Visual impression of whiteness and its colorimetric definition

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    Visual impression of whiteness and its colorimetric definitionR. Thielert and G. Schliemanr

    Unilever Forschungsgesellschaft mbH, Hamburg 50, W. Germany(Received 26 March 1973)

    Scale values D of whiteness have been determined visually by the method of paired comparisons of anumber of white samples that differed in hue, saturation, and lightness. Each sample was also specified byuse of a newly developed whiteness formula W = Y - 33.33p. W is the whiteness, Y is the luminousreflectance of the sample, and p is the ratio of two distances in the 1931 CIE chromaticity diagram,p = /. is the distance between the chromaticity point F of the sample and a point0 with the chromaticity coordinates x 4 = 0.3090, y o = 0.3170. Point 0 is the center of an ellipse witha major semiaxis a = 0.030 and a minor semiaxis b = 0.009. The angle of inclination of the major axiswith respect to the positive direction of the x axis of the chromaticity diagram is 0 = 48.0'. is thedistance between point 0 and the intersection E of the ellipse with the straight line through the points 0and F. Good correlation between D and W was obtained in all cases, even if samples were compared thatdiffered considerably in hue. This demonstrates the greater range of validity of the newly developedformula in comparison with current whiteness formulas.

    Index Headings: Color; Colorimetry.

    A great variety of colors are perceived as white. Tofind a measurable quantity that correlates well withthe results of the visual assessment of these manywhite colors is a well-known problem of colorimetry.There are several calorimetric formulas for evaluationof whiteness.' However, the most frequently used arevalid only within a more or less small part of thegamut of colors perceived as white. We tried, therefore,to obtain a whiteness formula having a greater range ofvalidity. To this end, we compared the tristimulusvalues of a number of white samples, which haddifferent hues, saturations, and lightnesses, with theresults of visual assessments of these samples.

    The samples were made from 8 cmX12 cm rec-tangular sheets of paper, each sample consisting of astack of ten sheets glued together at the edges. Thepapers of one sample had identical optical properties.Papers of different samples contained different amountsof different fluorescent brighteners; some containedalso small amounts of dyes.


    Color measurements were made by use of a Zeissspectrophotometer PMQ II with an integrating-sphereattachment RA 3 and a xenon-lamp attachment of aZeiss Elrepho calorimeter. The xenon lamp was placeddirectly in front of the illuminating aperture of theintegrating sphere. Thus, diffuse illumination of thesamples was obtained from an illuminant that corre-sponds approximately 2 to CIE illuminant D680. Becauseall samples contained fluorescing optical brighteners,the light reflected from the samples was combined withfluorescent light at certain wavelengths. The lightdiffusely reflected and emitted from the samples at O0was dispersed in a monochromator; the total relativespectral radiance Pa was measured by a photomultiplier.Pa is the sum of the spectral reflectance pa of the sample

    and the spectral radiance fx of the fluorescent radiationemitted at the same wavelength A relative to the spectralradiance of a nonfluorescent nonselective white standardin the same illumination,

    PX =pX+fX- (1)PX was measured between 380 and 770 nm at intervals

    of 10 nm. The bandwidth of the monochromator was5 nm. The measured values of the relative spectralradiance Pa were related by calibration of the whiteworking standard to the spectral reflectance px= 1 for aperfectly reflecting, perfectly diffusing, nonfluorescentsurface. From the Px, tristimulus values X, Y, Z ofthe 1931 CIE calorimetric system were calculated onthe basis of illumination3 with CIE illuminant D60 .The tristimulus values of all samples used in ourinvestigations are given in Table I.


    The whitenesses of seven sets with ten or twelvesamples each were visually assessed. One set consistedof ten either yellowish-white or bluish-white samples(B 1-B 10), one of ten bluish-white samples (B 1 1-B20),and one of ten violet-white samples (V1-V1O). Anotherset consisted of samples that were either greenish-whiteor reddish-white (RG1-RG10) and another consisted ofyellowish-white, bluish-white, violet-white, greenish-white, and reddish-white samples (F1-F12). Two setsof samples (H1-H10, H11-H20) were arranged insuch a way that observers had to compare neutralwhite samples with lighter but distinctly coloredsamples having different hues. The chromaticitycoordinates of all samples are shown in the Figs. 1-3.

    Whiteness was visually assessed by the method ofpaired comparisons.4 The samples were assessed by 40observers, 30 female and 10 male, from the laboratorystaff who were between 20 and 45 years old. All observ-




    TABLE 1. Tristimulus values, visually determined scale values of whiteness, and colorimetrically evaluated whiteness.

    Samiiple X Y z DI hb W.c TVd










































    sample I Y Z DA db W,7 WdRG7RG8RG9RG1O















































    D =visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressionsare normally distributed.

    b d= visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressionsare uniformly distributed.

    C W7=whiteness, calculated from the Vaeck-Van Lierde formula (see Ref. 15).d W =whiteness, calculated from Eq. (7).

    ers were tested for normal color vision by use of theIshihara test.5 The observers had no special experiencewith assessment of white samples, but had some generalexperience with visual assessment of colors by themethod of paired comparisons. For each observer, theconsistency of his judgments was evaluated by use ofthe coefficient of consistency 4 K, which was >0.70 inall cases.

    The samples were presented on a matte gray card-board, the tristimulus values of which were X=21.73,Y=23.95, Z=23.95. These values were based onillumination with CIE illuminant D60 and spectralreflectance p, = 1 for the perfectly reflecting, perfectlydiffusing surface. The samples were illuminated by aCL 20 luminaire 6 with an illuminance of 1600 lm mrn2 .This luminaire consists of a xenon lamp7 XBO 150W/1,a parabolic aluminum reflector, and a circular glasscover in front of the lamp having a diameter of 0.45 m,which served as diffuser and filter. The relative spectral-

    energy distribution of the luminaire is approximatelythe same as that of phase D60 of natural daylight. Thatmeans that measurements and visual assessments weremade using light sources, the relative spectral-energydistributions of which are nearly identical.

    All n samples of each set were presented to eachobserver in pairs in all possible 'it(n- 1) combinations.The observers had to decide which sample of each paircorresponded more to their idea of whiteness. Theresults of these experiments can be presented for eachset of samples as a matrix (mijk). Each element Mik ofthis matrix corresponds to the proportion of theobservers who reported that sample si caused an impres-sion of whiteness Si that was greater than the impressionof whiteness Sk caused by sample s*. From the matrices(Mik), scale values D of the visual impressions ofwhiteness were calculated' (Table I) with the assump-tion that for all pairs si and Sk of each set of samplesthe Thurstone-Mosteller model4 is valid:

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    (i) The differences Si-Sk observed by a greatnumber of persons are normally distributed for eachpair of samples.

    (ii) The normal distributions of the differencesSi-Sk all have the same standard deviation.

    (iii) The correlation between the sensations Si andSk excited in all observers, is the same for all pairs ofsamples.

    If these assumptions are valid, then the scale valuesD are a measure of the magnitude of the visuallyperceived whitenesses of the samples. Because it isdifficult to check the validity of the assumptions, wehave calculated' from the (mik) additional scale valuesd of the visual impression of whiteness that are basedon the entirely different assumption that the differencesSi-Sk are uniformly distributed.4 These scale valuesd are also listed in Table I. Good correlation existsbetween the scale values D and d for all sets of samples,as can be seen from the correlation coefficients r(D,d)listed in Table II. The correlation coefficients aredefined by

    r(D,d)=, (D--B)(di-d)li

    [EF (Di -B)) E (di -d)2, (2)i i

    where D is the mean of all Di and d is the mean of alldi of each set of samples. There is a good correlationbetween the scale values D and d in spite of the factthat they have been calculated with very differentassumptions concerning the distribution of the differ-










    + D60

    .0 0*0

    0.3i1-0.30 0631 0.32 0.33

    FIG. 2. Chromaticity coordinates of samples RG1-RG10 (-) andFl-F12 (o).

    ences Si-Sk. That means that the correlation betweenthe scale values D and the magnitude of the visuallyperceived whiteness would not be much influencedeven if the true distribution of the Si-Sk deviatedconsiderably from a normal distribution.


    It has already been mentioned that current whitenessformulas are valid only within a more or less small






    +:- 03O0


    0,33 0.2 a30 0.32

    FIG. 1. Chromaticity coordinates of samples Bi-B10 (o), Bit-B20 (X), and V1-V10 (e).

    FIG. 3. Chromaticity coordinates of samples Hl-H10 (o) andH11-H20 (0).

    al satto 1UxJI i

    December 1973 1609








    TABLE II. Correlation coefficients.

    Samples r(D,d)a r(D,Ws)b r(D,W2)o r(D,W:)d r(D,W4) r(D,W 5)f r(DW6)9 r(DW 7 )h r(DWV)!Bt-Blb 0.994 0.997 0.997 0.997 0.997 0.996 0.998 0.996 0.997B11-B20 0.996 0.983 0.989 0.990 0.984 0.942 0.970 0.977 0.988V1-VIO 0.986 0.990 0.985 0.986 0.976 0.950 0.986 0.986 0.891RG1-RG1O 0.997 0.510 0.298 0.254 0.134 0.284 0.320 0.706 0.957F1-F12 0.997 0.787 0.622 0.618 0.207 0.364 0.450 0.889 0.953H1-H10 0.996 0.412 0.322 0.246 -0.032 0.153 0.445 0.476 0.962H11-1120 0.997 -0.725 -0.670 -0.734 -0.447 -0.750 -0.057 -0.016 0.982

    a D = visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressionsare normally distributed. d= visually determined scale values of whiteness, calculated with the assumption that differences betweenwhiteness impressions are uniformly distributed.

    b WI= whiteness, calculated from the Berger formula (see Refs. 8 and 10).o W2:=whiteness, calculated from the Taube formula (see Refs. 8 and 11).d W3= whiteness, calculated from the Hunter formula (see Refs. 8 and 11).o W4=whiteness, calculated from the Stensby formula (see Refs. 8 and 12).f W5 =whiteness, calculated from the Stephansen formula (see Refs. 8 and 13).9 Wo= SCAN brightness (see Refs. 8 and 14).h W= whiteness, calculated from the Vaeck-Van Lierde formula (see Ref. 15).i W=whiteness, calculated from Eq. (7).

    part of the gamut of colors perceived as white. This hasbeen shown previously8 with the formulas suggested byBerger,'0 Taube,'" Hunter,'" Stensby,"2 and Stephansen'3and with the SCAN formula.'4 In Table II the correla-tion coefficients r(D,WI), r(D,W2), r(D,W3), r(D,W4 ),r(D,W5), and r(D,We) are listed, where D are thevisually determined scale values of whiteness (Table I)and W,, W2 , W3 , W4, W5, and W6 are the whitenessescalculated from the above-mentioned formulas. Fromthese correlation coefficients, which were calculated in amanner analogous to the correlation coefficients r(D,d)defined by Eq. (2), we conclude that only poor correlat-tions exist between D and W1, W2, W3, W4, W5, andW6, respectively, if samples are compared that differedconsiderably in hue. A whiteness formula having agreater range of validity has been published by Vaeckand van Lierdel5 :

    W7 = Y+ 5000AB- 7000AE, (3)where W7 is the whiteness and Y is the luminousreflectance of the sample. AE is the distance of thechromaticity point F of the sample from a mean blue-yellow axis in the 1960 CIE UCS diagram. This blue-yellow axis is defined by

    v = 2.9042 (u-0.2014)+0.3072. (4)AiB is the distance between two points F' and M,

    where F' is the point of intersection of the perpendicularfrom point F on the blue-yellow axis with this axisitself. M is the point of intersection between theperpendicular from the chromaticity point of standardilluminant C on the blue-yellow axis and this axis itself.The chromaticity coordinates of M are ugf =0.2014 andtilw-0.3072, AB is positive if point F' is below point Mand negative if point F' is above point M. In Table II,the correlation coefficients r(D,W7 ) are listed that aredefined in a manner analogous to the correlationcoefficients r(D,d). Good correlation between D and

    W7 is indicated in most cases, even if samples withdifferent hues are compared, as is the case with samplesRG1-RG1O and FI-F12. However, the correlationbetween D and W7 becomes poor if a bluish-whitesample is compared with other samples of the same huethat are less saturated but exhibit the same or evengreater lightness. This occurs with some samples of thesets Hl-H10 and Hi 1-H20. In this case, wrong valuesof whiteness are obtained from Eq. (3), because thewhiteness W7 of bluish-white samples increases withAB without limit when Y and AE are constant. Thusthe whiteness W7 of samples appearing distinctlybluish-white will be too great in comparison with thevisual impression of whiteness.

    We tried to obtain, therefore, a whiteness formulahaving a greater range of validity than Eq. (3). Thefirst step in our considerations was the assumptionthat the impression of whiteness is influenced by thelightness and the saturation of the samples. The nextstep was the selection of a certain point in the chromat-icity diagram as an origin of a colorimetric quantitythat correlates with the magnitude of the visuallyperceived saturation. The usual practice is to use thechromaticity coordinates of the illuminant as thisorigin when determining the excitation purity ofobject colors. However, it is doubtful whether thispractice is best for assessment of whiteness.

    From the results of the visual assessment of 18self-luminous colors of the same luminance, Honjyoand Nonakal' derived a white-perception region, theborder of which is, in the 1931 CIE chromaticitydiagram, approximated by an ellipse with a majorsemiaxis a=0.0 32 and a minor semiaxis b=0.008. Thechromaticity coordinates of its center P are xP=0.3110,yp=0.3 190 and the angle of inclination of the majoraxis with respect to the positive direction of the x axisof the chromaticity diagram is 0=41.40. These data'7can be interpreted to indicate that there is an ideal

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    white that has the chromaticity coordinates of point P.Presumably this point will shift when conditions ofobservation are used, different from those used byHonjyo and Nonaka. We have not considered influencesof this kind; we provisionally used point P as the originof a calorimetric quantity that correlates with the visualsensation of saturation. We defined this calorimetricquantity provisionally by the ratio






    where (PF) is the distance between point P and thechromaticity point F of the sample, and (PG) is thedistance between point P and the intersection G of theellipse with the straight line through P and F.

    We obtained a fairly good correlation between thevisually determined scale values D of whiteness and thequantity 1 -q, which we computed from the tristimulusvalues of Table I. This correlation could be improvedby minor changes of the shape and the location of theellipse published by Honjyo and Nonaka. The newellipse (Fig. 4) has a major semiaxis a=0.030 and aminor semiaxis b=0.009. The chromaticity coordinatesof its center 0 are x0 =0.3090, yo=0.3 1 70 and the angleof inclination of the major axis with respect to thepositive direction of the x axis of the chromaticitydiagram is 0=48.00. A straight line that coincides withthe major axis intersects the spectrum locus at 576 nm.In analogy to Eq. (5), we defined

    (OF)P=( (6)(OE)

    as a measure of the visually perceived saturation,where (OF) is the distance between points 0 and Fand (OE) is the distance between point 0 and theintersection E of the new ellipse with the straight line




    030 032

    Fia. 4. Tolerance ellipse and definition of p.

    Samples BI-B IO

    I 2 ' 6 ' e ' 1D

    1 Samples B11-Bf20 1 Samples Vl-VIO







    I. .0 2 4D

    Samples RG I - RG 10

    0I .2



    0 2 4 6

    Somples p.H-H1i

    Samples Ft - FR

    I. /

    0 2 4D

    0 2 4 6 2 4D 0 D

    FIG. 5. Relationship between visually determined scale values Dof whiteness and calorimetrically evaluated whiteness W.

    through the points 0 and F (Fig. 4). The influence ofboth saturation and lightness on the visual impressionof whiteness was taken into consideration by use of

    W= Y-c(lOOp), (7)where c is a constant. The nnantitv b has been multi-plied by a factor 100 because p usually is between 0and 1, whereas F usually is between 70 and 100 andcan even be greater, with fluorescent white samples.We assumed that Y is directly proportional to theimpression of lightness because the luminous reflectanceY of white samples is restricted to a relatively smallrange. The form of Eq. (7) was selected because itrepresents the simplest possibility of taking intoaccount the influence of both lightness and saturationon whiteness.

    In Fig. 5, the relationship between the visuallydetermined scale values D of whiteness and the white-ness W calculated from Eq. (7) with c=4 is shown.The correlation coefficients r(D,W) that were cal-culated analogously to the correlation coefficients r(Dd)are listed in Table II. As can be seen from Fig. 5and Table II, good correlation between D and Wwas obtained for all sets of samples. This demonstratesthat Eq. (7) has a greater range of validity than allother whiteness formulas that were tested by us.

    I .. -


    December 1973 1611


    As already mentioned, we used tristimulus valuesthat arc based on the CIE 1931 standard colorimetricobserver. This was dorne inl 3pite of the fact that thesamples were observed under conditions correspondingto a visual field of more than 4 angular subtense.The correlation between D and W, however, could notbe improved by using tristimulus values based onthe CIE 1964 supplementary standard calorimetricobserver.


    We are very much indebted to Dr. V. Bugdahlhis co-workers for the preparation of the samplesto F. Rudolph and his co-workers for plottingellipses.


    REFERENCES'G. Wyszecki and W. S. Stiles, Color Science (Wiley, New

    York, 1967), pp. 468-469.2H. Loof (private communication).3 Reference 1, p. 289. In this reference, the illuminant to which

    we refer is denoted as D .6- We use, however, the

    denotation D 60 because this is in accordance with thedenotations now in use with the CIE standard illuminants D.

    4H. A. David, The Method of Paired Comparisons (Griffin,London, 1963).

    'S. Ishihara, Tests for Colour-Blindness, 38 plates Edition(Kanehara Shuppan Co., Tokyo, 1967).

    6U. Schultz and R. Lehmann, in Proceedings of theInternational Color Meeting "Color 69," Stockholm 1969(Muster-Schmidt, Gattingen, 1970), Vol. 2, p. 845.

    7H.-G. Friihling, W. Munch, and M. Richter, Farbe 5, 41(1956).

    8R. Thielert and G. Schliemann, Farbe 21, 113 (1972).9 R. Thielert and G. Schliemann, J. Opt. Soc. Am. 62, 137

    (1972).'"A. Berger, Farbe 8, 187 (1959)."R. S. Hunter, J. Opt. Soc. Am. 50, 44 (1960).1 2P. S. Stensby, J. Am. Oil Chem. Soc. 45, 497 (1968).13G. Hansen, Zelistoff Papier 18, 393 (1938).

    14SCAN-P3: 62, Brightness of Paper and Paperboard(Scandinavian Pulp, Paper, and Board Testing Committee,Stockholm, 1962).

    "S. V. Vaeck and F. van Lierde, Ann. Textiles Belges No.3-9/64, 7 (Sept. 1964).

    16 K. Honjyo and M. Nonaka, J. Opt. Soc. Am. 60, 1690(1970).

    "We are very much indebted to Dr. Kazuo Honjyo of CentralResearch Laboratory, Hitachi, Ltd., Tokyo, forcommunication of these data.

    Technical CouncilCHARLES J. KOESTER (Chairman), Research Labora-

    tory, American Optical Corporation, P. 0. Box 187,Framingham Centre, Mass. 01701

    ROBERT V. POLE (Vice Chairman), IBM Corporation,Monterey & Cottle Roads, San Jose, California95114

    The chairmen of the Technical Groups comprise(ex officio) the Technical Council.

    Aeronautics and Space Optics-LLOYD G. MUNDIERand Corporation, 1700 Main Street, Santa

    Monica, California 90406Atmospheric and Space Optics-

    FREEMAN H. HALL, JR.NOAA, Wave Propagation Laboratory, Environ-

    mental Research Labs., Boulder, Colo. 80302Color-C. J. BARTLESON

    Kollmorgen Corporation, Macbeth Research Labo-ratories, Box 950, Newburgh, New York 12550

    Information Processing, Holography, & Coherence-JOSEPH W. GOODMAN

    Stanford Electronics Laboratories, Stanford, Calif.94305

    Lasers and Electro-Optics-ANTHONY J. DEMARIAUnited Aircraft Research Laboratories, East Hart-

    ford, Conn. 06108

    Lens Design-DAVID S. GREYDavid Grey Associates, 60 Hickory Drive,

    Waltham, Mass. 02154Optical Fabrication and Testing-FRANK COOKE

    66 Summer Street, North Brookfield, Mass. 01535Optical Materials-IRVING H. MALITSON

    A-251 Physics Building, National Bureau of Stan-dards, Washington, D. C. 20234

    Radiometry and Photometry-BRUCE W. STEINERB-312 Metrology Building, National Bureau of

    Standards, Washington, D. C. 20234Raman-ELLIS R. LIPPINCOTT

    Dept. of Chemistry, University of Maryland,College Park, Md. 20742

    Spectroscopy-JACK SUGARA-167 Physics Building, National Bureau of Stan-

    dards, Washington, D. C. 20234Thin Films & lnterferometry-

    PHILIP W. BAUMEISTERInstitute of Optics, University of Rochester,

    Rochester, New York 14627Vision-LORRIN A. RIGGS

    Hunter Laboratory, Brown University, Providence,Rhode Island 02912


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