@ VisionRes., Vol.36,No.17,pp.2713-2720, 1996 Pergamon Copyright 01996 ElsevierScienceLtd.Allrightsreserved PII: S0042-6989(96)00014-4 PrintedinGreatBritain 0042-6989/96 $15.00+0.00 Measurements of Human Sensitivity to Comb- filtered Spectra V. BONNARDEL,*? H. BELLEMARE,$ J. D. MOLLON* Received 9 March 1995; in revisedform 23 October 1995 Using a novel stimulator that incorporates a liquid crystal display, the spectral modulation sensitivity tlmction of the colour vision system was derived by measuring discrimination thresholds for comb-filtered spectra. This function shows a peak of sensitivity at 0.97 c/300 nm with a plateau that extends to 1.67 c/300 nm. Extrapolation of the curve gives an estimated high-frequency cut-off at 5 c/300 nm. The thresholds are also transformed to the CIE (1931) diagram and the elliptical isosensitivity contours thus obtained are compared with the classical discrimination ellipse of MacAdam for the corresponding region of colour space. Copyright @ 1996 Elsevier Science Ltd. Colourvision Comb-filtered spectra PsychophysicsSpectralmodulationsensitivityfunction INTRODUCTION More than 10 years ago H. Barlow (1982) suggestedthat the concept of Fourier transforms might be borrowed from spatialvision and applied to colourvision. He called for measurements of the sensitivityof the colour system using comb-filteredspectra,$ that is, sinusoidalmodula- tions of radiant energy over the full visible spectrum. Sensitivity measurements for comb-filteredspectra for a range of frequencies will give an indirect estimate of the modulationtransfer function (MTF) of the colour system in the same way that the contrast sensitivity function (CSF) determined by Campbell and Robson (1968) estimates the degree of demodulation imposed by the visual system on different spatial frequencies. In applying Fourier analysisto colour vision, Barlow’s *Department of Experimental Psychology, Cambridge University, DowningStreet, CambridgeCB23EB, U.K. ~Laforia, University Paris 6,4 place Jussieu, Paris 75005, France. $To whom all correspondenceshouldbe addressedat present address: PhysiologicalLaboratory,CambridgeUniversity,DowningStreet, Cambridge C132 3EG, U.K. IEmail [email protected]. AC.UK]. $Twoconsiderationsjustify the term “comb-filteredspectra” adopted by H. Barlow. First, from an historical point of view, the term directly recalls an experimentof Newtonwhere a combwas used to intercept some wavelength intervals while others were transmitted (Newton, 1704,Optick). His system served to demonstratethat the sensation of white was ASOelicited by a successive stimulationof coloured lights as long as the successionwas fast enough. Second, from comb-filtered spectra, Barlow derived “comb-frequency” which is a convenientway to avoid any confusionwith frequency of the electromagnetic radiations. 1ssthe present context although an actual comb would provide rectangular modulationsthe term is used to refer to sinusoidal spectral energy modulations. original motivewas to ask whether the dimensionalityof the system (the number of types of receptors) was constrained by the low-pass filtering imposed by the spectral sensitivity curves of the cones. Subsequently, Benzschawel et al. (1986) and recently Romero et al. (1995a) showed that comb-filteredspectra could be used to distinguish different models of post-receptoraloppo- nent processes.However, despite the potential interest of the frequency view of colour vision, it has not proved straightforward to develop an experimental set-up that generates sinusoidallymodulated spectra. A first attempt to measure sensitivity to comb-filtered spectra was reported by Barlow et al. (1983), using a Michelson interferometer.This device was able to produce sinusoi- dal modulations,but did not allowfrequencyand phase to be controlled independentlyand did not allow frequency to be held constantover the entire spectrum.Bonnardel et al. (1991) developed another device based on a linear interferencewedge and a cross-polarizationfilter system which avoided the previous limitations but produced square-wavemodulations. In the present experiment,we take advantageof liquid crystal display (LCD) technology to generate comb- filtered spectra that can be readily varied in frequency, phase and modulation depth. LCD technology offers a modern method of light modulation, but our device is similar in its principle to the early template calorimeters in which a mask was placed in the plane of the spectrum in order to obtain desired spectral profiles (Ives, 1921; Winch & Machin, 1940). Such instruments were primarily used for colour measurements, but more recently, colour discriminationexperimentswere carried out with the Spectral Colour Integratorwhere, according to the same principle, colour stimuli were produced by 2713
Measurements of Human Sensitivity to Comb-filtered SpectraV. BONNARDEL,*? H. BELLEMARE,$ J. D. MOLLON*
Received 9 March 1995; in revisedform 23 October 1995
Using a novel stimulator that incorporates a liquid crystal display, the spectral modulationsensitivity tlmction of the colour vision system was derived by measuring discrimination thresholdsfor comb-filtered spectra. This function shows a peak of sensitivity at 0.97 c/300 nm with a plateauthat extends to 1.67 c/300 nm. Extrapolation of the curve gives an estimated high-frequency cut-offat 5 c/300 nm. The thresholds are also transformed to the CIE (1931) diagram and the ellipticalisosensitivity contours thus obtained are compared with the classical discrimination ellipse ofMacAdam for the corresponding region of colour space. Copyright @ 1996 Elsevier Science Ltd.
More than 10 years ago H. Barlow (1982) suggestedthatthe concept of Fourier transforms might be borrowedfrom spatialvision and appliedto colourvision.He calledfor measurementsof the sensitivityof the colour systemusing comb-filteredspectra,$ that is, sinusoidalmodula-tions of radiant energy over the full visible spectrum.Sensitivitymeasurementsfor comb-filteredspectra for arange of frequencieswill give an indirect estimate of themodulationtransfer function (MTF) of the colour systemin the same way that the contrast sensitivity function(CSF) determined by Campbell and Robson (1968)estimates the degree of demodulation imposed by thevisual system on different spatial frequencies.
In applyingFourier analysisto colourvision,Barlow’s
*Department of Experimental Psychology, Cambridge University,DowningStreet, CambridgeCB23EB, U.K.
~Laforia,University Paris 6,4 place Jussieu, Paris 75005,France.$Towhom all correspondenceshouldbe addressedat present address:
$Twoconsiderationsjustify the term “comb-filteredspectra” adoptedby H. Barlow. First, from an historical point of view, the termdirectlyrecalls an experimentof Newtonwhere a combwas usedtointercept some wavelength intervals while others were transmitted(Newton, 1704,Optick). His system served to demonstratethat thesensation of white was ASOelicited by a successive stimulationofcoloured lights as long as the successionwas fast enough.Second,from comb-filtered spectra, Barlow derived “comb-frequency”which is a convenientway to avoid any confusionwith frequencyof the electromagnetic radiations. 1ssthe present context althoughan actual comb wouldprovide rectangular modulationsthe term isused to refer to sinusoidal spectral energy modulations.
originalmotivewas to ask whether the dimensionalityofthe system (the number of types of receptors) wasconstrained by the low-pass filtering imposed by thespectral sensitivity curves of the cones. Subsequently,Benzschawel et al. (1986) and recently Romero et al.(1995a) showed that comb-filteredspectra could be usedto distinguishdifferent models of post-receptoraloppo-nent processes.However, despite the potential interestofthe frequency view of colour vision, it has not provedstraightforward to develop an experimental set-up thatgenerates sinusoidallymodulatedspectra.A first attemptto measure sensitivity to comb-filtered spectra wasreported by Barlow et al. (1983), using a Michelsoninterferometer.This device was able to produce sinusoi-dal modulations,but did not allowfrequencyand phase tobe controlled independentlyand did not allow frequencyto be held constantover the entire spectrum.Bonnardeletal. (1991) developed another device based on a linearinterferencewedge and a cross-polarizationfilter systemwhich avoided the previous limitations but producedsquare-wavemodulations.
In the present experiment,we take advantageof liquidcrystal display (LCD) technology to generate comb-filtered spectra that can be readily varied in frequency,phase and modulation depth. LCD technology offers amodern method of light modulation, but our device issimilar in its principle to the early template calorimetersin which a mask was placed in the plane of the spectrumin order to obtain desired spectral profiles (Ives, 1921;Winch & Machin, 1940). Such instruments wereprimarily used for colour measurements, but morerecently, colour discriminationexperimentswere carriedout with the Spectral Colour Integratorwhere, accordingto the same principle, colour stimuli were produced by
2713
2714 V. BONNARDELet al.
LI
F2
LCD
IF
F1
IS
s’
A
v
Ys“
&4c/300nm,p=0°
FIGURE1. Experimentaldevice. The light from the source (S) located at the focal point of a Fresnel lens (Fl) is focusedby asecondlens (F2) to form a real image S’of S at the apertureof the integratingsphere(IS). The LCDis mountedin the collimatedbeam, directly after the interferencewedge(IF) whichgives a continuouslinearspectrumfrom400 to 700nm.The outputof theintegrating sphere, viewed through a lens (Ll) in Maxwellianview, produces an homogeneousfield of 2 deg diameter. Thefigure to the right shows examples of sinusoidalspectral modulationsachievedby applyingelectronic masks to the spectrum(symbolized by the colour initials). The masks presented here have f= 4 c and p =Odeg with three different levels ofmodulation.When the spectrum is unmodulated(m = O),the spot is perceived as achromatic. When m#O the spot appearscolouredand for a constant level of modulationits hue dependson the combinationof frequencyand phase, that is, the number
and the position of the spectral bands that are transmitted.
cardboard masks applied to a large spectrum (Holtsmark& Valberg, 1969).
The threshold measurements presented here wereperformed for a large gamut of frequencies combinedwith a full range of phases, which allowed us to derive aspectral modulation sensitivity function (SMSF) for anormal trichromat observer. A particular advantage ofcomb-filteredspectra is that the chromaticitycoordinatesfor a given frequencywith a constant level of modulationdescribe an ellipse in the CIE (1931) diagram, whenphase varies from O to 360 deg (Buchsbaum &Gottschalk, 1984). This convenient property allowed usto derive for the differentfrequenciesa set of discrimina-tion ellipses, which are compared to the classicalMacAdam ellipse (MacAdam, 1943) for the correspond-ing region of chromaticity space.
METHODS
Experimental device
The luminous source is a short-arc Xenon Lamp(Osram XBO, 150 W), located at the focal point of a
*Foreach relative sinusoidalspectral modulationat the thresholdlevel,the parameters were determined by calculating the best fittingsinusoidal function over 400-696 nm. The curve fitting was donewith Kaleidagraph–Macintosh software. For the overall 24sinusoidal fittings the mean correlation is 0.98.
Fresnel lens (157 mm x 157 mm). The collimated beamilluminates an interference wedge, which yields acontinuous spectrum (115 mm x 24 mm) that is linearin wavelength units. The rays are then collected by asecond identical Fresnel lens, which forms a real imageof the source at the aperture of an integrating sphere(50.8 mm in diameter).The output of the sphere, viewedthrough a lens in Maxwellian view, produces anhomogeneous field of 2 deg diameter (Fig. 1). A LCDis mounted in the collimated beam, directly after theinterference wedge. The LCD screen currently used isone commerciallyavailableas a peripheralfor displayingcomputer-generatedimages with an overhead projector(Sayett Datashow 480). It is of the double super twistednematic type and gives a contrast ratio of 15:1. Theextinction ratio of the LCD screen (i.e. the transmissionratio of black and white pixels) is wavelength-dependent,showing the highest residual transmission in the short-wavelengths and the lowest in the 450-550 nm intervalwith a transmissionof an intermediate level in the long-wavelengths. These characteristics slightly distort ourempirical modulations measured with a spectroradi-ometer. However, this effect is small, as is indicated bythe quality of fit found between the relative sinusoidalspectraldistributiongivenby the ratio E(l)/Eo(2) and thebest-fittingsine function.*
The screen (211 mm x 158 mm) is a passive-matrixaddressingsystem of 640 x 480 pixels on which sinusoi-
dal profilesare drawn in a rectanglewhose size fitsthat ofthe continuous spectrum. The software application hasbeen developed on an Apple Macintosh LC computer todisplay sinusoidal profiles of any frequency and phase.The level of modulation is set by the number of pixelscorrespondingto the width of the interference wedge ateach wavelength (see inset, Fig. 1).
Thus, the LCD acts as an electronic mask imposingsinusoidalmodulationsover the spectral power distribu-tion of the light source.The resulting illuminationE(2) isexpressed by the following formula:
E(A) = EO(A)[l+ resin@(A) +Po)] (1)
where Eo(l) is the spectral power distribution of thesource measured in the absence of modulation;m is thelevel of modulation which varies from O to 1; ~ is thefrequencyexpressed in cycles per 300 nm and denotedc;POthe starting phase which, by convention, is equal toOdeg when for a maximal modulation the sinusoidincreases from the mean level of modulation at the400 nm end. p(~) = (1.22A80) scales the spectral inter-val in a 0-360 deg interval.
In the case of comb-filtered spectra, two interestingquestionsarise that do not find an obviousanalogy in thecase of spatial vision. The first is whether a CSF forcolour vision should properly be based on modulationsthat are constant in wavelength units, or whetherfrequency or some other metric (such as log frequency)offers an appropriatebasis. In this firststudyour choice ismainly dictated by practical considerations: our inter-ference wedge is linear in wavelength, and the CIE(1931) chose this unit to describe spectral radiant powerdistributions.A second questionconcernsthe distributionof the unmodulated spectrum. Should it, say, be flat inenergy units or in quantum units or in luminance units?The last is certainly unrealistic if the results are to applyto naturalisticilluminantsor visual signals.In the absenceof any obvious theoretical consideration and in view ofthe difficulty of obtaining a flat equal-energy spectrum,we use here the spectral power distributionof the Xenonlamp after transmissionthrough IR and UV filters.
Light measurements
Calibrationsof the spectral power distributionand thechromaticitycoordinatesof the stimuliwere made with aspectroradiometer(model PR-650, Photo Research).Themanufacturer’scalibration of the spectroradiometerwaschecked at the Laboratoire de Physique Appliqu6e,Mus4umd’HistoireNaturelle (Paris) against a secondaryluminance standard (Pefferkorn, 1993).
Since light levels were too low to measure the spectraldistributionsat the position of the subject’s pupil, thesecalibrationswere made at the extremity of an optic fibre(Oriel, liquid fibre, 8 mm in diameter), which fitted intothe outputof the integratingsphere.Before and after eachexperimentalsessionthe chromaticitycoordinatesfor theunmodulatedspectrumwere recorded. For a total of 130experimentalsessions,the mean differencebetweenthesetwo chromaticitycoordinatesexpressedas distancein theCIE (1931) diagram is 0.0029. This small variability
testifiesto the stabilityof the light source for the durationof the testing session (1.5 hr). However, a slight drift inthe chromaticity coordinates over the period of theexperiment was noticed. For 130 measurements theaverage chromaticity coordinates of the unmodulatedspectrum are X. = 0.284,y. = 0.372 with SDSof 0.00675and 0.0085. This variability displaced the locus of theunmodulated spectrum to noticeably different positionsof the chromaticity diagram. To estimate the effects ofthis displacementon the sensitivityof the observer, thetheoretical MacAdam ellipses (MacAdam, 1943) werecomputed for the two extreme colour centres recorded.The two ellipses show a size difference of only 4%,which is insignificantfor our experiment.
Psychophysical procedure
The observer, her head resting on a chin-rest in dark-adapted conditions, saw the output of the integratingsphere in Maxwellianview as a homogeneousspot. Theabsolute luminance of the target was estimated at 5-6cd/m2by visually matching it to a white spot of similardiameter viewed directly and not in Maxwellianview.
In a three-alternative temporal forced choice, thereference (unmodulated spectrum) appeared twice andthe test (modulatedspectrum)once in the three temporalwindows (1 sec each) in a random fashion. The task wassimply to indicatewhich stimulusdiffered from the othertwo by pressing one of the three keys. Between stimuluspresentations the LCD was in its off state, giving aluminance level below 1 cd/m2.
In order to ensure that the observer did not usebrightness as a cue, the program introduced luminancevariationsby applyingpatternsto the electronicmask in arandomfashion.Luminancevariationsbetween the threeindividual presentations of a trial were of the order of25% for all frequencies except for 0.44 and 0.7 c forwhich they were double.
The threshold modulation difference between the testand the reference was determined by an adaptivestaircase procedure (Cornsweet, 1962).Twelve frequen-cies (from 0.44 to 3.96 c) combinedwith the full range ofphases (from Oto 330 deg, in 30 deg steps) provided atotal of 144 combinations of frequency and phase. Sixthreshold determinations were carried out for allfrequencies except for 0.44-0.7 c where only fivemeasurements were made after all the other data hadbeen gathered.
The observer (VB) is a female with a normal colourvision according to a battery of clinical tests (Ishihara,Farnsworth-Munsell100-Hue,Nagel anomaloscope).
RESULTSAND DISCUSSION
Spectral modulation sensitivity measurements
As has already been noted for the case of square-wavemodulations(Bonnardel& Varela, 1991),if sensitivityisplotted against frequency for constant phase, the curvesdisplay several local minima and maxima. The bumpyprofilesarise from a systematicchangeof directionin the
—
2716 V. BONNARDELet al.
—
—
—
3’
/
—
0.1 1 Frequency(c/ 300nm) 10
FIGURE2. SDectralmodulationsensitivityfunction.The oarameteraof the relative sDectralsinusoidalmodulationsmeasuredatthe threshold]evel @,/Eo)were estimatedby a fittingpro;edure. The reciprocalof th~estimatedamplitudeis plotted againstthefrequency.The upper curve describes the sensitivity to optimal phases and correspondsto the SMSFwhereas the lower curvecorrespondsto the sensitivityto peaaimalphases. The SMSFpeaks at 0.97 c and the lowercurve at 1.23c. Bothcurvesdisplayamaximumof sensitivityfor the medium-rangefrequencies.The phase dependenceof the coloursystemcan be appreciatedfrom
the difference between the two curves.
CIE (1931) diagram for a given phase when frequency isvaried, as illustratedfor Odeg phase in Fig. 4. Similarly,the sensitivity of the chromatic system shows a largedependencyon phase, as can be seen in thejagged curvesobtained by Barlow et al. (1983), whose interferometerproduced phase changes concomitantly with frequencyvariations.
Because our intentionwas to estimate the MTF of thechromatic system,we choose to representthe upper limitof sensitivity, that is, for each frequency we plot themeasurement for the optimal phase only. We also derivea similar curve describing the lower limit, whichcorresponds to the sensitivity measured at the leastfavorable or “pessimal” phase.*
Spectral modulation sensitivi~ jimction (SA4SF).Foreach of 24 combinations of frequency and phase, wemeasured the spectral power distribution of the modu-lated spectrum at the threshold level, Et(l), and of thecorresponding unmodulated spectrum, EO(2).The rela-tive sinusoidal spectral modulation is given by E~(l)/EO(2).A fitting procedure was then used to estimate theparameters of the best-fittingsinusoid and the reciprocalof the amplitude was plotted as a function of frequency(Fig. 2).
The upper curve, i.e. the SMSF peaks at 0.97 c with ashoulder at 1.67c and decreases on either side of thisinterval. The high-frequency cut-off, estimated byextrapolating the curve to y = 1, is five cycles. At thelower frequenciesthe fall in sensitivityis less steep thanat the higher frequencies. Because the threshold mea-surements at 0.44 and 0.7 c were performed after all theother data had been gathered, a practice effect may have
*Thisneologismisborrowedfrom Weale (1951).
led to overestimation of the sensitivity at these twofrequencies.
Compared to the previouscurve obtainedwith square-wave modulations for the same observer [see Fig. 5 inBonnardel & Varela (1991)], the SMSF presented hereshowsa general improvementof sensitivity,owing to themethod used (three-alternativeforced choice vs adjust-ment). In the middle range of frequencies, the sensitivitycurve for square-wave modulationsdisplayed two clearpeaks (0.8 and 1.8 c) which are not apparentin the SMSF.This last discrepancy was not expected and may needfurther experimental investigation.
With a peak at 1.23c anda decrease below 0.7 c andbeyond 1.67 c, the lower curve of Fig. 2 displaysa clearband-passprofile.The residual sensitivityfor the lowestfrequency allows us to estimate a low-frequencycut-offnear 0.4 c. The difference between the optimal andpessimal curves indicates the phase dependence of thecolour system. The shift of phase necessary to switchfrom maximal to minimal sensitivity depends onfrequency but always lies in the 60-120 deg interval. Itis worth noting that a shift of 180deg produces a colourstimulus of a complementary wavelength for which acomparable sensitivity can be assumed, as shown indiscriminationthreshold measurements for complemen-tary coloursperformedby Holtsmarkand Valberg (1969)with the Spectral Colour Integrator.
Remark on the spectral projile of stimuli included in0.97–1.67 c interval. Profiles of the relative spectralmodulationsfor the 0.97–1.67c intervalcorrespondingtooptimal and pessimalphases are plotted on two differentgraphs (Fig. 3, right) and, within each category, it can beseen that the seven different spectral power distributionsshow clear similarities. The optimal spectral profilesdisplay three lobes approximately centred on 420-430,
FIGURE3. Spectralprofileaof stimuli includedin the 0.97-1.67 c interval.Right, relative spectral modulationof optimal (top)andpessimal(bottom)stimuli.Left, the chromaticitycoordinatesof the correspondingspectralpowerdistributionsplottedin theCIE (1931) diagram form two distinct clusters. The chromaticity coordinates of the pessimal stimuli are located on an axisslightly tilted from the tritanopic axis and the chromaticitycoordinatesfor optimal SPDSform a cluster roughlyin the deutandirection. T and D lines correspondto the dichromaticconfusion lines (T, Tritan; D, Deutan) passing thoughthe locus of the
unmodulatedspectrum (cross) which is located for these measurementsat X. = 0.28 andy. = 0.376.
5OW51Oand 600-610 nm, and one of the crossoversoccurs in a tight interval at 560 nm. With three lobesoccurringwhere the crossoversof the optimalprofilesareobserved, the pessimal profiles exhibit a reverse profile.
0.9
0.s
0.7
0.6
0.5
Y
0,4
0.3
0.2
0.1
0.0
(_’’”\
550
;)0
\
Correspondingly, the chromaticity coordinates of thecorresponding spectral power distribution are shown tobe clustered in two distinct groups in the CIE (1931)diagram (Fig. 3, left).
J#””r(
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.s 0.9x
FIGURE4. Elliptical representationof fully modulatedspectra in the CIE (1931)diagram.The elliptical contoursfitted to thechromaticitycoordinatesmeasuredfor the 12 frequenciesat 30 deg steps are drawnin the CIE (1931)diagram.The axis ratio,the orientationand the colour centre of best-fittingellipses vary with frequency.For each frequencythe Odeg starting phase isindicated (dots). Variation in depth of modulationcorrespondsto movementalong a line that joins the unmodulatedspectmm(cross) to an elliptical contour in a given direction i.e. for a given phase. For these measurementsthe locus of the unmodulated
For comparisonthe parameters of the MacAdamellipse computedfor the same colour centre (x. = 0.275,y. = 0.358) are also given.
In summary, in spite of large differences in experi-mental procedures, the present data show features incommon with the empirical measurementsof the SMSFpreviously published for normal trichromats (Barlow etal., 1983; Gemperlein et al. 1990; Bonnardel & Varela,1991):sensitivitydecreases at the lower frequenciesandexhibits an optimum for the intermediate frequencies,while a high-frequencycut-off is observedbetween 4 and6 C.
This high-frequency limit is also consistent with thatbased on the Fourier transform of Smith and Pokomy’sfundamentals (Smith & Pokomy, 1975) computed byBarlow (1982) or that computed more recently byRomeroet al. (1992)from the colourmatchingfunctions.Although total demodulation is observed at differentfrequenciesaccording to the type of receptor, the criticalfrequency does not exceed 6 c. The conclusion thatBarlow derives from his analysis of individual cones ishere confirmed empirically for the whole colour system.
Elliptical representation of sensitivip
Chromaticity coordinates of fully modulated spectra.In order to determine the area covered in the CIE (1931)diagramby frequency-limitedfunctions,that is, functionsthat have no harmonic higher than a given order whenresolved by Fourier methods, Buchsbaum & Gottschalk(1984; see also Buchsbaum, 1985) computed thechromaticity coordinates of sinusoidal spectral powerdistributions (SSPDS)with O < f < 1.5 c. For a givenfrequency with a constant modulation, they showed thatchromaticitycoordinatesof SSPDSdescribe an ellipticalcontour in the CIE (1931)diagramas phase varies from Oto 360 deg.
By referring to Welter’s theorem (Welter, 1950),Brilland Benzschawel(1985), provided their own demonstra-tion that the chromaticity coordinates of SSPDS mustdescribe an ellipse in the chromaticity diagram. Thus,whatever the frequency, an elliptical contour can beperfectly fitted to the data points, as in fact was the case
—
with the chromaticitycoordinateswe measured for fullymodulated spectra (Fig. 4).
Chromaticity coordinates of minimally modulatedspectra. Full discrimination ellipses were also derivedby measuring the chromaticitycoordinatesat the thresh-old modulation. Since at least in one direction thesensitivitymeasurementswere limited by the maximummodulationavailable,the highestfrequencywas removedfrom this analysis. The actual chromaticity coordinatesare the means of the chromaticitycoordinatesof the sixthreshold determinations (or five for 0.44 and 0.7 c)recorded after each set of experimental data had beengathered (Fig. 5, left).
The best-fittingellipsesform a quite homogeneoussetwith an axis ratio variation of 2290 and an orientationvariationof 5.2 deg with a mean of 75.8 deg (see Table 1for values). Because the measurements were made atdifferent times there were small variations in the colourcentre of the ellipses.However the centres of the ellipsesestimated by our elliptic regression algorithm alwayscorresponded to the chromaticity coordinates of theunmodulatedspectrum.For the purposeof comparison,amean colourcentre is computedand the full set of ellipsesis plotted on the same graph (Fig. 5, centre).
From this set, a mean ellipse is derived and comparedto the MacAdam ellipse computed for the same colourcentre. To match the size of our ellipse, the MacAdamellipse in Fig. 5 (right) is enlarged seven times its actualvalue. It should be noted that the MacAdam ellipserepresents the standard deviations of chromaticitymatches.Thus, the size differencecan be partly attributedto the measureof discriminationused (standarddeviationof matchesvs mean of thresholdsfor discrimination),andpartly to the differencebetween successiveand simulta-neous methods. Several studies have shown that thecapacity to discriminatecolour is impaired in successivecomparison tasks (Uchikawa & Ikeda, 1981; Romero etal. 1986).
Finally, it is worth comparing the present results with
2720 V. BONNARDELet al.
those of Romero et al., (1995b)where, in contrast to ourempirical method, the spectral modulation sensitivitycurves are computed from the MacAdam discriminationellipses. For each combination of frequency and phase,Romero and his collegues calculated the amplitude ofmodulationneeded to bring the chromaticitycoordinatesof each SSPDto the ellipticalthresholdcontour.Two setsof curves were derived corresponding to thresholds ofeither three or ten MacAdam units. For the widertolerance, the maximal sensitivity function displays acut-off frequencyat 4.125 c with a peak at 1.5 c, whereasthe narrowertoleranceS1:OWSa peak value at 1.35c and ahigh-frequencycut-off at 6 c. Our empirical estimate of5 c for the high-frequencycut-off is thus consistentwithan absolutesensitivitycorrespondingto seven MacAdamunits.
CONCLUSION
Buchsbaum,G. (1985).Chromaticitycoordinatesof frequency-limitedfunctions: erratum.Journal of the Optical Society of America A, 2,95.
Bucbsbaum,G. & Gottschalk,A. (1984). Chromaticitycoordinatesoffrequency-limited”functions. Journal of the Optical Society ofAmerica A, 1, 885-887.
Campbell, F. W. & Robson, J. G. (1968). Application of FourierAnalysis to the visibility of gratings. Journal of Physiology(London),197,551-566.
Cornsweet, T. N. (1962). The staircase method in psychophysics.American Journal of Psychology, 75,485-491.
Gemperlein,R., Paul, R. & Steiner,A. (1990).Fourier InterferometricStimulation(FIS):The methodand its applications.In BlakemoreC.(Ed.), Vision: Coding and eflciency. Cambridge: CambridgeUniversityPress.
Holtsmark,T. & Valberg, A. (1969). Colour discriminationand hue.Nature, 224, 366-367.
Ives, H. E. (1921). A proposed standard method of calorimetry.Journal of the Optical Socie~ of America, 6, 469478.
MacAdam, D. L. (1943). Specification of small chromaticitydifferences in daylight.Journal of the Optical Socie~ of America,33, 18-26.
An LCD template offers the visual scientist aPefferkorn, S. (1993). Rapport Elalonde luminance. In Photom6trie
mt%opique,conventionde recherche BNM 91-2-46-0027(personalconvenient way of generating colour stimuli with any communication).required spectral power distributions and thus is an Romero,J., Hita, E. & Jimenez Del BarCo,L. (1986).A comparative
alternative to traditional calorimeters with three mono- study of successive and simultaneous methods in colour
chromatic primaries. The reliability of the stimulator was discrimination.VisionResearch, 26, 471476.
tested by measuring discrimination thresholds to sinu-Romero, J., Jimenez del Barco, L. & Hita, E. (1992). Mathematical
reconstructionof color-matchingfunctions.Journal of the Opticalsoidal spectral modulations and these results were Socie~ of America A, 9, 25–29.consistentwith classical discriminationdata. From these Romero, J., Nieves, J. L., Garcia-Beltrtin, A. & Hita, E. (1995a)
measurements an estimate of the MTF was deriveddescribingthe filteringpropertiesof the entire chromaticsystem in the frequency domain.
REFERENCES
Barlow,H. B. (1982).Whatcauses trichromacy?A theoreticalanalysisusing comb-filteredspectra. VisionResearch, 22, 635-643.
Barlow, H. B., Gemperlein,R., Paul, R. & Steiner, A. (1983).Humancontrast sensitivityfor comb-filteredspectra.Journal ofPhysioZo~,340, 5op.
Berrzschawel,T., Brill, M. H. & Cohn,T. E. (1986).Analysisof humancolor mechanisms using sinusoidal spectral power distributions.Journal of the Optical Society of America A, 3, 1713-1725.
Bonnardel,V., Martinoya,C. & Varela, F. J. (1991).Une m6thodedemesure de la sensibility aux modulations p&iodiques d’6nergielumineusespectrale chez l’Homme.ComptesRendus de l’Acad@miedes Sciences, Paris, 312, 695–700.
Bonnardel, V. & Varela, F. J. (1991). A frequency view of color:Measuring the bumarr sensitivity to square-wave spectral powerdistributions.Proceedingsof theRoyal SocietyLondon,B, 245, 165–171.
Brill, M. H. & Benzschawel,T. (1985).Remarkson signal-processingexplanations of the trichromacy of vision. Journal of the OpticalSocie~ of America A, 2, 1794-1796.
Analysis of colour-visionmechanisms in the chromatic frequencydomain.Journal of Optics (Paris),26, %15.
Romero, L., Nieves, J. L. & Garcia-Beltr6n, A. (1995b) Humanprocessing of colour information in the chromatic-frequencydomain. VisionResearch, 35, 867-871.
Smith, V. C. & Pokorny,J. (1975). Spectral sensitivity of the fovealcone pigmentsbetween400 and 500 nm. VisionResearch, 15, 161–171.
Uchikawa, K. & Ikeda, M. (1981). Temporal deterioration ofwavelength discrimination with successive comparison method.VisionResearch, 21,591-595.
Weale, R. A. (1951).Journal of Physiology (London),13, 115–122.Winch, J. T. & Machin, C. F. (1940).The physical realisation of the
C.I.E. average eye. Transactionsof the Illuminating EngineeringSocie~ of London,5, 93–104.
Welter, H. (1950).PhysikalischeBegrMdungeines FarbenkreisesundAnzatze einer physikalischenFarbenlehre.Annalen der Physi~ Ser6, 8, 11-29.
Acknowledgements—VB thanks Francisco Varela for his contributionand supportin the early phasesof this work.This workwas carried outwhile VB was supportedby fellowships from EuropeanCommissionand the Fondation Fyssen and by MRC grant G940661ONto JDM.Some of this work was presented at ECVP in Eindhoven,September1994.
