GREY, MARK, AND HASKELL

new type of element is1

R=b, . (11)

To form the network, several such elements areconnected in series. The reader can readily convincehimself that there is a one-to-one correspondencebetween the analysis of this case and the analysis ofthe conductance case treated in the body of the paper.Finally, it should be mentioned that the analysis ofeither the resistance or the conductance responsenetwork is independent of the sign of the exponent of

I in Eq. (1). Any transducer whose resistance variesas some power (positive or negative) of the input levelmay be used to establish a proportionality betweeneither the resistance or the conductance of the networkand the logarithm of the input level.

ACKNOWLEDGMENTS

The authors are indebted to Mr. V. K. Elorantaand Mr. C. P. Thomas for constructing the light-intensity meter described, to Lois Lee Mooney forconducting the calibration experiments, and to Dr.W. A. Shurcliff for his help in preparing the manuscript.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 50, NUMBER 1 JANUARY, 1960

New Reflectometer and Its Use for Whiteness Measurement*RICHARD S. HuNTER

Hasnter Associates Laboratory, Inc., McLean, Virginia(Received June 1, 1959)

A new 0450 blue- and green-light reflectometer has been built with S-4 vacuum phototubes in a ratio-measuring circuit. Where whiteness is of interest, materials are usually yellowish in hue. In these cases,precise reflectance measurements with just the blue and green tristimulus filters are adequate for whitenessdetermination. Investigators have found that, in general, yellowness detracts from perceived whiteness muchmore than does grayness. For best correlation with visual rankings, the green-minus-blue reflectance differ-ence corresponding to yellowness should receive four-to-five times the weight of luminous (green) reflectancealone. Because inadequate blue reflectance detracts so strongly from perceived whiteness, widespread use isnow made of blue fluorescing dyes for the whiteness enhancement of textiles, papers and plastics. These"fluorescent brighteners" absorb in the near ultraviolet and fluoresce in the blue. An ultraviolet-absorbingfilter in the new instrument may be alternated between the sample-viewing and incident light beams toinclude, and then exclude the near-ultraviolet which excites fluorescence. It is thereby possible to obtain ameasure of the contribution of these fluorescent brighteners to blue reflectance, and thence to whiteness.

THE INSTRUMENT

A NEW reflectometer with 0450t geometry hasbeen built primarily for measurements of white-

ness, reflectance, and opacity of white and near-whitepaints, papers, textiles, plastics, and porcelain enamels.It uses a two-beam, null method of measurement as didthe Multipurpose Reflectometer built by the writer 25years ago' and widely used for the same purpose.

Figure 1 is a photograph and Fig. 2 is a block diagramshowing the 450 right-triangle beam pattern of the newreflectometer. Structurally there are two housingsidentical in size and shape. From the front (Fig. 1), theleft housing is the optical unit with light source, sampleholder, filters, and phototubes. The right housing is theelectrical unit with vacuum-tube galvanometer, stand-ardizing rheostats, and ten-turn potentiometer withdigital dial giving Wheatstone bridge settings ofreflectance. Although the two housings are normallybolted together to provide a compact self-contained

*Paper presented before the Optical Society of America,New York, April 2-4, 1959.

t Equivalent to the reciprocal 45°0 geometry.1 R. S. Hunter, J. Opt. Soc. Am. 30, 536 (1940).

instrument, they can be unbolted and separated byseveral feet or more where necessary to accommodatelarge specimens.

FIG. 1. Photograph of reflectometer.

44 Vol. 50

January1960 NEW REFLECTOMETER AND WHITENESS MEASUREMENT

IELECTRICALI UNIT

STANDARDIZING REFLECTANCEI KNOB KNOB

-I

I

V I%%L_ - -_ - - - - - - - _

FIG. 2. Diagram of reflectometer-optical unit below,electrical unit above.

In the exposure unit, light from a single lamp reachestwo 1P39 phototubes by separate paths; one direct andthe other by way of the specimen. (See Fig. 2.) Actually,there are two pairs of phototubes; one with the greentristimulus filter and one with the blue tristimulus filter.

The 6-v instrument lamp is mounted outside thereflectometer housing for easy access and better cooling.A greenish phosphate-glass, heat-absorbing filter in theincident beam not only minimizes sample heating, butit helps with the spectral correction of the Y filter. Theblue and green tristimulus filters are, as in previoustristimulus instruments,2 4 bluer than they otherwisewould be so as to, in effect, change the illuminant fromthe incandescent yellow actually used to the bluishdaylight color of CIE Illuminant C.

Spectral characteristics of the combination of 3100'Klight source, 1P39 phototubes, and the two filters arecompared in Hunter's previous paper4 with the idealg and z functions for Illuminant C. The blue filter wasdesigned by Glasser and Troy,3 the green filter byHunter.4 There is no amber or X tristimulus filter. Aswill be shown in the following, there is little need forsuch a filter in the measurement of whiteness.

Because the filters are beyond the test specimen, theinstrument takes account of light modified in wave-length composition by specimen fluorescence. It doesnot, of course, measure fluorescence arising from day-

2 R. S. Hunter, Natl. Bur. Standards (U. S.) Circ. No. C429(1942).

3 L. G. Glasser and D. J. Troy. J. Opt. Soc. Am. 42, 652 (1952).4 R. S. Hunter, J. Opt. Soc. Am. 48, 985 (1958).

light illumination because the illumination is actuallyincandescent at 3100'K.

Nevertheless, this fluorescence sensitivity has inpractice proved useful. The near ultraviolet content of3100'K is closer to that of daylight than is indicated bythe difference in color temperature between the twosources. This is because natural daylight suffers appreci-able near-ultraviolet loss from atmospheric absorption.

In the instrument, the ultraviolet-absorbing com-ponent of the blue filter can be mounted in the mannershown in Fig. 2, so that it is movable from the specimen-incidence to the specimen-viewing beam. Blue-reflect-ance readings made before and after this movement ofthe ultraviolet absorbing filter will reveal any change ofreflectance arising from specimen fluorescence.

The specimen-positioning panel is of black plasticwith a window 2- in. in diameter. The specimen holdershown in Fig. 1 is a spring-loaded, plunger type. Forspecimens which are not in the form of flat sheets, coverglasses or cells may be used to form flat surfaces formeasurement. The optical unit may be separated fromthe electrical unit and turned with specimen windowhorizontal, either up or down, for convenience inhandling specimens of a variety of forms.

Figure 3 is a diagram of the Wheatstone-bridgecircuit used in the new apparatus. It will be seen thatcurrent from the lamp-viewing phototube passes throughthe digital-scale potentiometer, RL. By turning thefinger-hole knob attached to this potentiometer untilthe vacuum tube galvanometer shows balance, theoperator equates the voltage drop in RL to that in thearm Rs which carries current from the specimen-viewingphototube. The operator thus sets

ILRL=IsRs, or

RL= Is(RS/IL).

Since IL and Rs remain unchanged after the initialstandardizing adjustment of Rs, RL settings serve tomeasure Is, the specimen-phototube current. As will beseen from the circuit diagram, a twin triode, with a

150 V

SCALE G '

LG \ W B 132 /Cs~sa

B-~~~~~~~~~~~~~~~~~~~~~~~

LAPVEIGSEIEGIWN

LAMP VIEWING SPECIMEN VIEWINGPHOTOTUBES PHOTOTUSES

FIG. 3. Wheatstone-bridge circuit used to measurereflectance by RL=,,(R,/IL).

45

I L_ - - - -

*I

RICHARD S. HUNTER

zero-centered, pivot-type galvanometer in the platecircuit, is used to indicate voltage imbalances. A switchand zeroing rheostat are used to adjust for differences inconduction of the two sides of the twin triode.

A ceramic standard for 00450 directional reflectanceis used when adjusting the blue and green RL poten-tiometers. There are separate potentiometers for theblue and green scales. To hold the lamp close to thedesired color temperature of 3100'K, regulated power issupplied.

Although phototubes vary in response with tempera-ture, the two tubes of each pair are close to each otherin the small enclosure and, therefore, change temperatureand response at nearly identical rates. It has been foundin practice that temperature change has been diminishedand stability improved when the instrument lamp isburned continuously at one-half rated voltage betweenperiods of use. The two beams of light being comparedoriginate at the same source and pass through the samefilter. As a result of this and of the temperature pre-cautions, the precision and stability of the reflec-tometer are good.

In a test of stability, the standard deviations for aseries of 20 separate readings of a ceramic plaque madewithin one hour was 0.08% for green, 0.03% for blue.For a similar number of readings made over a periodof three days without intervening adjustment of thecalibrating potentiometers, the standard deviationswere 0.14% for green, 0.28% for blue.

MEASUREMENTS OF WHITENESS

Whiteness has been defined' as that attribute of asurface which denotes its similarity to preferred white.The white preferred in industry and commerce isalways high in diffuse luminous reflectance and eitherneutral or perhaps slightly bluish in chromaticity.

Most white materials are naturally yellowish. Evenafter adjustment with bluish dyes or pigments, thewhite materials encountered in everyday life are mostlikely to be yellowish, sometimes bluish, less oftengreenish or pinkish.

Not only are pinkish and greenish whites less pre-valent than yellowish and bluish ones, but there isconflicting evidence on how to assess properly the pink-green chromatic dimension in whiteness measurement.A study of commercial preferences for white paints,textiles, plastics, and papers reveals that, where thereis a choice between pinkish and greenish tints in white,pink is usually (though not always) preferred. Becausethe role of the pink-green dimension of chromaticity inwhiteness is generally small, and has not been quantita-tively assessed, it seems feasible to ignore this chromaticdimension in whiteness measurement.

Chromaticity departure from neutral in the yellowand blue directions is measured by differences betweengreen and blue (G and B) tristimulus reflectances. 4 The

5 R. S. Hunter, J. Opt. Soc. Am. 48, 597 (1958).

Q>

0

0 I 2 3 4 5 6G -B )) (Yellowness)

FIG. 4. One whiteness contour representing each of 6 relationsproposed for measurement of whiteness.

pink-green dimension involves a third tristimulus re-flectance, which may be amber (A) or CIE-X, de-pending on the instrument. If the third dimension isignored, a tristimulus reflectometer with only green andblue filters is adequate for whiteness measurement.

Several studies have yielded data bearing on thequestion of how properly to weigh yellowness (orsometimes blueness instead) and luminous reflectancein determining whiteness. Figure 4 is a graph on whichare plotted whiteness contours demonstrating a numberof relations proposed for the numerical measurement ofwhiteness. The five curves and one straight line on thisgraph are each identified in Table I.

In this graph, yellowness is measured by G-B, andluminous reflectance by G in percent. The curves havea common point on the gray axis near G= 74; thestraight line crosses this axis at G= 70. The data fromwhich the curves were prepared have been transformedto tristimulus G and B reflectances from CIE and L, a,

I,!~~~~~~~~~~~,

and b values of color using equations previously given.2 The chromaticity departures from neutral have beenmeasured only in the b dimension of the L, a, b coordi-nate system, and parallel to the dominant wavelength577-mu locus of the x, y diagram. In this direction, Xand Y Illuminant C reflectances are equal.

Three of the curves in Fig. 4 (Judd, Selling,and k = 3 8.6) are derived from the formula for whitenesswhich was proposed by Hunter' and first used by Judd.'

[600 /1-Y 2 W=1 -(a+2,1]2+

ki 22

6 D. B. Judd, Paper Trade J. 100, 266 (1935); 103, 154 (1936).

46 Vol. 50

January1960 NEW REFLECTOMETER AND WHITENESS MEASUREMENT

TABLE I. Identification of eight uniform-whiteness contours in Fig. 4.

Curve name Equation represented Source and reason for presentation

Judd 1 85(G-B) 12 i 100-G 121 i ki=20 Proposed by Huntera first used by Judd"Selling Wk 1= +1 k, 70 Recommended and used by Selling and Frieledki=38.6 kd(G+0.242B) I 200 J k= 38.6 Intermediate contour suggested by present studyMacAdam No equation MacAdame visual rankings of white textilesTaube W=G-4(G-B)=4B-3G Taube'sf best straight line for visual rankings of textiles

(CDM scales)AE W= 100-E[(100-L)2+b2]l Standard color-difference equation for CDM scalesb

a See reference 2.b See reference 4.

o See reference 6.d See reference 7.

e See reference 8.i See reference 9.

In the foregoing equation, the first of the two com-ponents within the curly brackets measures thechromaticity contribution to departure from perfectwhite; the second measures the luminous reflectancecontribution.

For yellowish whites with a dominant wavelength of577 (Munsell Hue 2Y to 5Y), the foregoing Hunter-Judd equation reduces to

r85(G-B) 12+ -l w=1{[ 2 j+ [1G]}

ki(G+0.242B) 2 J

where G and B are decimal fractions rather thanpercentages.

The constant ki in the foregoing equations may bevaried to fit the different specimen-proximity conditionsof visual whiteness judgment which the equation mayrepresent. When specimens are juxtaposed, ki is highcorresponding to the fact that reflectance countsheavily when there is no prominent line or area ofdivision between two specimens. As specimens areseparated, ki diminishes according to Hunter 4 in thefollowing manner: samples separated by barely visibledividing line, k,= 120; sample sseparated by contrasting,but narrow line, 90; samples separated by contrasting,broad patterned area, 40; and ratings of individualspecimens for whiteness without reference to othersamples, 20. Assuming that whiteness was an attributeof materials to be judged in practice without directintercomparisons, Hunter recommended a value fork, of 20 in whiteness measurement.

Although he allowed his observer to make directcomparisons, Judd6 found the above equation withk1=20 to give whiteness correlating well with visualrankings of paper specimens by a number of papertechnologists. Selling and Friele7 performed a similarexperiment, perhaps with better juxtaposition of speci-mens, and recommended use of the same equation, butwith ki= 70. Because of the small weight given toluminous reflectance, the slope of the Judd curve inFig. 4 is steep. The Selling curve, for which kl= 70, ismuch less steep. Of the contours in Fig. 4, two inaddition to the Judd and Selling curves were derivedfrom visual rankings of the whiteness of actual speci-

7 H. J. Selling and L. F. C. Friele, Appl. Sci. Research B1, 453(1950).

mens. MacAdam8 worked with white fabrics in 1934;Taube9 with the same types of materials in 1958. TheMacAdam curve is one of a family he drew to representthe results of his observer's rankings. The straight linesuggested by Taube represents the best of severalequations she tried-both straight line and curvilinear.The MacAdam and Taube curves, it can be seen, haveslopes midway between those of the Judd and Sellingcurves.

Of the six contours in Fig. 4, two do not involvevisual judgments of the whiteness of specimens. Thegraph labeled AE at the bottom is the locus of pointsequally different from the color of perfect white accord-ing to the widely used Judd-Hunter NBS Unit of ColorDifference.2 4"10 It is obvious from the relatively smallslope of this curve that color-difference measurementsaccording to the formulas widely used for chromaticcolors are unsuitable for measurements of whiteness.They give too little weight to chromaticity.

The contour labeled k1 =38.6 is, as can be seen inTable I, based on the Hunter-Judd whiteness equation.Its slope is intermediate between those of Judd andSelling curves, and about equal to those of the MacAdamand Taube curves. In the absence of any visual ratingsof whiteness during the present study, whitenessrelations giving slopes near the average of those foundby four different investigators are recommended.

The value, ki=38.6 was selected so that the fraction85/k, is an even number (2.20). If one desires a white-ness scale of from 0 to 100, this ratio becomes 220 andthe Hunter-Judd whiteness equation becomes

f 220 (G-B) 1 r o-G1 1 JW=_100-0 +

+0.242B 2 ,

where G and B are directional reflectances in percent.The foregoing equation and Taube's straight-line

equation of approximately the same slope,

W=G-4(G-B) =4B-3G,

are recommended for whiteness measurement. The

8 D. L. MacAdam, J. Opt. Soc. Am. 24, 188 (1934).9 K. Taube, Part of unpublished "Study of home-laundering

methods" (Housing and Equipment Laboratory, Institute ofHome Economics, U.S.D.A., Beltsville, Maryland).

10 D. B. Judd, Am. J. Psychol. 52, 418 (1939).

47

RICHARD S. HUNTER

80 7Y

70

G-B (%)FIG. 5. Whiteness chart with curvilinear contours

showing loss of whiteness.

chief difference between these two equations lies in thefact that the former curvilinear equation gives highestwhiteness ratings to neutrals; the straight-line equationrates bluish whites above neutrals of the same direc-tional reflectance.

Prior to the widespread use of fluorescent brighteners,colorimeterists tended to feel that neutral whites shouldreceive the highest whiteness ratings. Recently, how-ever, when bluish whites-usually having fluorescentbrightener-are compared with neutrals of the samelightness, observers have been found to prefer thosewith the bluish cast. This suggests that the straight-lineequation may be preferred, at least for evaluatingwhites with fluorescent brighteners.

The simplest way to obtain whiteness ratings withthe curvilinear equation is to use a chart with whitenesscontours such as is shown in Fig. 5. As an example ofthe use of the new instrument for whiteness measure-ments of nonfluorescent materials, this figure shows theloss of whiteness of a number of cotton fabrics whichhave been subjected to resin treatments. Figure 6 is astraight-line whiteness chart on which are plotted thechanges in whiteness from fluorescence in the presentinstrument of a number of fluorescence-brightenedspecimens discovered in the course of everyday life.

G - B (N)

FIG. 6. Whiteness chart with W=4B-3G contours showingwhiteness due to fluorescence-brightened specimen changes.

It is obvious that no single equation or chart forwhiteness can represent the many observing conditionsand observer preferences which exist. In the presentpaper, two equations,: and charts prepared from them,are proposed for reflectometer measurements of white-ness in average situations. The traditional Hunter-Juddtype of equation giving curved contours which rateneutrals highest in whiteness is expected to find usewhere fluorescent brighteners are not involved. Thestraight-line chart gives highest ratings to bluish tints,as do many observers when they evaluate materialstreated with fluorescent brightener. With either typeof whiteness function, the green-minus-blue reflectancedifference corresponding to yellowness receives aboutfour times the weight given luminous reflectanceincrements. Thus, a reflectometer like the present one,which measures green-minus-blue reflectance differenceswith high precision is needed for the measurement ofwhiteness.

t Nearly identical equations in the Color-Difference Meter4

coordinates areW=L-3b

andW= 100-[(100-L)2+ 10b2]I.

48 Vol. 50