Temporal modulation sensitivity and pulse-detection thresholds …€¦ · Temporal modulation sensitivity and pulse-detection thresholds for chromatic and luminance perturbations

1992 J. Opt. Soc. Am. A/Vol. 4, No. 10/October 1987

Temporal modulation sensitivity and pulse-detectionthresholds for chromatic and luminance perturbations

William H. Swanson*

Eye Research Laboratories, The University of Chicago, Chicago, Illinois 60637

Takehiro Ueno

Department of Psychology, Osaka City University, Osaka 558, Japan

Vivianne C. Smith and Joel Pokorny

Eye Research Laboratories, The University of Chicago, Chicago, Illinois 60637

Received November 10, 1986; accepted June 5, 1987

We studied temporal processing of chromatic and luminance perturbations of a 600-nm field, measuring bothmodulation sensitivity (sinusoidal frequencies from 0.25 to 40 Hz) and pulse-detection thresholds (pulse durationsfrom 5 to 2560 msec) for mean luminances of 0.9 to 900 Td and field sizes of 0.50 to 80. Chromatic stimuli were pro-duced by antiphase modulation of lights matched by heterochromatic flicker photometry. Both mean luminanceand field size affected sensitivity, and the magnitude of field-size effects increased with mean luminance. Wederived both luminance and chromatic impulse response functions for each set of experimental conditions, using themodulation-sensitivity data. At high mean luminances and large field sizes the chromatic impulse responsefunctions are complex, suggesting contributions from both chromatic and luminance mechanisms. Pulse-detectiondata were fitted by a peak detector model based on these impulse response functions.

INTRODUCTION

Temporal sensitivity to luminance perturbations' has fre-quently been studied with two different types of stimuli:periodic (flicker detection) and aperiodic (flash detection).For periodic stimuli, the relation between temporal frequen-cy and modulation sensitivity is referred to as a temporalcontrast-sensitivity function. For aperiodic stimuli, the re-lation between pulse duration and modulation threshold isreferred to as a threshold-duration function. A number ofinvestigatorsl"2 have attempted to relate these two functionsin terms of an underlying linear temporal filter definedmathematically as an impulse response function.

Chromatic perturbations are produced by antiphase mod-ulation of a pair of lights matched in luminance by hetero-chromatic flicker photometry.3-8 Temporal contrast-sensi-tivity functions for chromatic perturbations are distinctlydifferent from temporal contrast-sensitivity functions forluminance perturbations,3-7 and threshold-duration func-tions for chromatic pulses show integration over a longertime period than seen with luminance pulses.8 Smith et al.,8using the concept of a chromatic impulse response function,found that a wavelength-independent chromatic impulseresponse function fitted their threshold-duration data formodulation from white at 9 Td.

No previous study has directly compared temporal con-trast-sensitivity data and threshold-duration data for chro-matic perturbations, nor is there a study in which flicker-detection and flash-detection data have been compared for afull range of field sizes and retinal illuminances. We gath-ered flicker-detection and flash-detection data on two ob-

servers by using both chromatic and luminance perturba-tions. The use of chromatic and luminance impulse re-sponse functions and a peak detector model allowed us tointegrate two different types of data within a single concep-tual framework. To the extent that the impulse responsefunctions permit prediction of pulse-detection data frommodulation-sensitivity data, they provide a good approxi-mation of the temporal properties of mechanisms mediatingdetection of chromatic and luminance perturbations.

We varied retinal illuminance and field size. For lumi-nance perturbations, both temporal contrast-sensitivityfunctions and threshold-duration functions are strongly in-fluenced by retinal illuminance and spatial structure."9"0

Retinal illuminance and spatial extent also influence chro-matic temporal contrast-sensitivity functions."" 2 The useof impulse response functions allowed us to quantify theeffects of these stimulus parameters.

METHODS

EquipmentWe used a computer-controlled two-channel Maxwellianview system employing two light-emitting diodes (LED's,General Instrument Models MV64521 and MV5752). Lightfrom the two LED's was lightly diffused, combined by adichroic beam splitter, collimated, and then focused on a 2-mm artificial pupil. The field of view was defined by circu-lar field stops with diameters of 80, 2°, or 0.5° of visual angle.

A two-channel LED driver circuit gave precise linear con-trol of the radiance of each LED by controlling the density of

0740-3232/87/101992-14$02.00 ©) 1987 Optical Society of America

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Vol. 4, No. 10/October 1987/J. Opt. Soc. Am. A 1993

constant-amplitude, 2-,usec pulses. For each channel, amultiplier (Burr-Brown Model MPY100CM) was fed bythree 12-bit digital-to-analog converters that specified thewaveform (90 points per cycle for the sinusoids), mean lumi-nance, and modulation depth, permitting a large range ofmodulations without sacrificing precision of waveformspecification. A voltage-to-frequency converter (Burr-Brown Model VCF62CG) controlled the density of thepulses fed to each LED.

Two types of waveform were input by the computer to theLED driver circuit: sinusoids of 0.25 to 40 Hz and pulseswith durations of 5 to 2560 msec. Available sinusoidal fre-quencies were produced as fractions of 80 Hz (i.e., 80 Hz, 80/2 = 40 Hz, 80/3 = 26.67 Hz, etc). The sinusoidal frequencyvalues and pulse durations were measured with a frequencycounter (Racal 9900). The sinusoidal frequencies were ac-curate to three significant figures, and the pulse durationswere accurate to within 2%, except for the nominal 5-msecpulse, which was accurate to within 10%.

CalibrationsLED's are convenient as light sources in temporal experi-ments. However, there is the potential for a variety ofstimulus artifacts. In addition to their spatial inhomogen-eity, chromatic and luminance artifacts may occur."3 TheLED driver circuit was designed to provide color consistencyand linearity. Here we describe the performance of ourinstrument.

LED ChromaticityThe spectral emission characteristics of the LED's weremeasured with a laboratory-constructed spectroradiometerplaced at the eyepiece. The MV5752 LED had a peak at 560nm and a bandwidth at half-height of 27 nm; the MV64521LED had a peak at 630 nm and a bandwidth at half-height of38 nm. The metameric monochromatic equivalents of theLED's, computed for the CIE standard observer,'4 were 564and 625 nm, respectively. With these sources, all availablechromaticities were on the spectrum locus.

Color Consistency of the LED'sTo evaluate potential chromaticity shifts with luminance,we measured the spectral emission characteristics (2-nmintervals) of our LED's for steady outputs of 900 Td (themaximum value per LED used in our study) and 36 Td (forthe 564-nm LED) or 12 Td (for the 625-nm LED). Weobtained chromaticity shifts to longer wavelengths of 1.67nm for the 564-nm LED and 0.06 nm for the 625-nm LED.Calculations for the CIE standard observer indicate thatthese chromaticity shifts should result in luminance changesof less than 0.6%. In our experiments the LED's were modu-lated around a fixed mean luminance and reached the ex-tremes for only brief periods of time. Further, high modula-tion levels were required only for the highest flicker frequen-cy conditions and shortest pulses. Thus the calibrationmeasurements represent more extreme operating conditionsthan actually used in gathering the data.

Linearity of the LED'sLED driver parameters were adjusted to confine the operat-ing ranges to their linear region. As a statistic for linearity,we performed a linear regression analysis on these data and

obtained a correlation of 0.9997 for the 564-nm LED and0.9998 for the 625-nm LED.

Overshoot of the LED'sWe used a photodiode to examine the waveform for a lightpulse from 450 to 900 Td (the largest pulse used in ourexperiments). An overshoot was measurable but was lessthan 0.15%.

Field HomogeneityUniformity of the field was achieved by the use of lightdiffusers in front of the LED's, long-focal-length achromaticlenses, and precise alignment of the images in the pupil.Field homogeneity was assessed with a color-matchingmethod. We illuminated the surround of a 0.50 aperturewith a monochromatic light metameric to the field and ofequal luminance. The 0.5° aperture was moved throughoutthe central 8° of the field, and the color match was undis-turbed. Inhomogeneities larger than 5% would have dis-turbed the color match, so our result indicates field homoge-neity at least as good as this figure.

Photometric CalibrationRetinal illuminance of the 564-nm light was measured with atechnique described by Nygaard and Frumkes."5 We ob-tained a maximal retinal illuminance of 900 Td for the dim-mer LED (564 nm), giving a maximal mean luminance of 900Td (with 100% modulation) for the experiment. CalibratedInconel neutral-density filters were used to provide addi-tional mean luminances of 90, 9 and 0.9 Td, so the LED'soperated in a similar dynamic range for all stimulus condi-tions.

ProceduresObservers viewed the stimulus in a darkened room, using achin rest to maintain a constant head position. At the be-ginning of an experimental session, the 564-nm LED was setat half its maximum luminance (450 Td), and neutral-densi-ty filters were added to bring the field to the desired range.The observer then matched the two sources of heterochro-matic flicker photometry, adjusting the radiance by the 625-nm LED.'6 This setting (made with the same mean lumi-nance and field size used in the session) was then used for the625-nm LED throughout the session. The time-averagedchromaticity of the field was metameric to approximately600 nm.

We used perturbations of either chromaticity or lumi-nance; the LED's were modulated about a constant meanluminance and had identical modulation. For the sinusoids,the modulation of two LED's was either in phase or anti-phase: the in-phase condition gave luminance modulationwith no change in chromaticity, and the antiphase conditiongave chromatic modulation with no change in luminance (asdefined by heterochromatic flicker photometry) (Fig. 1,top). For luminance pulses both sources either increasedsimultaneously or decreased simultaneously, while for chro-matic pulses one source increased while the other sourcedecreased (Fig. 1, bottom).

Series I: Effect of Mean Luminance for a 20 FieldIn this series of experiments we evaluated the effect of meanluminance on detection of luminance and chromatic pertur-

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Ti meFig. 1. Temporal luminance profiles of stimuli: sinusoids shownon top, pulses shown on bottom. The solid lines represent theluminance profile of the 625-nm source; dashed lines represent theluminance profile of the 564-nm source. For luminance perturba-tions (left), the sources are modulated in the same phase, while forchromatic modulation (right) the sources are modulated in anti-phase.

bations. We measured sensitivity to sinusoidal flicker atmean luminances of 0.9, 9, 90, and 900 Td and pulse-detec-tion thresholds at 9 and 900 Td. Field size was held con-stant at 20.

We used the method of adjustment to measure temporalmodulation sensitivity (sensitivity is defined as the recipro-cal of the threshold modulation). The sinusoids were pre-sented at 97% modulation, and the observer adjusted modu-lation with a bidirectional switch. The observer rapidlydecreased the modulation depth to approximate thresholdand then carefully bracketed the flicker fusion threshold insingle 0.04-log-unit steps. Sensitivities were determined fora full range of frequencies (0.25 to 40 Hz), presented insemirandom order. In most experimental sessions for alltrials the modulation was either chromatic or luminance.Most conditions were repeated in two separate experimentalsessions. Data reported are the mean values, with two tofive settings per frequency.

We measured pulse-detection thresholds with a staircaseprocedure that randomly intermixed durations.8 For eachtrial, the observer initiated the trial by pressing a button andresponded by pressing a bidirectional switch to indicate ei-ther "seen" or "not seen." In a single 20-min session weused either chromatic or luminance pulses and measuredthresholds for 10 pulse durations ranging from 5 to 2560msec in 1-octave steps. Data reported are the medians of 10reversals for a single staircase at each duration.

Series II: Effect of Field SizeIn this series of experiments we evaluated the effect of fieldsize on detection of luminance and chromatic perturbations,using field sizes of 0.50 and 8°. We measured modulationsensitivity and pulse-detection thresholds at 9 and 900 Td.The procedures were as described for Series I.

ObserversTwo of the authors (TU and WS) served as observers for allexperimental conditions; both have normal color vision andnormal visual acuity (with their usual refractive correction).

DATA ANALYSIS

We used the modulation-sensitivity data to generate digitalimpulse response functions using the phase reconstructionmethod of Stork and Falk,'7 which generates the impulseresponse function for a linear minimal phase filter. Thephase-reconstruction technique assumes that a linear filteris responsible for detection and uses the flicker data to de-fine the amplitude spectrum of the filter. The phase spec-trum for the linear filter is then computed from the ampli-tude spectrum, and the inverse Fourier transform is per-formed to generate a digital impulse response function.Previous approaches involved postulating a suitable analyticfunction and adjusting its parameters to fit the amplitudedata. The Stork-Falk numerical-integration method hasthe advantage of being nonparametric and model free. Thetime course for these digital impulse response functions is inrelation to the onset of the response, not to the onset of thestimulus. We calculated the digital impulse response func-tions to a resolution of 10 msec. A digital impulse responsefunction was generated for each set of stimulus conditions.

The amplitude spectrum for a digital impulse responsefunction fits the corresponding flicker data exactly, so anyanalytic impulse response function that gives a good fit tothe digital impulse response function should also give a goodfit to the flicker data. We chose a convenient analytic func-tion to fit the digital impulse response functions, but thischoice of functions was not crucial to our analysis. Wederived analytic impulse response functions by fitting thedigital impulse response functions with a variation of theWatson-Nachmias' 8 model: each digital impulse responsefunction was fitted with a difference of two five-stage linearfilters, with a latency difference to between the two filters.As previously noted, 8 a five-stage filter is representative ofthe slope of the amplitude-sensitivity data for chromaticmodulation 4'7 "9 as well as for luminance modulation 2 0 (seealso Uchikawa and Ikeda2 l). The impulse response func-tion, I(c, t), for a single n-stage linear filter with cornerfrequency c is

(1)

where t is in seconds and c is in hertz. We normalized I(c, t)to its peak response. To form the analytic impulse responsefunctions we weighted the two filters by coefficients, A andB, and took their difference:

IRF(t) = A[I(cl, t)/kl] - B[I(cC, t -to)/k2 (2)

where cl and c2 are the corner frequencies (in hertz) of thetwo filters, to is the latency difference (in seconds) betweenthe onsets of the two filters, and kh and k2 are the normaliza-tion terms for the two filters. The Fourier transforms2 2 ofthe analytic impulse response functions are analytic tempo-ral contrast-sensitivity functions that we compared with ourflicker data.

The analytic impulse response functions were used in apeak-detector model to predict the pulse-detection data; thedigital impulse response functions gave virtually identicalpredictions. Each analytic impulse response function wasconvolved with pulses of various durations to derive theresponse amplitude. The prediction for threshold is thereciprocal of response amplitude. Thus each analytic im-

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Table 1. Scale Factors (in log units) Used to FitPulse-Detection Dataa

Series I: Effect of Mean Luminance for a 20 FieldMean Perturbation

Luminance (Td) Luminance Chromatic

900 -0.03 0.109 0.11 -0.19

Series II: Effect of Field SizeTU WS

Td/deg Luminance Chromatic Luminance Chromatic

900/0.5 -0.08 0.14 0.08 0.16900/2.0 0.03 -0.07 0.06 -0.08900/8.0 - -0.16 -0.08 0.059/0.5 -0.15 0.05 -0.13 0.029/2.0 -0.07 0.27 -0.05 0.219/8.0 -0.05 0.09 -0.12 -0.09

a These values were subtracted from the predicted threshold modulations(in log units) to fit the data.

pulse response function produced a template for the pulse-detection data gathered under the same field size, chroma-ticity, and mean luminance as was used for the correspond-ing flicker data. For each set of experimental conditions wefitted the template to the data by scaling it vertically (that is,letting sensitivity vary while keeping temporal propertiesfixed) with a least-mean-squares procedure. The verticalscaling factors required are given in Table 1; in all but onecase the scaling factors were less than 0.2 log unit. Theamplitude sensitivities for 9 to 900 Td are separated by 2 logunits, so the scaling factors are relatively small.

RESULTS

Series I: Effect of Mean Luminance for a 2° FieldThe top panels of Fig. 2 show the flicker data and corre-sponding analytic functions plotted as amplitude sensitivityversus frequency for luminance and chromaticity perturba-tions, and the bottom panels show the analytic functionsreplotted in terms of modulation sensitivity. Since the ef-fects of mean luminance were quite similar for the two ob-servers, the analytic functions were derived from the meansof the data for the two observers. The temporal contrast-sensitivity functions for luminance modulation resemblethose of Kelly,2 0 who used comparable luminance levels anda similar range of temporal frequencies but a larger field size.When the data are plotted in terms of amplitude sensitivity,the functions for 9 to 900 Td converge at high temporalfrequencies (Fig. 2, top left). The temporal contrast-sensi-tivity functions change from low-pass to bandpass as meanluminance is increased (bottom left), with little change insensitivity at low frequencies. When the data for chromaticmodulation are plotted in terms of amplitude sensitivity, the0.9- to 90-Td functions converge at high frequencies (Fig. 2,top right). The chromatic temporal contrast-sensitivityfunctions show a systematic dependence on mean lumi-nance. For mean luminances from 0.9 to 90 Td the chro-matic temporal contrast-sensitivity functions are low pass,and sensitivity increases with mean luminance for all tempo-ral frequencies. As mean luminance is increased from 90 to900 Td, chromatic sensitivity is increased only above 4 Hz; at

900 Td the chromatic temporal contrast-sensitivity functionis clearly bandpass (bottom right).

The digital impulse response functions are shown as filledsymbols in Fig. 3, and the analytic impulse response func-tions are shown as smooth curves. The impulse responsefunctions for luminance modulation show a distinct patternas mean luminance increases: the time from onset to peakresponse becomes shorter, and a negative lobe appears (Fig.3, left-hand panels). The chromatic impulse response func-tions also show a decrease in time from- onset to peak as meanluminance increases, and for 0.9-90 Td the negative lobe isquite small (Fig. 3, right-hand panels). We examined thefirst 2000 msec of the digital impulse response functions forringing resulting from noise in the data. The ringing wasalways of low amplitude (as seen beyond 200 msec in the 90-and 900-Td luminance impulse response functions shown inFig. 3), indicating very little noise in the data.

The digital chromatic impulse response function has adistinct negative lobe at 900 Td, and the positive lobe isbimodal (with one peak near 30 msec and a second peak near100 msec) and cannot be fitted by a difference of two n-stagefilters. The bimodality represents systematic tendencies inthe data for 2-16 Hz and is not due to random data variation(which produces ringing). Since the time course of the firstpeak is similar to the time course of the positive componentof the 900-Td luminance impulse response function, it ap-pears that the mechanism responsible for detection of lumi-nance perturbations may contribute to the response. Inter-actions between mechanisms sensitive to luminance pertur-bations and chromatic perturbations have frequently beenmodeled with a vector sum,2 3 but it is not obvious how tocombine the corresponding impulse response functions. Asan approximation we added a third filter whose corner fre-quency was identical to the positive component of the ana-lytic 900-Td luminance impulse response function and in-cluded a latency difference between onset of luminance andchromatic responses. Thus we modified Eq. (2) to obtain

IRF(t) = A[I(cl, t - t,)/kj] - B[I(c2 , t - tO)/k2]

where the terms are as defined for Eq. (2).Table 2 gives the amplitudes, corner frequencies, and rela-

tive latency differences of the analytic impulse responsefunctions. For both chromatic and luminance modulationthe amplitudes and corner frequencies increase as meanluminance increases, while the latency differences decrease.In all cases the amplitude of the first filter is greater thanthat of the second filter, and for chromatic modulation at900 Td the amplitude of the third filter is greater than thatof the first filter. The latency difference is larger for chro-matic modulation than for luminance modulation, and forboth types of modulation the latency differences tend toincrease as mean luminance decreases.

Pulse detection thresholds for luminance and chromaticperturbations are shown in Fig. 4, with mean luminances of900 Td (top) and 9 Td (bottom). Note that the data areplotted in terms of modulation sensitivity; on a scale ofamplitude sensitivity they would be separated by 2 log units.The solid lines are predictions from the corresponding ana-lytic impulse response functions, using the parameters de-

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rived from the modulation-sensitivity data (Table 2). Atshort durations, thresholds for luminance pulses decreasewith increased pulse duration, showing integration up to 40msec at 900 Td and up to 80 msec at 9 Td. Similarly,thresholds for chromatic pulses show integration up to 160msec at 900 Td and up to 320 msec at 9 Td. There were no

systematic differences between thresholds for luminance in-crements and luminance decrements or between thresholdsfor hue shifts toward red and toward green.

For luminance pulses at 900 Td, the data show a pro-nounced local minimum at 40 to 80 msec. The peak detectormodel described above predicts the shape of the pulse-detec-

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Luminance Modulation Chromatic ModulationMean Filter 1 Filter 2 Mean Filter 1 Filter2 Filter3

Luminance cl c2 to Luminance ci c2 to c3 t1(Td) (Hz) A (Hz) (msec) B (Td) (Hz) A (Hz) (msec) B (Hz) (msec) C

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0.9 10.9 273 7.2 49 49 0.9 4.53 78.2 - - - - - -

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tion function for all conditions except for this increase inthreshold for pulses longer than 80 msec. A number ofmodels have been proposed to explain this nonmonotoni-city,10'2 4-26 but, as our data do not allow us to distinguishamong these models, we did not attempt to derive a fit tothem. In the least-mean-squares program used to scale thepredictions vertically, for the 900-Td luminance pulses fitswere made only to data for pulses of 5 to 40 msec. Theresulting scaling factors are listed in Table 1; the variabilityis similar to that reported by Smith et al.

8 and may be due tocriterion shifts from day to day.

Series II: The Effect of Field SizeThe individual data for the two observers are plotted in Figs.5-8 for the 0.5° field (circles) and the 80 field (squares); thecorresponding analytic temporal contrast-sensitivity func-tions are plotted as solid lines. Each set of temporal con-trast-sensitivity functions is shown with the correspondingimpulse-response functions and threshold-duration func-tions. In general, modulation sensitivity increases withfield size for both luminance and chromatic perturbations,and the effect of field size is more pronounced at 900 than at9 Td. However, the effects of field size on the shape of the

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Fig. 5. Data and theoretical functions for detection of luminance perturbations by observer TU. Data were gathered at two mean luminances:900 Td (left) and 9 Td (right). Predictions from the analytic impulse response functions are shown as smooth curves. Modulation sensitivityis shown in the top panels as a function of frequency (hertz) for field sizes of 80 (squares) and 0.50 (circles). Analytic impulse responsefunctions derived from modulation-sensitivity data are shown in the middle panels, with response amplitude plotted as a function of time (inmilliseconds) from response onset, for field sizes of 80 (dashed curves), 2° (solid curves), and 0.50 (dotted curves). Pulse-detection data andthreshold-duration functions predicted by the impulse response functions are shown in the bottom panels; threshold pulse-modulation depth isplotted as a function of pulse duration (msec) for field sizes of 80 (squares), 20 (circles), and 0.50 (triangles). Threshold-duration functionsfrom the analytic impulse response functions are shown as smooth curves for field sizes of 80 (dashed curves), 20 (solid curves), and 0.50 (dottedcurves).

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luminance temporal contrast-sensitivity functions are dif-ferent for the two observers: increase in field size increasesthe bandpass characteristics of the temporal contrast-sensi-tivity functions at both luminance levels for subject TU (Fig.5), while for subject WS the bandpass characteristics changelittle with field size. For chromatic modulation, the effects

of field size are similar for both observers (Figs. 7 and 8). At900 Td, sensitivity at all frequencies increases as field size isincreased from 0.50 to 8°, giving a vertical shift of the tempo-ral contrast sensitivity functions by more than 0.5 log unit.At 9 Td the primary effect of field size is to increase thesensitivity to high frequencies.

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The parameters for the analytic impulse response func-tions are given in Table 3. Similar patterns are seen forchromatic and luminance impulse response functions atboth 9 and 900 Td. Increase in field size tends to increasethe amplitudes of both filters, an effect that increases with

mean luminance. A bimodality is seen in the 900-Td chro-matic impulse response functions for all three field sizes andin the 8° chromatic impulse response function at 9 Td.

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field sizes. Data and predictions are shown in Figs. 5-8. Several features evident in the temporal contrast-sensitiv-The vertical scaling factors used are given in Table 1. For ity functions and impulse response functions can also beluminance pulses, the predictions fit the data well (except noted in the pulse-detection data. Above 1 Hz, both lumi-for the nonmonotonicity at 900 Td). For chromatic pulses nance and chromatic temporal contrast-sensitivity func-the fits are reasonable except for the 80 data, where the tions show an increase in sensitivity with mean luminancesensitivity at long durations is greater than predicted. (reflected in the impulse response functions as an increase in

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Filter 1 Filter 2 Filter 1 Filter 2 Filter 3ci c2 to ci c2 to c3 ti

Subject (Hz) A (Hz) (msec) B Subject (Hz) A (Hz) (msec) B (Hz) (msec) C

900 Td 8°TU 27.5 3110 24.2 24 2490 TU 14.0 892 3.9 36 434 27.5 12 1450WS 24.4 3930 25.2 25 3560 WS 13.9 1410 4.0 21 100 24.4 18 1070

900 Td, 2°TU 21.6 2100 17.1 24 1520 TU 8.5 308 6.7 171 135 21.6 9 801WS 18.8 1520 16.7 22 1030 WS 7.5 379 5.0 153 170 18.8 5 705

900 Td, 0.50TU 21.8 731 19.2 21 442 TU 10.6 170 8.5 141 87 21.8 10 129WS 21.5 676 19.2 22 467 WS 9.6 188 12.9 140 32 21.5 10 150

9 Td, 8°TU 15.4 1220 9.6 34 855 TU 8.8 214 2.5 150 100 15.4 60 164WS 13.9 1090 9.9 13 410 WS 8.0 276 4.7 173 145 13.9 70 189

900 Td, 2°TU 12.1 598 7.4 36 250 TU 4.1 241 - - - - - -WS 10.9 521 8.2 36 249 WS 5.9 191 4.3 177 31 - - -

900 TD, 0.5°TU 13.1 385 12.9 58 228 TU 5.3 160 3.8 259 12 - - -WS 10.1 592 6.4 60 205 WS 4.7 156 3.3 297 15 - - -

a Generated as the difference between five-stage minimum phase filters. Terms are as in Table 2.

response amplitude); this is reflected in the pulse-detectiondata as consistently lower thresholds at 900 than at 9 Td. At900 Td, increases in field size tend to give increased sensitiv-ity at all durations, while the 9-Td data show less clearseparation with increasing field size; the pulse-detectiondata also show a greater increase in sensitivity with field sizeat 900 than at 9 Td. The individual differences observed inthe luminance temporal contrast-sensitivity functions arealso evident in the pulse-detection data. For the luminancetemporal contrast-sensitivity functions, subject TU showsan increase in sensitivity with increase in field size, whilesubject WS does not. The 9-Td data for luminance pulsesshow the same effect: for all durations, subject TU shows agreater increase in sensitivity with field size than does sub-ject WS.

DiscussionOur temporal contrast-sensitivity functions, impulse re-sponse functions, and pulse data for luminance modulationare similar to earlier data for human psychophysics1 andturtle cone respones.27 ,28 Our temporal contrast-sensitivityfunctions and pulse-detection data for chromatic modula-tion are also consistent with those of previous studies.4-8,11,12We have three new findings concerning the effect of meanluminance on chromatic modulation sensitivity. First, datafor 0.9 to 90 Td converge at high frequencies when plotted interms of amplitude sensitivity. Second, sensitivity to hightemporal frequencies increases faster with mean luminancethan sensitivity to low temporal frequencies. Finally, themagnitude of field-size effects is dependent on mean lumi-nance.

The analytic impulse response functions were generatedby fitting the digital impulse response functions using five-stage linear filters. The key factor is not the form of the

analytic filters but rather how closely they match the digitalimpulse response functions derived from modulation-sensi-tivity data. Similar (but not identical) mathematical func-tions have been used to fit psychophysical'8' 2 9 and physio-logical30 data. Following these earlier studies, we interpret-ed the first filter as representing an excitatory process andthe second filter as representing an inhibitory process. Theanalytic filters correspond closely to the digital filters (Fig.3), so the parameters A, B, C, to, and t, can be used tocharacterize the behavior of each filter. The digital impulsefunctions exactly fit the modulation-sensitivity data, whilethe analytic filters only approximate the data (smoothcurves in Figs. 5-8, upper panels). The degree to which thesmooth curves give poor fits to the modulation-sensitivitydata reflect the extent to which the modified Watson-Nach-mias model is unable to fit the digital impulse responsefunctions. These failures are primarily for chromatic mod-ulation under conditions that yield a luminance componentto the response, which as mentioned above are difficult tomodel.

The bimodal chromatic digital impulse response functionsat 900 Td suggest that chromatic modulation may be detect-ed in part by the mechanism that responds to luminanceperturbations. There are three sources that might intro-duce achromatic modulation in our chromatic stimulus:physical artifacts,7 temporal dependence of heterochromaticflicker photometry in this paradigm, and phase differencesbetween the cone responses. Physical artifacts could beproduced by poor alignment of the two chromatic sources,which might introduce a retinal mismatch of the images. Itis unlikely that these bimodal impulse response functionsreflect luminance artifacts due to retinal mismatch of theimages, since the chromatic thresholds above 6 Hz are nomore than two to three times smaller than the luminance

Swanson et al.


thresholds. In order for a luminance artifact to cause aluminance contribution to threshold, the artifact would haveto produce a luminance response to antiphase flicker thatwas one half to one third as large as the response obtainedwith in-phase modulation of the entire field. We had di-chromats make photometric matches at 8 Hz, and they wereable to eliminate flicker entirely by photometric matching.At this frequency, any significant luminance artifact due tomismatch of the retinal images would have been easily visi-ble for the dichromats. It is unlikely that the bimodal chro-matic impulse response function is the result of poor align-ment of the two chromatic sources. We defined chromaticstimuli as antiphase modulation of photometrically matchedsources, with a single high temporal frequency used to matchthe sources at each luminance level. However, it is recog-nized that the shape of the flicker photometric function isfrequency dependent.31' 32 Thus it is possible that in themidfrequency range a pure chromatic stimulus was not ob-tained. A third source of achromatic response to chromaticflicker might be that the cone types mediating the responsehave different phase responses to temporal modula-tion.23'33 -3 5 In this event, even if the flicker photometricmatch is independent of temporal frequency, pure chromat-ic modulation would not be obtained for the antiphase con-dition. It is possible that our data reflect both temporalvariations in flicker photometry and differences in thephases of the responses of the cone types mediating theresponse.

We compared our data for uniform field flicker with Kel-ly's31 analytical functions for the chromatic and luminancespatiotemporal surfaces at 68 cd/M 2 (about 465 effectivetrolands3 6). For luminance modulation our 90-Td data werefitted well by Kelly's luminance temporal contrast-sensitiv-ity functions for spatial frequencies of 4 to 5.7 cycles/deg.Similarly, our 90-Td chromatic data were fitted by Kelly'schromatic temporal contrast-sensitivity functions for spa-tial frequencies of 1 to 2.8 cycles/deg. Our data show thatfield-size effects are highly dependent on mean luminance inthe range 9 to 900 Td, so it is likely that the shape of thechromatic spatiotemporal surface will also depend on meanluminance.

The 80 field not only has a different spatial-frequencycontent from the 2° field but also permits stimulation ofperipheral retina. At high frequencies the peripheral retinais more sensitive than the fovea.37'38 This is consistent withthe effects of field size on our luminance impulse responsefunctions at 9 and 900 Td: the functions show shorter timeto peak and greater amplitude for the 80 field. The 900-Tdchromatic impulse response functions for the 8° field have agreater amplitude and a narrower bandwidth than the chro-matic impulse response functions; this pattern is what wouldbe expected if the 80 field increased the response of theluminance channel to chromatic flicker. Retinal inhomo-geneity (whether due to change in the relative population ofunderlying cone types and/or to changes in spectral sensitiv-ities accompanying changes in optical density with eccen-tricity39'4 0) suggests why the predictions give poor fits to the8° chromatic pulse data: there are several temporal mecha-nisms stimulated by the 8° field, so the linear systems theoryapproximation is inadequate.

The same effects of stimulus parameters were seen in theflicker data and the flash data, suggesting a common source.

What is most remarkable about the pulse-detection data isthat the impulse response functions derived from modula-tion sensitivity data are able to predict the pulse-detectiondata to within 0.2 log unit, using a simple peak-detectormodel. The pulse-detection data are plotted in terms ofmodulation sensitivity rather than amplitude sensitivity, forwhich the 9- and 900-Td data sets would be separated by 2log units; over such a large range, a 0.2-log-unit variation issmall. Thus effects of luminance and field size on detectionof flicker and flashes are not only qualitatively similar butthey are also quantitatively similar. The overall quality ofthe fits from a peak detector indicates that the impulseresponse functions do indeed reflect the underlying tempo-ral processes.

CONCLUSIONS

We have studied the effects of mean luminance and field sizeon sensitivity to chromatic and luminance temporal pertur-bations and have predicted pulse-detection thresholds fromimpulse response functions derived from modulation-sensi-tivity functions. The effects of field size and mean lumi-nance were similar for both modulation sensitivity andpulse-detection thresholds, with either chromatic or lumi-nance perturbations. In general, the magnitude of field-sizeeffects was dependent on mean luminance. For each experi-mental condition, the temporal dependence of pulse-detec-tion data was predicted by a peak detector model using animpulse response function derived from modulation-sensi-tivity data; analytic forms for the impulse response func-tions were produced by differences of linear filters. Thesepredictions fit the data well except for a nonmonotonicity inthresholds for the 900-Td luminance pulses.

ACKNOWLEDGMENTS

This research was supported in part by National Eye Insti-tute research grants EY00901 and EY07010 to J. Pokornyand by Grant in Aid for Scientific Researches no. 61510055,1986, from the Japanese Ministry of Education to T. Ueno.

* Current address and address for reprints, Retina Foun-dation of the Southwest, Presbyterian Medical Center, Suite414, 8230 Walnut Hill Lane, Dallas, Texas 75231.

REFERENCES AND NOTES

1. Reviewed by A. B. Watson, "Temporal sensitivity," in SensoryProcesses and Perception, Vol. I of Handbook of Perceptionand Human Performance, K. R. Boff, L. Kaufman, and J. P.Thomas, eds. (Wiley, New York, 1986), Chap. 6.

2. Reviewed by M. Ikeda, "Temporal impulse response," VisionRes. 26, 1431-1440 (1986).

3. H. deLange, "Research into the dynamic nature of the humanfovea-cortex systems with intermittent and modulated light. I.Attenuation characteristics with white and colored light." J.Opt. Soc. Am. 48, 777-784 (1958).

4. P. L. Walraven, H. J. Leebeek, and M. A. Bouman, "Somemeasurements about the fusion frequency of colors," Opt. Acta5, 50-54 (1958).

5. D. Regan and C. W. Tyler, "Some dynamic features of colourvision," Vision Res. 11, 1307-1324 (1971).

6. D. H. Kelly and D. van Norren, "Two-band model of hetero-chromatic flicker," J. Opt. Soc. Am. 67, 1081-1091 (1977).

Swanson et al.


7. J. J. Wisowaty, "Estimates for the temporal response character-istics of chromatic pathways," J. Opt. Soc. Am. 71, 970-977(1981).

8. V. C. Smith, R. W. Bowen, and J. Pokorny, "Threshold tempo-ral integration of chromatic stimuli," Vision Res. 24, 653-659(1984).

9. Early-literature reviewed by J. L. Brown, "Flicker and intermit-tent stimulation," in Vision and Visual Perception, C. H. Gra-ham, ed. (Wiley, New York, 1965), Chap. 10.

10. A. Gorea and C. W. Tyler, "New look at Bloch's law for con-trast," J. Opt. Soc. Am. A 3, 52-61 (1986).

11. G. J. C. van der Horst, "Chromatic flicker," J. Opt. Soc. Am. 59,1213-1217 (1969).

12. C. Noorlander, M. J. G. Heuts, and J. J. Koenderink, "Influenceof the target size on the detection of threshold for luminanceand chromaticity contrast," J. Opt. Soc. Am. 70, 1116-1121(1980).

13. C. F. Stromeyer, G. R. Cole, and R. E. Kronauer, "Second-siteadaptation in the red-green chromatic pathways," Vision Res.25, 219-237 (1985).

14. G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York,1982).

15. R. W. Nygaard and T. E. Frumkes, "Calibration of the retinalluminance provided by Maxwellian views," Vision Res. 22,433-434 (1982).

16. Heterochromatic flicker photometry was performed at the high-est available frequency for which the subject could detect flick-er, and modulation was set to a value that allowed the subject tomake a precise setting. In general, these frequencies variedwith mean luminance: 20-27 Hz at 900 Td, 10-13 Hz at 90 Td,8-10 Hz at 9 Td, and 8 Hz at 0.9 Td. For the 0.50 field, the 900-Td settings were made at 13-16 Hz, and for the 80 field, the 9-Td settings were made at 10-16 Hz.

17. D. G. Stork and D. S. Falk, "Visual temporal impulse responsesfrom flicker sensitivities," J. Opt. Soc. Am. A 4, 1130-1135(1987). The computer program was kindly provided by DavidStork.

18. A. B. Watson and J. Nachmias, "Patterns of temporal interac-tion in the detection of gratings," Vision Res. 17, 893-902(1977).

19. J. J. Wisowaty and R. M. Boynton, "Temporal modulationsensitivity of the blue mechanism: measurements made with-out chromatic adaptation," Vision Res. 20, 895-909 (1980).

20. D. H. Kelly, "Visual responses to time-dependent stimuli: I.Amplitude sensitivity measurements," J. Opt. Soc. Am. 51,422-429 (1961).

'21. K. Uchikawa and M. Ikeda, "Temporal integration of chromaticdouble pulses for detection of equal-luminance wavelengthchanges," J. Opt. Soc. Am. A 3, 2109-2115 (1986).

22. The Stork-Falki7 impulse-response functions are computed forminimal phase filters. Watson and Nachmias18 derived theirimpulse response function model by considering only the ampli-tude spectrum, not the phase spectrum. For a few parameterconditions our modified Watson-Nachmias model producessharp irregularities in the temporal contrast-sensitivity func-tions because of phase interactions of the component filters.The temporal contrast-sensitivity function data do not showlocal minima; therefore we smoothed the predictions by takingthe envelope of predictions with parameter to varying by ±5msec. This procedure was used for the following temporalcontrast-sensitivity functions: in series I, the 90-Td luminancetemporal contrast-sensitivity function and the 900-Td chro-

matic temporal contrast sensitivity function; in series II, the0.50 and 80 temporal contrast-sensitivity functions for lumi-nance modulation at 9 and 900 Td.

23. Reviewed by D. T. Lindsey, J. Pokorny, and V. C. Smith,"Phase-dependent sensitivity to heterochromatic flicker," J.Opt. Soc. Am. A 3, 921-927 (1986).

24. J. A. J. Roufs, "Dynamic properties of vision. IV. Thresholdsof decremental flashes, incremental flashes and doublets inrelation to flicker fusion," Vision Res. 14, 831-851 (1974).

25. D. H. Kelly and R. E. Savoie, "Theory of flicker and transientresponses. III. An essential nonlinearity," J. Opt. Soc. Am. 68,1481-1490 (1978).

26. J. Krauskopf, "Discrimination and detection of changes in lu-minance," Vision Res. 20, 671-677 (1980).

27. T. D. Lamb, "Properties of cone photoreceptors in relation tocolor vision," in Central and Peripheral Mechanisms of ColorVision, D. Ottoson and S. Zeki, eds. (Macmillan, London, 1985),pp. 151-164.

28. S. J. Daly and R. A. Normann, "Temporal information process-ing in cones: effects of light adaptation on temporal summa-tion and modulation," Vision Res. 25, 1197-1206 (1985).

29. J. R. Bergen and H. R. Wilson, "Prediction of flicker sensitiv-ities from temporal three-pulse data," Vision Res. 25, 577-582(1985).

30. D. A. Baylor and A. L. Hodgkin, "Reconstruction of the electri-cal responses of turtle cones to flashes and steps of light," J.Physiol. (London) 242, 759-791 (1974).

31. D. H. Kelly, "Spatiotemporal variation of chromatic and achro-matic contrast thresholds," J. Opt. Soc. Am. 73, 742-750 (1983).

32. W. B. Cushman and J. Z. Levinson, "Phase shift in red andgreen counterphase flicker at high frequencies," J. Opt. Soc.Am. 73, 1557-1561 (1983).

33. P. K. Kaiser, M. Ayama, and R. L. P. Vimal, "Flicker photome-try: residual minimum flicker," J. Opt. Soc. Am. A 3, 1989-1993 (1986).

34. We [W. H. Swanson, V. C. Smith, J. Pokorny and R. L. P. Vimal,"Phase shifts for heterochromatic flicker at intermediate fre-quencies," J. Opt. Soc. Am. A 2(13), P40 (1985)] extended thestudy of Lindsey et al.

2 3 and found that phase shifts at 900 Tdare larger than those at 90 Td.

35. C. F. Stromeyer, G. R. Cole, and R. E. Kronauer, "Chromaticsuppression of cone inputs to the luminance flicker mechan-ism," Vision Res. 27, 1113-1137 (1987).

36. Kelly's mean luminance of 68 cd/M2 results in an estimatedeffective retinal luminance of 466 Td. See Y. Le Grand, Light,Colour and Vision, 2nd ed., translated by R. W. G. Hunt, J. W.T. Walsh, and F. R. W. Hunt (Chapman and Hall, London,1968). Given the difference in mean luminance, field size, spa-tial structure, and subjects, the similarity between our 90-Tddata and Kelly's 466-Td data does not imply any contradictionbetween our calibration and Kelly's.

37. C. W. Tyler, "Analysis of visual modulation sensitivity. II.Peripheral retina and the role of photoreceptor dimensions," J.Opt. Soc. Am. A 2, 393-398 (1985).

38. J. Rovamo and A. Raninen, "Critical flicker frequency and M-scaling of stimulus size and retinal illuminance," Vision Res. 24,1127-1131 (1984).

39. J. Pokorny, V. C. Smith, and S. Starr, "Variability of colormixture data-II. The effect of viewing field size on the unitcoordinates," Vision Res. 16, 1095-1098 (1976).

40. J. Pokorny and V. C. Smith, "Effect of field size on red-greencolor mixture equations," J. Opt. Soc. Am. 66, 705-708 (1976).

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Temporal modulation sensitivity and pulse-detection thresholds …€¦ · Temporal modulation sensitivity and pulse-detection thresholds for chromatic and luminance perturbations