Original article J. Optics (Paris), 1994, vol. 25, n' 3, pp. 81-92

DEPARTAMENTO DE OPTICA, UNNERSWAD DE GRANADA

Granada, Spain

DIFFERENTIAL COLOR THRESHOLDS AND NEW RESULTS ON FAILURES

OF CHROMATICITY AND LUMINANCE PREDICTION L. JIMfhBZ DEL BARCO, E. HITA, I. R. IIM6NEZ and I. ROMERO

KEY WORDS : MOTS CL& : Colour vision Colour discrimination Discrimination chromatique Colorimeuy Colorimdtrie

Vision de la couleur

SUMMARY : The expedmental determination of differential chromaticity thresholds from metameric matches show discrepan- cies in colotimetric prediction using the stand& observers established by the CIE [Hita er al., J Opt Soc Am A 1986; 3 ~ : 1203-09 ; Jimenez delBarco etal.. I Optics 17, 1986 ; 247-541. In this work we have determined whether the discrepancies of co lo r ime~c prediction me contained in the differential color thresholds. To study the possibility of generalizing prior results to a wider range of experimental conditions we have carried out new experimen~ determining the differential color thresholds af an achromatic stimulus from metameric matches, using direct vision and a foveal field of 1.5'. The results are expressed in terms of the color-matching funclions of CIE-z' standard Obsewec. as well as those proposed by a'-Stiles and Burch and Nayatani et al. The discussion of the results is made taking into account different causes which may explain the failures of colorimetric prediction detected ! rod inhusion, interactions of the responses of cones sensitive to shoe-wavelengths, errors and matching imprecision. Results show that the failures of colorimeuic prediction obtained under our experimental conditions exceed the color differential threshold. These discrepancies increase with the relative difference of the S-cone excitation level for the matched stimuli.

Seuils diffbrentiels de chromaticite et nouveaux rhul- tats sur les d6fauts de pr6diction de chromaticite et de luminance

&SUM!?. : Les 6sultats obtenus par Hita et ai'(J Opt Soc Am A 1986; 3 : 1203-9) et par Jimenez del Barco el al (J Optics 1986 ; 17: 247-54) montrent les d€fants d'additivite colohdtrique a paair de la d6termination des seuils diffdrentiels de chromaticite pour stimuli metameres. Dans ce travail nous mons dtudie si les ddfauts de pfidiction colorim6trique son1 contenus dans le seuil diff6rentiel de chromaticii6. Pour audier la possibilii6 d'une generalisation des r€sultats pdalables ?a des autres conditions experimentales nous awns dalisd des ~ O U V B ~ U X expdriments avec un stimulus achromatique mvaillant avec champs visuels de 1.5'. luminance dans le niveau photopique bas et vision directe.

Les r6sultats ont 6t.6 exprimes pout I'obsetvateur de d€&ence colorimdtrique CE-2' et aussi pour les proposer, par 2a-Stilcs et Burch et Nayatani er al. Les defauts d'additivitd sont analysds seloo plusieurs facteurs : intrusion des bttonnets dans la vision de la couleur. interactions des fipponses des cones m a c maxime sensibilite aux longueurs d'onde counu, et erreurs dans la r6alisation d'dgalisations ooladmdtriques. Les r6sultats obtenus m4ntrent que ins ddfauu; de prddictions,

sous nos conditions exp&imentales, excedent le seuil diffdrentiel de la couleur. Les defauts trouv6s augmmentent avec la difference relative du niveau d'excitation des canes type S entre les deux stimuli dgauu.

IhTRODLJCTION prediction in the tristimulus values obtained from matches between monochromatic primaries and the

Practical Colorimetry is developed from CIE standard C for a visual field of 2" ; he used the Grassmann's laws of additive color mixtures. Several methods of Maxwell matches and of maximum authors have obtained results that show failures of saturation. Wyszecki and Stiles [21 made similar additivity and linearity in color vision and, C0np.e- experiments using the CIE standard source D65 and queatly, failures of colorimetric prediction in color also found failures of linearity similar to those matches. Crawford [I] found failures of colorimetric observed by Crawford. Other authors detected fail-

82 L. J I M ~ E Z DEL BARCO et al.

ures of additivity under experimental conditions such as large-field color vision (Clarke [3], Nimeroff [4], Palmer [5-6]), peripheral vision (Moreland and Cruz 171). low luminance levels (Aguilar and Stiles IS]), small sizes and.stimuli of short duration (Kaiser 191).

Different causes may explain the failures of additi- vity and linearity : rod intrusion (Palmer 15-61, Trezona [IO], Stabell and Stabell [ l l J ) ; post-recep- toral interactions of the responses of cones with a maximum of sensitivity to short wavelengths (Ingling and Dmm [12]) ; matching imprecision (Trezona 1131, Stiles [141).

Most authors who analyze this problem do colors matches and then study the failures of colorimemc prediction by analyzing the tristimulus values and the spectral radiances corresponding to the stimuli studied. However, from the viewpoint of practical colorimetry, a color match may be affected by the error associated with the limitation of the color discrimination capacity of the visual system; i.e. minimum perceptible differences or differential color threshold (MacAdam [15], Brown and MacAdam [16], Wyszecki and Fielder /17]). In short, for a representational system such as CIE-1931, a color stimulus (xo, yo, Y o ) is characterized by a group of color coordinate values (x, y, Y) which constitutes its differential threshold of color. Classically, the differential color threshold is represented by an error ellipsoid that contains stimuli of different spectral radiance Le,+ which an observer is unable to discrimi- nate completely (Brown and MacAdam [161).

Most of the studies which detect failures in Grassmann’s laws include only color matches. It is possible that, although discrepancies exist between the nistimulus values of both the reference and matched colors, these discrepancies are contained within the differential color threshold of the reference color. This situation would be tolerable from the point of view of differential colorimetry. In the present work we have carried out experiments which detect failures of additivity, but determining the differential color threshold of the color matches. Our aim is to determine if the magnitude of the color discrepancies is contained in the corresponding threshold. On the other hand, at the CIE’93 Sym- posium (Yiena) questions have been debated con- cerning brightness-luminance discrepancies found in some metameric matches of lights and non-additivity problems encountered in Colorimetry. Thus, we feel that the proposed study will be useful because there are few works in the literature which analyze additivi- ty failures in colorimetric prediction while taking into account the differential color threshold.

There are two important aspects of the classical experiments [15-171 which determine differential color thresholds : 1) most authors make initial iso- meric matches, thereby avoiding possible failures of linearity and additivity, and 2) because, in most

J. Optics (Paris), 1994, vol. 25, no 3

cases, the color-matching functions of the real ob- server are unknown, differential color thresholds are generally determined by employing the color-match- ing functions of the CE standard observers. These standard observers are an average of the color-match- ing functions of different real ,observers ; thus, it is possible to study whether the colorimetric discrepan- cies (found by real observers who took part in the experimental determination of the differential color threshold) are contained within the differential color threshold obtained with different standard observers.

Hita et al. [18] and Jimehez del Barco et al. [19- 201 found failures of additivity when they made metameric matches and determined the differential color thresholds with primaries produced by a group of interference filters with narrow bandwidth, and reference colors produced by filters with a large bandwidth. A bipartite foveal vision field of 3” was used with a low photopic luminance level (average retinal illumination of 30 Td) and Maxwellian vision was employed. These results were obtained using the CIE-1931 standard observer and CIE-Judd. These failures persisted even when rod intrusion was av- oided during the cone plateau period following bleaching [19].

In this article new results are shown. We have varied the experimental conditions (direct vision and 1.5” foveal fields) and extended the region of stimuli studied [19-201 to an achromatic stimulus to detect the possible additivity failures in the event that color vision mechanisms are excited in more balanced proportions. We have measured differential color thresholds for an achromatic stimulus, using three observers and different degrees of metamerism in the initial matching. For ow results we have used the C 5 1 9 3 1 standard observer, the color-matching functions of 2”-Stiles and Burch [Zl] and the C E - 1931 standard observer with the modifications of Nayatani et al. 122.1. The aim was to discover whether the possible failures of additivity are con- tained in the differential color threshold when differ- ent color-matching functions are employed. At the same time this study includes an analysis of lumi- nance thresholds and Abney’s laws which was not carried out in the previous works [18-19].

EXPERIMENTAL DEVICE

The experimental device consisted essentially of two visual colorimeters of a modified DonaIdson type (each with three primary colors), the purpose of which is to produce the two color stimuli that constituted the test : a reference stimulus and a variable stimulus presented in a circular bipartite field. A general schematic view is shown infigure I. The filters that wansmitted the light beam and produce the three primary colors in both colorimeters

J . Optics (Paris), 1994, vol. 25, no 3

S, METHOD

L. JIM~NEZ DEL BARCO et al. 83

i i

! ! r4f P -!- U c3--.(B--1=)+ ! b.

!

1 - ! O !

I !

FIG. I . -Schematic view of the experimental device.

were illuminated with normal incidence using two identical stabilized halogen lamps S, and S, (sylvaoia FFX 500 W). A diaphragm system with adjustable apertures was coupled to the color filters, enabling the luminous flux to be controlled in all of them. The colorimeters were refrigerated to avoid temperature variations in the filter transmittance. In each of the integrating spheres, E , and E,, a mixture of both primary sets was carried out. The field was futed at 1.5' by a diaphragm D situated at the exit of the photometric cube K, from which emerged two juxtap- osed beams, which constituted the color test. The exposure time was controlled by an electro- mechanical shutter 0 situated at the exit of the diaphragm D.

To avoid potentially small errors in estimating the filter transmittance, the device was calibrated by directly determining the spectral radiance Le, of the color stimulus produced by the experimental device at the exit of the photometric cube K. The calibration system consisted of a monochromator Jobin-Yvon with a 2 nm maximum resolution situated in the same position as the eye. The beam from sphere E , or Ez was focused into its entrance slit by means of an achromatic double-lens. Attached to the exit slit of the monochromator was a silicon photodiode EG&G (HUV-4OOOB) with good sensitivity, stability, linearity, and signal-to-noise ratio characteristics. The radiometric measurements were registered with a digital multimeter with 1 pV resolution. In the spectral measurement of the radiant flux we have taken into account the spectral responsivity of the instrument as a whole.

-

Experimental conditions and matchings

The results from these previous stages 118-191 were for stimuli with relatively high saturation. Therefore we might consider generalizing the results to less saturated stimuli, and thereby follow the rules set by the CIE for the generalization of colorimetric data 1231. For this reason we determined the differen- tial color thresholds from metameric and isomeric matches for an achromatic stimulus, since in previous works no stimulus corresponding to this region was studied. We must bear in mind that in an achromatic stimulus the effects of the primaries are in more balanced proportions. This is an important issue when studying the average response of the visual mechanism.

We chose an achromatic reference stimulus of chromaticity coordinates (x = 0.397, y = 0.425) in the CIE-1931 diagram. The luminance was in the low photopic level (average retinal illumination of 48Td). The visual field was 1 3 , thus avoiding possible rod intrusion, although previous experiments done with photopigment bleaching during the cone plateau period 1191 have demonstrated that results conceming failures in colorimetric prediction were independent of this possible interaction. The sur- rounding field was dark, and each observer was adapted to darkness for a period of 10 min before beginning the experimental session.

Measurements were taken with two observers (males, 35 and 37 years of age without any kind of ammetropia) with normal color vision according to the Ishibara, Famsworth Panel 15-D tests and Pickford-Nicolson anomaloscope, and some experi- ence in this type of experiment. For each observer four differential color thresholds were determined (one from an isomeric match and the other three from metameric matches with different degrees of metamerism [ZO]).

To obtain different matches with different degrees of metamerism, we carried ont three metameric matches and one isomeric match for each observer. In the metameric matches (M-VI, M-VU. and M- VIII) glass color filters of wide bandwidth were placed in the reference colorimeter and interference color-filters were placed in the variable colorimeter. In the isomeric matches, identical interference color- filters were placed in both colorimeters. Table I shows the spectral characteristics of the fdters employed in the different matches (wavelength of maximum transmission and bandwidth at 0.5 peak). Figure2 presents the triangles that determine the group of primaries employed in each match, while figure 3 shows the relative spectral ,radiance L,, of the diffeient matches for the observer L. J.

84 L. JIMBNEZ DEL BARCO et al. J. Optics (Paris), 1994, vol. 25, no 3

Experimental procedure and calculation of the differ- entia1 color thrcshold

TABLE I Spectrol chorocteristics of the filters used

in lhc different matchings.

I B3

1 Matching

21.0 474.3

20.0 662.7 nm Isomeric

B3

595.0 I Metameric M-VJ I E, I I 555.3 I

21.0 474.1

B1

Metameric M-VU

20.5 458.5 Metameric M-VUl

82 I (*)

115 421.3

R2 I 20.0 I I G 20.7

For each initial matching the differential color threshold was measured by means of the constant- stimuli method and was computed using the statistical method proposed by Wyszecki [%I. In this procedure there is an initial visual matching, for both chromati- city and luminance, by manipulating the controls of the variable colorimeter. From this match, the refer- ence stimulus is compared with a series of stimuli (which surrounded the reference one) selected from $5 different evenly distributed directions in the CIE- 193 1 color space, reaching distances that make them clearly distinguishable from the latter. Around 120 comparison stimuli were selected in each threshold determination, each of these obtained by varying the diaphragms of the colorimeter. To avoid tactile effects the variable colorimeter controls were ma- nipulated only by the experimenter and the observer’s task was only to judge whether the two stimuli (reference-variable) presented simultaneously were equal or not ; thus the observer participated as a zero instrument. Each variable stimulus was compared 10 times with the reference stimulus in order to assign to each variable stimulus a statistical weighted function

FIG. 2. -Triangles in the CIE (x-y) diagram, determined by the chromatid- ties of primary colors in eoch matching for the achromatic stimulus (SI.

Y

0.0 0.2 0.6 0.8 O m 4 x

J . Optics (Paris), 1994, vol. 25. n" 3

(2.0

10.0

z 8.0 x 6' z 2 3 4.0

E 6.0

Y z

2.0

0.0

A I .6

M-VI I

1.0

0 2

0.0

C

L. JIM6NEZ DEL BARCO et al. 85

equal to the number of times it was judged as being the same. We can consider this number a statistical evaluation made by each observer of the similitary between each comparison stimulus and the reference one. The exposure time of the test for stimuli comparisons was 1 sec C251, with a IO sec interval between presentations. The experimental sessions were distributed throughout different hours of the day in order to average out the possible effects of the psychological condition of the observer [25]. In order to avoid observer fatigue, the session lasted no more than 20 min. The differential threshold was deter- mined by means of a discrimination ellipsoid contain- ing 95 % of the affirmative answers in the (x, y, Y ) space, which was obtained by carrying out a statisti- cal adjustment based on a variance and covariance analysis of the (x, y , Y ) values weighted with the corresponding number of affirmative answers [26].

The equation for the discrimination ellipsoid takes the form :

A(x -xo)' + B(y -yo)' + C (Y - Yo)+'

+ 2 0 ( x -xo)cv - Y o ) + 2ECv -Yo)(Y - Yo) + 2 F (x -xO) (Y- Yo) = 7.81

where xo. yo represent the chromaticity coordinates and Yo the luminance of the center of the ellipsoid. The first member of the equation is distributed as ,yz (chi-square) with three degrees of freedom. When the value is set at 7.81, the discrimination ellipsoid will contain the 95 % of the distribution.

From the above equation we can also determine the values that correspond to the maximum and minimum luminance of the discrimination ellipsoids. These values allow us to check Abney's law regulating the luminance in color matches under our experimental conditions. The principal elliptical section, which results from cutting the ellipsoid on a plane perpen- dicular to the luminance axis in the CE-1931 system and passing through its center, provides a measnre- ment of the differential chromaticity threshold for the reference stimulus. Figure 4 shows, as an example, a discrimination ellipsoid obtained with a statistical adjustment of the cloud of points in the CIE-1931 system using the method described above. In this figure we can observe the principal elliptical section that passes through its center (no. yo, Yo), and the

4 FG 3 . -Relative spectral radiance of the srimuli corsponding to the different metameric matches and observer L. 3. : A) : M- VI : B : M - W ; and C : M-VIII. Solid curves correspond to the reference stimulus obtained with primaries with great spectral bandwidth. Dashed curves correspond to the matched stimuli obtained with primaries of narrow spectral bandwidth,

86 L. JR&NEZ DEL BARCO et d.

0.43

Y 0.41

0.39

J . Optics (Paris), 1994, vol. 25, no 3

- - - - - -

'i

x J WO. 4. -We can see, as an example, a discrimination dipsoid obtained with n stotisrical adjufment of the cloud of points in the CE-1931 system using the consfont-stimuli method, We observe the principal elliptical section (a mea.surement of fhe differential chromaticiq threshold for the reference stimulus) and the maxi- mum (Y-) and minimum (I",") luminance values of fhe discrimi- notion ellipsoid.

values Y,, and Y,, that represent the maximum and minimum luminance of the discrimination ellipsoid, respectively.

RESULTS

Concerning failures in chromaticity prediction

The chromaticity discrimination ellipses, which refer to the CIE-1931 standard observer, are shown for the observers L. J. and J. R. (Figs. 5(A) and (B)). An analysis of these figures shows significant inter and intra-individual differences in the discrimination ellipses when the degree of metamerism is changed in the initial matches. The elliptical sections are different in all the metameric matches analyzed for all the observers and for the same achromatic refer- ence stimulus. These variations are generalized in comparison to the isomeric match. The inter-ob- server variability for the same color match is adequately explained in the litteratme and it is in agreement with the results of Ruddock [27], Viknot [281, Nayatani et al. 1291. This variability could be caused by differences in pre-retinal photopigments, eye lens and macular optical densities. Nonetheless, in the present work we are more interested in analyzing the colorimetric discrepancies that appear in the thresholds determined for the same observer

0.45 L.J.

0.43

J 0.41

0.39

0.37 - 0.35 0.37 0.39 0.41

x

0.45 I I J.R.

t M-VI1

0.37 - 0.35 0.37 0.39 0.41

B x

FIG. 5. - Principol elliptical seefiom of discrimination ellipsoids for the differeef initial matches analyzed with reference lo the CIE-1931 standard observer for the achromatic stimulus : A : observer L. J . and B : observer J . R .

when we vary the degree of metamerism in the initial matching. In this sense, for any single observer, variations in area, orientation and semiaxes-relation- ships (except in the coordinates of the centers that will be discussed in great detail later) might be included among the intra-individual variations studied by Wyszecki and Fielder [17].

Since the center of the isomeric ellipse can be considered representative of the chromaticity of the stimulus matched to the reference stimulus 1181, it is important to note for all the observers the consider- able discrepancies between the chromaticity of the reference stimulus and the centers of the discrimi-

J. Optics'(Paris), 1994, vol. 25, no 3

nation ellipses in the case of metameric matches using the CIE-1931. These discrepancies do not occur with the isomeric match.

Figure 6 shows the results obtained for the ob- server L. J. using the CIE color-matching functions with the modifications of Nayatani et al. [22]. while infigure 7 we show the results referred to the color- matching functions of 2"-Stiles and Burch [ X I . We can deduce that the failures of colorimetric prediction

Stimulus Observer

Achromatic L. I.

J.R.

L. JWENEZ DEL BARCO et al. 87

Matching Y,, Y,, Yo

I Som. 4.04 3.95 3.99 M-VI 4.12 3.95 4.03 M - W 3.64 3.30 3.47 M-VIII 4.05 3.54 3.79 I som. 4.06 3.94 3.99 M-VI 4.03 3.86 3.95 M-VU 3.44 3.19 3.31 M-VUI 3.67 3.40 3,.54

0.45 L.J.

0.43

Y 0.41

0.39

0.37 0.35 0.37 0.39 0.41

x

FIG. 6. -Principal elliptical sections of discrimination ellipsoids for the different initial morches analyzed and observcr L. 3. with reference to the CE-1931 standard observcr with the modifi- carions of Nnvatani for the achromatic stimulus.

0.40 0.38 0.40 0.42 0.44

x

FIG. 7. -Principal elliptical sections of discrimination ellipsoids for the different initial matches analyzed and observer L. 3. with reference to the Stiles and Bwch color-matchingfuncrioions for the nehromatic stimulus.

88

the luminance-of all the stimuli withim the error ellipsoid. In the case of the isomeric match mentioned above the stimulus luminance within the error ellip- soid with the hikhest luminance is 4.04 cd/m2 and the luminance of the stimulus with the lowest luminance is 3.95 cd/m2. In the case of the ellipsoid correspond- ing to the metameric match M-VII, these values are 3.64 cd/m2 and-3.30 cd/mz respectively. Because the lowest luminance of the isomeric match (3.95 cd/mz) is higher than the highest luminance of the metameric match M-VI1 (3.64 cd/m2), we can deduce that the ellipsoids do not intersect, thus revealing important failures of luminance prediction. A similar situation occurs with theobserver J. R. and the matchs M-VLI and M-VIII. These discrepancies between the error ellipsoids were. the same for the two observers when the 2"-Stiles and Burch color-matching functions and the CIE-1931 standard observer with the modifi- cations of Nayatani were employed.

In view of these results and with the aim of generalizing them to other regions of the chromaticity diagram, we have revised the error ellipsoids ob- tained in our laboratory in previous works 1181. In these results we detected failures of colorimemc prediction but without having studied the luminance variable. In these experiments four differential color thresholds (three under metameric conditions) were determined for stimuli with hues : blue, purple, reddish-orange,: yellowish-green and yellow. In this case the foveal field was of 3' and maxwellian vision was used. Table 111 presents the results in luminance for two observers and different matches using stimuli of different regions of the chromatic diagram. These results were obtained using the CIE-1931 standard observer. We can observe the same failures of luminance predictions for all the different stimuli and all the observers (blue : M-IV ; purple M-I ; reddish- orange : M-I, M-11, M-111 ; yellowish-green : M-II for the observer L. J., M-IV for the observer J. R. ; yellow : M-IV, and M-I1 for the observer L. J.). The results, conceming the failures of luminance predic- tions, were the same when the CIEJudd color- matching functions were used.

L. JIM~NEZ DEL BARCO et al. J . Optics (Paris), 1994, vol. 25, ne 3

ANALYSIS AND DISCUSSION

The results from determining the thresholds of an achromatic stimulus, conceming the failures of chromaticity and luminance predictions, allow us to generalize the discrepancies to the larger group of experimental conditions and to other groups of color- matching functions. From these results it can be 'observed that inter-and intra-individual variations occur but we are more interested in analyzing the intra-individual ,ones : that is, the variations of the centers of the discrimination ellipses for the same observer and the same reference stimulus when the

TABLE 111 Experimental parameters corresponding to the luminance discri- miruffion ellipsoids (representative of differential color thresholds) for the different initio1 marches and the different observers : bhe. purple, reddish-orange, yellowish-green and yellow stimulus. Data are' referred to S ~ C P CIE-1931 (z. y , Y). Unirs in cd/m2.

Stimulus

Blue

Purple

Reddish-orange

Yellowish-gree

Yellow

- lbserve

L. 1.

1. R.

L. J.

J. R.

L. J.

J. R.

L. J.

J. R.

L. J.

I. R.

degree of metamerism

matching

I Som. M-I M-II M - N I Som. M-I M-II M-IV I som. M-I M-n M - N I som. M-I M-n M-IV I Som. M-I M-U M-m I Som. M-I M-U M-m I Som. M-II M-IV M-V I Som. M-n M-N M-V I som. M-II M-Ill M-IV I Som. M-II M-Ill M-IV

- y,,, - I s o 1.48 1.50 1.18 1.53 1.53 1.57 1.11 3.12 3.42 3.20 3.14 3.14 3.44 3.30 3.18 5.42 4.76 4.84 4.70 5.47 4.80 4.79 4.89 3.91 3.74 3.77 3.95 3.99 3.86 3.64 3.96 6.92 6.17 7.21 7.50 6.90 6.82 7.20 7.42 -

- Ymi. - 1.36 1.33 1.37 1.06 1.34 1.32 1.32 0.97 2.98 3.14 2.93 2.89 2.91 3.16 2.84 2.88 5.10 4.41 4.41 4.20 5.04 4.42 4.24 4.29 3.75 3.33 3.43 3.47 3.65 3.23 3.39 3.32 6.78 6.58 6.78 7.22 6.72 6.58 6.83 7.07 -

- YO -

I .43 I .40 1.43 1.12 1.43 1.41 I .44 I .04 3.05 3.28 3.07 3.01 3.02 3.30 3.08 3.04 5.25 4.59 4.63 4.45 5.26 4.61 4.52 4.56 3.84 3.53 3.60 3.71 3.82 3.54 3.51 3.64 6.85 6.67 6.99 7.36 6.82 6.69 7.01 7.24 -

varied [ZO]. in this sense we could justifiably expect that the centers of the dis- crimination ellipsoids might not be the same (partly because the color-matching functions of the standard observer do not perfectly fit the functions of reach real observer) ; but if the standard observer is rep- resentative (as an average value) of color matches done by real observers with normal color vision, the color coordinates corresponding to the center of the ellipsoids should be included in the differential color threshold. In this case, differential color thresholds obtained with different degrees of metamerism should intersect. However, this does not happen as may be deduced from figures 5-7 and table II.

Additivity failures in Abney's laws, under our experimental conditions, are consistent with the

J. Optics (Paris), 1994, vol. 25, no 3

results of Sanders and Wyszecki [30], Kayser and Wyszecki @I], Boynton and Kaiser [321 and Guth et al. [33]. It must be pointed out that these results were obtained through heterochromatic brightness matches. In some experiments the brightness of one achromatic stimulus was matched with a mixture of two monochromatic stimuli. In other experiments an achromatic stimulus was matched with a mixture of a monochromatic stimulus and the same achromatic stimulus hut with half the brightness. The experimen- tal conditions and the method by which we carried out our experiments were different, but the results are similar with regard to additivity failures of Grassmann’s and Abney’s laws with metameric matches.

In the analysis of the results there are several factors that we could take account as being the possible causes of the discrepancies between the predicted color matches for different metamerism degrees :

a) Small errors in the measured spectral radiance of the matchings

As indicated when we described the experimental device, we directly measured the spectral radiance of the stimuli at the exit of the device. An estimation of the instrumental error related to chromaticity coordi- nates and luminance values was x = 0.002, y = - + 0.002 and Y = 2 0.03 cd/m2, respectively. These values applied to the center of the discrimi- nation ellipses (those which previously did not in- tersect) allow some ellipses to intersect with the isomeric ellipse but the discrepancies between the centers of the ellipses for the different metameric matches persist. This happens also when we analyze the luminance values as can deduced from tabZe 11 and III. Thus, the magnitude of the discrepancies lead us to believe that this factor is not the cause of the discrepancies.

b) Rod intrusion Different authors have studied the influence of

rods in color vision (Palmer 15-61, Trezona [lo], Stabell and Stabell [ll]). That our results were obtained with previous adaptation to darkness and within the low photopic level suggest the possibility of rod influence in our experiments. But this factor has been analyzed in previous experiments developed to avoid the influence of rods through the photopig- ment bleaching technique and in which we took the measnrements during the cone-plateau period of the long-term dark-adaptation curve [ 191. The results showed that rod intrusion can be ruled out as a possible cause of color-prediction discrepancies be- cause with the photopigment bleaching technique, the orientation and sizes of the discrimination ellipses varied, but the discrepancies between the centers of the ellipses of the different matches persisted.

L. JIM~NEZ DEL BARCO et al. 89

c) Failures of the standard observer to predict an individual’s additive color match

It is well established that there are differences in color matching among individuals [29-331. Thus, some failures of the standard observer are to be expected due to the inter-observer variability that has been widely studied in the literature [27-291 : but the problem is that for any given observer the magnitude of the intra-individual variations, when the degree of metamerism is changed, is very great as can deduced from the fact that the ellipses do not intersect (i.e. : see thresholds for the initial matching M-W, fig. 5A and B). Although an inter-individual component is implicit in the representation, because the compari- sons depend critically on the average color-matching functions of other observers, this possibility could be eliminated if color-matching functions of each indi- vidual observer were obtained, but our aim is to analyze the results from the viewpoint of the Differ- ential Colorimetry as indicated in the introduction. Most results are referred to the color-matching func- tions of standard observers and therefore, we can analyse whether color discrepancies are included in the color tolerances obtained from differential color thresholds using a group of color p&aries with a narrow spectral bandwidth.

The cause of the discrepancies that we have found might be analyzed on the basis of the response of the color-vision mechanisms. From the results, we might expect the response from color vision mechanisms to di€fer in the following situations : i) when the match is made between stimuli of similar spectral-radiant power distribution and ii) when the match is made between a stimulus with smooth spectral radiant power distribution and a stimulus with sharp peaks in its spectral radiant power distribution. These differ- ences are greater especially in the region of short wavelengths (see f i g . 3, metameric matches M-VI, M-VI1 and M-VIII). Figure3 indicates that the relative excitation of S cones (with maximum sensiti- vity to short wavelengths) is higher in the metameric match M-VII. We should point out that in this metameric match we find the greatest discrepancies, both in luminance and chromaticity, as can be deduced fromfigure 5 ( A and B ) and table 11. In this match the achromatic reference stimulus has been matched to a stimulus which has only two maxima (498 nm and 583 nm) in its speceal radiant power distribution ; this may be explained because two of the three interference filters used as primaries have their wavelengths of maximum transmission very close as can be seen in table I. In the metameric match M-VI, the excitation of tbe S cones is lower and the discrepancies found are also lower because the ellipse corresponding to the metaheric match M- VI intersect with the ellipse obtained under isomeric conditions. In the metameric match M-VIII the rela- tive excitation of S cones with respect to the exci-

90

tatiod of M and L cones is similar and the discrepan- cies found are acceptable at least for the L. J. observer, although these are higher for the obser- ver J. R. This behaviour ma be clearly deduced from figure 8 where +. Ax2 + Ay IS the euclidean distance (in the CIE-chromaticity diagram) between the center of the ellipsoid obtained with the isomeric match and the center of the different metameric matches ; AS is the difference between the S-cone excitation level of each metameric match and the isomeric match, this difference is normalized with respect to the S-cone excitation of the isomeric match (the S-cone excitation level has been determined taking into account the cone-excitation space pro- posed by Boynton[34]). As figure8 shows. the chromaticity discrepancies obtained increase with

S VII. Results are similar for both observers.

Analyzing the discrepancies found in the metameric matches with respect to the relative exci- tation of the opponent-chromatic channel L - 2 M and the achromatic channel L + M, derived from Boynton's model [34], find the following. First, figure 9 shows the chromaticity discrepancies be- tween metameric and isomeric matches (following explanation in figure 8) with respect to L - 2 M . Here we see that an increase in the relative excitation of S-cones (fig. 8) with respect to the isomeric match

L. JIM~NEZ DEL BARCO ef al.

- *', and they are higher for the metameric match M-

A(L - 2 M )

0,03 -

0,025 -

0,02 -

0,015 -

0,Ol-

0,005 -

J. Optics (Paris). 1994, vol. 25, n" 3

causes a decrease in the relative excitation of L - 2 M channel (jig. 9). This result was expected because the metameric match' M-VII, in which discrepancies are higher, corresponds to the filter with maximum transmittance in the short wavelengths. Secondly, figure I O shows the discrep- ancies in function of A(L + M , (relative excitation

L + M level of the achromatic channel). Results agree with the discussion on the luminance variable (table U). The results were similar for both observers.

These results agree with those of Zaidi 1351 which show non-linearity phenomena (failures of Grassmann's laws of additive color mixtures that produce failures in colorimetric prediction) using tests with a high excitation of cones S. Nevertheless we think that the results may be more in agreement with the fact that the color-matching functions of real observers show a larger dispersion with respect to the different standard observers in the short wavelengths [27-291.

Thus, our results show that an additive mixture of three quasi-monochromatic lights can match a smooth spectral power distribution of wide bandwidth Ifig.3), but the great excitation of the photoreceptors in the case of the quasi-monochroma- tic primaries can distort the expected tristimulus values of the match.

We can conclude that the failures of colorimetric prediction under our experimental conditions (foveal

0 0

0 1 , 1 8 , I I I I 1

0 2 4 6 8 10 12 14 16 18 20

AS - (%) S

FIG. 8. - Chromoticiry differences between the center of the ellipsoid obtoinedfrom the isomeric match and the centers of Ihc ellipsoids obtainedfrom the metameric matches in relation to the relative difference of the S-cones excitation for each metameric match with respect to the isomeric motch (achromatic stimulus, 1. R. ond L. 1. obsemers).

.I. Optics (Paris). 1994, vol. 25, n” 3 L. JIM6NEZ DEL BARCO et al. 91

0’035 I 0,03 -

0,025- - h

% 0,02- U -I- 0,015- N X

4 Y 0,Ol-

0,005 -

. R Distled Llne L. J. solla Line .I. R.

w M - V I

0 0 6 12 18 24 30 36 42 48 54

(“4 A (L-2M)

(L-2M) FIG. 9. -Chromaticity differences bemeen the center of the ellipsoid obtainedfiom the isomeric match and the centers of the ellipsoids obtainedfiom the metameric matches in relation to the relative dqerence ofrhe L - 2 M excitationfor each metameric match with respect to the isomeric match (achromatic stimulus stimulus, 3. R. and L. 3. observers).

0,035

0,025 0’031 0,015

0,Ol

0,005

x - e ’\ I

/ I I

I Dished Llne L. J. Solld Llnc J. R.

I I / I

w M - V I

M - V I I

AM - v I I I

I , I , I I

2 4 6 8 10 12 14 0

0

A (L+W

&+MI (“4

FIG. 10. -Chromaticity diflepences bemeen the center of the ellipsoid obtained from the isomeric match and the centers of the ellipsoids obtainedfiom the metameric matches in relation to the relative difleereence of the L + M excitation for each metameric match with respect to the isomeric match (achromatic stimulus, 3. R. and L. 3. obsemers).

92 L. JIMGNEZ DEL BARCO et d.

fields between 1.5" and 3', direct or Maxwellian vision, luminance in the low photopic level and stimuli with high excitations of cones S) are of such magnitude that they exceed even the differential color threshold. We think that from the viewpoint of colorimetry a revision of color-matching functions would be useful.

J . Optics (Paris), 1994, vol. 25, n" 3

[16] Brown WRT, MacAdam DL. Visual sensitivities to combined chromaticity and luminance differences. J Opt Soc Am 1949 ; 39 : 808-34.

[17] Wyszecki G, Fielder GW. New color matching ellipses. J Opt Soc Am 1971 ; 61 : 1135-52.

[IS] Hita E, Jim6nez del Barco L, Romero J. Differential color thresholds from metameric matches : experimental results cancernine failures of colorimehic additivity. J Opt Soc

ACKNOWLEDGMENTS

The authors wish to thank the reviewer for the suggestions made to improve the manuscript.

This research was supported by the Direcci6n General de Investigaci6n Cientifica y T&cnica, DGICYT (Grant PB90-0871).

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(Manuscript received in September 19th 1993.)

0 Masson, Paris, 1994