Convergence of experimental multiple Rayleigh matches to. peak L- and M- photopigment sensitivity estimates

Transcription

1 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 1 VIÉNOT F, SERREAULT L., ARDO FERNANDEZ., 2006, Convergence of experimental multiple Rayleigh matches to peak L- an M- photopigment sensitivity estimates, Visual Neuroscience, 23: Convergence of experimental multiple Rayleigh matches to peak L- an M- photopigment sensitivity estimates FRANÇOISE VIÉNOT 1, LUCILE SERREAULT 2 an EDRO ARDO FERNANDEZ 3 1 Muséum National Histoire Naturelle, CRCDG, aris, France 2 Université aris-su, MST Optique physiologique, Optique e contact et Optométrie, Orsay, France 3 Universia e Extremaura, Departamento e Física, Baajoz, Spain Corresponing author Françoise Viénot Muséum National Histoire Naturelle Centre e Recherches et e Restauration es Documents Graphiques 36 rue Geoffroy Saint-Hilaire F aris France vienot@mnhn.fr Tel: Fax: Abstract Shift in the wavelength of peak sensitivity of the cone photopigments is a major cause of inter-iniviual variations in the Rayleigh match. Normal colour observers performe

2 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 2 multiple Rayleigh matches, i.e. a series of seven Rayleigh-type colour matches using various sets of test an primary lights, in orer to erive estimates of the M- an L- photopigment wavelengths of maximum absorbance. We preicte the ratio of incient raiances r / g for a range of plausible values in terms of wavelength of the peak sensitivity of the M-cone an L- cone. An algorithm allowe us to ajust the values of the peak wavelength of the cone photopigments in orer to minimize the sum of square ifferences between preicte an real results of matches. To create caniate M-cone an L-cone photopigments that best preict the set of equation values, we use the low ensity spectral absorbance curves of the M-cone an L-cone photopigments respectively, as tabulate by Stockman an Sharpe 2000, an shifte each template along a logarithmic wavelength scale. For all observers, the system of 7 Rayleigh-like equations converges to a unique solution. M- an L- cone photopigments are estimate separately. The istribution of the wavelength of maximum sensitivity of the photopigments inclues a cluster. Only a few women s results lie outsie the cluster. The choice of the template has a consierable influence on the convergence of the algorithm. Keywors Multiple Rayleigh colour matches, Cone photopigments, Spectral absorbance template, Colorimetry, Human colour vision Introuction Normal colour vision is trichromatic. Colour matches are explaine by the absorption of photons in three families of photopigments: the S-cone photopigment, the M-cone photopigment, the L-cone photopigment. During the past 20 years, a polymorphism of the M- cone an L-cone photopigments has been shown in humans, by molecular genetics an psychophysical stuies see a review in Sharpe et al., 1999, table 1.3. Its consequence on

3 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 3 metameric colour-matches Neitz & Jacobs, 1990 an the spectral luminosity function Carroll et al., 2000 has been moelle an verifie. Shift in the wavelength of peak sensitivity of the cone photopigments is recognise as a major cause of inter-iniviual variations in the Rayleigh matches. Neitz & Jacobs 1990, comparing two ifferent colour-matches from colour normal male observers an consiering together finings from molecular biology, suggeste that there are iscrete variations in both mile an long wavelength cone pigments. He an Shevell 1994, measuring the ratio of two particular Rayleigh-type matches the Dual-Rayleigh, investigate iniviual ifferences in cone photopigments of normal trichromats. Specifically, they showe that the range of the results for 17 observers was too large to be explaine by only iniviual ifferences in photopigment optical ensity an pre-receptoral filtering. Their results were accounte for quantitatively by a small ifference 3-5 nm in the maximum of the L-cone photopigment. He an Shevell left one question unsolve: Which photopigments varies in lambamax? Rayleigh matches are constraine by the spectral positioning both of the M-cone an L- cone photopigments. In this stuy, we aress the inverse problem. We explore a screening metho that specifically estimates the M-cone an L-cone photopigment wavelengths of maximum absorbance in the absence of known genotype. We propose to ask observers to make multiple colour matches, i.e. a series of Rayleigh-type colour matches using various sets of test an primaries, in orer to reveal variations in M-cone an L-cone photopigments. We investigate the convergence an iscuss the accuracy of the metho. Methos Rayleigh- type colour matches The Rayleigh match is a match between a near-monochromatic yellow light an an aitive mixture of near-monochromatic green an re lights. The classical proceure makes use of

4 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb nm, 670 nm an 545 nm raiations. The test an the mixture are presente to the observer on a bipartite fiel. A match is achieve when the same number of photons is absorbe on the left an right half-fiels, in each family of cones. For Rayleigh-like matches where the S- cones are insensitive to the primary an test lights, this necessary conition can be expresse using two equations. We use the term cone funamental to mean the spectral sensitivity of the cones measure at the cornea. Any inert pigment inclue in the eye acts as a filter that transmits a fraction τ of the light at wavelength. It reuces the sensitivity of the eye compare to the sensitivity of the cones. Thus the number of photons absorbe by the L-cones, for example, can be calculate either as the prouct of the raiance incient at the cornea by the L-cone funamental l or as the prouct of the raiance by the spectral transmission factor τ of the inert pigments an by the cone spectral sensitivity. For a Rayleigh-like match, given the raiances y, g, r of the lights an the sensitivity l y, l g, l r an m y, m g, m r of the L- an M-cones to the lights, for L-cones for M-cones l = rr + l gg l yy eq. 1 m = rr + mgg myy eq. 2 With matrices, the equations can be written in terms of ratios of raiances as m l r r lg r m g g y y = ly my eq.3 When l y, l g, l r an m y, m g, m r are known, the system has a unique solution for the ratios of raiances, provie the matrix is non-singular. In most real experiments, test an primary lights are not monochromatic, an the spectral raiance of the light shoul be multiplie by the spectral response l an m of the cone funamentals so as to accurately express the total energy absorbe by the cones. Then, equations 1 an 2 are written as

5 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 5 = + y y l g g l r r l eq.4 = + y y m g g m r r m eq.5 In orer to simplify further calculations, it is possible to normalize the raiance to unity as r0, g0 y0 an multiply by an ajusting factor α, β, or γ. = + γ β α y l g l r l eq.6 = + γ β α y m g m r m eq.7 Written with matrices in terms of ratios of multiplying factor, it is r m r l 0 0 g m g l 0 0 γ β α γ = y m y l 0 0 eq.8 Again, when l an m are known, the system has a unique solution for the ratios of multiplying factors α/γ an β/γ, as long as the matrix is non-singular. The inverse problem consists of recovering the sensitivities of the cones from the raiances obtaine for one Rayleigh match. In this case, the system is uner-etermine. We woul expect that with several Rayleigh-like matches, the inverse problem, i.e. recovering the sensitivities of the cones from multiple Rayleigh match settings woul become over-etermine. Moelling of small variations in L-cone an M-cone photopigments. We nee to reconstruct the cone funamentals, i.e. the spectral sensitivity of the cones at the entrance to the eye. Cone funamentals epen on - the low ensity spectral absorbance of the photopigment, - the effective optical ensity of the photopigment in the outer segment of the cones, - the macular pigment optical ensity, - the lens optical ensity.

6 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 6 It has been shown empirically that the low ensity spectral absorbance of the photopigment can be represente by a unique template or nomogram Dartnall, 1953, when plotte on a logarithmic scale versus some function of wavelength: either the logarithmic value of the wavelength Stockman & Sharpe, 2000, or the normalize wavelength Govarovskii, 2000, or the fourth root of wavelength Barlow, 1982; Dartnall et al., 1983, or the logarithmic value of the wave number Baylor et al. 1987, or the normalize frequency Lamb, 1995; Carroll et al., The nomogram rule greatly facilitates the moelling since the low ensity spectral absorbance of an unknown photopigment can be simply calculate from the wavelength of peak sensitivity uniquely. Here, to create caniate M-cone an L-cone photopigments, we use the low ensity spectral absorbance curves of the M-cone an L-cone photopigments respectively, in log quantal units an in 5 nm steps, as propose by Stockman an Sharpe Then we shifte each template along a logarithmic wavelength scale, interpolate in 1 nm steps using the cubic spline metho, transforme to a linear scale, an obtaine the low ensity spectral absorbance curves A 0 of each caniate photopigment. Increasing the ensity of the photopigment in the cone outer segments broaens the banwith of the relative spectral absorptance. We calculate the cone absorptance spectrum, i.e. the fraction F q of the incient photons absorbe at the retinal level in cones of effective optical ensity D as F q DA0 = 1 10 eq.9 The lens an the macular pigment absorb light as two filters in front of the photoreceptors. So at the corneal level the cone funamental sensitivity is obtaine by multiplying the cone absorptance spectrum F q by the transmittance of the macular pigment τ mac an by the transmittance of the lens τ lens l q = F q,l-cones τ mac τ lens eq.10

7 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 7 m q = F q,m-cones τ mac τ lens eq.11 which can be converte then to energy units as l an m in orer to be inclue in a prouct with the spectral raiance of the incient light measure in energy. roceure As explaine previously, we expect that with several Rayleigh-like matches, it will be possible to recover the sensitivities of the cones from the raiances of the matches. The avantage of moelling the spectral sensitivities of the cone funamentals using a template for the photopigment sensitivity is that all l values, as all m values, are linke to 2 inepenent variables the wavelength of the peak sensitivity of the M-cone photopigment, the wavelength of the peak sensitivity of the L-cone photopigment, an 3 parameters the effective optical ensity of the photopigments, the lens optical ensity, the macular pigment optical ensity. Thus, we propose the following proceure: 1. First, the observer performe several real matches an obtaine several values for r / y an g / y, from which we use only the ratio of raiances r / g 2. Secon, we preicte the ratio of raiances r / g for a range of plausible values in terms of wavelength of the peak sensitivity of the M-cone an L-cone photopigment from 515 to 535 nm an from 540 to 570 nm respectively, in 1 nm steps. We coul simplify the proceure by fixing at typical values the effective optical ensity of the photopigment in the outer segment of the cones, the lens optical an the macular pigment optical ensity. 3. Finally, we programme in Matlab an algorithm to minimise the sum of square ifferences between observe an preicte values of the ratio of raiances r / g.

8 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 8 Experimental setup Observers were aske to perform colour-matches between a yellow test light an an aitive mixture of re an green lights. We chose 5 wavelengths in the mile- an long-wave range of the visible spectrum. Among the 10 possible layouts that coul be achieve with 5 lights, only 7 that yiele photopic luminance levels were assesse, with a yellow light as the test light 1. Y1586nm + G551nm = Y2580nm, at about c.m R1617nm + G551nm = Y2580nm, at about c.m R3639nm + G551nm = Y2580nm, at about c.m R1617nm + G551nm = Y1586nm, at about c.m R3639nm + G551nm = Y1586nm, at about c.m R1617nm + Y2580nm = Y1586nm, at about c.m R3639nm + Y2580nm = Y1586nm, at about c.m -2

9 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 9 Fig. 1. Layout of the three-channel optical system use for multiple Rayleigh matches. The moifie Maxwellian view layout with iffusers inserte before the Lummer cube allows enlarging the exit beam at the entrance of the pupil so that the observer coul see the 10 eg matching fiel in nearly natural viewing. One neutral wege allows ajusting the amount of "Re" light in the Re an Green mixture. Another neutral wege allows ajusting the amount of "Yellow" light. A three-channel optical system Fig. 1 was use an calibrate. A moifie Maxwellian view layout iffusers were inserte before the Lummer cube allowe enlarging the exit beam at the entrance of the pupil so that the observer coul see the 10 eg matching fiel in nearly natural viewing. Compare to the stanar 2 match, the 10 eg match offers some comfort to the observer an improves the repeatability of his matches. A im white surroun allowe for stabilising the state of aaptation of the observer. The quasi-monochromatic test an primary lights were obtaine using interference filters. One neutral wege allowe ajusting the amount of "Re" light an controlling the hue of the Re an Green mixture. Another neutral wege allowe ajusting the amount of "Yellow" light an controlling the brightness equilibrium of the Rayleigh match. Spectroraiometric calibration was achieve in situ. Subjects Fourteen colour normal observers 5 men, 9 women were aske to perform 7 Rayleigh-like matches 6 repetitions for 12 observers, 15 repetitions for observers FV an F. Their colour vision was screene using Ishihara plates, D15 an Nagel anomaloscope Table 1. Anomaloscope settings were normal for all but two observers CD an who set the regreen mixture scale of the anomaloscope at the borer between normal an protanomalous ranges. A euteranomalous observer serve as a control subject.

10 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 10 Table 1. Description of the group of observers. Normal setting on the anomaloscope is An anomaloscope setting at 46 yiels an anomalous quotient equal to 0.74 an efines the borer between normal an protanomalous observers. Known inheritance is reporte in the text. Wavelengths of M-cone an L-cone peak sensitivity estimates are obtaine using tabulate photopigment spectral absorbance. Observer Sex Age Ishihara anel Nagel Known M-cone L-cone D15 anomaloscope inheritance max max CD F 28 Normal Normal 46 YES DO M Normal Normal Normal FR F 58 Normal Normal Normal YES FV F 58 Normal Normal LS F 23 Normal Normal MH F 23 Normal Normal NB H 27 Deutan Deutan NG F 21 Normal + Normal YES NK M 28 Normal Normal Normal M 21 Normal Normal F M 30 Normal Normal Normal RD M 59 Normal Normal Normal SJV F 27 Normal + Normal & 45 SV F 23 Normal Normal Normal VB F 44 Normal Normal Normal YES

11 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 11 Results The algorithm allowe us to ajust the moel parameters of the putative factors of variation in orer to minimize the sum of square ifferences between preicte an real results of matches. rovisionally, we fixe at typical values Stockman & Sharpe, 2000 the effective optical ensity of the photopigment in the outer segment of the cones 0.38 for a 10 eg fiel, the lens optical ensity at 400 nm an the macular pigment optical ensity at 460 nm for a 10 eg fiel. Fig. 2. 3D mesh plot of the sum of square ifferences between observe an preicte values of the ratio of raiances r / g for observer F.

12 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 12 Fig. 2 shows a 3D mesh plot of the sum of square ifferences between observe an preicte values of the ratio of raiances r / g for one observer. We notice the elongate shape of the hollow region. Fig. 3 isplays the contours of the sum of square ifferences between observe an preicte values of the ratio of raiances r / g for this observer. Here, a minimum is visible at Optimum max,m-cones = nm Optimum max,l-cones = nm Fig. 3. Contours of the sum of square ifferences between observe an preicte values of the ratio of raiances r / g for observer F.

13 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 13 For all observers we foun qualitatively similar contours as in figure 3, with the elongate shape of the hollow space. Nevertheless, the minimisation proceure yiels a unique solution for the wavelength of the peak sensitivities of the M- an L-cone photopigments. Fig. 4. Ajuste wavelengths of the L-cone an M-cone peak sensitivity of all observers. Square symbols for male observers. Diamon symbols for female observers. Only results of observers whose initials are mentione in the text are labelle. Thirteen observers lie within the cluster efine by a circle.

14 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 14 In fig. 4 we present the results of all observers on one graph. Remarkably, observer CD shows a result positione about the upper left corner of the graph, which means that the optimum peak wavelength for the M- an L-photopigments are close to each other. All other normal observers results lie in a cluster about 8 nm wie. As an aitional check of the multiple Rayleigh match proceure, a euteranomalous observer NB on the Nagel anomaloscope was teste. Since the caniate abnormal photopigment can be erive from the M- or the L-template, the solution epens on whether the anomalous photopigment is base on the M- or the L- template. Assuming a small ifference in wavelength of peak sensitivity between the anomalous M-cone photopigment an the normal L-cone photopigment DeMarco et al., 1992, we erive the anomalous photopigment spectral absorbance from the L-cone pigment template. Then, the euteranomalous observer s multiple Rayleigh match settings coul be preicte with a pair of L-cone max = nm an intermeiate cone photopigments max = nm. Discussion Experimental results showe that multiple Rayleigh matches allow ientifying the pair of photopigments that satisfy the iniviual settings. We also examine whether the istribution of the optimum wavelength of peak sensitivity reveals iniviual ifferences in M- an L- cone photopigments. After iscussing the sources of uncertainty, we will concentrate on iniviual ifferences. Sources of uncertainty The raiometric calibration of the equipment, the assume input values of the fixe parameters an the choice of photopigment spectral absorbance templates, are sources of uncertainty which may be of importance consiering the small number of Rayleigh-like equations an the limite repeatability of the observer s settings.

15 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 15 We checke that propagation of error of the spectral position of the maximum transmittance of the filters as little as 1 nm results in a shift of 1 or 2 nm of the L-cone photopigment sensitivity. Although the matches were easy to perform, an although the observations were reproucible, we face several ifficulties to erive iniviual factors of variation. At first, we ignore four factors of variation: the macular pigment that has little effect on large fiels beyon 551 nm, the peak optical ensity of the visual pigments, the peak optical ensity of the macular pigment, an the optical ensity of the lens. In a previous stuy Viénot, 2001, we showe that, with careful control of the colour-matching functions, the preiction of all factors of iniviual variation can be precise. Here, since our observers performe 7 equations, we moifie the software in orer to ajust, in aition to the wavelength of peak sensitivity of the photopigments, the optical ensity of the lens, or the effective optical ensity of the M-cone photopigment, or the effective optical ensity of the L-cone photopigment. Inee, ifferent estimations of the effective optical ensity of the M-cone an L-cone photopigments have alreay been accounte for in the literature Smith et al., Three observers were oler than 58 years FR, FV, RD. Observer FV lies at the borer of the cluster, the other two insie. We verifie that multiplying the lens optical ensity by 1.56 as for a 60 years ol observer okorny, Smith & Lutze, 1976 change only moerately the spectral position of the M-cone photopigment less than 1.8 nm an the L-cone photopigment less than 0.7 nm. In aition, it is known that a change of effective optical ensity of the photopigment affects notably the ajuste ratio of raiances in Rayleigh-type matches. In the case of the ual match which resembles equation #5 in our experimental stuy, He an Shevell 1994 calculate that the effect of a 5 nm shift in the L-cone funamental on the ratio of two particular Rayleigh-type matches is about as large as the effect of the normal extreme

16 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 16 variation in optical ensity an pre-receptoral filtering. Thomas an Mollon 2004 insiste on the impossibility to ientify a unique pair of photopigments that satisfy a given Rayleigh match because the match is etermine by the max of the photopigment an also its optical ensity. Here, we evaluate the observers who mae the largest number of repetitions. As anticipate, optimizing the effective optical ensity of a single photopigment results in a noticeable spectral shift up to 9 nm for the M-cone photopigment an up to 2.5 nm for the L- cone photopigment. Although ajusting aitional parameters allows reuction of the resiuals of the fit, such results must be consiere with caution as the system of 7 equations with 3 or more unknowns becomes only slightly over-etermine with respect to the variability of the observer s experimental settings. The choice of the template has a consierable influence on the final convergence of the algorithm. Alternatively, we moele the optical ensity spectrum t x of the ilute photopigment using analytical expressions. From Stockman an Sharpe 2000, we use log10t x = a + bx 2 + cx 4 + x 6 + ex 8 + fx 10 + gx 12 + hx 14 eq.12 where is the wavelength, max is the wavelength at peak sensitivity a, b, c,, e, f, g, h are the constant terms propose by Stockman an Sharpe 2000 x = log10 *558 / max. From Lamb 1995, we use S x = expa A x + expb B x + expc C x + D 1 where a, b, c, A, B, C, D are the constant terms propos by Lamb 1995 x = max /.

17 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 17 Then the photopigment sensitivity only epens on the wavelength at peak sensitivity max. Surprisingly, the spectral positions of the M-cone an the L-cone photopigment maximal absorbance collapse to the same peak wavelengths for 3 female observers CD, MH, FV when using the Lamb s template an for two observers CD, MH when using Stockman & Sharpe s template. For the remaining 11 observers, the algorithm yiels shifte wavelengths of the M-cone an L-cone photopigment peak sensitivity, epening upon the choice of template Fig. 5. Respective ranges are [519.5 : 524.3] an [555.4 : 561.9] with the tabulate templates, [529.3 : 538.8] an [556.7 : 567.8] with Stockman an Sharpe s polynomial template, [523.7 : 533.7] an [547.5 : 559] with Lamb s analytical template. Such isagreements reflect variations in the esign of the template, mainly in the positioning of the maximum of the template with respect to the slope at long wavelengths. The template that serves to moel photopigment absorbance is as critical to change the slope at long wavelengths as the cone effective optical ensity.

18 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 18 Fig. 5. Ajuste wavelengths of the L-cone an M-cone peak sensitivity are higher using Stockman an Sharpe s polynomial template than using their tabulate template. Figure 5 also shows that the range of M-cone an L-cone photopigment sensitivity is more restricte with the tabulate template than with Stockman an Sharpe s polynomial template. Thus, an accurate template is necessary for the multiple Rayleigh match proceure to converge. In the ignorance of a template base on soun theoretical principles, our ecision to relate the M-cone pigment an the L-cone pigment to inepenent patterns is probably wise.

19 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 19 Iniviual ifferences For all observers, the system of 7 equations converges to a unique solution. The istribution of the wavelength of maximum sensitivity of the photopigments inclues a cluster with 13 observers as shown in figure 4. Sources of uncertainty make it ifficult to rely on the absolute location of the wavelengths of peak sensitivity of the photopigments. Nevertheless, compare to the ata reporte in the literature, from for the normal M-cone photopigment to nm for the hybri M-cone photopigment an from for the hybri L-cone photopigment to nm for the normal L-cone photopigment after Sharpe et al, 1999, the multiple Rayleigh matches yiel somewhat shorter peak wavelengths for the M-cone photopigment: to nm an a quite plausible range for the L-cone photopigment: to nm. The case of observer CD nees to be explaine. rotanomaly coul be suspecte from the spectral position of her photopigments. However it is not obvious from her anomaloscope settings. We note that CD an have anomaloscope settings at the borer of the normal range but only CD s point is outsie of the cluster. Four observers are aware of eficiencies in their family. Observer CD has a colour blin uncle, from the mother s sie, an observer NG is aware of some colour vision efect for her father, with no more information, so some extra anomalous pigment might well be operative. Nevertheless, only CD is out of the cluster. Observer VB who has a euteranopic brother, an observer FR whose father an two sons are euteranopes lie insie the cluster. As expecte they are not carriers of an anomalous photopigment. Most instructive is the istribution between men an women within the cluster. All men s multiple Rayleigh matches yiel well separate L-cone an M-cone photopigments. For a few women FV an NG, an possibly MH, the minimum ifference between observe an preicte results occurs when both L an M optimum peak wavelengths move towar each

20 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 20 other. Observer NG was recruite because she coul rea the theoretically conceale igits of plate 45 of the Ishihara album without any hesitancy but observer SJV who coul rea conceale igits of plates 5 an 45 has well separate photopigments. We note that for FV an MH, algorithms using a unique analytical template for L-cone an M-cone photopigments converge to the same peak wavelength estimates for the two photopigments. Shifts of L-cone an M-cone optimum peak wavelength seem to be correlate, as if the pigments were attracte by a unique generic photopigment. Several explanations can be given. One possibility is that the variability of the matches is too high to allow the fit to converge. Alternatively, the Rayleigh-type colour matches are highly correlate an the equations cannot be regare as inepenent. Or, the assumption that a unique L-cone photopigment an a unique M-cone photopigment oversimplifies the analysis. Although genetics has shown that multiple pigments are not rare in the colour normal population: 8% for males Sjoberg et al., 1998, the pattern is expecte to be complex with women since about 15% of them inherit an X-chromosome carrying an abnormal opsin gene array from one parent Sharpe et al., Therefore, the female pattern is complex. The fact that in our reuce sample, only females ten to have close L-cone an M-cone photopigments might reflect multiple pigments. Conclusion In conclusion, with simple assumptions, multiple Rayleigh matches from a colour normal observer converge to a pair of L-cone an M-cone photopigments that satisfy the iniviual s settings. The locations of the wavelength of peak sensitivity of the L- an M- cone photopigments are preicte separately which represents an avantage for multiple Rayleigh matches versus ual Rayleigh matches. In our sample, the istribution of optimum preicte wavelengths of peak sensitivity inclues a cluster. The case of one observer is ambiguous. Nevertheless, in the face of the sources of error an uncertainty, it remains ifficult to

21 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 21 accurately preict the L-cone an M-cone photopigment wavelengths of maximum absorbance. Accurate tabulate templates are essential to ensure convergence to precise positioning of iniviual M-cone an L-cone photopigments.

22 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 22 Acknowlegments We thank colleagues an stuents who volunteer as observers. We acknowlege the contribution of Estelle Michon from the MST Optométrie at Université Orsay to a preliminary phase of this stuy, Ken Knoblauch an the reviewers for their valuable comments.

23 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 23 References Barlow, H.B What causes trichromacy? A theoretical analysis using comb-filtere spectra. Vision Research, 22, Baylor, D.A., Nunn, B. J. & Schnapf, J.L Spectral sensitivity of cones of the monkey Macaca fascicularis. Journal of hysiology, 390, Carroll, J., McMahon, C., Neitz, M. & Neitz, J Flicker-photometric electroretinogram estimates of L:M cone photoreceptor ratio in men with photopigment spectra erive from genetics. Journal of the Optical Society of America A, 17, Dartnall, H.J.A The interpretation of spectral sensitivity curves. British Meical Bulletin, 9, Dartnall, H.J.A., Bowmaker, J.K., & Mollon, J.D Human visual pigments: microspectrophotometric results from the eyes of seven persons. roceeings of the Royal Society, Lonon, Series B, 220, DeMarco,., okorny, J., & Smith, V.C Full spectrum cone sensitivity functions for X-chromosome linke anomalous trichromats. Journal of the Optical Society of America A, 9, Govarovskii V.I., Fyhrquist N., Reuter T., Kuzmin D.G. & Donner K In search of the visual pigment template. Vis Neurosci. 17: He, J.C. & Shevell, S.K Iniviual ifferences in cone photopigments of normal trichromats measure by ual Rayleigh-type color matches. Vision Research, 34, Lamb, T. D hotoreceptor spectral sensitivities: common shape in the longwavelength region. Vision Research, 35, Neitz, J. & Jacobs, G.H olymorphism in normal human color vision an its mechanisms. Vision Research, 30,

24 23/04/ :27igments e cônes_vns _vienotserraultaro_siteweb 24 okorny J., Smith V.C. & Lutze M Aging of the human lens. Appl. Optics 26: Sharpe, L. T., Stockman, A., Jägle, H., & Nathans, J Opsin genes, cone photopigments, color vision an colorblinness. In Color vision: From Genes to erception, e. Gegenfurtner K.R. & Sharpe L. T., pp Cambrige, UK: Cambrige University ress. Sjoberg, S.A., Neitz M., Baling S.D. & Neitz J L-cone pigment genes expresse in normal colour vision. Vision Research, 38: Smith V.C., okorny J. & DeMarco Full-spectrum cone sensitivity functions for X-chromosome-linke anomalous trichromats. Journal of the Optical Society of America A, 9, Smith V.C., okorny J. & Starr S.J Variability of color mixture ata I. Interobserver variability in the unit coorinates. Vision Research, 16, Stockman, A. & Sharpe, L. T Spectral sensitivities of the mile- an longwavelength sensitive cones erive from measurements in observers of known genotype. Vision Research, 40, Thomas.B.M. & Mollon J.D Moelling the Rayleigh match. Visual Neuroscience, 21, Viénot F Retinal istribution of the macular pigment an the cone effective optical ensity from colour matches of real observers. Color Research an Application, 26, S264- S268.