whiteness: photometric specification and colorimetric evaluation

Whiteness: photometric specificationand colorimetric evaluation

Ernst Ganz

Though basic problems of the perception of whiteness are as yet unsolved, this paper attempts to survey the

present state and the requirements of industrial whiteness measurement. Generic formulas with adjustable

parameters for the evaluation of whiteness and tint are presented.

Introduction

Whiteness is an attribute of colors of high luminousreflectance and low purity situated in a relatively nar-row region of the color space along dominant wave-

lengths of 570 nm and 470 nm approximately. Al-though colors perceived as white thus constitute a setin a three-dimensional space, most observers are able

to arrange white samples of different luminous reflec-tance, purity, and/or dominant wavelengths in a one-dimensional order according to whiteness.1 This ordermay vary for a given group of white samples not only

between observers but also for the same observer be-tween various methods of assessment (ranking, paircomparison, difference or ratio scaling, etc.). Moreover

the assessment of whiteness also depends on individualpreference and on such widely varying conditions as the

level and spectral power distribution of sample irra-diation, the color of the surround of the whites, and theacquired preconceptions in various trades. Howeverthere is fairly general agreement that samples are con-sidered less white the darker and the yellower they are.

Three peculiar observations are made if samplesdiffering only moderately in whiteness are compared:

(1) Although a difference in lightness and/or in

blueness may be clearly perceived, it is possible to rank

the samples according to their whiteness. Differentweight may be attributed to lightness and blueness bydifferent observers.

(2) Differences in hue often give rise to contradictory

assessments of whiteness, some observers preferringwhites with a greenish tint and others those with areddish tint. Samples with an intermediate bluish orneutral tint are however assessed more consistently.

The author is with CIBA-GEIGY, Ltd., CH-4002 Basle, Switzer-

land.Received 5 February 1976.

(3) Independently of the individually perceiveddifference in whiteness, there is fairly general agreementamong observers on differences in hue. Most observersperceive the same samples greener than others, whichin turn appear redder than the first. However, theremay be disagreement about samples that appear neithergreenish nor reddish (i.e., neutral or bluish white).

These three effects probably explain why samplesdiffering in luminous reflectance, purity, and/or dom-inant wavelength can be ordered linearly according totheir whiteness as perceived under given conditions byindividual observers, although no general agreement on

whiteness can be reached.White is a ubiquitous color, and its production in

textiles, paper, plastics, and coatings is a major indus-trial task paralleled in importance by the restoration ofwhiteness by laundering.

Before the advent of fluorescent whitening agents(FWA's), whiteness was enhanced by bleaching andbluing the substrates and by selecting and purifyingpigments to be incorporated. The perfect diffuserapproximated by magnesium oxide or barium sulfatecould then be considered as the ideal or preferred white.

The additional use of FWA's enlarged the range ofwhites far beyond the whiteness of the perfect diffuser.But the search for a generally accepted preferred whiteor rather for typical individually preferred whites hasnot yet yielded definite results.

Nevertheless, instrumental methods for an objectiveevaluation of whiteness and tint replacing possiblycontroversial visual assessments became more signifi-cant. Two steps of the procedure must be distin-guished:

(1) The spectral radiance factors are measured, andthe tristrimulus values are calculated. Instead ofspectrophotometers, colorimeters directly indicatingapproximate tristimulus values are frequently used for

routine measurements. Standard spectrophotometricand calorimetric techniques can be applied if samplesare bleached and blued only or contain nonfluorescent

September 1976 / Vol. 15, No. 9 / APPLIED OPTICS 2039

500 X nm 600

Fig. 1. Sample number 12 (210) of the CIBA-GEIGY Plastic WhiteScale2 measured with a Zeiss DMC 25 spectrophotometer: (1)spectral radiance factor with xenon lamp(the depressions near 465nm being due to xenon lines); (2) conventional reflectance with de-tector for visible range (S10 sensitivity); (3) conventional reflectance

with detector for uv range (5 sensitivity).

pigments and have not been treated with FWA's. Withfluoroescent samples, however, the spectrophotometricand colorimetric specifications require special attention.

(2) Evaluation of whiteness and tint by suitableformulas based on tristimulus values and equipped withparameters yielding sufficient correlation with visualassessments by a significant group of observers.

Photometric Specification of WhitenessReflectance is measured with most conventional

photometers by monochromatic irradiation of thesample and of the reference white at a wavelength X.For nonfluorescent samples the ratio of the undispersedreflected fluxes is equal to the spectral radiance factorf3(X) at the irradiated wavelength. For fluorescentsamples this procedure does not yield spectral radiancefactors in the wavelength ranges in which fluorescenceis excited and/or emitted. In the range of excitation thereflected monochromatic flux is increased by the poly-chromatic power of the emitted fluorescence, which isnot recorded at its proper wavelengths in the range ofemission (see Fig. 1).

The value actually measured was termed conven-tional reflectance by Grum and Patek3 and defined byBillmeyer.4 It is a function of both the spectral prop-erties of the sample and of the spectral responsivity ofthe photodetector. Therefore, it is unsuitable for thephotometric specification of fluorescent samples. It isgenerally accepted that the spectral radiance factors ofwhite fluorescent samples must be measured withpolychromatic irradiation using a photodetector fittedwith a monochromator or with suitable filters.

The spectral tristimulus values of the CIE 1931standard colorimetric observer or of the CIE 1964 sup-plementary standard colorimetric observer are used forthe calculation of tristimulus values applied to theevaluation of whiteness.

Influence of Sample IrradiationFor fluorescent samples treated with FWA's the vi-

sually perceived color as well as the spectral radiancefactor and the calculated or approximately measuredtristimulus values depend on the spectral power dis-tribution of the irradiation. The contribution of fluo-rescence is the more important the higher the power ofthe irradiation in the wavelength range of fluorescenceexcitation, and the lower it is in the wavelength rangeof fluorescence emission. Therefore, it is not sufficientto check whether the spectral power distribution of theirradiation corresponds in the visible range only withthat of the standard illuminant (e.g., D65) for which thespectral radiance factor or the approximate tristimulusvalues should be valid. The irradiation must alsoconform with the standard illuminant in the whole uvrange giving rise to excitation of fluorescence.

This has been known for at least 15 years5 6 and wasalso stressed in the introductory lecture7 of the 1972"ISCC Conference on Fluorescence and the Colorimetryof Fluorescent Materials." The discrepancies betweenwhiteness measurements made with different instru-ments still arise mainly because the dependence of thespectral radiance factors of fluorescent samples on thespectral power distribution of the irradiation in bothabsorption and emission wavelength ranges is neglected.

As an example, chromaticities of sample 12 (210) ofthe CIBA-GEIGY Plastic White Scale measured withvarious instruments fitted with xenon lamps are plottedin Fig. 2. The large deviations from the chromaticitycomputed for D65 are due to differences in the relativeuv contents of the effective sample irradiation in theinstruments. Since Z(sample)-Z(substrate) is ap-proximately proportional to the relative power of thefluorescence, the ratio Az (instrument)/Az(D65) is an

.33

.32

y

7QD65 A

_ Q504

E 633

%2

I I.29 .30 .31

.30

.31

x

Fig. 2. Apparent D65 chromaticities of sample number 12 (210) ofthe CIBA-GEIGY Plastic White Scale measured with various in-struments: (1) Spectromat SP-3; (2) Zeiss RFC 3 with AGB-filters;(3) Zeiss Elrepho; (4) Spectromat SP-3 with adjustable uv filter8 ; (5)Zeiss DMC 25; (6) Zeiss DMC 25, but transformed to D65 by themethod of Eitle and Ganz.9 All chromaticities of the nonfluorescent

substrate for sample 12 lie within the circle 7.

2040 APPLIED OPTICS / Vol. 15, No. 9 / September 1976

-

Table I. Chromaticities of Twenty White Papers Measured by Berger with a

Filtered Xenon Lamp (Zeiss Elrepho) and by Grum, et al. with aMacbeth D65-Simulator Fluorescent Lamp

Berger

Sample

AchromSubstr.

40103228361112332937

7134243303438393135101213

x

0.31270.31570.31340.31300.31280.31300.31280.31170.31140.30750.30760.30730.30610.30640.30650.30610.30330.30260.30220.30040.30000.29940.31300.31140.3064

y

0.32900.33350.32970.330.00.32940.32890.32910.32840.32700.32140.32070.32070.32120.31970.31910.31830.31480.31400.31360.31130.31050.30950.33000.32700.3197

Az

0.00000.00610.00620.00700.00730.00730.00910.01080.02030.02090.02120.02190.02310.02360.02480.03110.03260.03340.03750.03870.04030.00000.00460.0169

x

0.3164(0.3202)0.32010.31820.31950.31960.31950.31640.31760.31700.31710.31700.31500.31500.31800.31830.31480.31470.31460.31400.31400.31340.31820.31760.3150

Grum et al.

y

0.3345(0.3396)0.33880.33670.33820.33840.33810.33450.33540.33470.33500.33470.33390.33190.33540.33550.33230.33180.33170.33140.33150.33040.33670.33540.3319

Ratio

Az(G)/Az Az(B)

0.00000.00090.00490.00210.00180.00220.00890.00680.00810.00770.00810.01090.01290.00640.00600.01270.01330.01350.01440.01430.01600.00000.00190.0080

0.150.790.300.250.300.980.630.400.370.380.500.560.270.240.410.410.400.380.370.40

0.410.47

Note: Since the chromaticity of the substrate was not measured by Grum et al., it wasapproximated by shifting the Berger values corresponding to the mean chromaticity differ-

ence of the achromatic point and of the two blued nonfluorescent samples 10 and 11.

Samples 7, 12, 13 are blued and treated with FWA's, sample 10 being the substrate for

samples 12 and 13.

index of the relative uv contents of the irradiation ef-fective in the instruments ranging from 0.80 to 1.25.Although the chromaticities plotted in Fig. 1 are char-acteristic for the type of instrument, the actual valuesdepend on the state of the source and of the integratingsphere at the time of the measurement.

Another example is given in Table I, which shows the

chromaticities of the same twenty paper samples mea-sured by Berger10 with a filtered xenon lamp (Zeiss El-repho) and by Grum et al." with Macbeth D65-simu-lator fluorescent lamps. Within the limits of attainableaccuracy the ratio Az (Grum)/Az (Berger) for nonfluo-rescent samples 10 and 11 is near unity (as to be ex-pected). For blued samples 7, 12, 13 containing alsoFWA's it is approximately 0.55, and for fluorescentsamples it is on the average 0.40. (For samples 40, 42,43 treated with a different FWA it is even lower.) The

power of fluorescence measured with irradiation by theMacbeth D65-simulator fluorescent lamp is diminishedat least by 50% compared to true D65 irradiation, ac-counting for an excess of about 10% measured using theZeiss Elrepho with a filtered xenon lamp (see Fig. 2).The increased effect on samples 40, 42, 43 is probablydue to displaced absorptance and/or emittance spectraof the applied FWA, with respect to the line spectrumof the fluorescent lamp.

For some industrial routine work such discrepancies

are without consequence. Relative visual assessmentsand relative instrumental measurements of whitenessare sufficient for comparing the whitening effect ofsimilar products, evaluating various application pro-cedures, assessing fastness properties, etc. Relativewhiteness determinations based on reproducible sam-ples of graded concentrations of FWA's or on stablewhite scales are often made with various irradiationsroughly approximating to daylight even if the relativespectral power distribution of the source and the re-flectance of the luminaire or of the coating of the inte-grating sphere change due to aging. However, the fol-lowing restrictions should be kept in mind:

(1) Comparison of samples prepared with FWA'sdiffering in the excitation and/or fluorescence spectrummay be influenced by the spectral power distributionof the irradiation.

(2) Comparison of fluorescent samples producedwith substrates differing in reflectance and/or con-taining different concentrations of nonfluorescent dyes(e.g., for bluing) will in general be heavily influenced bythe spectral power distribution of the irradiation.

(3) As a consequence of restrictions (1) and (2)agreement of visual assessments and instrumentalmeasurements of whiteness is likely to be impaired ifthe spectral power distribution of the irradiations isdifferent.


(4) Whiteness formulas based on assessments andmeasurements of fluorescent white samples with irra-diations diverging spectrally from a standard illuminant(e.g., D65) will generally yield different results withmeasurements using an irradiation with a standard il-luminant or with another different spectral power dis-tribution.

(5) To avoid mistaking spectral radiance factors andtristimulus values of fluorescent white samples deter-mined at spectral power distributions diverging fromthat of a standard daylight illuminant, they should becharacterized by a suffix (ADL) for artificial daylightwith an optional indication of the approximate colortemperature. Unless conformity in the uv range ischecked, a suffix denoting a standard illuminant shouldnot be used even if the actual source is labeled to rep-resent a standard illuminant in the visible part of thespectrum. The same applies if the method of approx-imate illuminant transformation suggested by Berger12and discussed later is used.

Standardization of Sample IrradiationThe relative spectral power distributions of the

standard illuminants D representing the differentphases of daylight has been defined numerically by theCIE, but no physical source has yet been adopted torepresent such illuminants with sufficient accuracy andconstancy. Various methods have been developedhowever for checking the influence on color of the di-vergence of the spectral power distribution of physicalsources from that of the standard illuminant D65 andfor setting tolerances:

(1) Based on a paper by Berger and Strocka,13 theprovisional 1973 version of the German Standard DIN6173, Blatt 2 (Farbabmusterung: Beleuchtungs-bedingungen fur knstliches Tageslicht) uses the meancolor difference of ten metameric pairs in order tocharacterize the deviation in the visible spectrum ofartificial daylight sources from illuminant D65. To testconformity in the uv range, the color difference betweena fluorescent white test color introduced by Ganz andEitle1 4 and the perfect diffuser is computed for D65 andfor the source of artificial daylight to be tested.

(2) Richter15 suggested extending the method ofGanz and Eitle14 for determining a special color ren-dering index related to the uv range. The deviationsof the spectral power distribution are tested by evalu-ating the color differences of the original fluorescentwhite test color and of three fluorescent colors me-tameric in D65. The latter are characterized by fluo-rescence spectra identical with that of the test color andby idealized uniform quantum absorptance in theranges of 320.0-362.1 nm, 360.0-392.2 nm, and400.0-418.4 nm, respectively.

(3) In a second paper by Berger and Strocka,1 6 threesimulated functions of quantum absorptance are de-fined (Fig. 3), subdividing the experimental data ofGanz and Eitle14 in order to provide more informationon the conformity of artificial daylight sources with il-luminant D65 in the uv range. Instead of color differ-ences the number of quanta absorbed by the threesimulated absorptance functions is taken as a criterion

for the tolerated deviations in the uv range of the day-light source as compared with the number of quantaabsorbed from the spectral power distribution of illu-minant D65 adjusted for equal power at 560 nm. Thetolerances are chosen so that D75 and D60 are admittedas substitutes for D65. The narrower tolerance forsources with a low uv content is selected in order to ex-clude artificial daylight sources that do not sufficientlyexcite the fluorescence of FWA's. This method su-persedes the one mentioned before (1) in the provisional1974 version of DIN 6173.

Tolerances in chromaticity and/or spectral powerdistribution of artificial daylight sources for the as-sessment of color have been set:

(1) British Standard BS 950, Part 1 (1967) sets tol-erances for sources approximating to D65. It requiresper luminous flux of 100 lm a radiant power of 11.2 mWin the range of 300-340 nm and of 43.2 mW in the rangeof 340-400 nm. The tolerance in both ranges is 30%and 15% in the six visible ranges. The tolerance el-lipse in the chromaticity chart just excludes D60 andD70 as substitues for D65. But the tolerance in the340-400-nm uv range in which fluorescence of FWA'sis mainly excited almost admits sources as different asD55 and D75 (-33% and +32%, respectively).

(2) The French Tentative Standard T30-061 definesthe same chromaticity range for sources approximatingto D65 as BS 950, Part 1 mentioned above. No toler-ances are set however for the spectral power distribu-tion.

These methods requiring measurements of spectralpower distribution are useful for manufacturers ofsources and luminaires. The colorist needs simplermethods:

(1) Japanese Industrial Standard JIS Z 8902 specifiesa special type of xenon lamp in combination with a filteras standard source for visual assessments of fluorescentwhite samples based on two scales of fluorescent whitereference samples. Effective lamp life is estimated tobe 300 h or more.

(2) A device for controlling the relative uv contents

G E1" 9)'

0.2 >~ \ \

300 400 A

Fig.3. Quantum absorption Q(X') of the sample by Ganz and Eitlel4(full line) and of the three simulated functions by Berger and Stroc-

ka16 (dotted lines).


of the sample irradiation in a photometer has been de-vised by Gartner and Griesser.8 With an adjustable uv

filter the excitation of the fluorescence of a stable whitereference sample is attenuated sufficiently to keep thetristimulus values of this sample constant. The longterm reproducibility of the measurements lie within thethreshold limits of perceptible whiteness differences.

(3) Sources used for the visual assessment and in-strumental measurement of fluorescent white samplescan be tested by a method developed by Anders andGanz.1 7 The metameric match between one of a series

of fluorescent white samples graded in FWA concen-tration and a blued, nonfluorescent white sample isobserved or calculated. The higher the relative uvcontents of the irradiation, the lower is the FWA con-centration necessary for matching the nonfluorescentsample. The accuracy of the method depends on theprecision of the hue match of the samples.

Restriction (1) set forth in the introductory discussionof routine measurements applies here also and may limit

the usefulness of methods (2) and (3).

Conversion of Experimental Data to StandardIlluminants

Spectral radiance factors and tristimulus values ofwhite fluorescent samples for physically nonreprodu-cible standard illuminants can be calculated frommeasurements with irradiations moderately divergingfrom a standard illuminant. Since the reflectance ofthe samples is not influenced by the irradiation, only thecontribution of fluorescence to the spectral radiancefactor has to be corrected. The contribution of fluo-rescence measured with polychromatic irradiation is not

determined directly. It is easier to exclude fluorescence

and to measure the true reflectance of the fluorescentsample. The spectral radiance factors due to fluores-cence are subsequently calculated as the differencebetween the measurements including and excludingfluorescence.

Several methods for the measurement of true re-flectance of fluorescent samples have been suggested:

(1) Grum18 measures true reflectance with two mo-nochromators placed in the beams irradiating thesample and measuring its radiance, respectively, setting

both monochromators to the same wavelength.(2) Simon1 9 uses one monochromator placed in turn

in the beams irradiating the sample and measuring itsradiance. By this method the true reflectance is mea-sured in the wavelength ranges of emission and of ex-citation of fluorescence, respectively. The true re-flectance must be interpolated in the range of super-posed excitation and emission.

(3) Allen20 determines a correction function basedon measurements of the spectral radiance factor offluorescent samples with the unfiltered source and usingin turn two filters in the beam of irradiation attenuating

and excluding fluorescence, respectively. This methodpermits calculation of true reflectance exactly in therange of superposed excitation and emission. Since the

correction function is a ratio of two differences, it cannot

be applied if both numerator and denominator becomesmall and pass through zero.

(4) Eitle and Ganz9 measure true reflectance ap-proximately in the range of superposed excitation andemission by using a series of cutoff filters. The errorsintroduced by neglecting the corrections applied byAllen (3) tend to increase the measured values of truereflectance a little. The influence on further evalua-tions of white fluorescent samples is insignificant.

(5) Berger1 2 substitutes true reflectance in the range

of superposed excitation and emission by the spectralradiance factor of either the nonfluorescent substrateor the sample including fluorescence, whichever is thesmaller. For testing this method Berger computedtristimulus values by the method of Eitle and Ganz9 fortwelve samples and six illuminants based on measure-ments made with a source of a spectral power distribu-tion of Xe(10).21 The differences between the colori-metric values calculated with true reflectance andsubstitute true reflectance, respectively, for illuminantsD65, D75, and A are on the average less than 0.0001 in

chromaticity coordinates and 0.02 in luminance factor.The differences may be considerably larger accordingto the overlap of excitation and emission for illuminantslike Xe(2), F(13), or F(17), which diverge more fromXe(10) used as the source for measurement. The resultof this investigation makes the measurement of the truereflectance of fluorescent white samples obsolete formost industrial applications if suitable sources are usedto irradiate the samples.

Alman et al. 2 2 discussed the feasibility of thesemethods applied to colored fluorescent samples.

In order to correct the contribution of fluorescenceto the spectral radiance factors for a standard illumi-nant, the ratio of the number of quanta absorbed by theFWA at measurement and at irradiation by the stan-dard illuminant must be determined. For this purposethe fraction of the spectral absorptance of the sampledue to the FWA has to be calculated. Therefore, thespectral radiance factors of the substrate in the state inwhich it is effective in the sample must be measured. It

is generally known that the absorptance of a substratemay be both decreased by laundering and increased bydyes or impurities in the liquors and/or in the subse-quent heat- and after-treatmentg. What is needed,therefore, is not to measure the substrate in the state asdelivered, but rather to treat it before measurement ina blank bath containing all components of the actualbath including dyes for bluing and tinting if used butexcluding FWA's. All after-treatments (heat etc.) must

be applied.In spite of these precautions a difference in reflec-

tance is sometimes observed between sample andtreated substrate at wavelengths uninfluenced by flu-orescence. It is advisable to correct such differencesover the whole 300-700-nm wavelength range by as-suming that a constant difference in the absorptioncoefficient (as determined by a Kubelka-Munk analysisin the range of no fluorescence) has to be added to, orsubtracted from, the experimental spectral absorptioncoefficients of the treated substrate.


Methods for Conversion

With these provisions, methods of different degreesof approximation have been devised for computingspectral radiance factors and/or tristimulus values offluorescent white samples for physically nonreprodu-cible standard illuminants:

(1) Eitle and Ganz9 determine the relative spectralpower distribution of fluorescence F (X) with thespectral radiance factors of the sample including fluo-rescence AM(X) and excluding fluorescence T(X) cor-responding to the true reflectance

FM(X) = [M( - (X)I - SM(X). (1)

The relative number of quanta absorbed in polychro-matic irradiation is proportional to the sum over thewavelength range ' of excitation

Q = k E [1 - T(X')I * |1 - flT(X) [1-3o(X')] 2

A' fo(X')* [1- T(XI)J2

- S(X') ' * AX', (2)

where o(X') are the spectral radiance factors of thesubstrate treated in a blank bath. Neglecting the in-fluence on the reabsorption of fluorescence excited bydifferent spectral power distributions of the irradia-tion,23 the spectral power distribution of fluorescenceFN(G) for the standard illuminant N is approximatedby

FN(X) = FM(A) QNIQM. (3)

The spectral radiance factor AN(X) is calculated for thestandard illuminant

flN(X) = T(A) + FN(X)/SN()

= AT(X) + [M(X)- iT() QN S . (4)QM SN(X)'

The error introduced by the approximation of Eq. (3)is less than 0.02 in the luminance factor and 0.0002 inthe chromaticity coordinates if tristimulus values arecomputed for illuminants D75, D65, D55, and even Abased on measurements with a suitably filtered xenonlamp similar to the spectral power distribution ofXe (10).

(2) Errors in colorimetric measurements of fluo-rescent white samples due to an incomplete fit of thespectral power distribution of the irradiation to that ofa standard illuminant can be approximately correctedby a method proposed by Ganz.24 Three correctionfactors each for reflectance and for fluorescence can be

calculated based on true standard (e.g., D65) or refer-ence data of A, G, B, and those actually measured forboth a fluorescent white sample and its nonfluorescentsubstrate. The three correction factors for reflectancewith an instrument and a given kind of sample (gloss,surface-structure) are fairly constant. The three cor-rection factors for fluorescence depend on the spectralpower distribution of the irradiation and must be re-determined from time to time due to the aging of thesource and the integrating sphere.

The effectiveness of the method was tested witheighteen samples prepared with different FWA's onpolyester, polyamide, and acetate fibers and on pig-mented plastic sheets. The samples were measuredwith six photometers of four different types. The meanand the standard deviation of the computed differencesof chromaticity, luminance, and whiteness betweenuncorrected and corrected measurements, respectively,and true D65 values are given in Table II.

The sign of the uncorrected means is due to the ex-perimental spectral power distributions. In five of thesix instruments tested the relative uv contents of thesample irradiation was smaller than in D65. The cor-rection reduces the mean whiteness difference ap-proximately to the threshold value of three units. Thespread is reduced only to about half of that for uncor-rected data if the correction factors are determined withone calibrated pair only and used for the correction ofall other samples differing in FWA and substrate. Thespread is further reduced if the correction factors em-ployed are specifically determined for each FWA andeach substrate.

The correction method may also be applied to tris-timulus values X, Y Z since fluorescence of FWA's ismainly centered in the short wavelength section of ,and the correction for reflectance is nearly independentof wavelength.

Both methods (1) and (2) are applicable only if thenonfluorescent substrate used for the preparation of thesamples is available and the contributions of fluores-cence and reflectance can be separated. Moreover itis necessary to calibrate either the spectral power dis-tribution of the irradiation at measurement or thewhiteness of stable reference samples for a standardilluminant.

(3) Considering these difficulties, Berger1 2 suggestedcomputing tristimulus values T = X, Y, Z of fluo-rescent white samples with spectral radiance factorsOM(X) measured with an irradiation differing only

Table II. Mean ,i and Standard Deviation a of Computed DifferencesBetween Experimental and True D65 Chromaticity, Luminance,

and Whiteness (CIBA-GEIGY units)

Colorimetric Ax Ay AY AWdata Au O Fu a A a u a

Uncorrected 0.0014 ±0.0026 0.0031 ±0.0045 -1.05 ± 1.80 -18 ± 23Generally -0.0004 ±0.0013 0.0003 ±0.0031 -0.11 ±2.14 3 ±12corrected

Specifically -0.0011 ±0.0009 -0.0008 ± 0.0014 -0.30 ± 0.30 4 ±7corrected


Table Ill. Differences Between Values Measured with Irradiations Indicated

and Transformed to D65 by Formula (5) of Berger2 and True D65 ChromaticityLuminance and Whiteness (CIBA-GEIGY units) for CIBA-GEIGY

White Scale Samples 210 Plastic (P) and 240 Cotton (C)

Ax Ay AY AW

Irradiation P C P C P C P C

D75 -0.0020 -0.0030 -0.0031 -0.0040 0.35 0.73 8 11

D55 0.0026 0.0037 0.0040 0.0051 -0.40 -0.80 -10 -14

A 0.0070 0.0099 0.0105 0.0135 -1.08 -2.10 -26 -36Xe(2) -0.0066 -0.0116 -0.0114 -0.0183 0.78 2.10 27 45

Xe(10) -0.0021 -0.0009 -0.0035 -0.0012 0.28 0.26 8 3

F(2) -0.0024 -0.0031 -0.0051 -0.0065 0.04 0.08 11 14F(6) -0.0132 -0.0162 -0.0232 -0.0265 1.44 2.64 55 65

slightly from that of a standard illuminant SN(X) usingthe standard method for nonfluorescent samples

Tci = k E 3M(X)SN(X)ti(X)AX, (5)

where

k = 100 /E SN(X)Y(X)AX.x

This procedure corresponds to a transformation of thechromaticity of the sample irradiation M at measure-ment to that of the standard illuminant N. As pointedout by Berger this method does not correct the colori-metric deviations due to differences in the relative uvcontents between the irradiation at measurement andthe standard illuminant.

The magnitude of these deviations can be estimatedby the method of Eitle and Ganz (1).

AT =Tci-TNi = k E [fm(X)-N(X)I . SN(X) * ti(X) . AX. (6)x

According to Eqs. (1) and (3)

ATj =k FN(X) [QMSN(X) 1 (X) AX.X 1QN -SM(X

(7)

The deviations of the tristimulus values vanish forsources M for which the ratio of the spectral powerdistribution S(X) to that of the standard illuminant Nis equal in the mean to the ratio of the number of quantaQ absorbed by the FWA contained in the sample

SM (X) QM

SN(X) QN(8)

They are proportional to the integrated product of thespectral power distribution of the fluorescence, of thespectral tristimulus values and of the deviations from(8).

The differences of chromaticity, luminance, andwhiteness determined for various irradiations andtransformed to D65 by formula (5) from true D65 values

are computed for strongly fluorescent plastic and cottonsamples of the CIBA-GEIGY whiteness scales, TableIII. Sources developed specifically for the assessmentof fluorescent white samples like Xe(10) and F(2) yield.differences of a magnitude similar to that caused by D75

and D55, respectively. Deviations produced by in-candescent and unfiltered xenon sources as well as bymost fluorescent lamps cannot be adequately corrected.

Conversely the transformation (5) suggested byBerger is useful for demonstrating the influence of thespectral power distribution of the irradiance on thechromaticity of white fluorescent samples. Thetransformation to the Adams-Nickerson chromaticvalue space was used for the same purpose (see Fig.4).

Summing up, the requirements for a reproducible andcorrect determination of colorimetric data of fluorescentwhite samples are:

(1) The spectral power distribution of the sampleirradiation as produced by the source, filters, and thecoating of the integrating sphere (if used) should bewithin the tolerances specified for a standard illuminant(e.g., German Standard DIN 6173).

(2) Stable fluorescent white reference samples arerequired for routine checking deviations of the spectral

- -, n --1616 (Vy-Vz)-14 -12 -10 -B -6 -4 -2

A A - -- ----- -

A ......

D5S00 --4 D0 -Z05500 .4

05500 -6 ;>

D7500 -90

D7500 -10

94

D75000 05500 92

0 A07500 goD~

05500 ...... . . J

tg S0 A . . .aBe

-6 -4 -'

-22 -2 -: -1 14 -2 1 -22 *io -11 -10 -14 -12 -10 Vz

Is (Vy-Vz)

Fig. 4. Influence of the spectral power distribution of the irradiance

on the effect of FWA's and of bluing.9 Chromaticities for illuminants

D75, D65, and A of a sample: & untreated, E treated with FWA, X

blued, ® treated with FWA and blued.


-S -4 -=

power distribution of the irradiation due to aging of thesource and of the coating of the integrating sphere.

(3) Photometers should be fitted with adjustablefilters for compensating minor changes as detected by(2) before replacing sources and/or coatings.

Colorimetric EvaluationThe establishment of whiteness formulas correlating

visual assessments with clorimetric measurements washeavily influenced by fortuitous circumstances such aschoice of test samples, personal, and/or trade prefer-ences of the observers, sample irradiation by sourceswith unsuitable or insufficiently defined power distri-bution differing sometimes between visual assessmentand measurement, type of instrument used, and theamount of time and effort expended on the evaluation.

Review of Existing Whiteness FormulasWhiteness formulas were developed along two dif-

ferent lines:(1) The aim to reach a preferred or ideal white led to

formulas defining whiteness as the proximity in a uni-form chromaticity space,

W = 100 - [(AL)2 + k(AC)2 ]1 /2 , (9)

of the sample to the preferred white. The perfect dif-fuser was considered as the preferred white before theadvent of FWA's.

(2) The observation that whiteness could be in-creased by bleaching, bluing, and by the application ofFWA's led to formulas based on reflectance measure-ments with a filter of maximum transmittance at 457nm (Tappi method) or with the A, G, B filters used foran approximate determination of the tristimulus valuesTi:

in the domain of chromatic colors is no argumentagainst their validity.

Seve26 compared a formula of the first type (9) withten formulas of the second (10) by constructing the linesof intersection of an equiwhiteness surface defined bythese formulas with two suitably chosen planes in the1964 CIE (U* V* W*) space. In both the planes W =100 and Xd = 576.5 nm, the formula of the first type isrepresented by a circle and each of the ten formulas ofthe second type by a straight line. The lines in theplane Xd = 576.5 nm can be characterized by their slopep, which is a function of the parameters of the formulaand of W* of the sample.

On the yellow side of the neutral axis attainable bybleaching and bluing, all formulas evaluate whitenesssimilarly, whereas on the blue side the evaluation by theformulas of the two types is contradictory. As Frankedid not include in his survey samples treated withFWA's, he did not find significant differences betweenthe correlation coefficients for formulas of the two types.

Seve discusses the shortcomings of both types ofwhiteness formulas. Those of the first type fail in theevaluation of samples treated with FWA's if the perfectdiffuser is considered to represent the preferred white.By formulas of the second type, samples are evaluatedthe whiter, the bluer they are. Although this is incor-rect on principle, these formulas have been used suc-cessfully for the evaluation of samples containingFWA's since the power of the blue fluorescence is lim-ited by the power of the radiations exciting fluorescenceavailable in daylight and in artificial sources. Svesuggests bending the equiwhiteness lines upward on theblue side in order to avoid possibly false evaluations.

Ganz24 examined three generic whiteness formulasof the second type:

W= ZkTi. (10)

Functions combining luminance and chromaticitycoordinates were also tried.

Franke25 collected 116 whiteness formulas of bothtypes and tested them with twenty-two nonfluorescentwhite paper samples. No effects of spectral powerdistribution have to be accounted for in this case. Theaverage of the visual assessments of fifty observers wascorrelated with the whiteness computed by the differentformulas based on measurements with a spectropho-tometer fitted with three different sample geometriesand with a three-filter photometer. Approximately 80%of the formulas tested yield correlation coefficients inthe range of 0.90-0.98, the remainder being spread downto values of 0.20. The formulas are grouped accordingto the number of colorimetric parameters used and tothe complexity of the calculation. Hits and failures areevenly spread over all groups, and no systematic supe-riority was found.

Every whiteness formula,

W = (XYZ),

defines surfaces of constant whiteness in the whole colorspace. However they may be used reasonably in a verylimited range of near-white colors only. Potential abuse

W1 = 1*-B+ y.G + a -A + Ki,

W2= X-L+ v-b+ g-a+ K2,

W3= E. Y+ P -X + a + K3,

(11)

(12)

(13)

in which B, G, A are the photometer values read withthe corresponding filters and linked with the tristimulusvalues by

X = fxA -A + fxB. B,

Y = G

Z = fZB - B

and calculated by

A = gAX * X + gAZ -Z

G= Y,

B =gBz-Z,

where

gAX = 1/fXA,

gAZ = -fXB/(fXA -fZB),

gBZ = 1/fZB-

L, b, a are the Hunter coordinatesstimulus values by

(14)

(15)

(16)

linked to the tri-


Table IV. Factors for Converting AGB in XYZ and Vice Versa

CIE 1931 (2°) CIE 1964 (100)fXA fXB fZB fXA [XB fZB

A 1.0447 0.0539 0.3558 1.0571 0.0544 0.3520D55 0.8061 0.1504 0.9209 0.8078 0.1502 0.9098D65 0.7701 0.1804 1.0889 0.7683 0.1798 1.0733D75 0.7446 0.2047 1.2256 0.7405 0.2038 1.2072C 0.7832 0.1975 1.1823 0.7772 0.1957 1.1614E 0.8328 0.1672 1.0000 0.8305 0.1695 1.0000

Fig. 5. Lines of intersection of theequiwhiteness surfaces defined bythe whiteness formulas of Stensby,Tappi, and Berger with the planesY = 100 and Xd = 470 nm, respec-tively.24 The whiteness formulaW = B was derived from theTAPPI brightness R457. There-fore it is called the Tappi white-ness formula although it is not en-

dorsed by Tappi.

STENSBY TAPPI BERGER

L = 10.0. y/2,

a = 17.5 -Y 1/2 [X/(fXA + fXB) - Y] - 0-01, (17)

b = 7.0 y-1/ 2 (Y - Z/fZB) 0.01,

the factors fxA, fxB, fzB being functions of the illumi-nant and the colorimetric observer employed (see TableIV).

The parameters (&y,ca), (Xvg), (,p,a) are chosendeliberately or determined by regression analysis ofvisual whiteness assessments vs colorimetric measure-ments. K are constants depending on the normalizationof the whiteness scale and, for Eq. (13), on the chro-maticity of the illuminant also.

The properties of three specific forms of the genericEqs. (11) and (12) are compared in Fig.5. The lines ofintersection of the equiwhiteness surfaces of the for-mulas by

Stensby W= L - 3b + 3a;TAPPI W = B,Berger W= 3B + G - 3A,

with the planes Y = 100 and Xd = 470 nm, respectively,are shown.

The equiwhiteness lines of the three formulas for Xd= 470 nm are approximately parallel and equally spacedflat curves. Although their slope and spacing are dif-ferent, the three formulas agree in attributing increasedwhiteness to samples of higher luminance and/or en-

hanced blueness. The equiwhiteness lines for Y = 100are straight lines in the chromaticity chart approxi-mately equally spaced and parallel for the three for-mulas. However, their slope is very different accordingto the preference for reddish whites of the Stensbyformula and for greenish whites of the Berger formulaas compared with the TAPPI formula.

For a quantitative characterization of specific for-mulas the whiteness W was calculated in the range ofnear whites as a function of luminance Y, dominantwavelength Xd, and colorimetric saturation

(18)

x, and yI denoting the chromaticity of the illuminantI. S is positive on the blue side and negative on theyellow side.

The partial derivatives (WlaY), (W/aS), and(aW/aH) were numerically computed. The colorimetricsaturation S is defined for a suitable line Xd = const(reference dominant wavelength, e.g., 470 nm) and thecolorimetric hue H in the same units as S but perpen-dicular to it, H being positive on the green side andnegative on the red side (see Fig. 6).

A whiteness formula can be characterized at eachpoint of the color space by (aWlaY), by the slope w ofthe equiwhiteness lines in the plane Xd = const,

W = (dW/aS)/(aW/dY), (19)


90

85

80AD =470

75

S = [(XI - X)2 + (y, - y)2]1/2,

The parameters 0,-ya or v,,4, which will be requiredfor the construction of a whiteness formula with pre-determined properties, can be estimated from the di-agrams. Precise values of these parameters can becalculated. 2 4

The existence of the second derivatives is due to thestructure of the formulas. It is neither experimentallyproved nor theoretically motivated excepting (a2W/aY2)of the L, b, a formulas where L = 1OY'1/2 . In view of thisand considering that Y varies for whites over a verylimited range only, the simple Eq. (13) linear in Y, x, ywas constructed which can also be written

W3 = (W/aY) Y + (W/S) S + K3

Fig. 6. Definition of 0 characterizing hue preference sin(-A) =(AWH/AH); cos(-O) = (AWs/AS).

and by their angle 0 in the chromaticity chart relativeto the normal on the line Ad = const,

-=-arctandW/aH)/(aW/0S)],

or by the angle A relative to the x axis,

P= p + + 7r/2,

(20)

(21)

where is the angle between the reference dominantwavelength d and the x axis. This definition of characterizing hue preference is equivalent to the onegiven in Ref. 24 due to a goniometric identity.

Since the equiwhiteness surfaces defined by Eqs. (11)and (12) are not actually equidistant planes, the secondderivatives of whiteness do not vanish, and the pa-rameters (W/aY), o, and are functions of the tri-stimulus values. It is advisable to characterize andcompare whiteness formulas of different types by thevalues (aW/aY)i, ci, and /s for the perfect diffuser withilluminant I and to standardize the whiteness of theperfect diffuser W = 100 by adapting the constants K.The existence of the following relations can be shownfor formulas:

30

20

10

0

-10

-20

-30

-40

= (aW/aY)-(Y+ W*S) + K3

with (aWlAY) as unit of whiteness, andS = (xi - x) sin2 - (y - y) - cos

sin( - )(xi -x) -cos(/ + 0) + ( -) sin(k + )

cost

(23)

(24)

1000 2000 3000 4000 w

Fig. 7. B, G, A whiteness formulas defined by their parameters fi,y, a (with = 1) and characterized by wj and fi for dominant wave-

length Xd = 470 nm (or ;pI, respectively). 2 4

L, b, a [Eq. (12)]

(aW2 /aY) 1 = X/2

due to L = 10Yl/2 (22)

K2 = 100(1 - X).

Taking the values wj and As (or I, respectively) ascoordinates, each whiteness formula as defined by itsparameters (,-y,a) or (,v,pt) can be represented by apoint in such a diagram (Figs. 7 and 8). Specific for-mulas frequently used are marked

TI TAPPICR CroesST StephansenBE BergerTA Taube

W= BW = B + G - A,W= 2B -A,W= 3B + G - 3A,W = 4B - 3G,

50 -

40 -

30 -

20 -

10 -

0-

-10 -

-20 -

-30 -

-40 -

V= -1 -2 _3 i' SY -4- 10

- 0

-- 10 .0-- 20~~~~~~~~~~~~.

_ 30

-40 -.

-50 -1.0

-60 -1.5

-70 .

1000 2000 3000 4000 W

and

HU Hunter W = L - 3b,SY Stensby W = L - 3b + 3a.

Fig. 8. L, b, a whiteness formulas defined by their parametersP, and characterized by wj and us for dominant wavelengthXd = 470 n (or q/, respectively). 2 4 Stensby (SY)cow = 3.38 X

103 and X = 56°.


y

B, G, A [Eq. (11)]

(OWl/aY), = 6

with = j3 + -y + a

K = 100(1 - 6)

2.0

Substituting in Eq. (13) we get formulas for the pa-rameters

= (aW/ay),

p = -(oW/aY) o cos(1, + 77)/COSO,

= -(oW/aY) c o * sin(o + 7)/cosk, (25)

K3 = 100(1 - 0 P x - a yI.

as functions of (aW/aY), co, 0, i7 and conversely

0 = arctan(a/p) -,

co = (COSk) . (p2 + a2)1/2/E. (26)

Meaning and Determination of Parameters

The implicit values of the hue angle 0 vary over a wide

range from 560 for red preference (Stensby) to -30° for

green preference (Berger). Values up to +900 have

been observed for persons with extreme hue preference.Their equiwhiteness lines in the chromaticity diagramrun approximately parallel to the line Xd = 470 nm.Such exceptional sensation of whiteness is dominatedby the red/green tint of the samples and is rather in-dependent of the intensity of the fluorescence of FWA's

or of the bluing. The average hue preference is in therange of about 100 as defined by the formulas of TAPPI,Taube, and Hunter, and 300 corresponding to the po-sition of the tangents to the curves of constant Munsellchroma at Xd = 470 nm for near whites. The choice of

0 is not very critical in general. It is decisive only if the

calculated whiteness is used, e.g., for assessing the rel-ative efficacy of FWA's differing in hue, for evaluatingthe influence on whiteness of tinting with dyes, or forthe determination of the maximum whiteness attainableby a FWA in increasing concentrations giving rise to anincreasing greenness.

The implicit values of the factor co relating the relative

contributions of blueness and lightness to the sensationof whiteness cover a range of approximately 650 (W =

B) to 3400 (Stensby). The values most frequently usedlie in the range of 1800-2500. No information on in-

dividual preferences influencing the value of w isavailable yet. A minimum value of X is indicated by the

slope of the MacAdam limit in the range of light blues.Since the locus of samples increasing in whiteness dueto increasing concentrations of blue dyes runs ap-proximately parallel to the MacAdam limit, the slopeof the equiwhiteness lines must be considerably greaterthan that of the MacAdam limit at the correspondingdominant wavelength. This slope coMA is for Xd = 470nm approximately:

WAMA = AY/AS - 10/0.017 600.

The formula W = B with co = 650, although quite sen-sitive to the effects of bleaching and of FWA's, is stillinsensitive to the effect of bluing. For the same reasonthe conception of whiteness presented by Stenius2 7

must be doubted. Defining equiwhiteness lines parallel

to the MacAdam limits, it attributes to a series of sam-ples which increase visually in whiteness due to in-

creasing concentrations of a blue dye, decreasing values

of whiteness on the yellow side of the achromatic axisand approximately constant values on the blue side.

The four parameters of each whiteness formula (11),(12), (13) can be determined by multiple regressionanalysis of calorimetric data and visual assessments ofwhite'samples, provided that they are well distributedin the color space, i.e., that all three of their coordinates(luminance factor Y, calorimetric saturation S, andcolorimetric hue H, see Fig. 6) vary sufficiently andindependently. The samples prepared by Berger'0

satisfied this condition exceptionally well. With thesesamples the CIE TC-1.3, Subcommittee on Whiteness,carried out various investigations. Reports are inpreparation.

Usually the samples available for such work are suf-ficiently differentiated in saturation and to a lesserdegree in luminance caused by a variation of FWAconcentration and by differences in substrate luminanceby bleaching and/or by bluing. The variation in hue ismostly limited and often nil. A complete regressionanalysis is not feasible therefore.

Since the hue preference angle 0 is a function of theratios of the parameters2 4 a/l, ,g/v, p/u [Eqs. (26)], thevalues of the latter can be tabulated as a function of 0for a given color (e.g., the perfect diffuser I, see TableV). Selecting such ratios as constants, the remainingthree parameters of the whiteness formulas can be cal-culated for tentative values of PI:

Table V. Ratios of Parameters af/:, p/v, p/a as a Functionof the Hue Preference Angle /, for Reference Dominant

Wavelength 470 nm and for the Perfect Diffuser Irradiatedby D65 and CIE 1931 20 Observer

0I oU/: p/v p/a

Greenpreference

-35 -1.1796 0.4556 2.7184-30 -0.9941 0.3974 2.1254-25 -0.8318 0.3431 1.7184-20 -0.6867 0.2914 1.4178-15 -0.5542 0.2415 1.1835-10 -0.4310 0.1926 0.9932-5 -0.3143 0.1439 0.8333

0 -0.2021 0.0946 0.69515 -0.0924 0.0439 0.5728

10 0.0164 -0.0090 0.462115 0.1261 -0.0651 0.360120 0.2384 -0.1257 0.264325 0.3552 -0.1924 0.172830 0.4785 -0.2673 0.084035 0.6112 -0.3536 -0.003440 0.7566 -0.4557 --0.090945 0.9191 -0.5804 -0.179950 1.1051 -0.7388 -0.271655 1.3236 -0.9507 -0.367960 1.5882 -1.2538 -0.4705

Redpreference

Note: If applied to D65 irradiation and CIE 1964 10° ob-server, the values of 0I refer approximately to a referencedominant wavelength of 463 nm.


Table VI. Luminance Factors Determined byGrum etal. 1 1,

8 for a D65-Simulator Fluorescent Lampand CIE 1964 100 Observer

Sample Y Sample Y

7 94.21 A 93.3810 91.87 B 92.3911 90.77 C 89.0612 92.14 D 90.5413 92.73 E 91.0828 95.35 F 93.7529 96.12 G 85.7430 96.49 H 90.9831 97.09 J 87.4032 94.84 K 89.4833 95.96 L 88.7234 96.9635 96.7536 95.3837 96.0838 96.7539 97.1540 95.0342 95.3043 95.08

E ' -Gi + fi- [Bi + (a/p),.-Ai] + Ki - Wjj2 = Min,

E X - Li + v [bi + (/v) 1 - a I + K2 -W]J 2 = Min, (27)

E {* Yi + a- [Yi + (P/l) - Xi] + K3 - WI2 = Min.

The optimal value of XI is determined subsequently byfinding the highest coefficient of correlation betweenthe visually assessed whiteness values Wi and thosecomputed by the formulas with the parameters corre-sponding to the tentative values of kI.

This procedure has been applied to the visual as-sessments and measurements published by Grum etal. 1 supplemented by the luminance values2 8 shown inTable VI. Complete regression analysis cannot becarried out since the twenty samples 7 to 43 on which

the analysis is based did not include colored whites.The inclusion of the eleven samples A to L visually as-sessed in four different laboratories by the ISCC Sub-committee for Problem 18 was particularly valuablesince it allowed the whiteness formulas to be tested byan independent set of data. The mean of the results ofpair comparison in laboratories 1, 2, and 3 was used inthis investigation, the results of laboratory 4 disagreeingwith the other three and yielding also a low coefficientof correlation with the computed values. The colori-metric data of the twenty-two samples of the oldGEIGY textile white scale (Table VI of the originalGWS paper") appear to be erroneous probably owingto deterioration of the samples. The coefficient ofcorrelation found between the nominal (visual) andcomputed whiteness based on these colorimetric datais as low as 0.94 compared with values above 0.995 forflawless white scales of that particular type and of alllater types.3

The parameters and the coefficients of correlationwere computed with the three generic whiteness for-mulas (11), (12), (13) for values of I equal to 600, 150,and -300 for red, neutral, and green hue preference aswell as for Grum's original formula and a simplifiedformula, which will be discussed later (Table VII). Thewhiteness of the eleven ISCC samples used for corre-lation was calculated with the indicated parametersdetermined by regression analysis of the twenty Bergersamples. All formulas yield approximately the samehigh degree of correlation with visual assessment, thecoefficients of the ISCC samples being at least as highas those of the Berger samples. A very slight neutral(0 = 150) hue preference may be noticed, but the ex-clusion of colored white samples, also apparently trueof the ISCC samples, does not allow any conclusions tobe drawn concerning hue preference or dependence ofwhiteness on chromaticity except in the narrow rangecovered by the samples. The differences between themean coefficients of correlation of the two samplegroups for Grum's formulas and for the generic formulas

Table VII. Parameters and Correlation Coefficients Based on Data by Grum etal.for Various Whiteness Formulas and Hue Preference Angles I

20 11Samples Berger ISCCWhiteness Correlationformulas coefficientsGrum et al. original (33) 0.991 0.991Grum et al. simplified (34) 0.989 0.991BGA -I hiy 0o K160 6.42 -13.71 10.19 -172.0 0.986 0.98915 4.94 -2.59 0.62 -178.2 0.989 0.993-30 4.12 3.02 -4.09 -184.6 0.985 0.987Lba 0I X v pu K,60 5.64 -5.71 7.16 -446.1 0.986 0.98915 5.77 -6.71 0.44 -458.6 0.989 0.992-30 5.91 -7.06 -2.81 -471.5 0.985 0.986Yxy E e p a K,60 2.93 2818 -5988 935.9 0.986 0.98715 3.00 -1052 -2922 1129.5 0.989 0.991-30 3.07 -2912 -1370 1193.0 0.986 0.986


0.38 0.39 0.40 0A1 S*

Fig. 9. Graphical method for determining adjusted parameters p,

a, and 3 of Eq. (13) based on measurements of plates 5 to 12 of the

CIBA-GEIGY Plastic White Scale with instruments A, B, C of dif-

ferent types and CR with instrument C after reconditioning and re-placing the xenon lamp (measurements by Griesser).

with As = 150 are insignificant. This indicates that thesystematic errors introduced by the different whitenessformulas are small as compared with the uncertainty ofthe visual assessments, even if averaged. However, thisagreement between the formulas might be slightly im-paired if the calorimetric data used had been deter-mined at a D65 sample irradiation with standard uvpower.

Linear arrays of samples produced by applying var-ious concentrations of one FWA on one substrate areunsuitable for multiple regression analysis (27) since theluminance factor Y and the calorimetric saturation Sdo not vary independently. White scales produced bythis technique may be used for a simple linear regressionanalysis, however, if the unit e = (aW/aY) of the visuallydetermined nominal whiteness Wi of the samples isknown. With values of p/a for the selected hue pref-erence 0 taken from Table V or calculated by

p/a = tan(o + i7), (28)

the parameters a and K3 can be found by the last of Eqs.(27) or by a graphical method. For applying the latter,

Si* = xi I p/a + Yi (29)

and

Wi* = Wi- Yi

are calculated and plotted. The regression line isdrawn, and the values S1*, W1* and S2*, W2* are readfor two points situated on it. The parameters of thewhiteness formula (13) are determined by

-= (W1* - W2*)/(Sl*-S2*),

p = a- (p/c), (30)

K3 = W*-a *-Si*.

With parameters found by this procedure, Eq. (13)yields values of whiteness for the chosen hue preference

angle 0 conforming approximately to the values of thewhite scale used for calibration.

The graphical method is shown in Fig. 9 and TableVIII. The fluorescent samples 5 to 12 of the CIBA-

GEIGY Plastic White Scale are measured with variousinstruments. Sample irradiation corresponds ap-proximately to D65 (filtered xenon sources). Tri-stimulus values are determined for illuminant D65and for the CIE 1931 standard colorimetric observer.The values of Wi* are calculated with the nominalwhiteness values of the samples and with the scale unite = 2. The values of Si* are determined for a neutralhue preference 0 = 200 yielding p/ = 0.2643. Thevalues of Si* and S2* are read on the regression lines forvalues of W1* =-100 and W2* = 30, respectively. Theparameters p and ar are larger, the smaller the relativeuv content of the sample irradiation is in the instru-ment. Thus conforming values of whiteness are at-tained.

The nonfluorescent samples 1 to 4 of the CIBA-GEIGY Plastic White Scale are not used since theirchromaticity and whiteness are independent of therelative uv content of the sample irradiation. The sameapplies for the contribution to whiteness caused bybluing the substrates (see, e.g., Table I samples 7, 12,and 13). As the contribution of fluorescence to white-ness is not determined separately in this simple method,contributions to whiteness possibly caused by bluing areerroneously treated as depending on the relative uvcontent of the sample irradiation. Furthermore, therestrictions (1) and (2) stated in the paragraph on thestandardization of the sample irradiation also applyhere. Differences in the excitation and/or fluorescencespectrum of FWA's as well as in substrate reflectancemay influence the correlation of the whiteness deter-mined visually and computed by this method. Themagnitude of such errors, although often systematic,may be compared with the standard deviation of visualassessments of whiteness using the CIBA-GEIGYPlastic White Scale. Depending on the differencesbetween scale and sample in surface structure and intint, and also depending on the experience of the ob-servers, standard deviations of +2 to +7 units are found.

This method based on colorimetric measurements offluorescent white scales is frequently used and is anasset for industrial routine work. It enables moderatedifferences in whiteness to be corrected using variousinstruments equipped with filtered xenon sources. Itmust be kept in mind, however, that this method is nota proper calibration, but rather a useful adjustment of

Table VIII. Calculation of Parametersp, a, and K, forWhiteness Eq. (13) Based on Measurements (by Griesser)of Plates 5 to 12 of the CIBA-GEIGY Plastic White Scale

with Instruments A, B, C, and CR (see Fig. 9)with e = 2, 0 = 200, and p/u = 0.2643

Instru- S, * for S,* forment W,* = 30 W,* =-100 p U K3

A 0.3780 0.4146 -939 -3552 1373B 0.3827 0.4145 -1081 -4088 1594C 0.3862 0.4145 -1215 -4594 1804CR 0.3816 0.4139 -1064 -4025 1566

Sample irradiation in instruments B and CR correspondsapproximately to D65. In instrument A there is an excess,and in instrument C there is a deficiency in the relative uvcontent of the sample irradiation.


0.308

0 in 0

0.306

0.0 16 18020 022 024

Fig. 10. Equiwhiteness lines and line of the preferred hue corre-sponding approximately to a dominant wavelength of 472 nm (llu-

minant C) presented by Vaeck.2 9

the parameters of the whiteness formula to the actualstate of an instrument.

Hue Preference-Preferred Hue-PreferredWhite

These terms have been used with different meanings.White samples of a group treated with various com-mercial products and selected by customer panels mostfrequently have been termed preferred whites for in-stance. The terms as used in this paper must be definedtherefore:

(1) The preferred white is the chromaticity of thestimulus which is considered the whitest possible for agiven luminance factor by a single observer or by a groupof observers under given conditions of observation. Thepreferred white will vary for different observers orrather for different groups of conforming observers, andpossibly for different conditions of observation. Itshould not depend on the possibility of materiallyrealizing such a stimulus.

(2) The preferred hue is given by the dominantwavelength of the preferred white. If the preferredwhite is identical with the chromaticity of the perfectdiffuser or is undefined, the preferred hue may be foundas the line representing the chromaticities of the stimuliattributed the highest hue preference.

(3) Hue preference is a characteristic of observersand of whiteness formulas giving different preferencein whiteness to stimuli of equal luminance and of equalcolorimetric saturation but of varying dominant wave-length. Red, neutral (blue), or green hue preference canbe represented as the angle between the tangent to theequiwhiteness curves in a point of the chromaticitychart and the normal to a reference dominant wave-length (e.g., 470 nm) representing a mean preferred hue(Figs. 7 and 8).

The whiteness formulas of the first (9) and of the

second type (11, 12, 13) do not define a preferred huealthough those of the second type display a definite huepreference implied by the parameters of the formulas(Table V). In the formula by Vaeck29

W= Y+k-E(u,v), (31)

the equivalent luminance E(u,v) representing thecontribution of chromaticity to whiteness is defined byequiwhiteness lines in the CIE 1960 uniform chroma-ticity diagram (Fig. 10). The apexes of the angularequiwhiteness lines lie on a line corresponding ap-proximately to a dominant wavelength of 472 nm forilluminant C. Thus stimuli of equal luminance factorand of equal colorimetric saturation but of differentdominant wavelength are evaluated less effective forenhancing whiteness. The dominant wavelength of 472nm defines the preferred hue of the whiteness formulaby Vaeck although no preferred white is indicated.

McConnell3 0 investigated the preference of observersvisually assessing paper samples varying in blue re-flectance over a wide range (58 B 91). For givenvalues of blue reflectance B, the best white papers areselected, and their chromaticities are plotted in the a,bdiagram as defined by the cube-root color coordinatesystem by Glasser et al. The selected whites are cen-tered along the yellow-blue axis a = 0. They are sit-uated on the yellow side b > 0 for low values of B and onthe blue side b < 0 for high values of B. The chroma-ticity of the best white paper at a given level of bluereflectance B is found to be represented as a functionof the value of blue reflectance B by the line ap = 0 andbp = 0.36 (80 - B) which is called the preferred whiteline. Whiteness was then defined

W = B - 2(a2 + [b - 0.36(80 -B)121/2 (32)

as the value of blue reflectance B diminished by twicethe distance in chromaticity between the sample andthe preferred white at the level of blue reflectance B.Equiwhiteness lines are computed with this formula andshown in Fig. 11 for the plane Y = 100 and for the planeof the preferred hue Xd = 479 nm defined by the pre-ferred white line and the achromatic axis. A discussionof the formula shows that the equiwhiteness surfacesare cones. Their points lie on the preferred white line,and their axes are perpendicular to the equi-whitenesssurfaces W = B (see Fig. 5, Tappi) on which the pointsof the cones stand. This is understandable since thebest whites have been selected from papers with thesame blue reflectance B and not from papers with thesame luminance factor Y. The formula of McConnellallots decreasing whiteness for blueness increasing be-yond the preferred white only if luminance decreasesalso.

The whiteness formula published by Grum et al."

W = 3.80Z - 3.647P,,, - 270.1

is similar in structure to that of McConnell. P,, is thepurity as determined in MacAdam's geodesic chroma-ticity diagram. Thus no preferred hue is explicitly in-troduced. Contrary to the original paper, the constant270.1 has to be negative to yield the computed values


(33)

.34

.33

.32

.31

.30

.29y=100 2 3 1

.28

105Y NL

100

90

85

80

75.27 .28 .29 .30 .31 .32 x .27 .28 .29 .30 .31 .32 x

Grum, Witzel + Stensby Mc Connell

of whiteness published in the paper. Since the com-putation of the equiwhiteness lines in the CIE Yx,ycolor space is rather involved, a simplified formula wasderived analogously:

W = 3.80 -Z - 1201 -S - 270.1 (34)

in which Pt, is replaced by the colorimetric saturationS (18). The transformation of circles S < 0.012 in theCIE chromaticity diagram yields ovals in the MacAdamgeodesic chromaticity diagram centered at the illumi-nant. The long axis is approximately parallel to the tcoordinate axis and about 1.7 times larger than the smallaxis. Therefore, it is not surprising that the same highcorrelation is found for the whiteness calculated by boththe original [Eq. (33)] and the simplified [Eq. (34)]formula with the visually determined values (TableVII).

The equiwhiteness lines computed for the simplifiedformula are also shown in Fig. 11. As in McConnell'sformula, the equiwhiteness surfaces are cones with axesalso perpendicular to the equiwhiteness surfaces W =k-Z, but the points of all cones are located in the chro-maticity of the illuminant. The spacing of the equi-whiteness lines is narrower on the yellow side and wideron the blue side. This is the main difference betweenthe simplified formula and probably also the originalformula by Grum et al. as compared with the formulaW = B, the equiwhiteness lines in the chromaticity di-agram being bent only slightly. No preferred white andno preferred hue are implied by this formula.

Thielert and Schliemann31 visually assessed thewhiteness of seventy-two samples in seven groups bypair comparison and related the results with thewhiteness calculated by various formulas. Sample ir-radiation corresponding approximately to the spectralpower distribution of illuminant D60 was used for boththe visual assessment and for the measurement. Based

.2:

1 I U . t• 21 Fig. 11. Lines of intersection ofthe equiwhiteness surfaces defined

60 1 ooW by the whiteness formulas of Grumet al. (simplified); McConnell;Thielert and Schliemann with theplane Y = 100 and the plane of thepreferred hue or of constant dom-

inant wavelength.

60

7 .28 .29 .30 .31 .32 .33 x

ielert + Schliemann

on the observations of Honjyo and Nonaka3 2 of stimuliappearing white in a dark surround the authors pre-sented a new whiteness formula

W= Y- 33.3-p. (35)

p = (OF)/(OE) is the ratio of the distances from' 0 inthe CIE chromaticity diagram of the stimulus F to beevaluated and the radially correlated point E on theperiphery of an ellipse centered at 0 (xo = 0.3090, yo= 0.3170 for D60 with xI = 0.3217, y' = 0.3378) with along axis a = 0.060 approximately parallel to a dominantwavelength of 476 nm and a short axis b = 0.3-a. Theequiwhiteness lines of this formula implying both apreferred hue and a preferred white 0 are shown in Fig.11. The equiwhiteness surfaces are cones also, but theiraxes are parallel to the coordinate axis of the luminancefactor Y.

The correlation coefficients of the visual assessmentsvs the whiteness computed by various formulas werecalculated for the seven groups of samples. For neu-trally blue fluorescent whites of chromaticities situatedbetween the preferred white 0 and the illuminant D60,uniformly high correlation was found with all whitenessformulas tested. For samples with distinctly greenishor reddish tints, the formula of Thielert and Schliemannas well as the formula of Vaeck based on a preferred hueyield significantly higher correlation with visual as-sessments than any formula (11) or (12) implyingroughly linear equiwhiteness lines. For groups in-cluding samples of chromaticities on the blue side of thepreferred white 0, higher correlation with the formulaby Thielert and Schliemann than with the other for-mulas was found for all sample groups but one.

For illuminant D65, the preferred white 0' accordingto Thielert and Schliemann would be expected atchromaticity coordinates x0, - 0.30 and yo' - 0.31shifting the preferred white correspondingly with the


illuminants. No decrease of whiteness ass(under normal conditions of observation inbeen reported, however, if the chromaticitof higher luminous reflectance passed tlpreferred white O' due to increasing conc(FWA's. It is probable therefore that the (of the preferred white (as defined in this pa]also on the luminous reflectance Y as McConnell as a function of the blue reflec

Mori33 correlated visual rankings of wlobserved by several authors with rankincomputed whiteness. Applying formulasconventional type (10), (e.g., Tappi, Taube,of the color difference type (9), Kendall'slation coefficient was computed. Bychromaticity of the reference white useddifference formulas, the preferred white the reference white yielding the higheKendall's r. Mean preferred whites with cixp, yp were found for the data of

Friele

Vaeck and Van LierdeVaeck and Van LierdeShinada

(nonfluoresc. andfluoresc. samples)

(nonfluoresc. samples)(fluoresce samples)(nonfluoresc. samples)

Since it is not possible to reach high values,with nonfluorescent samples, the chromapreferred white found with the fluorescen-Vaeck and Van Lierde is most informative

The representation of equiwhitenesscones implies discontinuities of (W/oS) iiof the cones. Friele3 4 avoided this shortcornthe equiwhiteness surfaces as halves of toperboloids:

W2 = AL2 - (M/b)2 - (SC) 2 .

This procedure has the additional advantage that thedifferent sensitivity of white perception to yellow-blueand red-green hue differences can easily be accountedfor, M and S meaning the coordinates of the long andshort axes of the equiwhiteness ellipses in the chroma-ticity diagram. For the preferred hue at the dominantwavelength of 575 nm and 473.8 nm, respectively, on theblue side, the formula is reduced to

W2 = 0.298L 2- 30.393K2 ,

with

essed visuallydaylight has;y of sampleshis tentativemntrations ofchromaticityper) dependsobserved by-tance B.iite samplesgs based on, of both the

Taking account of the work of Friele, Vaeck,McConnell, Mori, Thielert, and Schliemann, it appearsadvisable to construct a generic whiteness formulabased on the relevant preferred white and on the dif-ferentials of whiteness in suitably. chosen coordinatesof the color space. The values of most parameters re-quired are still unknown, but they can be estimated.The equiwhiteness surfaces of this generic formula arerepresented by halves of two-sheet hyperboloids in theCIE Y, x, y color space,

(Y - YA)2- [(S - SA)] 2- (xH)2 = (Yv) 2 ,

Hunter) and where S is the colorimetric saturation, and H is therank corre- calorimetric hue as defined in Fig. 6. The axes of the

varying the hyperboloids are assumed to lie in the plane of thein the color preferred hue and to be parallel to the achromatic axis.vas found as YA and SA are the coordinates of the apex of the as-st value of ymptote cone. AYv is the difference of luminanceiromaticities between the vertex of the hyperboloid and the apex of

the asymptote cone. The vertices of all hyperboloidsXp Yp represent the line of the preferred whites. The factor

0.309 0.305, w does not directly specify the equiwhiteness surfacessince their (oW/aS) is not constant and changes sign at0.305 0.307, the preferred white. By analogy with the formulas of

0.293 0.296, the second type, is defined as the slope of the as-0.315 0.312. ymptote cone of the equiwhiteness hyperboloids on theof whiteness yellow side of the preferred white in the plane of theticity of the preferred hue. The factor X evaluates the reductionst samples of of whiteness caused by deviations of the hue H from the

preferred hue H = 0. The factor determines the slopesurfaces by 0 of the line of the preferred whites. Both X and r de-n the points pend on the derivatives (S/oW), - (S'/oW), andLing defining (AH/oW) which indicate the distances of the asymptote7o-sheet hy- cones differing by one whiteness unit [Fig. 12(a)].

With(36)

a = [(AS/IW) + (S'/AW)]/2,b = [(AS/AW) - (S'/AW]/2,c =(H/Am,- = (Y/AS)yeliow = d/b,

x/w = b/c; = d/a,

we get

H

zvIAS ASAw AWI: IM

I H

L = 0.53517X + 0.54587Y + 0.64468Z, (37)

K = 0.41046X + 0.49896Y - 0.76322Z.

Thus the equiwhiteness lines are represented by de-generate hyperbolas. The value of W = 0 is reached ifboth terms of the first Eq. (37) are equal (for illuminantC and CIE 1931 standard colorimetric observer x1 =0.3311, y = 0.3419 and x2 = 0.2886, Y2 = 0.2905).Outside this range whiteness is undefined, the value ofW2 being negative. The preferred white is located onthe blue side of the illuminant. However, Friele re-ferred to the probable influence of chromatic adaptationon whiteness evaluation.

Fig. 12. (a) Relations between the differentials of whiteness and theasymptote cones of the equiwhiteness hyperboloids. (b) Relationsbetween the equiwhiteness point Y on the achromatic axis and the

apex of the asymptote cone A and the preferred white P.


^ - -

(38)

l.

S

(AS/AW) - (AS'/AW)X 2(AH/AW)

T =u)0 ab (AS/AW) + (AS'/AW) (39)= d = a/b = (AS/AW) - (AS'/AW)

If it should prove that the slope of the line representingthe preferred white cannot be approximated by 0 = w/s,the assumed parallelism of the axes of the hyperboloidswith the achromatic axis is not valid. A more intricateformula based on tilted hyperboloids would then haveto replace Eq. (38).

Assuming the validity of Eq. (38), one suitably se-lected preferred white characterized by its luminancefactor Yp and its chromaticity xp, yp is sufficient todefine the line of preferred whites [Fig. 12(b)] as well asthe preferred hue with

n = arctan[(y - yp)/(xI - xp)].

Whiteness of a color Y, x, y is then calculated in twosteps:

(1) Transformation of coordinatesS = Ax cosi7 + Ay sing,

H = Ax sini - Ay cosn,

withAx = x,-x Ay = yI-y,

and determination of the coordinates SA and YA of theapex of the asymptote cone of the equiwhiteness hy-perboloid passing through the given point Y, S, H by thetwo Eqs. (38) and

SA = SP - (YP - YA - AYV)r/l,

where Sp is the colorimetric saturation (18) of the se-lected preferred white.

(2) With the coordinates of the apex, the luminancefactor YW of the equiwhiteness point on the achromaticaxis is found, and the whiteness is calculated

YW = YA + [(WSA)2 + (AYV)2 ]1/2,

W = (W/aY) * Yw + 100i - (aW/aY)].

with Eqs. (38)-(41) for illuminant D65 and CIE 1931or 1964 standard observer. It is implemented withdefault options for the parameters Yp to aH/OW if oneor more are unknown and set equal to zero. The fol-lowing values have been tentatively chosen:

Yp = 100, xp = 0.2899, yp = 0.2961, Hi = 0, AYv = 10,

OY/OW = 1, S/OW = 5 x 10-4, OS'/OW =

-1.67 X 10-4, OH/OW = 0.67 X 10-4,

yielding

aWlaY = 1, (D = 2000, X = 10,000, = 0.50,

Sp = 0.0400, X = 55.1°, Xd = 470 nm for 1931 standard observer.

Equiwhiteness surfaces were computed with the in-dicated tentative values of the parameters. The linesof intersection with the plane Y = 100 and the plane ofthe preferred hue are shown in Fig. 13. The trend andthe spacing of the equiwhiteness lines in the vicinity ofthe preferred hue on the yellow side of the preferredwhite are quite similar to the trend and the spacingprovided by the BGA, Lba, or Yxy formulas (11), (12),or (13) of average hue preference. In contrast, theequiwhiteness lines run approximately parallel to thepreferred hue on the red and on the green side. Thisis in agreement with visual assessments in attributingreduced whiteness to samples of a stronger reddish orgreenish tint. For samples that are bluer than thepreferred white, whiteness decreases with increasingblueness at all levels of luminous reflectance.

Observers with extreme red and green hue preference,respectively, give conflicting assessments of thewhiteness of samples with chromaticities lying between

.34y

.33

(40) .32

Deriving these formulas it was assumed that thepreferred hue is defined by the line of dominant wave-length of the preferred white. This is in agreement with

the findings of McConnell. However, Vaeck andThielert and Schliemann found the line of preferred hue

passing the chromaticity of the illuminant on the redside, thus attributing a greenish tint to the perfect dif-fuser. Therefore, the parameter HI indicating the hueattributed to the chromaticity of the illuminant wasintroduced. The formulas for Sp, -q, H, and Yw arereplaced by

Sp = [(XI - Xp) 2 + (y' - yp)2- H,211/2

= arctan[(yj - yp)/(xI - p)] - arctan(HI/Sp),

H = Ax - sin7-Ay cos- + Hi,

Yw = YA + [(WSA)2 + (XHI)2 + (AYV)2 ]/2

(41)

A program (FUNCTION WHYPO, FORTRAN IV) is

available for computing whiteness,

W = WHYPO(YX,y,YpXpypHIAYV

aY/OW,OS/OW,aS'/OW,aH/dW,OBS),

.31

.30

.29

.28

105Y

100

95

90 1

.27 .28 .29 .30 .31 .32 .33 x

Fig. 13. Lines of intersection of the equiwhiteness surfaces defined

by the hyperboloid whiteness Eq. (38) with the plane Y = 100 and the

plane of the preferred hue. The parameters of Eq. (38) are thoseincluded in function WHYPo as default options.


their preferred hues. It is not unlikely that the as-sessments of samples of chromaticities on the red andgreen sides of the achromatic axis will differ similarly.This would indicate that the planes approximating thepreferred hue are not a family of planes through theachromatic axis as defined above in this paper. Thepreferred hues would probably be better representedby planes parallel to the achromatic axis and approxi-mately parallel to the line of the chromaticities of theD illuminants or of the blackbody radiators as observedby Honjyo and Nonaka. 3 2

Special configurations of the equiwhiteness surfacesare produced in the following cases:

(1) For 9S'/aW =-8S/8W, we find = 0 and thepreferred white Sp = SA = const. independent of theluminance factor.

(2) For S'/aW = 0, the asymptote cones touch eachother in the plane of the preferred hue on the blue side.Thus whiteness is not defined for chromatic'ities beyondthe limiting envelope of the asymptote cones.

(3) For A Y = 0, the hyperboloids degenerate to theasymptote cones. Equation (7) in Thielert andSchliemann for instance can be reproduced for illumi-nant D60 and 1931 CIE standard observer (x = 0.3217,y = 0.3378) by setting

Yp = 100, xp = 0.3090, yp = 0.3170, H = 0.00448, AY = 0,

OY/OW = 1, S/OW = 0.0009, S'/OW = -0.0009, OH/OW= 0.00027,

yieldingdW/dY = 1, = 1111, X = 3704,r = , Sp = 0.0240, = 48°.

For industrial applications, the hyperboloid white-ness formula may be useful if the whijgeness of stronglytinted samples has to be determined. For routineevaluations of samples not approaching the boundariesof whiteness, one of the simple Eqs. (11), (12), or (13)is quite satisfactory.

Tentative Evaluation of TintAlthough strongly influencing the assessment of

whiteness, the reddish or greenish tint of white sampleshas not been characterized adequately. Approximatevisual assessments of tint were specified by the lettersRR, R, B, G, GG for reddish, neutral (blue), and greenishwhites on analogy with evaluating the cast of dyes andof the effect of fastness tests on dyeings. Attemptsusing dominant wavelength to specify the tint of whiteswere unsuccessful. Equally reddish tints, or equallygreenish tints, were found at widely varying dominantwavelengths depending on the excitation purity.

The fifty-six paper samples prepared by Berger'0covering the range of whites up to the limits were par-ticularly suitable for investigating methods for thespecification of tint. The samples were assessed in turnby seven persons engaged in routine evaluation ofwhiteness. The samples were presented in daylight,one by one, backed by a neutral gray of value 8.0 andcompared with the plates of a CIBA-GEIGY PlasticWhite Scale. The majority of the observers eliminatedsamples 51, 53, 54, 55, 56 as being too red, sample 48 as

being too yellow, and samples 4, 25, 26, 27 as being toogreen. The observers were then asked to grade the re-maining forty-six samples into one of the eleven tintgroups, 5R .. . 1R, B, 1G ... 5G, and award them ratingson a -5 to +5 scale, zero meaning neutral (bluish) white.Means and standard deviations of these gradings areshown in Table IX. A comparison with the chroma-ticities' 0 of the samples shows that the scatter of thegradings increases the whiter and the more tinted thesamples are. The average standard deviation of a singleassessment is 0.8 and of the mean of seven assessments0.3. This appears to be rather high for colorists but ananalysis of the assessments by observers (Table X) in-dicates that this is probably due to small individualdifferences in hue preference. The number of and theratings allotted to samples valuated as reddish andgreenish, respectively, vary more than the average ratingper sample. Excepting observers 1 and 7 characterizedby a slight green and red preference, respectively, theratings allotted per sample vary only by 10% of themean 2.0. The scaling is equal on either side of theneutral white. This is an indication that the symmetryof the hyperboloid whiteness formula (38) with respectto colorimetric hue H is admissible.

The scaling of tint is also fairly independent of thecolorimetric saturation S of the samples. An attemptwas therefore made to represent the tint T by

T=m-x + n-y+k.The parameters were determined by linear regression

Table IX. Means and Standard Deviations of VisualAssessments of Tint of Forty-six Paper Samples by

Berger'0 vs the CIBA-GEIGY Plastic White Scaleby Seven Observers

Sample Standard Sample Standardnumber Mean deviations number Mean deviations

1 -0.1 0.4 28 -0.3 1.02 2.0 0.6 29 0.1 0.43 3.4 0.5 30 0.4 0.85 3.0 1.2 31 0.9 0.96 3.1 0.9 32 0.0 0.07 1.4 0.5 33 0.1 0.48 1.7 0.8 34 -0,3 0.89 2.3 1.0 35 0.1 0.9

10 0.0 0.6 36 -0.3 0.811 -0.1 0.4 37 0.0 0.012 -0.1 0.4 38 0.4 0.813 -0.3 0.5 39 0.4 0.814 0.6 1.1 40 -0.3 0.815 0.4 1.0 41 -0.6 0.816 -0.7 0.5 42 -1.0 1.017 -1.7 0.5 43 -1.3 1.018 -1.4 0.5 44 0.0 0.019 -1.6 1.0 45 0.6 0.520 -1.7 1.3 46 -0.1 0.421 -2.0 1.0 47 0.0 0.022 -2.3 0.5 49 -1.9 0.923 -3.0 0.8 50 -3.3 1.024 -2.7 0.5 52 -2.9 0.9

Note: Redness 5R to 1R is marked by negative values -5to -1, neutral (blue) whiteness B by 0, and greeness G toG5 by positive values 1 to 5 (contributed by Anders andEckhardt).


(42)

Table X. Individual Assessments of Tint by Seven Observers of a Set of Forty-six PaperSamples from Berger'0 vs the CIBA-GEIGY Plastic White Scale

Observer 1 2 3 4 5 6 7 Mean

SamplesReddish 17 20 16 16 14 10 12 15.0Neutral 19 18 19 22 21 25 19 20.4

Greenish 10 8 11 8 11 11 15 10.6

RatingsReddish -44 -36 -35 -29 -27 -19 -25 -30.7Greenish 20 14 22 18 22 20 37 21.9

Ratings/sampleReddish -2.6 -L8 -2.2 -1.8 -1.9 -1.9 -2.1 -2.0Greenish 2.0 1.8 2.0 2.2 2.0 1.8 2.5 2.0

analysis of the mean of the visual assessments of tint vsthe chromaticities of Berger

m = -1048, n = 705, k = 95.8,

and vs the chromaticities measured in Basle

m = -964, n = 679, k = 78.3.

Unlike whiteness, tint is rather independent of theuv contents of the sample irradiation since chromatic-ities are shifted approximately parallel to the equitintlines by uv variations. The standard deviations of thevalues of tint computed by both sets of parameters withrespect to the visually observed means is less than 0.4.This indicates that the tint calculated by Eq. (42) fromthe chromaticity is about as significant as the mean ofvisual assessments of tint by four observers.

The equitint lines are approximately parallel to thedominant wavelength Xd = 470 nm (see Fig. 14). Theperfect diffuser is found to be neutral (T = 0.1), whereasthe samples of the CIBA-GEIGY Plastic White Scaleturn out to be slightly tinted. The width of the equitintbands may easily be adapted to more or less stringenttolerances 3 5 by adjusting the parameters of Eq. (42). Apossible dependence of tint on luminance was not yetinvestigated. Keeping the equitint planes parallel Eq.(42) could be modified allowing for such an effect. Therelationship with the presumed parallelism of the planesof preferred hues of the hyperboloid whiteness formulais apparent.

ConclusionsThe main problem of visual assessment and of in-

strumental measurement of white fluorescent samplesis the spectral power distribution of the sample irra-diation in the spectral ranges of excitation and ofemission of fluorescence. Since it is difficult to repro-duce the spectral power distribution of standard day-light illuminants (e.g., D65) by physical sources withadequate approximation and sufficient stability,methods for calibration, tolerances for checking, andmeans for controlling the actual spectral power distri-bution of the sample irradiation are required. Con-sistency of results can only be achieved if assessmentsand measurements are made at standardized spectralpower distributions of the sample irradiation.

Several types of formulas are successfully used for thecolorimetric evaluation of whiteness. Three lineartypes of formulas (BGA, Lba, Yxy) were discussed.The choice of one of these is a question of conveniencerather than of accuracy as the differences between thewhiteness calculated by these formulas fitted withsuitable parameters is small as compared with the dif-ferences of visual assessments by various observers.The additivity of whiteness calculated by the BGAformulas is desirable if the contribution to whiteness ofdifferent effects is studied. Both the BGA and Lbaformulas are handy to use with some types of photom-eters. The ease of interpretation and of adaptation ofthe Yxy formulas is appreciated if photometers areequipped with small dedicated computers.

The parameters of the formulas of all three types can

0.29 0.30 0.31 0.32 x

Fig. 14. Chromaticities of the paper samples by Berger' 0 0 and ofplates 2 to 12 of the CIBA-GEIGY Plastic White Scale3 x measuredby an Elrepho photometer with xenon lamp, computed for D65 illu-

minant and CIE 1931 standard observer A. The equitint lines are

determined by a linear regression analysis of the chromaticity and the

visual tint assessments of the samples. The lines separate the tints5G14G,3G,2GI 1G,N,1RI 2R,3R,4R1 5R.


be selected for matching the desired hue preference andsaturation to luminance ratio. The unit of whiteness

= n(oW/aY) should be defined as a small integermultiple or fraction of (oW/A Y), preferably with n = 1.W = 100 for the perfect diffuser is generally acceptedas reference point for the whiteness scale.

A hyperbolic whiteness formula based on the conceptof a preferred white and an attempted colorimetricdefinition of tint have to be checked by further experi-ments.

References1. D. L. MacAdam, J. Opt. Soc. Am. 24,188 (1934).2. CIBA-GEIGY Rev. 1, 13 (1973).3. F. Grum and J. M. Patek, Tappi 48, 357 (1965).4. F. W. Billmeyer, Jr., Appl. Opt. 13,1007 (1974).5. L. F. C. Friele, Die Farbe 8,171 (1959).6. A. Berger and 0. Koch, Die Farbe 9, 259 (1960).7. G. Wyszecki, J. Color Appearance 1 (5), 8 (1972).8. F. Grtner and R. Griesser, submitted to Die Farbe.9. D. Eitle and E. Ganz, Textilveredlung 3, 389 (1968).

10. A. Berger, samples and measurements made for CIE TC-1.3Subcommittee on Whiteness (1972).

11. F. Grum, R. F. Witzel, and P. Stensby, J. Opt. Soc. Am. 64, 210(1974).

12. A. Berger, Die Farbe 22, 213 (1973); Colour 73 (London), 331(1973).

13. A. Berger and D. Strocka, Die Farbe 21, 131 (1972); Appl. Opt.12, 338 (1973).

14. E. Ganz and D. Eitle, Die Farbe 19,103 (1970).15. K. Richter, submitted,to Die Farbe 00, 000 (197?).16. A. Berger and D. Strocka, Appl. Opt. 14, 726 (1975).17. G. Anders and E. Ganz, to be submitted to Appl. Opt.18. F. Grum, in Proceedings of the 17th Session CIE 1971 (CIE, Paris,

1972).19. F. T. Simon, J. Color Appearance 1 (4), 5 (1972); Colour 73

(London), 337 (1973).20. E. Allen, Appl. Opt. 12, 289 (1973).21. G. Wyszecki, Die Farbe 19, 43 (1970); for F(17) see Berger and

Strocka.1322. D. H. Alman, F. W. Billmeyer, Jr., and D. G. Phillips, submitted

to Proceedings of the 18th Session, CIE, 1975.23. E. Allen, J. Opt. Soc. Am. 54,506 (1964); L. F. C. Friele, Vezelin-

stituut TNO, Delft, Netherlands, private communication(1968).

24. E. Ganz, J. Color Appearance 1 (5), 33 (1972).25. W. Franke, Thesis, Darmstadt (1966); W. Brecht and W. Franke,

Wochenbl. Papierfabr. 95, 829 (1967).26. R. Sve, Color 69, (Gbttingen), 335 (1970).27. A. S. Stenius, J. Opt. Soc. Am. 65, 213 (1975).28. F. Grum, Eastman Kodak; private communication.29. S. V. Vaeck, Ann. Sci. Textiles Belges 1, 95 (1966).30. D. J. McConnell, Color 69, (Gbttingen), 329 (1970).31. R. Thielert and G. Schliemann, J. Opt. Soc. Am. 63,1607 (1973).32. K. Honjyo and M. Nonaka, J. Opt. Soc. Am. 60,1690 (1970).33. L. Mori, Acta Chromat. 2, 25 (1969).34. L. F. C. Friele, Die Farbe 8, 171 (1959) concluding "The formula

is ... only given to stimulate further thoughts on whitenessevaluation and cannot be recommended for use, the confusionwith respect to this subject being already intolerable."

35. G. Anders, Textilveredlung 9, 10 (1974).

THE FRONTIERS IN EDUCATION SYMPOSIUM '76, OctobeA25-27, 1976, n Tuczon, kAdz. Spooted by the'Education Gtoup o the IEEE and the Educationa2 Re-zeatch and Methods Dviion o the ASEE, wth thePa'tcipaton o the Co2eage o Engineeing o ftheUniZvexQty o Azona. The pu.pose is uto bngtogethe pone, concerned wth education n6chooZ, cotCege,6 and unveuitie, n nduwty andgoveAnment, to dcu new devetopment6 and newdxecation6 n engineeving education. Fomr ithe-inoAmation, contact Roy G. Post, epatneynt oJNucteaA Engineeving, UnZveity Auizona, Tuacon,A'uiz. 85721, o phone 602/884/3054.


whiteness: photometric specification and colorimetric evaluation

Documents