Pendellosung pattern superposed on the basic form of thecurve; (iii) there is an anomalous increase in the amount oflight reflected by a layer near the edges of the reflection band.In their paper' 0 the authors use the dynamical approach de-veloped by Jones" and furthered by Chandrasekhar andRao.12 With the first model presented, it is not feasible toobtain enough data points to demonstrate the Pendellosungfringes. The second, approximate approach precludes thiseffect since, as mentioned earlier, the loss of correct phaserelationship is one of the prices paid for fast solutions.

ACKNOWLEDGMENTS

This work was supported by the National Research Councilof Canada, the U.S. National Science Foundation andPrinceton University.

*Present Address: Department of Mechanical Engineering, TheUniversity of Calgary, Calgary, Alberta, Canada T2N 1N4

'A. C. Eringen and J. D. Lee, Liquid Crystals and Ordered Fluids,Vol. 2, edited by J. F. Johnson and R. S. Porter (Plenum, New York,1974), pp. 383-401.

2A. C. Neville and S. Caveney, "Scarabaeid Beetle Exocuticle as anOptical Analogue of Cholesteric Liquid Crystals," Biol. Rev. 44,531-562, (1969).

3A. A. Kozinski, G. J. Kizior, and S. G. Wax, "Separations with ProteinLiquid Crystals," A.I.Ch.E. 20, 6, 1104-1109, (1974).

4L. E. Hajdo and A. C. Eringen, "A Theory of Light Reflection byCholesteric Liquid Crystals Possessing a Tilted Structure," (un-published).

5G. H. Conners, "Electromagnetic wave propagation in cholestericmaterials," J. Opt. Soc. Am. 58, 875-879, (1968).

6L. M. Brekhovskikh, "Waves in Layered Media" (Academic, NewYork, 1960).

7D. W. Berreman, "Optics in stratified and anisotropic media: 4 X4-matrix formulation," J. Opt. Soc. Am. 62, 4, 502-510 (1972).

8D. W. Berreman, "Optics in smoothly varying anisotropic planarstructures: Application to liquid-crystal twist cells," J. Opt. Soc.Am. 61, 11, 1374-1380, (1973).

9R. Nityanda, "On the Theory of Light Propagation in CholestericLiquid Crystals," Mol. Cryst. Liq. Cryst. 21, 315-331, (1973).

OS. Mazkedian, S. Melone, and F. Rustichelli, "On the Circular Di-chroism and Rotatory Dispersion in Cholesteric Liquid Crystalswith a Pitch Gradient," J. Physique 37, 731-736, (1976).

"R. C. Jones, wrote a series of eight noteworthy papers on optics, thelast of which is in J. Opt. Soc. Am. 46, 126, (1956).

12S. Chandrasekhar and K. N. S. Rao "Optical Rotatory Power ofLiquid Crystals," Acta. Crystallogr. A 24,445-451, (1968).

Spatial summation in human vision: simple reaction timemeasurements

Takehiro UenoOsaka City University, Department of Psychology, Faculty of Letters, Sumiyoshi-ku, Osaka 558, Japan

(Received 17 November 1978)

The reaction-time technique was applied to examine spatial summation or area-intensity recip-rocity at suprathreshold levels in the fovea. A family of reaction time vs luminance curves wasmeasured in two experiments, and the luminance required to produce a criterion reaction time wascomputed from these curves to estimate the extent of summation. The first experiment showed thatthe upper level of spatial summation, the Ricco area, defined for constant reaction time increaseswith decreasing luminance level and that the upper limit of temporal summation is independent ofthe change in target size. The second indicated that the Ricco area decreases with increasing pulseduration up to 20-30 ms and then remains constant.

INTRODUCTION

Ricco's law states that the luminance (L) and area (A)of a light stimulus have a reciprocal relationship (L X A =const) for a constant visual effect. This implies completesummation of the visual response over a given retinal region.The maximum region in which complete spatial summationoccurs is termed the Ricco area or diameter. A number ofstudies have demonstrated that Ricco's law holds over areasof limited extent, but estimates of the summation area havevaried considerably: 30'-20 in the scotopic parafovea and2'-6' in the photopic fovea.1' 2 It has also been known thatRicco area varies with background luminance and target du-ration. Blackwell 3 found that critical area decreased withincreasing adaptation level. Barlow4 demonstrated thatcritical area for a brief flash exceeded that for a long flash atvarious background intensities. These findings indicate thecomplicated interrelations between spatial and temporalsummation.

The present study was designed to examine the mutualrelationships between area and duration at suprathreshold

levels by using reaction time (RT) as a measure of visual in-tegration. The results suggest that the RT measure becomesan effective tool for analyzing the spatial as well as temporalcharacteristics of the visual system.

GENERAL METHOD

The apparatus was a modification of that used in previousstudies,5 -7 which could present to the subject light flashes inthe form of circular targets of varying luminance and size.The flash source was a glow-modulator tube (Sylvania,R1131C) that was operated at 40 mA with rise and decay timesshorter than 30 ,us. Light from the glow-modulator tube,essentially a square wave, was sharply focused onto a smallground-glass plate fastened to the front wall of a light-tightbox. The subject could view target light with dark surroundthrough the observational window cut from the wall oppositeto that where the light pulse was presented. Two small dimred spots (0.150 in visual angle) served as fixation points, lo-cated symmetrically on both vertical sides 20 from the center

1023 J. Opt. Soc. Am., Vol. 69, No. 7, July 1979 0030-3941/79/071023-06$00.50 � 1979 Optical Society of America 1023

of the target. The subject was instructed to gaze with his righteye at the midpoint between the fixation points, so that themonocular field was foveally fixed.

The target stimulus consisted of a circular hole, drilled inthin aluminum plate, and was projected through a 640-nminterference filter (Vacuum Opt. Corp. Jap., type S) withhalf-power bandwidth of 10 nm to block rod intrusion. Thetarget was mounted to the front of the ground-glass plate onthe side toward the subject. The luminance of the filteredlong pulses measured at the target location by a photometer(Tektronix, J16) was 30 cd/m2. In order to control the lu-minance, Kodak Wratten neutral density filters (No. 96) wereused, which were calibrated through the overall optical systemagainst the 640-nm monochromatic light by means of twokinds of probe units supplied with the photometer. Thecalibrated values agreed within less than 12%.

The glow-modulator tube was electronically triggered bya signal from a six-channel time regulator (Sanwa, DTR-6)driven by a 100-kHz crystal clock. A random generator wasemployed to control the variable foreperiod between thewarning signal and stimulus onset: a random (exponential)distribution foreperiod ranging from I to 7 s, with an averageof 3 s. The light pulse was delivered with an intertrial intervalof 4.2-11.5 s. The subject sat in front of the light-tight boxwith his head held rigid by means of an adjustable biteboard,and he was instructed to respond as quickly as possible to eachflash by pushing a microswitch with his right fingertip. Re-action time from stimulus pulse onset to the button-pushingresponse was measured by a TKK digital counter (TW-7010A)and recorded by a TKK digital printer (DP-18).

The experimental paradigm was similar to that adopted inprevious experiments 5 -7: the main purpose of the study wasto collect a family of the RT vs L curve with target area (orduration) as a parameter. A block of 18 identical light pulseswas presented to find a single mean value of RT for a givenarea with a fixed luminance. Data for the trial block wereprocessed as follows: The first RT was skipped, and then thegeometric mean of the remaining 15 RTs was computed afterexcluding the longest and shortest of them. Data obtainedwere analyzed by the function

RT = k/L- + RTo, (1)

where k and n are constants and RTo represents the asymp-totic latency. The reducible latency RT-RTo refers to theintensity-dependent component.8' 0 The initial values ofRTo were carefully estimated for each curve by smoothing thedata and graphically estimating the asymptote. The valuesof k and n were then calculated by the use of least squaremethod. Furthermore, an attempt was made to improve thefit of Eq. (1) to the data points by varying the values of RTofrom those obtained by the graphic analysis.

Two well-practiced subjects, AH and TU, served in theexperiments. Both subjects had normal vision, except forrefractive errors that were adequately corrected by glasses.After a period of about 10 min of dark adaptation, the ex-periments were begun. The subjects performed 40 warm-upRT responses to the flashes with moderate intensity beforestarting the proper experiment. Data for TU alone are re-ported in the present paper. However, the main findings wereconfirmed with AH's data.

EXPERIMENT I

The purpose of the experiment was twofold. First, it wasto investigate how the Ricco area varies with the criterion RT- RTo levels selected. Second, it was to examine, on the basisof the same data, the effects of target area on the critical du-ration at which the upper limit of complete temporal sum-mation (Bloch's law L X t = const) is defined.

MethodEleven targets were used: 2.7', 4.5', 7.1', 8.9', 10.7', 13.4',

17.9', 26.8', 35.7', 44.6', and 60' in visual angle. Each of themwas presented with the 5- and 500-ms durations, noting thatthe brief duration is within the Bloch region, whereas the longone is a duration for which the relation L = const holds.6"0"1

The subjects served in five sessions under each duration, andonly one session was run per day. Within one session, two orthree of the 11 targets were randomly selected. For eachstimulus condition, luminance was varied in steps of 0.5 logunits or less from 30 cd/M2 to such a low level that average R Tsexceeded 300 ms, but the subjects could still detect flashes100% when presented 18 times. An irregular but descendingsequence of the luminance levels was employed, and there wasone block of 18 RT trials at each level. If the subjects madeanticipatory responses, the sequence was extended until 18RTs were obtained. No feedback was given to them con-cerning the anticipations. A rest period of about 1 minelapsed between trial blocks.

ResultsPart (a) of Fig. 1 presents an example of the data obtained

for subject TU: the geometric means of RT are plotted as afunction of log L, taking duration and target size as a param-eter. Parts (b) and (c) of Fig.1 show the estimated n and RTovalues for TU as a function of target size with duration as aparameter: the values of n are nearly constant under the500-ms condition, whereas under the 5-ms condition theydecrease with increasing target size; the exponent n shows adifference between brief and long durations for targets lessthan 30', whereas it is approximately equal for larger targets;and RTo values decrease with increasing target.

In order to examine spatial summation at suprathresholdlevels, the luminances required to produce six criterion valuesof the difference RT - RTo were calculated from the RT vsL curves fitted to the data by Eq. (1). Figure 2 presents plotsof these luminances as a function of log area of the target. Thestraight lines running among the data points are Ricco's lawL X A = const for A S Ac, and the relation L = const for A >A,, where A, represents the Ricco area, or the critical pointat which the lines intersect. The vertical bars about datapoint in RT -RTo = 10 ms represent + 1 S.E. of estimate,which was computed from the least-square regression linesfitted to the data obtained at each target area. The magni-tude of these bars was utilized to draw straight lines of slopes-1 and 0 through the data points for small and large areas,respectively, because we wanted to avoid an a priori choiceof the points that belong to one of the two segments. Figure2 indicates that the Ricco area increases as the criterion RT- RTo value increases. Under the 5-ms condition, the valueof A, increases from 4.3' (for RiT - RTo = 10 ms) to 15.8' (forRT - RTo = 100 ms) with increasing RT - RTo level, whereasit ranges from 4.9' to 11.7' under the 500-ms condition. In

1024 J. Opt. Soc. Am., Vol. 69, No. 7, July 1979 Takehiro Ueno 1024

4001

-3 -2 -1 0 1LOG LUMINANCE (cd/rm2)

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general, the Ricco areas are found to be larger under briefduration condition.

Part (a) of Fig. 3 shows the data corresponding toRT - RTo= 50 ms which are extracted from Fig. 2. In Fig. 3(b), thecritical duration, tc, based on Eq. (2), is computed from thedifference between the 5-ms duration data [open circles, Fig.3(a)] and the 500-ms duration data [filled circles, Fig. 3(a)]:

logtc = log Lb - log Lm + log tb (2)

where tb and Lb represent the duration and threshold iumi-nance of a stimulus brief enough for Bloch's law to be valid,and Lm represents the threshold luminance at a long durationfor which the relation L = const. holds. Equation (2) has itsorigin in the threshold studies,12' 1 3 but it has been utilized for

the RT study.7 Of particular interest is the finding that thecritical duration is independent of the variation in target area,as shown in Fig. 3(b). The horizontal line is a mean log du-ration, which indicates the expression for the boundaries de-fined by Anglin and Mansfield14 and Mansfield.'5 "16

EXPERIMENT 11The present experiment was designed to examine the re-

lationship between the Ricco area and the duration of stim-ulus.

MethodEleven durations, ranging from 1 to 1024 ms in steps of 0.3

log units, were investigated. It would be a very time-con-suming experiment if we were to obtain the Ricco area A, for

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FIG. 2. Luminance as a functionof target area under 5- (a) and500- (b) ms-duration conditions,taking RT - RTo level as a pa-rameter for subject TU. Data forsmall areas are fitted with a line of-1 slope: data for large areasare fitted by a horizontal line.

-2 -1 0

1025 J. Opt. Soc. Am., Vol. 69, No. 7, July 1979

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FIG. 1. (a) Reaction time as afunction of log luminance, withpulse duration and target size asa parameter for subject TU. Thesolid curves drawn through thedata points represent the RTvs Lcurve, Eq. (1), fitted by the methodof least squares. (b) Estimatedexponent n in Eq. (1) as a functionof target size for TU. Open cir-cles are for 5-ms duration andfilled circles for 500-ms duration.(c) Estimated asymptote RTO inEq. (1) as a function of target sizefor TU. The legends are similar tothose in (b).

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FIG. 3. (a) Luminance required to produce the criterion RT-RTO = 50 msas a function of target area for subject TU. Open circles are for 5-ms du-ration and filled circles for 500-ms duration. Data for small areas are fittedwith a line of -1 slope: data for large areas are fitted by a horizontal line.(b) Critical duration as a function of target area for TU. The horizontal linerepresents the mean.

each of these durations by using the paradigm in ExperimentI. Therefore, the following economical measure was em-ployed:

log A, = log Ls - log Li + log A,, (3)

where A, and Ls represent the area and threshold luminanceof a stimulus small enough for Ricco's law to be valid, and Llrepresents the threshold luminance at a large area Al for which

the relation L = const holds. The log area A, enters only asa scaling factor. This equation is a spatial analog of Eq. (2)on temporal summation. Judging from the data in Experi-ment I, we used 4.5' as A, and 44.6' as Al, respectively. Theextrapolation involved in Eq. (3) may be justified by thefinding that, as can be seen in Fig. 4(a)-(c), the RT vs L curvewith the 44.6' target shifted sufficiently to the left of the 4.5'target curve as L decreases. Two luminances (L, and LI)required to produce a RT value of 50 ms above the asymptoticRTo were calculated from the two RT vs L curves in order toestimate the size of the Ricco area at one suprathresholdlevel.

The subjects served in five sessions, and only one sessionwas run per day. Within one session, two or three of the 11durations were randomly selected, and two RT vs L curves,one with the 4.5' target and the other the 44.6' target, wereobtained under each of them. Other aspects of the methodwere the same as those used in Experiment I.

ResultsParts (a)-(c) of Fig. 4 show an example of the data obtained

for TU. The solid curves drawn in the figure represent Eq.(1). In Figs. 3(d) and 3(e), the estimated values of n and RTofor TU are plotted as a function of log duration: both n andRTo show a difference between the 4.5' and 44.6' targetsthroughout the durations; the values of n are essentiallyconstant for both the targets, with the exception of extremebrief (1 and 2 ms) and long (512 and 1024 ms) durations.

Figure 5(a) shows the luminances required to produce thedifference RT - RTo = 50 ins, as a function of log duration.The straight lines connecting the data points are Bloch's lawL X t = const for t < t, and the relation L - const for t 2 tc,where t, represents the critical duration, or the critical pointat which the lines intersect. The vertical bars about the datapoint represent * 1 S.E. of estimate, derived from the re-gression lines fitted to the data. The magnitude of these barswas considered to fit straight lines with slopes -1 and 0 to thebrief and long durations, respectively. From the graph, the

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FIG. 4. (a)-(c) Reaction time asa function of log luminance, withpulse duration and target size asa parameter for subject TU. Thesolid curves drawn through thedata points represent the RTvs Lcurve, Eq. (1), fitted by the methodof least squares. Open circlesare for 4.5' target and filled circlesfor 44.6' target. (d) Estimatedexponent n in Eq. (1) as a functionof log pulse duration for TU.Open circles for 4.5' target andfilled circles for 44.6' target. (e)Estimated asymptote RTO in Eq.(1) as a function of log pulse du-ration for TU. The legends aresimilar to those in (d).

LOG DURATION(msec)

1026 J. Opt. Soc. Am., Vol. 69, No. 7, July 1979

-1

1)

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2

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300

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FIG. 5. (a) Luminance required to produce the criterion RT-RTo = 50 msas a function of pulse duration for subject TU. Open circles are for 4.5'target and filled circles for 44.6' target. Data for brief durations are fittedwith a line of -1 slope; data for long durations are fitted by a horizontal line.(b) Ricco area as a function of pulse duration for TU. Data for brief durationsare fitted with a line of -1/3 slope; data for long durations are fitted by ahorizontal line.

values of t, are found to be 23.7 ms for the 4.5' target and 8 msfor the 44.6' target. Part (b) of Fig. 5 presents a plot of theRicco area as a function of log duration: the magnitude of theRicco area A, is computed by Eq. (3) from the difference be-tween the 4.5' target data (open circles, Fig. 5) and the 44.6'target data (filled circles, Fig. 5). It is found that the Riccoarea decreases as the -1/3 power of duration up to 20-30 msthen remains constant. The solid line connecting the datapoints represents the line based on the analysis by Mans-field.' 6

DISCUSSION

The results of two experiments for TU are summarized inFig. 6. The four distinct RT - RTo relations for differentregions of spatial and temporal variables are shown in the formof a diagram. The exponents are expressed as simple frac-tions. The expressions for the boundaries are defined by theprocedure of Anglin and Mansfield14 based on the propertyof continuity for the RT - RTo component. The schematicrepresentation shown in Fig. 6 is essentially similar to that ofMansfield,' 6 but several comments must be made on the di-agram of Fig. 6, referring to the data of the present experi-ments.

REACTION TIME FUNCTION

As is apparent from Fig. 1(b), the exponent n is above 1/2for the smallest target 2.7' under the 5-ms condition, whichcontradicts the exponent denoted in the Quadrant III of Fig.

6. This high value is largely due to the restriction that thestimulus range of less than 1.5 log units was used. If a rangeof more than 3 log units is employed, this value would be ex-pected to reduce to the value of 1/2.10 The same holds truefor the case of the 1-ms duration in Experiment II, as is seenin parts (a) and (d) of Fig. 4.

As Fig. 1(b) indicates, the exponent for smaller targets than10'is below 1/2 under the 500-ms condition. There is a similarfinding for the 4.5' target under durations of more than 500ms in Experiment II, as is found in Fig. 4(d). These resultsare inconsistent with the exponent denoted in the QuadrantII, based on the finding by Mansfieldl0 : he reported that forthe point source target of 0.050, the exponent remains closeto 1/2 over the range from 0.3 to 300 ms. The present datastrongly suggest that under longer durations than 500 ms, theexponent for small targets approximates 1/3, as indicated bythe point (4.5' and 500 ms) of the star mark in the QuadrantII.

It is clear from Fig. 1(b) that the exponent for targets largerthan 17.9' converges to 1/3 under the two durations, corre-sponding to the exponent in the Quadrants I and IV. Thisconfirms the results obtained by Vaughan et al,9 Mansfield,' 0

and Ueno.6 Part (d) of Fig. 4 shows that the exponent for the4.5' target is approximately 1/2 over the range 4-256 ms, afinding that is consistent with the value in the Quadrants IIand III; the data for the 44.6' target, ranged from 4 to 256 ms,show exponents of the order of 1/3 consistent with the expo-nent in the Quadrants I and IV.

At the outset of the analysis, the asymptotic RTo was ex-pected to keep a fixed, constant value throughout every con-dition, because it has been implicitly assumed as a motor re-sponse component.8 -10 -Inspection of Figs. 1(c) and 4(e),

z0

a

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FIG. 6. Schematic representation of the RT - RTo component for thesubject TU. The abscissa represents area in visual angle and the ordinaterepresents duration in ms. The constant of proportionality is omitted ateach of the four functions. For two star marks see text.

1027 J. Opt. Soc. Am., Vol. 69, No. 7, July 1979

I IB

0 07 I - -

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Takehiro Ueno 1027

I

. . . . . . .

USA.

I

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however, shows that the estimates of RTo (and those of thecorresponding exponent value) depend upon the stimulusconditions used: the range and spacing of stimuli. In orderto increase the accuracy of RTo value, therefore, a stimulusrange of more than 3 log units, if possible, would be requiredfor every combination of area and duration.

SPATIAL SUMMATION

Figure 2 indicates that the upper limit of spatial summationincreases with any increase of the criterion RT - RTo level.This finding is in the same line as the previous RT data6 ontemporal summation in which linearity holds between theupper limit of Bloch region and the criterion RT level. It isto be noted that, as is seen in Fig. 3(a), the magnitude of theRicco area is roughly the order of 10' at the suprathresholdlevel of 50 ms above the asymptotic RTo, because this valueis not always large, compared with the data of threshold andRT studies on cone summation.2'7

From the line with two distinct branches of Fig. 5(b), it isclear that the Ricco area is affected by the change in pulseduration: the summation area decreases nearly as the-1/3power of duration up to 20-30 ms then remains constant, 8'in visual angle. In Fig. 6, this relationship is specified by theexpressions for the boundaries between Quadrants I and IIand between III and IV. The threshold data obtained byBlackwell3 and by Barlow4 are in accord with the relationdepicted in Figs. 5(b) and 6.

TEMPORAL SUMMATION

Part (b) of Fig. 3 shows that the critical durations t, calcu-lated from Eq. (2), are essentially independent of area. Thisrelation is depicted in Fig. 6 by the expression for theboundaries between Quadrants I and IV and between II andIII. The puzzling problem is concerned with the magnitudeof a mean critical duration in Fig. 3(b), 20 ms; this value issomewhat large in comparison with the order of 10 ms in theprevious RT studies.6'1 0 "'1 In fact, Fig. 5(a) indicates that thecritical duration for the 4.5' target is approximately 22 ms; onthe other hand, the critical duration for the 44.6' target isnearly 8 ms, though a considerable partial summation con-tinues up to about 30 ms. Obviously, this is inconsistent withthe relations shown in Figs. 3(b) and 6. Such a contradiction

between the data in Experiments I and II may be caused bythe extrapolation involved in Eq. (2), or the difference in theexperimental paradigm employed. It appears, however, thatthe data in Fig. 5(a) are more general, considering thethreshold data obtained by Barlow4 in which the upper limitof complete temporal summation is decreased by increasingthe area of the stimulus. The location (44.6' and 8 ms) of thestar mark in the Quadrant IV indicates the possibility thatcritical duration decreases for a relatively large target.

ACKNOWLEDGMENT

Supported by a Grant in Aid for Scientific Researches (No.361044, 1978), Ministry of Education.

'G. S. Brindley, Physiology of the retina and visual pathway (EdwardArnold, London, 1970).

2p". E. Hallett, "Spatial summation," Vision Res. 3, 9-24 (1963).3H. R. Blackwell, "Contrast thresholds of the human eye," J. Opt. Soc.

Am. 36, 624-643 (1946).4H. B. Barlow, "Temporal and spatial summation in human vision

at different background intensities," J. Physiol. Lond. 141, 337-350(1958).

5T. Ueno, "Luminance-duration relation in reaction time to spectralstimuli," Vision Res. 16, 721-725 (1976).

6T. Ueno, "Reaction time as a measure of temporal summation atsuprathreshold levels," Vision Res. 17, 227-232 (1977).

7T. Ueno, "Temporal summation in human vision: simple reactiontime measurements," Percept. Psychophys. 23, 43-50 (1978).

8H. Pieron, The sensations (Trans. M. H. Pirenne and B. C. Abbot)(Yale University, New Haven, 1952).

9H. G. Jr. Vaughan, L. D. Costa, and L. Gilden, "The functionalrelation of visual evoked response and reaction time intensity,"Vision Res. 6, 645-656 (1966).

'OR. J. W. Mansfield, "Latency functions in human vision," VisionRes. 13, 2219-2234 (1973).

"M. L. Kietzman and B. J. Gillam, "Visual temporal integration andsimple reaction time," Percept. Psychophys. 11, 333-340 (1972).

12 J. Krauskopf and J. D. Mollon, "The independence of the temporal

integration properties of individual chromatic mechanisms in thehuman eye," J. Physiol. Lond. 219, 611-623 (1971).

3T. Uetsuki and M. Ikeda, "Adaptation and critical duration forStiles 7r mechanisms," J. Opt. Soc. Am. 61, 821-828 (1971).

14J. M. Anglin and R. J. W. Mansfield, "On the brightness of short andlong flashes," Percept. Psychophys. 4, 161-162 (1968).

'5 R. J. W. Mansfield, "Brightness function: effect of area and du-ration," J. Opt. Soc. Am. 63,913-920 (1973).

16R. J. W. Mansfield, "Measurement, invariance, and psychophysics,"In Sensation and Measurement-Papers in honor of S. S.; Stevens(Ed. H. R. Moskowitz, B. Scharf and J. C. Stevens) (Reidel, Dor-drecht-Holland, 1974), p. 113-128.

1028 J. Opt. Soc. Am., Vol. 69, No. 7, July 1979 Takehiro Ueno 1028