only to indicate their general nature and toconsider the few studies that are related to ours.M. D. Vernon's7 finding that monocular critical flickerfrequency was reduced by the introduction of a dot or asquare into the flickering field is in line with ours, butsince her study was concerned largely with binoculareffects, the data on this point require further experi-mental elaboration. Crozier and Wolf8 have performedflicker experiments with subdivided fields. They wereinterested primarily in changes in the shape of flicker-logI curves as a function of light-dark ratio. They showedin one experiment that a 30 square field, presented in theperiphery, gave, when divided into 4 equal squares byvertical and horizontal hairlines, changes in the CFF vslog I curve as compared with an unpatterned 30 field.The changes were an enlarged rod branch, a steeper conesegment, and a shift of the curve to higher luminances.In another experiment they used a 10° foveally regardedsquare field divided in one case by three opaque bars and

$ W. J. Crozier and E. Wolf (see reference 8) reported apparentmovement effects when flicker measurements were made withstriated fields, and obtained thresholds for two kinds of movement.

in the second case by six opaque bars, alternating withequally sized illuminated bars. The flicker curve for thesix narrower bars showed a shift to the right along theluminance axis, a steeper cone curve, and a moreextended rod branch compared with the curve for thefield with only three bars. (It should be noted thatCrozier and Wolf do not report data for a comparableunpatterned field in this case.) The general finding isthat the introduction of more patterning in the field,which Crozier and Wolf interpret in terms of increasedlight-dark perimeter, causes a change in the shape of thecurves and a shift to higher luminances. Our data areconsistent with Crozier and Wolf's data in showing adecreased CFF for our coarsest gratings (which mostclosely approximate the ones they employed). Ourmore extensive series of observations, however, show ashift in the opposite direction along the log trolandsaxis for the more finely striped fields.§

Crozier and Wolf's argument in terms of a neuralenhancement due to an increased perimeter of light-darkcontrast would seem difficult to reconcile with theirfinding of a reduced CFF with an increase in patterning.In addition it should be noted that the area effectsreported in their series of experiments on subdividedfields are contrary to established results."

In the type of situation that prevailed in the presentexperiment in which illuminated areas alternated withopaque areas of the same size, it may be assumed thatvarious retinal interactions occurred. It is probable(e.g., Adrian and Matthews,12 Granit," Granit andHarper 4 ) that summation effects extended across theunstimulated areas. In addition, it is possible, if we areto judge by many experiments in which adjacent retinalareas were differentially excited that a condition ofinhibition existed in the opaque areas (Graham andGranit,15 Fry and Bartley, 6 Beitel,17 and Hartline andRatliff' 8). The interaction between these processes musthave been complicated (e.g., disinhibition and abalance between summation and inhibition) and musthave depended upon a great many factors. Theseprocesses which exist at the retinal level must bethought of as having representations in the lateral

§ It should be mentioned that Crozier and Wolf determinedcritical luminance for fixed flash frequencies while the presentauthors obtained critical frequencies for fixed luminance levels.See W. J. Crozier and E. Wolf, J. Gen. Physiol. 24, 635-654(1941).

1l S. Hecht and E. L. Smith, J. Gen. Physiol. 19, 979-988 (1936);R. Granit and P. Harper, Am. J. Physiol. 95, 211-228 (1930);S. Kugelmass and C. Landis, Am. J. Psychol. 68, 1-19 (1955).

12 E. D. Adrian and R. Matthews, J. Physiol. 65, 273-298(1928).

1 R. Granit, Am. J. Physiol. 94, 41-50 (1930).14 R. Granit and P. Harper, Am. J. Physiol. 95, 211-228 (1930).1 C. H. Graham and R. Granit, Am J. Physiol. 98, 664-673

(1931).10 S. A. Fry and S. H. Bartley, J. Exptl. Psyclhol. 19, 351-356

(1936).17 R. J. Beitel, J. Gen. Physiol. 14, 31-61 (1936).18 H. K. Hartline and F. Ratliff, J. Gen. Physiol. 40, 357-376

(1957).

584 Vol. 49

CRITICAL FLICKER FREQUENCY

geniculate body and in the visual cortex. (See Polyak19

for references to this literature.)It would not be profitable to analyze our results

further in terms of such a complex hypothetical system.It is sufficient to state that stimulation by a gratinginvolves a sequence of interactions beginning at theretina and represented at higher levels of the visualsystem.

How these processes relate to the problem of inter-mittent light stimulation must also be considered.Data on the electroretinogram (see a summary byRutschmann 2 0 ) show considerable correspondence be-

19 S. Polyak, The Retina (University of Chicago Press, Chicago,1941).

20 J. Rutschmann, Arch. Psychol. 35, 93-192 (1955).

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

tween perceived flicker and flicker in the electricalresponse of the retina. The problem of how well theelectroencephalogram gives evidence of intermittentstimulation is probably controversial as yet.20 In anycase, we do not now have information on how suchphenomena as interactions at contours and acrossunilluminated areas might influence the neural responsesto intermittent light. Despite this fact, our data, whenelaborated by future experimentation and theory, mayprovide an improved basis for understanding flicker.

ACKNOWLEDGMENT

We wish to express appreciation to Dr. Donald Dillonfor help in the preliminary stages of the experiment.

VOLUME 49, NUMBER 6 JUNE, 1959

Some Multivariate Statistical Techniques Used in Color Matching DataJ. EDWARD JACKSON*

Color Technology Division, Eastman Kodak Company, Rochester, New York(Received January 29, 1958)

In color matching studies, statistical tests of significance should not be made on each variable separatelysince these variables are related and, in general, correlated. Instead, one test should be made for all variablessimultaneously. Multivariate generalizations are given for the basic significance tests and are illustratedby examples from actual color matching studies.

INTRODUCTION

SEVERAL members of the Color TechnologyDivision of the Eastman Kodak Company have

recently written four papers dealing with the variousaspects of color matching under different viewingconditions.- 4 The evaluation of the data from theseexperiments entailed the use of many statistical testsof significance, including several multivariate tests.The multivariate test is used when differences are beingcompared on two or more related variables. In thesesituations, as has already been pointed out,5' 6 thesignificance tests should not be applied to each variableseparately, because the probabilities associated withunivariate tests no longer apply. If the variables arecorrelated, these probabilities are further affected.

It is the purpose of this article to summarize a fewof the basic significance tests since the original papersin which these tests were proposed are found in journals

* On leave of absence at Virginia Ploytechnic Institute, Blacks-burg, Virginia. Revision of this manuscript sponsored by the Officeof Naval Research under the Contract with the Virginia Poly-technic Institute on Statistical Methods in Quality Control andSurveillance Testing.

I Burnham, Evans, and Newhall, J. Opt. Soc. Am..47, 35 (1957).2 Newhall, Burnham, and Clark, J. Opt. Soc. Am. 47, 43 (1957).3 Burnham, Clark, and Newhall, J. Opt. Soc. Am. 47, 959 (1957).R. W. Burnham, J. Opt. Soc. Am. 48, 215 (1958).J. E. Jackson, Ind. Qual. Control 12, 4 (January, 1956).

6 Brown, Howe, Jackson, and Morris, J. Opt. Soc. Am. 46, 46(956).

with which the majority of readers of the Journal ofthe Optical Society of America are probably unfamiliar.The original papers will be referred to, of course, sothat anyone wishing to investigate these methods morefully may do so. Examples will be used to illustrate thetests. To facilitate the printing of this article, con-siderable rounding has been done in the computations.Therefore, the numerical examples may not checkexactly.

Greek letters generally refer to population valuesof given parameters such as the population mean u andvariance o-2. The corresponding Roman letters refer tothe sample estimates of these same parameters; inthis case X and s2. Upper case boldface charactersrepresent matrices. For instance X represents the pxppopulation covariance matrix,

1012012

T,=

0,lp

012 ... 0 .1p0`2

2...

02p

0.2p ... UP2

Lower case boldface characters represent row vectors.For instance La represents a lxp vector of populationmeans:

vp= EgL2 . . ./I,].

June 1959 585