Visual impression of whiteness and its colorimetric definition

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<ul><li><p>JOURNAL OF THE OPTICAL SOCIETY OF AMERICA</p><p>Visual impression of whiteness and its colorimetric definitionR. Thielert and G. Schliemanr</p><p>Unilever Forschungsgesellschaft mbH, Hamburg 50, W. Germany(Received 26 March 1973)</p><p>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.</p><p>Index Headings: Color; Colorimetry.</p><p>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.</p><p>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.</p><p>COLOR MEASUREMENTS</p><p>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</p><p>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,</p><p>PX =pX+fX- (1)PX was measured between 380 and 770 nm at intervals</p><p>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.</p><p>VISUAL ASSESSMENT OF WHITENESS</p><p>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.</p><p>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-</p><p>1607</p><p>VOLUME 63, NUMBER 12 DECEMBER 1973</p></li><li><p>R. THIELERT AND G. SCHLIEMANN</p><p>TABLE 1. Tristimulus values, visually determined scale values of whiteness, and colorimetrically evaluated whiteness.</p><p>Samiiple X Y z DI hb W.c TVd</p><p>B1B2B3B4B5B6B7B8B9BlO</p><p>BllB12B13B14B15B16B17B18B19B20</p><p>VIV2V3V4V5V6V7V8V9V10</p><p>RG1RG2RG3RG4RG5RG6</p><p>85.2885.8386.4987.0187.1187.5987.7488.1888.4888.55</p><p>86.5286.2787.3486.9687.7687.5187.5187.6289.1089.05</p><p>80.5980.9581.2781.7381.7182.3182.7382.7882.9482.81</p><p>76.0083.0685.6982.5574.4287.13</p><p>89.5689.8390.2590.6490.5390.9290.9391.1291.3291.36</p><p>89.6289.3090.3089.7790.4290.2790.3190.4391.9892.18</p><p>82.2982.6182.6583.0782.8583.4383.8583.8984.1984.24</p><p>78.5388.5286.9282.7078.1789.20</p><p>85.7588.4591.2893.6294.5596.9797.82</p><p>100.32101.26102.25</p><p>96.4396.6598.9598.96</p><p>100.62100.64101.18101.63104.96104.75</p><p>91.6292.5695.0496.5698.0899.39</p><p>100.59100.97101.70101.29</p><p>89.8094.17</p><p>101.6599.8689.65</p><p>102.69</p><p>01.963.604.055.466.567.528.879.40</p><p>00.721.251.932.242.602.683.003.893.87</p><p>01.282.383.073.944.364.754.965.925.62</p><p>0.02-0.92</p><p>0.66-0.32-0.38</p><p>1.18</p><p>-0.45-0.35-0.25-0.15-0.05</p><p>0.050.150.260.370.41</p><p>-0.42-0.33-0.23-0.10-0.01</p><p>0.080.100.190.370.36</p><p>-0.44-0.35-0.22-0.14-0.01</p><p>0.080.170.200.370.33</p><p>0.02-0.27</p><p>0.20-0.11-0.14</p><p>0.35</p><p>13.522.831.537.642.148.351.259.162.364.5</p><p>50.652.457.059.462.163.063.364.468.565.2</p><p>63.364.570.974.878.881.485.586.390.387.4</p><p>54.517.278.468.637.676.5</p><p>50.656.261.665.767.972.073.678.279.981.5</p><p>72.573.476.577.479.679.980.581.284.883.2</p><p>70.371.273.274.273.173.674.373.875.477.1</p><p>71.254.477.063.458.984.0</p><p>sample I Y Z DA db W,7 WdRG7RG8RG9RG1O</p><p>FlF2F3F4F5F6F7F8P9110FitF12</p><p>H1H2H3H4H5H6H7H8H9H10</p><p>HitH12H13H14H15H16H17H18H19H20</p><p>84.0288.4476.9484.08</p><p>89.0082.4986.6290.8890.6389.1589.6580.8484.6089.2586.5888.32</p><p>90.6377.5376.8388.6876.5388.4570.7789.5275.9988.36</p><p>72.4268.2376.0077.9879.4076.9476.7186.9383.3087.13</p><p>83.4992.2179.6985.27</p><p>88.4785.2389.5690.7591.5290.0791.2782.1488.0892.0991.8592.16</p><p>91.5280.0278.9292.2178.5991.0673.1790.4778.4091.25</p><p>77.4469.9478.5380.5080.6679.6978.6989.7086.8189.20</p><p>99.02100.5093.0997.73</p><p>101.51102.40104.3597.1497.05</p><p>103.19101.4194.5488.28</p><p>105.4892.8999.79</p><p>97.05100.2295.64</p><p>101.2893.46</p><p>103.7083.16</p><p>100.9689.80</p><p>102.15</p><p>102.1596.1689.80</p><p>100.0999.8393.0995.4997.98</p><p>104.20102.69</p><p>-0.900.440.34</p><p>-0.12</p><p>0.672.623.1901.122.232.322.251.413.140.961.98</p><p>00.391.381.951.312.140.120.540.922.03</p><p>00.171.611.711.982.132.262.272.332.86</p><p>-0.290.130.12</p><p>-0.02</p><p>-0.290.180.33</p><p>-0.40-0.20</p><p>0.110.120.11</p><p>-0.120.32</p><p>-0.220.06</p><p>-0.33-0.18</p><p>0.070.230.050.32</p><p>-0.24-0.16-0.06</p><p>0.28</p><p>-0.40-0.37-0.05-0.03</p><p>0.050.090.130.130.150.31</p><p>49.048.957.867.7</p><p>39.971.968.719.934.566.066.669.330.070.015.546.8</p><p>34.576.973.553.469.370.247.256.056.763.3</p><p>49.995.054.575.591.157.875.257.964.176.5</p><p>57.074.571.973.2</p><p>59.377.483.356.763.974.276.571.559.386.057.974.2</p><p>63.966.273.477.676.684.765.271.472.481.6</p><p>34.641.271.268.570.271.973.575.872.884.0</p><p>D =visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressionsare normally distributed.</p><p>b d= visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressionsare uniformly distributed.</p><p>C W7=whiteness, calculated from the Vaeck-Van Lierde formula (see Ref. 15).d W =whiteness, calculated from Eq. (7).</p><p>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 &gt;0.70 inall cases.</p><p>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-</p><p>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.</p><p>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:</p><p>1608 Vol. 63</p></li><li><p>VISUAL IMPRESSION OF WHITENESS</p><p>(i) The differences Si-Sk observed by a greatnumber of persons are normally distributed for eachpair of samples.</p><p>(ii) The normal distributions of the differencesSi-Sk all have the same standard deviation.</p><p>(iii) The correlation between the sensations Si andSk excited in all observers, is the same for all pairs ofsamples.</p><p>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</p><p>r(D,d)=, (D--B)(di-d)li</p><p>[EF (Di -B)) E (di -d)2, (2)i i</p><p>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-</p><p>0.34-</p><p>0,33-</p><p>y</p><p>432-</p><p>0.34-</p><p>Q33-</p><p>y</p><p>032-</p><p>0.32-</p><p>+ D60</p><p>.0 0*0</p><p>0.3i1-0.30 0631 0.32 0.33</p><p>FIG. 2. Chromaticity coordinates of samples RG1-RG10 (-) andFl-F12 (o).</p><p>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.</p><p>COLORIMETRIC DEFINITION OF WHITENESS</p><p>It has already been mentioned that current whitenessformulas are valid only within a more or less small</p><p>PD60</p><p>9</p><p>9</p><p>x*Ify</p><p>+C</p><p>+:- 03O0</p><p>0.32x</p><p>0,33 0.2 a30 0.32</p><p>FIG. 1. Chromaticity coordinates of samples Bi-B10 (o), Bit-B20 (X), and V1-V10 (e).</p><p>FIG. 3. Chromaticity coordinates of samples Hl-H10 (o) andH11-H20 (0).</p><p>al satto 1UxJI i</p><p>December 1973 1609</p><p>to</p><p>so</p><p>0</p><p>go</p><p>ao</p><p>0</p></li><li><p>R. THIELERT AND G. SCHLIEMANN</p><p>TABLE II. Correlation coefficients.</p><p>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</p><p>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.</p><p>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).</p><p>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 :</p><p>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</p><p>v = 2.9042 (u-0.2014)+0.3072. (4)AiB is the distance between two points F' and M,</p><p>where F' is the point of intersection of the perpendicularfrom point F on the blue-yellow axis with this axisitself. M i...</p></li></ul>

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