Vol. 7, No. 12/December 1990/J. Opt. Soc. Am. A 2223
Luminance and chromatic modulation sensitivity of macaqueganglion cells and human observers
Barry B. Lee
Department of Neurobiology, Max Planck Institute for Biophysical Chemistry, D-3400 Gbttingen, FederalRepublic of Germany
Joel Pokorny and Vivianne C. Smith
Eye Research Laboratories, The University of Chicago, Chicago, Illinois 60637
Paul R. Martin* and Arne Valbergt
Department of Neurobiology, Max Planck Institute for Biophysical Chemistry, D-3400 Gottingen, FederalRepublic of Germany
Received October 12, 1989; accepted April 24, 1990
We measured the sensitivity of macaque ganglion cells to luminance and chromatic sinusoidal modulation. Phasicganglion cells of the magnocellular pathway (M-pathway) were the more sensitive to luminance modulation, andtonic ganglion cells of the parvocellular pathway (P-pathway) were more sensitive to chromatic modulation. Withdecreasing retinal illuminance, phasic ganglion cells' temporal sensitivity to luminance modulation changed in amanner that paralleled psychophysical data. The same was true for tonic cells and chromatic modulation. Takentogether, the data suggest strongly that the cells of the M-pathway form the physiological substrate for detection ofluminance modulation and the cells of the P-pathway the substrate for detection of chromatic modulation.However, at high light levels, intrusion of a so-called luminance mechanism near 10 Hz in psychophysical detectionof chromatic modulation is probably due to responses in the M-pathway, arising primarily from a nonlinearity ofcone summation. Both phasic and tonic ganglion cells responded to frequencies higher than can be psychophysical-ly detected. This suggests that central mechanisms, acting as low-pass filters, modify these cells' signals, thoughthe corner frequency is lower for the P-pathway than for the M-pathway. For both cell types, the response phase atdifferent frequencies was consistent with the cells' description as linear filters with a fixed time delay.
INTRODUCTION
If the luminance of a stimulus is modulated in time, sensitiv-ity of the human observer is maximal at approximately 10Hz.",2 For chromatic modulation between two lightsmatched in luminance by heterochromatic flicker photome-try, sensitivity is maximal at a low frequency and falls off atfrequencies greater than 5 Hz.1-3 Such differences in tem-poral characteristics led to the proposal that separable psy-chophysical mechanisms are involved in the detection ofchromatic and luminance modulations.4
In the visual pathway of the primate, there exist two maincell systems. The parvocellular pathway (P-pathway) con-tains tonic wavelength-opponent retinal ganglion cells thatproject to the parvocellular layers of the lateral geniculatenucleus. The majority of P-pathway cells receive antago-nistic input from medium-wavelength-sensitive (M) andlong-wavelength-sensitive (L) cones. The minority receiveinput from short-wavelength-sensitive (S) cones opposed bysome combination of M and L cones. Phasic, nonopponentganglion cells project to the magnocellular (M-pathway) lay-ers of the geniculate nucleus.5'10 M-pathway cells receivecombined input from M and L cones to both center andsurround.
Although both M-pathway and P-pathway cells are re-sponsive to both luminance and chromatic modulations,previous research suggests strongly that the M-pathway
forms the physiological substrate of heterochromatic flickerphotometry. 1 These cells are relatively unresponsive tochromatic modulation at equal luminance but may display aresidual frequency-doubled response attributed to a nonlin-earity of M- and L-cone summation.'2 With luminancemodulation, M-pathway cells are much more responsivethan are P-pathway cells, whereas P-pathway cells are themore sensitive to chromatic modulation.' 3- 7 This differen-tial sensitivity led to the proposal that the mechanisms re-sponsible for psychophysical detection of luminance andchromatic modulations have as a physiological substrate theM-pathway and the P-pathway, respectively. 7"18
Additional evidence for this hypothesis may be gained byshowing that, on changing stimulus conditions, each path-way shows alterations in sensitivity that parallel the psycho-physical changes observed. For example, the effect of de-creasing retinal illuminance level is different for luminanceand chromatic modulation.3 For luminance modulation,there is a loss of sensitivity only at high temporal frequen-cies, the contrast-sensitivity function becoming more lowpass in shape. For chromatic modulation, contrast sensitiv-ity at all frequencies diminishes with decreasing retinal illu-minance. In the experiments reported here, we measuredthe sensitivity of M-pathway and P-pathway cells to lumi-nance and chromatic modulations at retinal illuminancesbetween 2 and 2000 trolands (Td) and found results consis-tent with the hypothesis that, under most conditions, M-
2224 J. Opt. Soc. Am. A/Vol. 7, No. 12/December 1990
pathway and P-pathway cells underlie the detection of lumi-nance and chromatic modulations, respectively.
Temporal-contrast-sensitivity functions can be used toderive impulse-response functions, either by assuming somesort of filter model or by numerical methods.3"19 Such anal-yses can predict phase. Psychophysically phase is indeter-minate, but the phase of a cell response is measurable direct-ly. We assess this approach in terms of its ability to describethe phase of the cell responses.
METHODS
Ganglion-cell activity was recorded from the retinas of juve-nile macaques (Macaca fascicularis). After initial intra-muscular injection of ketamine, anesthesia was maintainedwith halothane or isofluorane in a 70%:30% N20:0 2 mixture(1-2% during surgery and 0.2-1% during recording). Localanesthetic was applied to points of surgical intervention.The electroencephalogram and the electrocardiogram werecontinuously monitored as a control for anesthetic depth.Muscular relaxation was maintained by intravenous infu-sion of gallamine triethiodide (5 mg/kg/h) together withapproximately 3 mL/h of dextrose Ringer. End-tidal PCO2was kept near 4% by adjusting the rate and depth of ventila-tion, and body temperature was maintained near 37.5 deg.
A contact lens with the internal radius matched to thecorneal curvature was used to focus the eye on a backprojec-tion tangent screen that was 57 cm from the animal. Thescreen was used for mapping receptive fields and for project-ing stimuli for cell classification. Positions of the fovea andthe optic disk were ascertained with the aid of a funduscamera. Clarity of the optic media was checked frequently,and, if the smaller retinal vessels could no longer be recog-nized, recording from that eye was terminated and the sec-ond eye prepared. On completion of recording the animalwas sacrificed with an overdose of barbiturate.
Details of the recording technique and the cell classifica-tion are given elsewhere.'7 Briefly, after extracellular activ-ity of a ganglion cell was isolated, the cell type was deter-mined by using flashed spots. Cell responses to stimuli ofdifferent, equiluminous colors were then recorded as an aidto cell classification. We recorded ganglion cells from para-foveal retina, typically at eccentricities of between 3 and 10deg.
Equipment and CalibrationStimuli were generated in a two-channel Maxwellian-viewsystem similar to that described elsewhere,3 except that thelight-emitting diodes used had dominant wavelengths of 553and 636 nm, with half-widths at half-height of 18 and 23 nm,respectively. Colorimetric purity was greater than 97%.With changes in intensity achieved by frequency modula-tion of a constant-amplitude pulse train, a high degree oflinearity is realized. Stimulus waveforms were generated bya computer (for 19.6 Hz or less, 128 values per cycle; forhigher frequencies, 64 values per cycle) through 12-bit digi-tal-to-analog converters. The image of the diodes had adiameter of approximately 3 mm in the plane of the pupil.
The two diodes were adjusted to equal luminance by usingheterochromatic flicker photometry of one of the authorswhose luminosity function matched closely that of the Juddobserver.2 0 We confirmed this calibration by placing thefront lens of a Photo Research scanning radiometer in the
plane of the pupil and comparing the luminances of the twodiodes. The time-averaged chromaticity of the field wasapproximately 595 nm. For luminance modulation, the di-odes were modulated in phase. For chromatic modulation,the diodes were modulated in counterphase. Frequenciesavailable ranged from 0.61 to 78.1 Hz. Field stops permittedthe adjustment of field size; the maximum stimulus diame-ter was approximately 25 deg.
Retinal illumination was measured as described byWestheimer.2' In view of the smaller size of the monkeyeye, one would expect retinal illuminance in the macaque tobe approximately 1.7 times that in humans.2 3 Time-aver-aged maximal illuminance was approximately 2000 humanTd or 3400 monkey Td. For convenience, values cited in thetext and the figures are in human trolands; monkey trolandsare cited in the figure legends if appropriate.
Sensitivity has been plotted in terms of physical diodemodulation. With amplitude sensitivity, a value of 1 (100) isequivalent to a 2000-Td modulation of each diode (peak topeak), a value of 10' to 200-Td modulation, and so forth.Modulation sensitivity has been calculated as for Michelsoncontrast. In the case of luminance modulation this is (Lmax- Lmin)/(Lmax + Lmin), which is the same for both diodes.For chromatic modulation, contrast is calculated in a similarmanner, as (max - Imin)/(Imax + Imin), where Imax and Imincorrespond to the maximum and minimum excursions inintensity of each diode. This gives the same value for bothdiodes. Chromatic modulation of 100% corresponded toapproximately 65% cone contrast in the M cone and 23%cone contrast in the L cone, these values being derived fromthe Smith-Pokorny cone fundamentals 2 0 as for Michelsoncontrast values described above.
The macaque luminosity function has not been deter-mined with precision, though available evidence suggeststhat it is similar to that of humans,23 consistent with theresemblance between the cone pigment spectra of the twospecies.24' 25 Individual phasic cells differ to some extent intheir spectral sensitivity."",1 6 However, for all cells we usedthe diode luminance calibration described above, in order toparallel the behavioral situation in which chromatic modula-tion presumably evokes activity from a population of M-pathway cells showing some spectral sensitivity variability.
Procedure: Physiological MeasurementsAfter isolation of a ganglion cell's activity, the cell's recep-tive-field location was plotted on the tangent screen, and theMaxwellian view stimulator adjusted to be centered on thepupil. The stimulator was then rotated about the pupiluntil its optic axis was approximately in line with the recep-tive field. Precise alignment of the stimulus on the recep-tive-field center was achieved by modulating a small spot(0.6 deg) and adjusting its position in the object plane of theoptical system in order to give maximal response. In theresults reported here, the spot size was then enlarged (4.6deg) to encompass both the center and the surround of thereceptive field.
The computer controlling the stimulus also averaged andstored cell responses. At each temporal frequency, activitywas averaged at a range of contrasts between 1.56% and 98%in 0.15-log-unit steps, and approximately 6 sec of data werecollected for each contrast level in an interleaved manner.At each level of retinal illuminance, an interleaved sequenceof frequencies was used to measure the temporal-contrast-
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Vol. 7, No. 12/December 1990/J. Opt. Soc. Am. A 2225
sensitivity function, one such run taking approximately 20-30 min. Neutral-density filters (Schott) were used to de-crease retinal illuminance from 2000 Td to 2, 20, or 200 Td.Some minutes were permitted to elapse after changing adap-tation level, which was decreased in 1-log-unit steps. Al-though anesthetics such as halothane have been reported todelay dark adaptation,2 6 our adaptation levels provided, atmost, a 1% bleach, so that kinetic effects on pigment regener-ation can be neglected.
Cell responses were stored with a resolution of 32 or 64bins per cycle (the former at frequencies of greater than 19.8Hz) and Fourier analyzed, and measures of cell sensitivitywere derived as described below.
Procedure: Psychophysical MeasurementsTo provide psychophysical data at a comparable retinal lo-cus with that of the cells recorded, observers viewed a 4.6-deg stimulus with its center 5 deg nasal to a fixation point.The head was stabilized with a bite bar. Subjects wereencouraged to make vertical eye movements of a few degreesto prevent fading of the flicker. Each observer adjusted the636-nm diode to match the 553-nm diode by flicker photom-etry. Temporal contrast sensitivity to luminance or chro-matic modulation was then measured by a method of adjust-ment. Starting at high modulation, buttons permitted asubject to increase or decrease modulation depth in 0.02-log-unit steps. After setting threshold, the observer proceededto the next frequency, frequencies being presented in semi-random order. For most data, repeat measurements weremade in two experimental sessions. Data reported aremeans of two estimates on each of three subjects (two male,one female) with normal color vision.
RESULTS
We measured cell responses at several levels of retinal illu-minance. We first describe the methods adopted to analyzeresponses and measure cell sensitivity and how resultingtemporal-contrast-sensitivity curves were derived. Wethen attempted to relate these data to detection thresholds.
Cells were classified as belonging to the parvocellular ormagnocellular systems by using a battery of tests, not just onthe time course of responses. These included measurementof achromatic contrast sensitivity and responses to alter-ations between a white field and equal-luminance lights ofdifferent dominant wavelengths. Since we recorded fromganglion cells, it might be argued that our classification ofcells into phasic and tonic did not necessarily correspond tomembership of the M-pathway or P-pathway. We are, how-ever, confident that this was the case. The visual stimuliused in cell classification have previously proven effective indistinguishing between cells of the parvocellular and magno-cellular layers of the lateral geniculate nucleus.9 4, 5,27 Wewill refer here to cells putatively belonging to the M-path-way as phasic ganglion cells and cells belonging to the P-pathway as tonic ganglion cells. The terms M-pathway andP-pathway will be used for discussing the properties of thesetwo cell systems as a whole.
Measurement of Cell SensitivityUnder each condition, cell responses were recorded at aseries of different contrasts, the amplitude of these respons-es then being derived from a Fourier analysis of peristimulustime histograms. Typical examples of the relationship be-tween response and contrast are shown in Fig. 1 for a phasic
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Fig. 1. Amplitude of first harmonic from Fourier analysis of peristimulus time histograms at three temporal frequencies: A, on-center phasicganglion cell as a function of luminance modulation; B, tonic ganglion cell for luminance and chromatic modulation. Modulation wascalculated as for Michelson contrast as described in the methods section. Solid curves indicate Naka-Rushton functions fitted by using least-squares nonlinear regression, provided that a criterion of 10 impulses/sec was exceeded. They describe the data satisfactorily.
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2226 J. Opt. Soc. Am. A/Vol. 7, No. 12/December 1990
Fig. 2. First- and second-harmonic components of phasic on-center cell response at two frequencies: A, chromatic-modulation function; B,luminance-modulation function. In the former case, the second harmonic is dominant; in the latter, the first harmonic. Solid curves areNaka-Rushton fitted curves.
cell for luminance modulation and for a tonic cell for chro-matic and luminance modulation. It should be noted that,for luminance modulation, luminance contrast is the abscis-sa, while for chromatic modulation physical contrast, interms of modulation of each diode, is used. Three temporalfrequencies are displayed for each condition.
Naka and Rushton2 8 showed that the Michaelis-Mentenfunction with an exponent of unity can be used to describethe radiance-response functions of individual neurons. Kap-lan and Shapley2 9 found responses of M-pathway and P-pathway cells as a function of luminance contrast to be wellfitted by this function. We also found that this functionfitted our measurements well at all temporal frequenciesand for both luminance and chromatic modulation. Since afirst-harmonic amplitude of 0-4 impulses/sec was typicallypresent in the absence of stimulation, curves were made tooriginate at 2 impulses/sec, so that the function used was
R(c) - 2 = Rmc/(c + b), (1)
where c is contrast, Rm is maximal response, and b is thecontrast evoking a half-maximal response. Curves were fit-ted on the basis of Eq. (1) by using a least-squares criterionand are drawn in each case. The curves provide a reason-able description; both R,, and b vary with frequency. Pro-vided that the first harmonic reached a criterion level of 10
impulses/sec, such a curve was fitted for each cell and condi-tion. In approximately 80% of cases (n = 1345) 95% or moreof variance could be accounted for by using this fitting pro-cedure, exceptions largely being instances for which re-sponses were weak.
For the phasic cell (Fig. 1A) at 9.8 and 39.1 Hz, responseamplitude rises steeply initially but then tends toward anasymptote. Responses are much weaker at low frequencies.For tonic cells, less response saturation was observed' 3'2 9
(Fig. B). Temporal-contrast-sensitivity curves for chro-matic modulation were low pass, and, for luminance modula-tion, they were bandpass; this difference can be seen oncomparing the temporal frequencies shown in Fig. B. Withluminance modulation at 1.22 Hz the criterion of 10 im-pulses/sec was not reached.
For responses to chromatic modulation in phasic cells,second-harmonic responses were of significant amplituderelative to the response at the fundamental frequency. InFig. 2 we compare the relationship between these two com-ponents on the modulation for one such cell. For chromaticmodulation, at both 1.22 and 9.76 Hz the second-harmoniccomponent is larger; such responses at twice the modulationfrequency may be attributable to a nonlinearity of M- and L-cone summation.'2 For comparison, we show also the first-and second-harmonic components to luminance modula-tion. At 1.22 Hz little second harmonic is present, whereas
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at 9.8 Hz it becomes significant only a higher contrasts, andexamination of the original peristimulus time histogramssuggests that it was associated with distortion of the funda-mental rather than a frequency-doubled response per se.Curves were fitted in the same way as for Fig. 1 and provideda reasonable account of the data. It should be noted thatthe magnitude of frequency-doubled responses is directlyrelated to the IM - LI cone-excitation difference and thatthe responses are thus vigorous for the red-green modula-tion used here. For chromatic modulation along a tritano-pic confusion line, they are absent.'2
We would stress that the harmonic composition of re-sponses of phasic cells to chromatic modulation was vari-able, although significant second-harmonic componentswere always present for the pair of wavelengths used here.'2
We observed some cells for which the second-harmonic com-ponent was dominant at only some frequencies, or for whichthe ratio of first- to second-harmonic components variedwith contrast. For some cells, the first-harmonic compo-nent was substantial at all frequencies. This variabilitymay originate from two sources (at least). First, the sur-round mechanism of phasic cells may exhibit opponency at
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low temporal frequencies,3 0 resulting in a response at thefundamental frequency. Second, there is some variabilityin spectral sensitivity among phasic cells, which may beattributable to a variation in the weighting of M- and L-coneinputs."',3' Such variation would also lead to variation inthe relative magnitude of first- and second-harmonic com-ponents. In averaging phasic-cell sensitivities to chromaticmodulation, we used the component with the higher value.
A 20-impulses/sec modulation in firing (i.e., 10-impulses/sec first-harmonic amplitude) has been used elsewhere'7 as ameasure of cell sensitivity. This cell response correspondsto 4-10 times the amplitude of the first Fourier componentobtained on analysis of maintained activity. Instead of sen-sitivity estimates obtained by direct extrapolation from thedata,' 7 curves fitted as for Fig. 1 appear to provide a satisfac-tory description of the relationship between contrast andresponse. Use of parameters from these curves permitscalculation of contrast gain'3' 29 as well as the contrast neces-sary to generate some criterion response. Contrast gain isdefined as the slope of the initial section of the contrast-response function Rm/b and is expressed as impulses persecond/(percent modulation). If an arbitrary cell threshold
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Frequency (Hz )Fig. 3. Sensitivity of ganglion cells to luminance modulation, expressed in terms of amplitude sensitivity [4000/(Lm£ - Lmin)] and Michelsoncontrast sensitivity and contrast gain, as a function of frequency at four retinal illuminances: A, phasic cells; B, tonic cells. Sensitivity was esti-mated from the modulation required to evoke a 20-impulses/sec modulation, that is, 10-impulses/sec in first harmonic. In the upper panels, avalue of unity (100) represents a modulation amplitude at criterion of 4000 Td (peak to peak). In the lower panels, sensitivity is expressed asthe luminance contrast required to reach the criterion and also as contrast gain; this is the slope of the initial segment of the curves in Fig. 1.Note that retinal illuminance in the monkey eye is probably approximately 1.7 times the values quoted here. Means and standard deviationswere derived from usually at least 10, and always at least 5, cells. All cells measured under a given condition were included. Tonic cells rarelyresponded to luminance modulation at 2 or 20 Td (imp, impulses).
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2228 J. Opt. Soc. Am. A/Vol. 7, No. 12/December 1990
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Fig. 4. Sensitivity of ganglion cells to chromatic modulation, expressed in terms of amplitude sensitivity (top) and modulation sensitivity(bottom), as a function of frequency at retinal illuminances indicated: A, phasic cells; B, tonic cells. In responses of most phasic cells the sec-ond harmonic was dominant; we used for sensitivity estimation whichever component (first or second) was the larger. Sensitivities werederived as in Fig. 3, except that they are expressed in terms of diode modulation instead of contrast sensitivity. Second-harmonic responses ofphasic cells were small at 2 and 20 Td. Monkey troland values are approximately 1.7 times the values shown here (imp, impulses).
is defined as the contrast evoking a criterion response Rthr,then the threshold is given byRthr/(RI/b), provided that Rtlris small in comparison with R.. This was generally the case.The criterion level used, a 10-impulses/sec first-harmonicamplitude, was on average 5-15% of R,. In Figs. 3 and 4 theordinates show sensitivity in terms of the threshold criterionand in terms of contrast gain.
Cell Sensitivity as a Function of FrequencySensitivity of 27 phasic and 25 tonic cells to luminance andchromatic modulation was measured. Not all cells weretested at all frequencies at all levels of retinal illuminance.Values depicted in Figs. 3 and 4 represent averages fromusually more than 10, and always more than 5, cells. Allcells recorded were included in the analysis, with the excep-tion of those tonic cells receiving S-cone input. No substan-tial difference was observed between on- and off-center pha-sic cells or between tonic cells with +M - L or +L - M coneinput, and data from these groups have been combined.
Figure 3 compares the sensitivity to luminance modula-tion of phasic and tonic cells at four levels of retinal illumi-nance. In the top panels amplitude sensitivity has beenused as the ordinate (points + 1 standard deviation) and inthe lower panels luminance contrast sensitivity and contrastgain have been used.
In all phasic cells at low frequencies, sensitivity remainedsimilar or showed a small increase as retinal illuminance wasdecreased. However, sensitivity to higher frequencies de-
creased, and curves became more low pass in shape, so thatin the amplitude plots the descending limbs of the curvestend to superimpose. It is noteworthy that at 200 and 2000Td cells responded to frequencies (as high as 80 Hz) substan-tially in excess of flicker-fusion frequencies observed psy-chophysically under similar conditions.
For tonic cells, luminance-modulation responses could beevoked at 200 and 2000 Td, although sensitivity was muchlower than for phasic cells. The response of tonic cells toachromatic modulation at 2 and 20 Td was weak, only 2 of 9cells tested reaching criterion at 100% luminance modula-tion. At 200 and 2000 Td, tonic-cell sensitivity remainedlow at first and then increased to a maximum at 10-20 Hz.This characteristic has been attributed to a center-surroundlatency difference.32' 33 At low frequencies, the opponentmechanisms are activated in phase and cancel each other; athigh frequencies a phase delay is present, and the vector sumof the opponent signals, which is now no longer in preciseantiphase, results in a more vigorous response.
Estimates of sensitivity to chromatic modulation areshown in Fig. 4. The top panels show amplitude sensitivityand the lower panels modulation sensitivity and gain, ex-pressed in terms of diode modulation. For tonic cells, sensi-tivity to chromatic modulation is little attenuated at lowtemporal frequencies, producing a low-pass characteristic.With chromatic modulation the opponent mechanisms actsynergistically, and a small phase delay between their sig-nals does not much affect the response, at least up to 20 Hz.32
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With decreasing retinal illuminance, a progressive decreasein sensitivity occurs, and there is an accompanying decreasein the maximum frequency that evokes a response. It isagain noteworthy that cells responded to chromatic modula-tion as high as 40 Hz at 2000 Td, which is a much higherfrequency than can be observed psychophysically underthese conditions.
Sensitivity of phasic cells to chromatic modulation is alsoshown. Phasic-cell sensitivity to chromatic modulation waslower than that of tonic cells and resembled in shape theirtemporal-contrast-sensitivity curves to luminance modula-tion.12 Data are shown for 200 and 2000 Td; at lower retinalilluminance, frequency-doubled responses were small or ab-sent.12 We noted in some phasic ganglion cells a response tochromatic modulation at 2 Td that might be attributable torod intrusion.
In terms of the modulation required to reach a response of20 impulses/sec, the cell sensitivities shown in Figs. 3 and 4are similar to those that we reported elsewhere.'7 Lumi-nance-modulation sensitivity is directly comparable. Interms of contrast gain, at 5 Hz, values are comparable withthose found on recording from S potentials in the lateralgeniculate nucleus.2 9 For chromatic modulation, compari-son must be in terms of cone contrast. Mean-diode-modu-lation sensitivity of tonic cells at 10 Hz, 2000 Td was 5.9%,and this corresponds to 1.4% modulation of the L cone and3.8% modulation of the M cone. These values are also com-parable with those reported previously.'7
A Luminance Modulation
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If compared with psychophysical sensitivity in the fovea,3
results in Figs. 3 and 4 are consistent with phasic cells'supporting detection of luminance modulation and with ton-ic cells' supporting detection of chromatic modulation. Toprovide a more direct comparison, we measured psycho-physical sensitivity in the parafovea.
Psychophysical Measurements in the ParafoveaAlthough much variation in psychophysical data with reti-nal eccentricity can be unified by taking the cortical magni-fication factor into account,3 4 variation in modulation sensi-tivity with eccentricity may not be simply explicable on thisbasis.3 536 Since detection thresholds in the fovea depend onstimulus size,3 it is uncertain to which foveal diameter a 4.6-deg stimulus in the parafovea best corresponds and whetherthe same scaling factor is appropriate for luminance andchromatic modulation. To provide psychophysical data ateccentricities comparable with those of the cellular measure-ments, we determined temporal-contrast-sensitivity func-tions, shown in Fig. 5, with a 4.6-deg spot centered 5 deg intothe peripheral retina. In the two top panels, amplitudesensitivity is plotted against frequency for luminance andchromatic modulation, and in the two lower panels the datahave been replotted in terms of modulation sensitivity.
For luminance modulation, these parafoveal data resem-ble those reported for 2-deg stimuli in the fovea.3 Withdecreasing retinal illuminance, functions become more lowpass. In the case of chromatic modulation, as with foveal
B Chromatic Modulation
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Fig. 5. Sensitivity of human observers expressed as in Figs. 3 and 4: A, luminance modulation; B, chromatic modulation. Shown are meansand standard deviations of 2-3 settings of three subjects. The arrow shows the characteristic inflection near 10 Hz in chromatic-modulation-sensitivity curves at 2000 Td.
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2230 J. Opt. Soc. Am. A/Vol. 7, No. 12/December 1990
data, sensitivity functions are low pass in shape. Modula-tion sensitivity decreases with decreasing illuminance, butthe effect is less marked than with 2-deg fields viewed fo-veally,3 and the results resemble more closely the human 0.5-deg data. A notch in the descending limb of the curve, seenat 10-20 Hz with foveal viewing, is also visible (arrow) in theparafoveal data presented here.
Comparison of Physiological and PsychophysicalMeasurementsFor luminance modulation, contrast-sensitivity curves forphasic cells clearly resemble the psychophysical data. Inboth, the bandpass character visible at 2000 Td becameprogressively more low pass as retinal illuminance was de-creased. Tonic-cell sensitivity to chromatic modulationalso resembles psychophysical data. Both sets of curves arepredominantly low pass in shape, and the sensitivity de-creases with the retinal illuminance level. However, thisdecrease is less rapid in the psychophysical than the physio-logical data. For both comparisons, cell cutoff frequenciesare higher than with psychophysical curves.
A modulation in firing of approximately 20 impulses/sechas been observed at contrast levels near the detectionthreshold for a human observer.' 7 However, comparisonsbetween psychophysical and physiological data are madedifficult by uncertainties in relating cell sensitivities to hu-man detection thresholds. Partly to avoid assumptions re-
garding so-called thresholds, one may employ another mea-sure, contrast gain, to describe cell sensitivity. 3
To compare human and cell sensitivities, we calculatedtheir ratio. Such ratios are thus relative values, which makeno assumption concerning cell thresholds. Figure 6A showsrelative sensitivities for luminance modulation. Sensitivityratios for phasic cells are clearly lower than those for toniccells. At 200 and 2000 Td this is so by a factor of 2-10, andthis factor would become larger as retinal illuminance de-creased further, because few tonic cells responded to lumi-nance modulation at 2 or 20 Td. Up to 20 Hz, adaptivebehavior and temporal-frequency tuning of phasic cells re-semble psychophysical data in that there is relatively littlechange in ratio with frequency or adaptation level. Thesedata are consistent with phasic cells' forming the physiologi-cal substrate for detection of luminance modulation.
Figure 6B shows a similar comparison for chromatic mod-ulation. For tonic cells, the sensitivity ratio remains con-stant until approximately 5 Hz with similar ratios (approxi-mately unity) as with phasic cells and luminance modula-tion. These data are consistent with the detection ofchromatic modulation having the tonic, P-pathway as itsphysiological substrate at these frequencies.
From Fig. 6B it can be seen that the ratio of sensitivity tothe chromatic modulation for phasic cells is higher than thatfor tonic cells at a low frequency but decreases until, near 10Hz, the sensitivity ratio is approximately unity. Such ratios
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Fig. 6. Ratio of psychophysical (psy) to physiological (phy) cell sensitivity for different cell types: A, luminance modulation; B, chromaticmodulation. The cell sensitivities used as a basis for the calculations were as in Figs. 3 and 4. For phasic cells and luminance modulation, thesensitivity in ratio is similar (close to unity) at all illuminances up to 20Hz. Above 20Hz, ratios fall steeply. The sensitivity ratio for tonic cellsis much higher and dependent on retinal illuminance, few tonic cells responding at 2 or 20 Td. For tonic cells and chromatic modulation, at lowfrequencies, ratios are close to unity up to 5 Hz. Near 10 Hz, ratios for second-harmonic responses for phasic cells reach a level (approximatelyunity) consistent with their participation in detection. The curves shown indicate characteristics of hypothetical filters that may be presentmore centrally.
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Fig. 7. Illustration of variability in phase of response as a function of temporal frequency: A, phasic cells and luminance modulation; B, tonic
cells for chromatic modulation; C, tonic cells for luminance modulation. For each condition, the response phase was averaged over the three
contrast levels immediately above that at which a criterion modulation of 20 impulses/sec was attained. Variation was typically 5-30 deg. Atlow frequencies, phasic cells respond with a phase advance relative to tonic cells; with increasing frequency, response phase shows an increasing
lag. On- and off-center phasic cells show a half-cycle phase difference, as do +M-L and +L-M tonic cells. D, Phase of the second-harmonic
component of the phasic cell response to chromatic modulation as a function of temporal frequency. All data for 2000 Td (3400 monkey Td).
would be consistent with the participation of phasic cells indetection at and greater than this frequency. It has beensuggested that the notch in psychophysical chromatic-mod-ulation-sensitivity functions between 10 and 20 Hz is due tointrusion of a luminance mechanism into chromatic-modu-lation detection,3 and so cells of the M-pathway may formthe substrate for this effect. Psychophysically, the intrud-ing mechanism has the temporal characteristic of that sup-porting luminance-modulation detection.3 From Figs. 3and 4 the temporal-contrast sensitivity curves of phasic cellscan be seen to be similar for luminance and chromatic modu-lation. Those points for which a luminance mechanism maymediate detection have been drawn in parentheses in Fig.6B.
For phasic cells and luminance modulation, minor butsystematic variability was observed as temporal frequencywas increased to 20 Hz. This was associated with smalldifferences in optimal temporal frequency between cell andpsychophysical sensitivities. However, at greater than 20Hz, a much more striking discrepancy develops because, at200 and 2000 Td phasic ganglion cells responded to frequen-cies well above flicker-fusion frequency of human subjects.The sensitivity ratio thus falls steeply with similar ratios atall retinal illuminances, consistent with the hypothesis thatsome central mechanism, with properties independent ofretinal illuminance, is acting on cell responses in limiting
temporal resolution. In an attempt to define this mecha-nism, we show the characteristic of a fourth-order filter inFig. 6A. The filter had a corner frequency of 20 Hz andwould account for the steep fall in sensitivity frequencies atgreater than this value. As retinal illuminance was de-creased to 20 and then to 2 Td, the cutoff frequency of phasiccells and human subjects became similar. The results thussuggest that the limit of temporal resolution to luminancemodulation is set at central or peripheral levels dependingon retinal illuminance.
In the case of chromatic modulation, sensitivity of toniccells to chromatic modulation at 2 Td was low in comparisonwith the psychophysical data. The reason for this discrep-ancy is unclear. A more striking difference was present atfrequencies of greater than 5 Hz at all levels of illuminance.As can be seen from Fig. 5, tonic ganglion cells were able torespond to as much as 40 Hz (at 2000 Td), implying that, asin the case of phasic cells and luminance flicker, some cen-tral mechanism acts to make high-frequency signals in theP-pathway unavailable for use in detection. The possibilitythat phasic cells participate in detection of chromatic modu-lation near 10 Hz complicates comparison of P-pathway andpsychophysical sensitivity. Chromatic modulation is seenas color alternation at less than 10-15 Hz.37 On the assump-tion that this reflects the cutoff frequency for a central filter,we have drawn in Fig. 6B a filter characteristic, as in Fig. 6A,
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of the fourth order and with a corner frequency of 10 Hz.We propose that the action of such a filter on tonic-cellsignals reveals intrusion of the M-pathway into chromaticmodulation detection at a high retinal illuminance.
Several possible central mechanisms could limit the tem-poral resolution of ganglion-cell signals. For example, cen-tral, presumably cortical, neurons may integrate incomingimpulses over a finite time period. An alternative possibili-ty is that, owing to intercell variability in the response phase,their averaged signal, summed by some central detectionmechanism, is only weakly modulated. To examine thispossibility, we analyze response phase at different temporalfrequencies in Fig. 7.
Figures 7A and 7B show, respectively, response phase ofphasic ganglion cells to luminance modulation and tonicganglion cells to chromatic modulation as a function of tem-poral frequency, plotted relative to physical modulation ofthe diodes. Phasic ganglion cells tend to respond with aphase advance in comparison with tonic ganglion cells.32
On- and off-center phasic cells respond to luminance modu-lation with a 180-deg phase difference, and this applies also
to the responses of +L - M and +M - L tonic cells tochromatic modulation.
With increasing temporal frequency, an increasing phasedelay of the response is apparent. Variability between cellsis similar in Figs. 7A and 7B, making an explanation in termsof phase variability unlikely. To provide a more quantita-tive analysis, we calculated the degree of attenuation thatmight be expected from phase scatter.
If mean response phase at a given frequency is , weassume that among the cell population response phase isnormally distributed about this value but that the responseR of all cells is identical. For a given cell with responsephase 0 + , there will be a response component at 0 of Rcos 0. The orthogonal component, R sin 0, will be canceledby another member of the population with response phase 0- 0. For different angular standard deviations, we calculat-ed the resulting attenuation of R by integrating over thenormal distribution.
For the phasic cells in Fig. 7A, for less than 19.6 Hz, thephase standard deviation varied between 5 and 20 deg.From 19.6 to 39.1 Hz the standard deviation for on- and off-
Phasic Cell.A Luminance Modulation
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Fig. 8. Amplitude sensitivity and response phase as a function of temporal frequency: A, on-center phasic cell and luminance modulation; B,+L- M tonic cells and chromatic modulation; C, +L - M tonic cell and luminance modulation. The curves for these individual cells are simi-lar to the mean curves in Figs. 3 and 4. With decreasing retinal illuminance, the response phase develops an increasing delay.
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Fig. 9. Comparison of response phase expected of a minimum-phase filter with measured response phase as a function of temporal frequency,
using the data from Fig. 8. Measured phase was corrected for a time delay of 20 msec to the impulse response. Data and curves have been dis-
placed vertically for clarity. In lower panels are plotted the differences between measured and predicted phase values.
center cells approximately doubled from 20 to 40 deg. Thepredicted degree of attenuation of an averaged signal is 6%for a standard deviation of 20 deg and 23% for 40 deg. Thesensitivity ratio for luminance modulation decreases by afactor of 5 from 20 to 40 Hz, indicating an 80% attenuation of
sensitivity. A standard deviation of greater than 90 degwould be required in order to cause this degree of attenua-tion. Thus phase variability among phasic ganglion cellscan be rejected as the major cause of the rapid decrease inthe sensitivity ratio at greater than 20 Hz. Introduction offurther variability on the way to some central point of sum-mation may occur but would imply a timing variability ofseveral tens of milliseconds to cause the attenuation ob-served.
For tonic cells and chromatic modulation, phase variabili-ty had a standard deviation of 10 deg or less for 9.8 Hz orbelow and increased from 24 deg at 19.6 Hz to 34 deg for 39.1Hz (mean of +M - L and +L - M cells). Again, thesedegrees of variability are inadequate to account for the de-crease in the sensitivity ratio observed.
The response phase of tonic cells to luminance modula-tion, shown in Fig. 7C, becomes variable as the frequency is
increased.3 2 This can be described in terms of a vectormodel in which a center-surround latency difference ispresent.3 0 '3 2 The phase standard deviation increased sys-tematically from 15.4 deg for 0.61 Hz to 65 deg for 39.1 Hz.The latter figure would correspond to approximately 45%attenuation of the summed signal, a further indication thatsummed signals in the P-pathway are an unsuitable sub-strate for detection of achromatic modulation.
The phase of the second-harmonic response of phasic cellsto chromatic modulation is shown in Fig. 7D. The phase ofresponse of on- and off-center cells is similar and changesmore rapidly than that for luminance modulation. It mightbe expected that phase should change at twice the rate as inFig. 7A, but inspection shows a somewhat greater phasechange than this.
Cell Sensitivity and Response PhasePsychophysical studies of temporal modulation have oftenused linear systems analysis to describe sensitivity curves.3 8
It is possible to predict the response phase and the impulse-response functions from such curves,3 "19 if it is assumed thatthe system behaves as a minimum phase filter. We beginhere such an analysis of ganglion-cell behavior. Although itis possible to use linear analysis to model cell behavior interms of center and surround components, as has been donefor cat ganglion cells,39 in what follows we do not considercenter and surround separately.
We made predictions of response phase based on datafrom individual ganglion cells rather than their average sen-sitivities. Sensitivity functions and phase of response areshown in Fig. 8 for a phasic ganglion cell and luminancemodulation, a red-on ganglion cell for chromatic modula-tion, and a red-on ganglion cell for luminance modulation.Sensitivity curves resemble the averaged data shown in Figs.3 and 4. Phase relative to diode modulation is plotted as afunction of temporal frequency in the lower panels. As inFig. 7, at low temporal frequencies the phasic cell respondedin a manner that was somewhat phase advanced relative to
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the tonic cells. With increasing temporal frequency, re-sponse phase lags to an increasing extent. As illuminance isdecreased, the phase curves are displaced downward, indi-cating an additional phase delay. Such a phase delay withdecreasing luminance has been postulated to account forstereo-depth effects if a neutral-density filter is placed be-fore one eye.40' 41 It has been described in cat ganglioncells,39 and Fig. 8 shows it also to be present in those of themonkey.
Response phase and impulse-response functions were de-rived from the sensitivity data of Fig. 8.19 Impulse responsefunctions so produced begin immediately after the pulse.Measured responses to flashes showed a time delay beforethe firing rate rises to greater than the maintained level.This will also produce a phase delay, proportional to tempo-ral frequency, and has to be taken into account for compar-ing predicted and measured response phase. From flashresponses of a sample of phasic and tonic cells, we found thedelay to the beginning of the response to be approximately20 msec at all illuminances. We therefore assumed for allcells of Fig. 8 that a fixed time delay of 20 msec was presentat the beginning of the impulse-response function. We cor-rected measured response phase to allow for this delay. Theresulting values are compared with the predicted curves inFig. 9. To facilitate comparison, we plotted in the lowerpanels the deviations between measured and predicted val-ues.
The predicted curves show some irregularities, primarilybecause of noise in the sensitivity data. The fit between themeasured and the predicted values is reasonable, althoughfor luminance modulation a small but consistent overesti-mate of the phase lag is present at 2 and 20 Td. No consis-tent deviations appear with increasing frequency or decreas-ing retinal illuminance, indicating that a fixed delay of 20msec was a reasonable approximation. A similar analysiswas carried out on two other phasic and two other tonicganglion cells with similar results.
The agreement shown in Fig. 9 indicates that, to a firstapproximation, the ganglion cell may be treated as a linearfilter. It would be predicted that the impulse-responsefunction of phasic ganglion cells should become of longerduration with decreasing retinal illuminance. We have ob-served this to be the case, although detailed comparison ofpredicted and observed impulse-response functions have yetto be carried out.
The data of Figs. 8 and 9 indicate that change in responsephase with temporal frequency arises from both the timedelay of a cell's response and its action as a temporal filter.The change in response phase with decreasing retinal illumi-nance probably arises from a change in the time course of theresponse rather than a latency increase per se. It has indeedbeen suggested that the apparent depth effect observed withthe Pulfrich pendulum may be associated with a change intime course of cell responses rather than a simple delay ofsignals from the filtered eye.4 2
DISCUSSION
Linking physiological and psychophysical data requires cer-tain assumptions. For detection paradigms, a class A com-parison4 3 may be invoked, but the demonstration that agiven cell system I is more sensitive than another, J, is not by
itself sufficient to show that I forms the physiological sub-strate of the detection task in question. There remains thepossibility that system J can contribute to detectionthrough, for example, some kind of summation. Alterna-tively, activity in system I may not be utilized centrally, sothat detection may be determined by system J; we haveshown an example in Fig. 6 for which high-temporal-fre-quency signals in the P-pathway do not seem to be utilized,and detection of high-frequency chromatic modulation isdetermined by the M-pathway. Thus corollary evidence asto the participation (or otherwise) of each system must besought. One way is to show that, under changing stimulusconditions, system I undergoes changes in behavior similarto that observed psychophysically, whereas system J doesnot. Other kinds of ancillary evidence can also be envis-aged.
Here we have provided such evidence, consistent with thehypothesis that detection of luminance modulation has as aphysiological substrate in the phasic, M-pathway, whereasdetection of chromatic modulation has a physiological sub-strate in cells of the tonic, P-pathway. For luminance mod-ulation, phasic ganglion cells form the most sensitive cellclass, and their adaptive behavior resembles psychophysicaldata as retinal illuminance is decreased. Not only are toniccells relatively insensitive to luminance modulation buttheir sensitivity falls rapidly at lower levels of retinal illumi-nance. Thus only the phasic, M-pathway possesses the ad-aptation characteristics required of a mechanism underlyingluminance modulation detection. For chromatic modula-tion, the P-pathway is the more sensitive, and its sensitivitydecreases with retinal illuminance in a way that resemblespsychophysical data.
There are additional reasons why the P-pathway is unlike-ly to support luminance flicker detection through some kindof summation process. For chromatic modulation, at lowfrequencies sensitivity ratios were approximately unity, sim-ilar to phasic cells and luminance flicker. It would thus benecessary to postulate that a summation process should op-erate for luminance but not for chromatic modulation. Thisis implausible. Second, the variability in response phase oftonic cells shown in Fig. 7C would not favor such a process.
We also infer that the characteristic notch at approxi-mately 10 Hz in chromatic-contrast-sensitivity functions isdue to participation of the M-pathway in detection, owing totheir response at twice the modulation frequency. Sensitiv-ity ratios found are consistent with this explanation. Thedisappearance of the inflection at low levels of retinal illumi-nance and its dependence on field size3 also parallel thephysiological results.1 2
The comparisons of Fig. 6 do illustrate some differencesbetween physiological and psychophysical data. First, forluminance modulation up to 20 Hz there are minor differ-ences in shape and peak frequency between M-pathway andpsychophysical curves. One possible source of this differ-ence might be that we measured sensitivity with the stimu-lus spot centered on the receptive field. If the receptive-field center were near the edge of the spot, some change inshape of the sensitivity function might result. A few cellswhose curves were compared for these two conditions didnot encourage such an explanation, however. Second, withchromatic modulation, tonic-cell sensitivity decreased withdecreasing retinal illuminance rather more rapidly than with
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psychophysical observations on humans. Although avail-able evidence suggests that psychophysical performance ofhuman and macaque are similar,2 3'44 a detailed comparisonis lacking. Until such data are available for the macaque,the significance of these minor inconsistencies between ma-caque physiology and human psychophysics is difficult toassess.
The most striking difference, revealed in Fig. 6, is thehigher cutoff frequency of macaque cells in comparison withpsychophysical measurements; there is evidence that this isnot a species difference.44 For luminance modulation, itwould appear that the behavioral limit of temporal resolu-tion is set at central or peripheral levels depending on retinalilluminance. At 2000 Td, some filter later in the visualpathway presumably attenuates high-frequency compo-nents in the M-pathway signal. This attenuation increasessteeply at greater than 20 Hz, as seen in the upper panel ofFig. 6A. Below 20 Td, our results are consistent with limitsof temporal resolution's being set at the level of the phasicganglion cells themselves.
For chromatic modulation, divergence between P-path-way and psychophysical sensitivities occurs at greater than 5Hz, although interpretation is somewhat complicated by theprobable intrusion at approximately 10 Hz of detection me-diated by the M-pathway. With the filter curve shown inFig. 6B, the sensitivity ratio rises steeply at greater than 5Hz. Since the cutoff frequency of tonic ganglion cells usual-ly exceeded 5 Hz, it is likely that the limit of temporalresolution for detection of chromatic modulation throughthe P-pathway is set primarily at a later stage than for theganglion cell. This applies not only to red-green modula-tion but also to modulation along a tritanopic confusionline.17 It is probable that such temporal filtering of the P-pathway signal occurs not only for chromatic modulationbut also under other stimulus conditions. There is somepsychophysical evidence that this is the case. The criticalduration for a chromatic perturbation4 5 is similar to thatfound for red or blue increment thresholds on a white back-ground,46 implying similar temporal characteristics.
Measurement of cell sensitivity in Figs. 3 and 4 is in termsof contrast gain or the modulation required to evoke a crite-rion modulation of firing (20 impulses/sec). Since cell re-sponses are statistically variable, determining cell thresh-olds has fallen into disrepute, so much so that sensitivity ofindividual cells has been thought to have little relevance forbehavior. With the approach shown in Fig. 6, we have triedto avoid this difficulty. It is possible, however, to analyze acell's sensitivity in terms of the signal-to-noise ratio in itsspike train, as originally attempted by Barlow and Levick47
for ganglion cells of the cat. More precise information of thenoise characteristics and variability in response is requiredbefore one can begin such an analysis for cells of the P-pathway and the M-pathway. As a first step, it appears thatthe maintained activities of phasic and tonic ganglion cellshave similar noise characteristics (Troy and Lee, unpub-lished; J. Troy, Northwestern University, Evanston, Ill.60208).
We have attempted to define what kind of operation mustbe performed on the ganglion-cell output in order to predictpsychophysical performance. However, the locus and thenature of central filters of P-pathway and M-pathway sig-nals remain uncertain. Temporal properties of cells in the
geniculate nucleus appear to be similar to retinal ganglioncells14"16; responses of area-17 cortical cells to temporal mod-ulation have been little studied. In Fig. 6, we suggest thatthe corner frequencies of filters acting on signals from theM-pathway and the P-pathway must differ by at least afactor of 2 (20 versus 10 Hz). Presumably, in contrast to thetemporal properties of the ganglion cells themselves, timeconstants of central mechanisms remain independent of illu-minance. There are precedents for the concept that affer-ent signals to the cortex are not utilized for perception.4 8
Psychophysically, temporal processing in the visual path-way has been described in terms of linear filters by usinglinear systems analysis. The results presented in Figs. 8 and9 suggest that, to a first approximation, ganglion cells them-selves may be treated in this way, for we have derived rea-sonable predictions of response phases from sensitivityfunctions after adding a constant delay. It remains neces-sary to show that impulse-response functions of ganglioncells may be derived through transformation of their con-trast-sensitivity functions. Form a physiological viewpoint,filters may operate at many stages in the visual pathway. Acomparison of late receptor potential recordings and psy-chophysical results led to the suggestion that at least twosuch processes are cascaded,4 95 0 resulting in a distributedmechanism with a time constant r longer than that of eitheralone. We did not make sufficient measurements to be ableto estimate r precisely for the different cell classes, but itsvalue (for phasic cells and luminance flicker) appeared to beintermediate between those calculated for the late receptorpotential and for the psychophysical results.4 9 Thus multi-ple sequential filters may be cascaded within the visual sys-tem.
ACKNOWLEDGMENTS
This research was partially supported by North AtlanticTreaty Organization collaborative research grant 0909/87and by U.S. Public Health Service NEI grant 00901 to JoelPokorny. We thank Bill Swanson for assistance in generat-ing response phase predictions, and Barbara Roser for tech-nical assistance. Some of these results were presented at the1989 Annual Meeting of the Association for Research inVision and Ophthalmology.
* Current address, Department of Neuroanatomy, MaxPlanck Institute for Brain Research, Frankfurt, Federal Re-public of Germany.
t Permanent address, Department of Biophysics, Instituteof Physics, University of Oslo, Norway.
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