H. P. FRANK AND R. ULLMAN

At 135' to the incident beam s is given by

2 -(x+y) if -x<y<-w -x

Po=-(wV2-x-y) if -2 -xy<w--x.

Using Eqs. (Al) and (A3), we obtain

Iiat=Iofias exp[-k(do+so)]Ž1 fexp[7xj

X{f(12)z exp[k( 4+)y] (x+y)dy

+j(,- eXP[( 1 y] (¶2- y-.X dy dx

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

(B3)

(B4)

Upon integration, Eqs. (2) and (B4) become

145= Zk3w(kv2 )3exp{ -[doso-('2 )(+w)I}

+sinh[( 2 )kh] sinh2[( I )hw]

and

135=I°ftk32rl)3 exp{ -k[do+ so-(+) (h+w)]}

Xsinhwhih a)kr(] sinh2ae r + )kw]

which are Eqs. (4) and (5) of the text, respectively.

VOLUME 45, NUMBER 6

(E5)

(B6)

JUNE, 1955

Subtractive Color Photography: Spectral Sensitivities and Masks*

W. T. HANSON, JR.,t AND W. L. BREWERtEastmnan Kodak Company, Rochester, New York

(Received October 15, 1954)

In linear photographic masking theory it is assumed that the cyan, magenta, and yellow dyes in the proc-essed film are deposited in amounts which are linear functions of the logarithm of each of the red, green,and blue exposures. Metameric pairs of colors will be reproduced alike in the photographic process only if thespectral sensitivities of the red-, green-, and blue-exposure emulsions conform to a set of visual color-mixturecurves. Optimum colorimetric reproduction is obtained through utilization of the combination of color-mixture curves and photographic masks, relating dye amounts to exposure, which minimize calorimetricreproduction errors.

It is shown that significant changes in the choice of color-mixture curves may be largely compensated forby corresponding changes in the masks. Optimum choices of masks depend in part upon the gamut of colorsto be reproduced. Emulsion spectral sensitivities departing from color-mixture curves may also yieldessentially equivalent calorimetric reproduction provided that the masks are suitably chosen.

INTRODUCTION

ADVANCES in photographic technology during thepast few years make possible the incorporation of

color-correcting masking in color-photographic proc-esses.1' 2 Color reproduction or masking equationsserve as a guide in indicating the kinds and amounts ofmasking which should be employed. Numerous methodshave been suggested for determining optimum sets ofequations.' One of these methods involves the applica-tion of the method of least squares to obtain equationsfor the approximate reproductions of a number of objectcolors.4

The purpose of the study reported here was to investi-gate more fully the usefulness of the least-squaresmethod in determining masking equations. Special

* Communication No. 1696 from the Kodak Research Labora-tories.

t Research Laboratories, Eastman Kodak Company, Rochester,New York.

t Color Technology Division, Eastman Kodak Company,Rochester, New York.

' W. T. Hanson, Jr. and P. W. Vittum, PSA Journal, 13, 94-96(1947).

2 W. T. Htaison, Jr., J. O1p. Soc. Anm. 40, 166-171 (1950).3 Evans, Hanson, and Brewer, Principles of Color Photography

(John Wiley and Sons, Inc., New York, 1953), pp. 639-661.4 Brewer, Hanson, and Horton, J. Opt. Soc. Am. 39, 924-927

(1949).

attention has been given to the effects of (1) the par-ticular selection of object colors, and (2) the assumedset of film spectral sensitivities.

EQUATION DERIVATIONS

Color-reproduction equations for color-photographicprocesses may be written in the form of:

c= gio+g1D+g12D 0+gu3Dbm= g20+g21Dr+g22 D,+g23Dby= g30+g31Dr+g32Dg+g33Db.

(1)

The quantities c, in, and y denote the amounts of thecyan, magenta, and yellow dyes in any small area of thephotographic film. The dyes are deposited as functionsof the exposure densities, D, D0, and Db, of the corre-sponding small region of the scene photographed. Theexposure densities are defined in terms of the exposuresR, G, and B as

Dr=-logR D,=-logG Db=-logB, (2)

where

R=fSrPTdX G= JSPTdX B= {SbPTdX. (3)

476 Vol. 45

SUBTRACTIVE COLOR PHOTOGRAPHY

Each of the quantities inside the integral signs is afunction of wavelength, ; Sr, S, and Sb denote thespectral sensitivities of the component emulsions of thefilm; P denotes the energy distribution of the incidentillumination of the scene; and T is the reflectance ortransmittance of the small region of the scene underconsideration. The energy distribution P is so nor-malized that for T= 1.00 throughout the region of thespectrum to which the film is sensitive, the values of R,G, and B are also equal to 1.00. For this same value ofT, Dr=D,=Db=O.

The constants g, g2o, and g30 pertain to the colorbalance of the film. The remaining g's indicate thegammas to which the various dyes should be developedas functions of the various exposures.

For a chosen set of object colors whose reflectances areknown, Eqs. (3) and (2) are applied to determine theexposure densities. The tristimulus values X, Y and Zfor each of the same object colors are also determined.From the known spectral densities of the cyan, magenta,and yellow dyes of the photographic film, values of c,m, and y are determined which yield the same X, Y, andZ values as each of the object colors. For each objectcolor, an equation can then be written which includesthe undetermined coefficients gio, gl, g2, and g3, andnumerical values for c, Dr, Dg, and Db. If there are morethan four object colors involved, all of the equations arenot apt to be satisfied by the same set of values for theunknown coefficients. Unique sets of coefficients can bedetermined, however, by application of the method ofleast squares to minimize color-reproduction errors (interms of c) for all the object colors. Similarly, values forthe remaining gs can be found using the same Dr, Dg,and Db values, along with the values of m and y for eachof the object colors.

SELECTION OF OBJECT COLORS

Ideally, the values of the coefficients in the color-reproduction equations would be relatively independentof the sampling of object colors for which they are de-rived. Under such conditions, any one set of objectcolors would be about as good as any other. If, however,the coefficients are markedly dependent upon the set ofobject colors chosen, these colors should be carefullyselected for their importance in the completed colorphotograph.

Three sets of object colors, of twenty colors each,were selected for this study. The first two sets werechosen on the basis of being important in a colorphotograph. Specifically, they were selected as follows:A group of engineers and supervisors concerned withquality control in the processing of photographic printswere asked to name the object colors which they con-sidered to be most important in color photographs.Based upon examinations of a large number of colorprints and tabulations of the frequency with whichvarious object colors appeared, they provided a list of

TABLE I. Recommended object colors.

N'umber Description

1 Flesh2 White3 Green4 Red5 Blue6 Brown7 Gray8 White9 Yellow

10 Light blue11 Black12 Pink13 Blue-green14 Blond15 Natural wood16 Sand17 Orange18 Peach19 Cream20 Lavender

Clothing of high reflectanceGrass, leaves, or clothingBrick, clothing, or paintSkyHair or clothingConcrete or clothingPaint of medium high reflectanceFlowers or clothingClothingClothing or paintClothing or flowersWater or clothingHair

Clothing or flowersClothingClothingFlowers

twenty colors.§ Table I gives this list. Recommendedweighting factors were also given, but were not used inthe subsequent calculations. Based upon this list, theauthors selected two sets of colors, each color repre-senting a particular object corresponding to one of thetwenty given in Table I. The chromaticities and visualdensities of these two sets of object colors are given inFigs. 1 and 2.

The third set of object colors was selected to span thecolor space of colors which could be reproduced by thedye set used for the study. The chromaticities and visualdensities of this set (Color Set 3) are given in Fig. 3.The spectral densities of unit concentrations of thethree dyes from which they were derived are given inFig. 4. This same dye set was assumed for the colorphotographic processes for which all the color-repro-duction equations were derived,

.50

.40

.30

.20

.10 *0 .10 20 .30 .40 .50 .60 70

FIG. 1. Chromaticities of Color Set 1. Visual densities are1 0.414 6 0.246 11 1.719 16 0.5032 0.122 7 0.788 12 0.340 17 0.4603 0.915 8 0.097 13 0.124 18 0.2704 0.821 9 0.345 14 0.623 19 0.1185 0.338 10 0.377 15 0.562 20 0.752

§ The authors are particularly indebted to Mr. John H. Baker,of the Color Print and Processing Department, of the EastmanKodak Company, for this list.

June 1955 4'77

W. T. HANSON, JR.,

.30 .40 .50 .60 .70

of Color Set 2. Visual densities are1.156 31 2.000 36 0.6450.456 32 1.311 37 0.5620.155 33 0.100 38 0.2480.315 34 0.941 39 0.1791.163 35 0.253 40 0.690

SENSITIVITY DISTRIBUTIONS

Six sets of sensitivity distributions were included forinvestigation. Three of these conform to color-mixturecurves. Such choices are required for "exact colorimetricreproduction" in a color-photographic process.5 Each setof color-mixture curves has a corresponding set of pri-maries. Chromaticities of the primaries are shown inFig. 5. The three sets of spectral sensitivities are shownas 1, 2, and 3 in Fig. 6. Sensitivities 1 are the color-mixture curves, x, y, and z, for the CIE standard ob-server. They have been renormalized so that, for theassumed illuminant, CIE Illuminant C, the values of R,G, and B in Eqs. (3) are all equal to 1.00 when T= 1.00.Sensitivities 2 are the color-mixture curves correspond-ing to the monochromatic primaries, R= 620 mp,G= 530 mu, and B = 455 mtt. Sensitivities 3 are the color-mixture curves corresponding to block-dye primaries,the red primary extending from 585 to 700 my, thegreen from 495 to 585 mA, and the blue from 400 to495 mtt.

1.0 --- i - - -

0.8

,.:0.60.2 - - - - - - - -

0.0- - --400 20 40 60 80 500 20 40 60 80 600 20 40 60 80 700

Wavelength (mpu)

FIG. 4. Spectral densities of dye set used for Color Set 3 andfor dye system of assumed color-photographic process.

Sensitivities 2 and 3 contain negative portions whichare not found in real processes. Furthermore, eventhough color-mixture curves are required for exactcolorimetric reproduction, they may not provide the bestreproduction in processes with available dye systems.Sensitivities 4, 5, and 6, also shown in Fig. 6, werechosen to investigate sensitivities approaching those ofreal photographic processes. Sensitivities 4 are the chiefpositive portions (renormalized) of Sensitivities 2.Sensitivities 5 are the chief positive portions of Sensi-tivities 3. Sensitivities 6 are those of an actual colorphotographic process.

COLOR-REPRODUCTION EQUATIONS

Color-reproduction or masking equations were deter-mined for each of the three sets of object colors witheach of six sets of sensitivity distributions. The coeffi-cients for all the equations (g's) are given in Table II.The method of least squares, as described in the intro-ductory section, was employed. Reproduction errors in

1.00

.90

.80

.60

y.5

1

0 .10 .20 30 40 .50 .60 .70

x

FIG. 3. Chromaticities of Color Set 3. Visual densities are41 0.165 46 1.681 51 3.089 56 0.69842 2.056 47 1.327 52 0.659 57 0.75543 175A 48 23 8 53 2,1 3 in 2a50744 0.881 49 0.642 54 0.293 59 0.85045 0.057 50 1.974 55 1.836 60 2.517

5 A. C. Hardy and F. L. Wurzburg, Jr., J. Opt. Soc. Am. 27,227-240 (1937); see also reference 3, pp. 617-618.

0 J0 .20

Gil I I I - I I - I IN I I

Izo --------I - -

L

570500

1\\1�81 0 11 1

- __ I 1

3 I ICIE 111 C 0 - 1

90 0 1

F

I I I

FIG. 5. Chromaticities of primaries corresponding toSensitivities 1, 2, and 3.

.50 oo

> l.40

.30

.20 L

.100 .10 .20

FIG. 2. Chromaticities21 0.466 2622 0.097 2723 0.410 28 124 0.851 2925 0.398 30

478 AND W. L. BREWER Vol. 45

.3

.2

.90 Loo.30 .40 .50 .60 .70 .80

SUBTRACTIVE COLOR PHOTOGRAPHY

terms of Ac2 , Am2 , and Ay2 , each summed for the 20colors, were minimized. Goodness-of-fit measures, inthe form of root-mean-squares of the deviations (orstandard deviations or sigmas), are shown under eachset of equations as Uc, Um, and rye

EFFECTS OF CHOICE OF OBJECT COLORS

In Table II the color-reproduction equations forColor Set 1 and Color Set 2 are similar to each other formost of the sets of sensitivities. The sigma values arealso of the same general order of magnitude. For ColorSet 3, however, almost all the terms in the equations aregreater in absolute magnitude than for the other twocolor sets. Greater masking corrections are called for.Also, the sigma values are somewhat larger, showingthat these equations did not give as good reproductionsof the colors of Color Set 3. Reference to Figs. 1-3indicates that the chromaticity and visual densitygamuts for Color Sets 1 and 2 are more restricted thanare the chromaticity and visual density gamut of ColorSet 3. The choice of colors to be used in determining thecolor-reproduction equations does affect the coefficientsin the equations. The effect appears to be associatedwith the gamut of the colors to be covered. Color Sets 1and 2 sample more or less the same region of color space,and, even though no pairs of individual objects areexactly alike, give comparable results.

The only marked inconsistency between the equationsobtained for Color Set 1 and Color Set 2 are for Sensi-tivities 3. The magenta-dye reproduction equations are:

Color Set 1:

m= 0.007-0.169D,+ 1.327D, - 0.180.Db. (4a)

Color Set 2:m=-0.003-0.405D,+ 1.796D -0.392Db. (4b)

The goodness-of-fit values for Color Set 1 were muchworse, being 0.068 (am) as compared to 0.011 for ColorSet 2. Examination of the reproduction errors for theindividual object colors revealed unusually large errorsof 0.137 in the magenta reproduction for Object Color4 and -0.146 for Object Color 20. Both of these colorsare seen to be relatively saturated purples, having high-green exposure densities.

To ascertain the effects that these two colors had onthe reproduction equations, they were eliminated fromColor Set 1, and a recalculation of the masking equa-tions was made. The equation for the magenta dye thenwas

m= 0.003-0.392D,+ 1.740Dg-0.353Db, (4c)

with m =0.011. Reasonably good agreement with theequations for Color Set 2 was thus obtained. Changes inthe coefficients in the equations for c and y were notlarge, but were all in the direction of giving closeragreement with the equations of Color Set 2.

It should be pointed out that Object Color 32, also asaturated purple, was eliminated in the first calculationfor the masking equations with Color Set 2 and Sensi-tivities 3. The elimination was necessary because, forSensitivities 3, its green exposure value, G, was negative.No value for D, could, therefore, be assigned to it. Theonly other colors eliminated from any of the calculationswere Object Colors 42, 47, and 48 from Color Set 3.These were also for Sensitivities 3 and for the reasonthat some of the exposures had negative values.

cn

.U

700 400 500

Wavelength (mP)

FIG. 6. Spectral distributions of Sensitivities 1, 2, 3, 4, 5, and 6.

These results [Eqs. (4a), (4b), and (4c)] again em-phasize the importance of sampling the same region ofcolor space if comparable sets of equations are to beobtained with different starting object colors. Theyalso are indicative of the large changes which can beproduced in the equation coefficients and goodness-of-fit values by a very small number of colors of highsaturation.

June 1955 479

W. T. HANSON, JR., AND W. L. BREWER

TABLE II. Table of color-reproduction equations.

Numbers tabulated glglgl213 c =gio+giiDr+g12D,+g3Dbcorrespond to g20g21g22923 where n =g2s+gnDr+g22D,+g2Dbg3g331g32g33 y =gso+g3iDt+g932D,+g33Db

Color Set 1 (natural objects) Color Set 2 (natural objects) Color Set 3 (dye combinations)

Sensitivities 1 0.027 3.619 -2.338 -0.297 0.014 3.719 -2.369 -0.335 0.187 4.477 -2.759 -0.605(CIE mixture curves) -0.009 -3.585 4.753 -0.162 -0.003 -3.692 4.880 -0.198 -0.059 -3.299 4.285 0.021

-0.006 0.498 -1.459 1.969 -0.004 0.484 -1.467 1.992 -0.021 0.074 -1.107 2.013

ac=0.056 am=0.057 er =0.034 ac=0.036 am =0.050 a5,=0.018 ac=0.24 2 am =0.169 a-=0.081

Sensitivities 2 0.003 1.783 -0.884 0.109 0.005 1.719 -0.831 0.112 -0.019 1.930 -1.112 0.270(Primaries 620, 530, 0.004 -0.685 2.118 -0.441 -0.001 -0.626 2.071 -0.443 0.041 -0.656 2.140 -0.521

455mp) -0.005 -0.249 -0.628 1.884 -0.004 -0.263 -0.624 1.894 -0.020 -0.321 -0.562 1.890

ac=0.036 r,,,=0.023 a , =0.008 ac=0.052 .m=0.032 a,=0.005 ac=0.177 am=0.102 ay=0.027

Sensitivities 3 -0.018 1.328 -0.378 0.067 -0.001 1.442 -0.593 0.153 -0.044 1.215 -0.298 0.096(Block-dye primaries) 0.007 -0.169 1.327 -0.180 -0.003 -0.405 ,1.796 -0.392 -0.012 -0.245 1.382 -0.214

-0.001 -0.326 -0.392 1.730 -0.003 -0.271 -0.529 1.807 -0.004 -0.267 -0.431 1.736

c=0.026 am,=0.068 a,,=0.030 ac=0.014 am=0.OII a,=0.005 ac=0.138 arn;=0.177 av=0.076

Sensitivities 4 0.010 1.929 -1.022 0.096 0.008 1.910 -1.036 0.127 0.017 2.247 -1.431 0.259(Positive portions 0.002 -0.856 2.365 -0.513 0.000 -0.860 2.429 -0.566 0.033 -0.889 2.486 -0.602Monochromatic -0.006 -0.228 -0.740 1.976 -0.005 -0.234 -0.741 1.982 -0.016 -0.327 -0.660 1.987

primaries)

acr=0.038 a,=0.018 a,=0.009 aec=0.04 5 a.=0.009 a.,=0.005 ac=0.16 2 a,=0.075 au =0.037

Sensitivities 5 0.009 1.691 -0.747 0.058 0.009 1.711 -0.808 0.101 0.008 1.889 -1.029 0.188(Positive portions 0.002 -0.635 2.106 -0.473 0.000 -0.680 2.229 -0.547 0.029 -0.686 2.240 -0.552Block-dye primaries) -0.006 -0.254 -0.696 1.957 -0.006 -0.252 -0.712 1.970 -0.014 -0.306 -0.662 1.973

sac=0.025 c,=0.018 a,=0.005 ac=0.037 a,=O.OO6 7=°0.007 s-C=0.llI am=0.056 ,,=0.027

Sensitivities 6 0.005 1.421 -0.380 -0.034 0.010 1.438 -0.444 0.010 0.009 1.610 -0.618 0.076("Real 0.007 -0.494 1.902 -0.414 -0.001 -0.656 2.153 -0.492 0.064 -0.584 2.186 -0.661

sensitivities") -0.031 -0.221 -0.632 1.867 -0.013 -0.134 -0.678 1.804 -0.060 -0.392 -0.666 2.276

ac =0.034 am =0.026 a, =0.048 a, =0.060 a, =0.021 a, =0.090 a, =0.107 em =0.089 a5 =0.043

EFFECTS OF CHOICE OF SENSITIVITYDISTRIBUTIONS

Large, and fairly systematic, differences in coefficientvalues are obtained for the different sensitivity distri-butions. For the color-mixture curve sensitivities, thereis a downward trend in coefficient value size betweenSensitivities 1 and 2 and between Sensitivities 2 and 3.These sensitivities, in the same order, correspond toprimaries of decreasing saturation (see Fig. 5). Withinthe range studied, the more desaturated the primaries,the smaller will be the masking corrections. Sensitivitiescorresponding to the less saturated primaries, however,have larger and more extensive negative portions. Asalready indicated, these negative portions (even ifobtainable) would have the effect of eliminating highlysaturated colors from the gamut of colors for whichpositive exposures are obtainable. Such colors areoutside the range of colors which can be reproduced bypositive amounts of the primaries assumed in estab-lishing the sensitivity distributions; they are outsidethe triangle formed on the chromaticity diagram by thethree primaries.

With few exceptions, coefficient values for Sensi-tivities 4 and 5 are larger than for the correspondingsensitivities which include the negative portions. Thisseems reasonable to expect because the negativeportions of the curves, in effect, perform some of themasking. Their elimination means that greater amountsof masking will be required. Coefficient values forSensitivities 6 are, in general, smaller than for Sensi-tivities 4 and 5. This probably results from the greater

spectral separation of the red, green, and blue spectralsensitivities for Sensitivities 6. The red, green, and blueexposures are more fully separated, and therefore lessmasking is required. The coefficient values are largerthan for Sensitivities 3, but the negative portions of thecurves for Sensitivities 3 have an even greater effect inexposure separation.

Trends in goodness-of-fit values with changes insensitivities are not readily evident. There is anapparent slight tendency for the sigma values to becomesmaller for sensitivities corresponding to primaries ofdecreasing saturation. For the most desaturated pri-maries (Sensitivities 3), however, some of the moresaturated colors must be eliminated from consideration.Even those colors which are near the outer limit ofcolors for which positive exposure values are obtainedcan cause decided increases in the sigma values. Thiseffect is both direct and indirect in that, by effectivelyaltering the masking equations, goodness-of-fit valuesfor other colors are made worse.

Elimination of the negative portions of the sensitivitydistributions resulted in slightly better goodness-of-fitvalues in most cases. It is therefore evident that sensi-tivities which are color-mixture curves, as required forexact calorimetric reproduction, do not necessarily givethe best approximations to colorimetric reproductionwhen exact reproduction is not obtainable. Sensitivities6 depart materially from color-mixture curves. Thespectral regions of their peaks of absorption are con-siderably displaced from those of any possible set ofcolor-mixture curves. Even so, the color reproductions

480 Vol. 45

SUBTRACTIVE COLOR PHOTOGRAPHY

obtainable with such sensitivities are not materiallyworse than those for the color-mixture curves giving thebest color reproduction. Compared to Sensitivities 1,the only color-mixture curves which are positivethroughout the spectrum, Sensitivities 6 appear to givecalorimetric reproductions which are definitely better.

NEUTRAL SCALE REPRODUCTION

Neutral colors in a scene give red, green, and blueexposure density values which are equal to each other.For a perfectly reflecting, perfectly diffusing white,Dr=Dg=Db=O. For other members of the series ofgrays, the exposure density values equal each other butare greater than zero.

Reproduction of the high-intensity white depends onlyon the values of glo, g20, and g3o. For Color Sets 1 and 2 inTable II, the absolute value of most of these quantitiesis less than 0.01, showing a reproduction which is verynearly neutral. Somewhat larger values are obtainedfor Color Set 3, but the largest is less than 0.20.

The gamma of the neutral-scale reproduction equalsthe sum of the coefficients of Dr, Do, and Db. If non-selective grays are to be reproduced at constant-colorbalance, the neutral-scale gammas for the c, m, and yequations in each set must all equal each other. If thegrays are to be reproduced at their true relative lumi-nances, these gammas will all be equal to 1.00.

Most of the neutral-scale gammas for the naturalobject sets of equations in Table II differ from unity byless than 0.01; the largest differs by only 0.022. Thus,true relative luminance reproductions of gray scales atessentially constant-color balances are indicated.

Departures from neutral-scale gamma values of unityare slightly greater for Color Set 3. The greatest de-parture is in the equation for y for Sensitivities 6 wherethe value is slightly over 1.2. This departure from unitycan probably be accounted for as follows:

The twenty colors of Color Set 3 represent differentcombinations of the dyes of Fig. 4. The neutral for thisdye set is somewhat selective, having a rather markeddrop-off at the short-wavelength end of the visiblespectrum. The blue spectral sensitivity curve forSensitivities 6 is displaced toward the short-wavelengthend of the spectrum as compared to all the other sets ofsensitivities. Because of the displacement and the low-density values in this spectral region for neutral colors,the blue-exposure densities will tend to be low in value.To provide adequate yellow dye for reproduction of the

neutral scale (and other colors), the coefficient of Dbmust therefore be unusually large.

The relatively high neutral-scale gamma for theyellow dye of Color Set 3 and Sensitivities 6 is thus seento be an artifact of the particular set of colors chosen forreproduction. The spectral characteristics of these colorshave a consistency of pattern not found among naturalobject colors. The equations derived for them do notproperly apply to natural objects.

SUMMARY AND CONCLUSIONS

Using the method of least squares, color-reproductionequations for three different sets of object colors for eachof six different sets of sensitivity distributions havebeen determined. For sensitivity distributions which arecolor-mixture curves, the mask gammas tend to de-crease in size with decreasing saturation of the primariescorresponding to the color-mixture curves. Althoughthere also appears to be a slight tendency for goodness-of-fit values to improve with decreasing saturation ofthe primaries, the results are erratic and we doubt thatthe differences are significant. We therefore believethat, for a dye set such as used in this investigation,there is no unique set of primaries, or correspondingsensitivity distributions, which is most satisfactory.

Elimination of the negative portions of the sensitivitydistributions tends to increase the values of the maskgammas, but not to worsen the goodness of reproductionobtainable. Sensitivities similar to those used in practice,which depart materially from color-mixture curves ortheir abridgments, give color reproductions essentiallyas good as any of the other sensitivities studied.

The gamut and nature of the object colors used indetermining color-reproduction equations by the least-squares method have a marked influence on the maskvalues and on the goodness-of-fit measures. Sets ofcolors with spectral patterns not characteristic ofnatural objects may give results which are not properlyapplicable to natural objects. If special spectral patternsare avoided and the color gamut is restricted to theless-saturated colors which appear to have greatestimportance in color photography, consistent results areobtained, even though the specific sets of object colorsare different. If sensitivities which are color-mixturecurves are used, the colors must also be restricted tothose well within the gamut which can be matched bymixtures of the primaries corresponding to the color-mixture curves.

June 1955 481