Quantitative Estimates of Saturation

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Quantitative Estimates of Saturation*JUDITH WHEELER ONLEY, CARL L. KLINGBERGt, MARVIN J. DAINOFF, AND GARY B. ROLLMAN

University of Rochester, Rochester, New York(Received 18 June 1962)

Scales relating saturation to clorimetric purity have been derived from magnitude estimations for red(W29) and green (W65) test stimuli of 4° and 1.50 subtense. Scales based on homochromatic comparisonsat several luminance levels follow a power-law form, with exponents ranging from 1.80 to 2.30. There isevidence that saturation scales for red and green light differ in slope, with the red scale being of consistentlyhigher slope than the green. This difference is demonstrated clearly by heterochromatic saturation matchesfor a large number of clorimetric purities, but is not substantiated by magnitude estimations utilizingheterochromatic comparisons. It is suggested that observers are not able to apply a ratio definition of satura-tion in making quantitative comparisons of heterochromatic stimuli by the method of magnitude estimation,and that real differences between saturation scales for differing hues may be masked by the adoption ofmedian magnitude estimations as a quantitative index of perceived saturations.

INTRODUCTION

AMONG the basic psychophysical data relevant toa description of color are the functions which

relate the psychological aspects of hue, brightness, andsaturation to a corresponding aspect of the lightstimulus (usually, dominant wavelength, luminance,and clorimetric purity, respectively). Although it hasbeen shown that each psychological aspect of color maybe influenced by interactions among the perceptionsproduced by all three major psychophysical correlates,it is nonetheless possible to estimate how each aspectvaries with its closest correlate by controlling the othertwo variables while manipulating the most relevantone. The function relating brightness to luminance hasbeen extensively investigated in this way.2 The relationbetween hue, expressed by color names descriptive ofvariations in color across the spectrum, and dominantwavelength is widely accepted. Saturation is, however,a much less familiar concept and has been given some-what conflicting definitions.3 It also is the least fre-quently abstracted of the three perceptual aspectsmentioned. Given a constant luminance and dominantwavelength, what changes in saturation result when wevary the clorimetric purity of the stimulus over thefull range from white to a spectrally pure light?

The subjective judgment of relative saturation forstimuli of the same dominant wavelength but differingcolorimetric purities can be made with considerableaccuracy. Most observers would agree on an ordinalscale of saturation with little or no difficulty: increasesin the colorimetric purity of a given color are accom-

* These experiments were conducted in the Department ofPsychology, University of Rochester, under the support of a grantfrom the National Institute of Neurological Diseases and Blind-ness, United States Public Health Service.

t Now at The Boeing Company, Seattle, Washington.I Committee on Colorimetry, The Science of Color (Thomas Y.

Crowell Company, New York, 1953), p. 252.2 cf. R. M. Hanes, J. Exptl. Psychol. 39, 438, 719 (1949); S. S.

Stevens, Psychol. Rev. 64, 153 (1957); R. G. Hopkinson, Nature178, 1065 (1956); J. W. Onley, Science 132, 1668 (1960).

3 Morton C. Bradley, Tech. Studies in the Field of the FineArts, Fogg Art Museum, Harvard University, April 1938, Vol. VI,No. 4.

panied by systematic increases in its saturation. Whenwe ask observers to make more quantitative judgmentsof saturation, however, the definition of saturationwhich has been adopted by each observer becomescritically important. The problem of the definition ofsaturation has been widely recognized.4' 5 It has beencustomary when dealing with empirical evaluations ofthe subjective magnitude of specific clorimetricpurities to distinguish between what we might call a"chroma" definition and a "saturation" or "amount ofcolor" definition. 6 In the former, saturation is definedas ". . . the attribute determining the degree of differ-ence from the achromatic color perception most re-sembling it. . . ."I This definition corresponds to thedefinition of Munsell chroma, and would imply thatequal Munsell chromas would appear equally saturated.The second definition states that saturation is ". . . theattribute of a visual sensation which permits a judgmentto be made of the proportion of pure chromatic color inthe total sensation. . . ."8 Whereas the first definitionimplies the psychophysical operation of interval judg-ments of difference from gray, the second implies ratiojudgments, abstracting the chromatic component froma complex perception. There is no reason to expect thatthese two classes of psychophysical operations wouldyield identical estimates of the relation between satura-tion and clorimetric purity, especially when appliedto stimuli which differ in dominant wavelength. It hasbeen demonstrated that the two definitions produceconflicting results when applied to stimuli of differingluminances. 6

For a wide range of sensory continua, it has beenempirically demonstrated that psychophysical judg-ments of intervals and of ratios result in differing

4 W. D. Wright, The Measurement of Colour (The MacmillanCompany, New York, 1958), p. 153.

'A. Pope, The Language of Drawing and Painting (HarvardUniversity Press, Cambridge, Massachusetts, 1949). See alsofootnote 3.

6 cf. R. M. Evans, J. Opt. Soc. Am. 49, 1049 (1959).7 D. B. Judd, Color in Business, Science and Industry (John

Wiley & Sons, Inc., New York, 1952).8 British Standard 1611, 1953, quoted by W. D. Wright,

reference 4, p. 154.

487

VOLUME 53, NUMBER 4 APRIL 1963

ONLEY, KLINGBERG, DAINOFF, AND ROLLMAN

SCALING - MAGNITUDEESTI MATION

SATURATIONMATCHING

Std.,Comp. l Std. Comp.

OBSERVER 1/ dSEES /L R E=

Target. LE REI

(FUSED)

TIME FIXATIONRELATIONS:

DURATION: 0.30 SOc

MONOCULARLYVIEWED I HAPLOSCOPICALLY

FIXATION

Poli .,0.30 sc

HAPLOSCOPICALLY

JUDGMENTS: NUMERICAL ESTIMATES ADJUSTMENTS TORE: STD. "100" MATCH STOS.

FUNCTIONS: SATURATION SCALES" RELATIVE C.P. FOREQUAL SATURATION

FIG. 1. General procedures.

estimates of the subjective magnitude scale.' Thequestion of which scale is the more fundamental re-mains unanswered. It appears quite probable that thepractical choice of scale will continue to be dictatedby the conditions of each specific application.' 0 At amore basic level however, there is mounting evidencethat a number of sensory experiences evaluated in theratio sense can be adequately described by a singlegeneral law whose parameters vary with the modalityand conditions of stimulation.9 Although this psycho-physical power law has not as yet been demonstratedto have unequivocal physiological significance, it istempting to attribute the generality of the power-lawfindings to some general underlying discriminativeprocess, and to consider ratio judgments to be themore fundamental.

To derive a psychological ratio scale relating satura-tion to its psychophysical correlate calorimetric purity,we may adopt any one of several methods, all of whichrequire the observer to abstract from a complex colorperception that aspect which represents its saturation(where saturation is defined as the relative amount ofchromatic color in the total sensation). Two suchscaling methods are those of ratio production andmagnitude estimation. Galifret has reported saturationscales for red surface colors obtained by each of thesemethods and compared to a scale synthesized fromdiscriminability data." While the scale obtained frommagnitude estimations was found to approximate apower-law form (with slope, and thence exponent ofthe power law equal to 1.0), that derived from theproduction of ratios was found to be curvilinear on a

I S. S. Stevens and E. H. Galanter, J. Exptl. Psychol. 54, 377(1957).

10 B. S. Rosner, "Psychophysics and Neurophysiology," inPsychology: A Sttdy of a Science, edited by S. Koch (McGraw-HillBook Company, Inc., New York, 1962), Vol. 4.

11 Y. Galifret, L'Annce Psychologique 59, 35 (1959).

log-log plot, and suggestive of a somewhat higher slope.Data of the magnitude-estimation procedure werefound to agree with the scale obtained from discrimina-bility data, a result accepted by the author as evidencefor the tentative labeling of saturation as a metatheticsensory continuum.9

Scales derived by the method of magnitude estima-tion and the method of ratio production for the visualdimension of brightness have been shown to agreewithin the errors of measurement of either procedure.' 2

The discrepancy in scales obtained by the two methodsfor the saturation dimension is disturbing. Although itis not clear from Galifret's report that stimuli for thetwo procedures were totally equivalent, his findingsraise serious questions concerning the application oftraditional scaling procedures to the saturation dimen-sion. A complete empirical investigation of the satura-tion scale should include some procedure which providesan independent verification of its form and the values ofits parameters.

The present study utilizes the methods of magnitudeestimation and saturation matching to investigate theform and parameters of a ratio scale relating saturationto colorimetric purity of stimuli yielding color percep-tions of red and green hues at several luminance levels.The magnitude estimation procedure is applicable to thederivation of scales for stimuli of each dominant wave-length and luminance level independently, but offers noinformation as to how the saturations of differingdominant wavelengths may be related. The psycho-physical investigation of this question has been carriedout both by the use of heterochromatic saturationestimations and by a direct saturation-matchingprocedure. While it is in no way implied that this studyoffers a complete picture of saturation relations, itslimited data present information of serious methodo-logical implications by providing an evaluation of theconsistency of the scales and scale parameters predictedby these differing judgmental procedures.

PROCEDURES

Three independent experiments were performed. Thegeneral procedures employed in the study are sum-marized in Fig. 1, and their specific conditions will bedescribed briefly.

Magnitude Estimates-4° Test Field

Each of the 18 color-normal observers was instructedto make numerical estimates of the saturation producedby test stimuli of three different dominant wavelengths(those of Wratten filters W29 red, W65 green and W48blue, as illuminated by tungsten light, and of varyingcolorimetric purities). All judgments were made relativeto a standard of the same dominant wavelength 1 and

2 cf. J. W. Onley, Science 132, 1668 (1960).13 Note, however, that particularly for the blue stimulus (results

of which are not reported here), there is a marked shift in hue with

;

488 Vol. 53

QUANTITATIVE ESTIMATES OF SATURATION

were nominally based on a ratio definition of saturation.Observers were told to define saturation as the "relativeamount of color" in each sample, and were shown colorsamples of varying purities to provide some degree offamiliarization with the saturation dimension.

Observations were made monocularly, with the pre-ferred eye. Each observer made one estimate for eachof 10 clorimetric purities of the three dominant wave-lengths, at each of two luminance levels (68 and 6.8mL). Dominant wavelength, luminance level, andcolorimetric purity were randomized in the design ofthis experiment.

Magnitude Estimates-1.5' Test Field

Each of 17 color-normal observers was instructed tomake numerical estimates of the saturation of red andgreen (W29, W65) test stimuli of varying clorimetricpurities. Judgments were made relative to both homo-chromatic and heterochromatic standards, and were asin the above procedure, based on a ratio definition ofsaturation. Familiarization with the saturation dimen-sion was accomplished by the use of color chips andsample stimuli provided by the actual experimentalapparatus.

Observations were made haploscopically; that is, theobserver viewed the standard test stimulus with oneeye, then viewed the comparison stimulus with theother eye. The haploscopic procedure was adoptedbecause of the complex after-image problems en-countered with the high luminance level in this experi-ment. For this study, each observer made one estimatefor each of eight calorimetric purities of the two domi-nant wavelengths at each of two luminance levels (680and 68 mL). Dominant wavelength, luminance level,colorimetric purity, and type of judgment (i.e., homo-chromatic or heterochromatic) were randomized in thedesign of this experiment, with specific restrictions beingplaced on successive stimulus presentations (e.g., ahomochromatic series always began each experimentalsession; heterochromatic comparison of a given teststimulus never immediately followed its homochromaticcomparison).

For both magnitude-estimation procedures, the fixa-tion target was a dim (0.18 mL) tungsten-illuminatedannulus, viewed for 5 min prior to a given stimulusseries.

Saturation Matches-1.5° Test Field

Each of two color-normal observers adjusted a com-parison stimulus to match in saturation each of a seriesof standard stimuli. Homochromatic judgments providethe baseline against which heterochromatic comparisonsmay be evaluated. The observers in this experimentwere highly trained in making clorimetric matches

changes in colorimetric purity. See W. DeW. Abney, Researchesin Colour Vision and the Trichromatic Theory (Longmans Green& Co., London, 1913) for data bearing on the Abney Effect.

F

AF

WALL

Eye

FIG. 2. Schematic diagram of the apparatus used in the scalingexperiments. Projectors: Pf (fixation field), P, (white componentof test field), P, (chromatic component of test field); F filter racks:S (standard), C (comparison); L lens; Sh shutter; GG groundglass slides; Af fixation aperture; At test aperture.

and experienced in the complex judgments required byheterochromatic photometry.

Observations were made haploscopically, as shownin Fig. 1. Red and green (W29 and W65) test stimuli ofvarying clorimetric purities were studied at a lumi-nance level of 74 mL. Hue, colorimetric purity, and typeof judgment were randomized, and the experimentaldesign included six judgments by each observer for eachof the experimental conditions.

For the matching procedure, fixation targets weredim hairline reticles, illuminated by a tungsten sourceat a level which was just visible to the observer. Teststimuli were delivered in an otherwise darkened field,and were preceded by a 5-min period of adaptation tothe surround prior to each series.

APPARATUS

For the scaling experiments, stimulus fields were pro-vided by three 35-mm slide projectors arranged asshown schematically in Fig. 2. Filter mountings forstandard and variable stimuli were positioned to allowrapid substitution of one for the other. Test-flashduration was controlled by an electromechanical timingunit, activating a rotary solenoid shutter. The presenta-tion of each test flash was under the control of theobserver, who pressed a control button when he con-sidered his fixation on the target to be adequate. A fine-ground glass slide positioned across each of the aperturesassured that the normally viewed stimuli appeareduniformly bright.

For the matching experiment, stimulus fields wereobtained by means of a multiple-channel Maxwellian-view optical system which has been described in detailelsewhere. 4

Light Sources

The light sources used for the three experiments weretungsten-filament lamps, all operated at approximately

14 J. W. Onley, J. Opt. Soc. Am. 51, 667 (1961).

April 1963 489


the same color temperature.' 5 For the 40 scaling study,projectors W and C contained 750-W 105-V spiral-filament projection bulbs. To obtain better field uni-formity, these projectors were converted to utilizevertical-ribbon-filament microscope lamps (6-V, 18-A)for the 1.50 scaling study. Light sources in the matchingapparatus were 12-V 50-cp auto bulbs with a V-shapedfilament that is particularly adapted to the stimulusrequirements of the Maxwellian view.

Calibrations

Luminance calibrations of all stimulus fields wereobtained by direct-matching procedures, by using theMacbeth illuminometer and monocular viewing. For thechromatic components of each stimulus field, thisnecessitated heterochromatic brightness matching,which was carried out independently for each of thetwo observers in the matching experiment. Specifica-tions of colorimetric purity throughout this report arebased on the judgments of these observers, and probablydepart at least slightly from measurements based onthe standard observer.

Colorimetric purity for spectral-plus-white combina-tions of lights is defined as follows:

Pc=Bv/(Bx+B.), (1)

where By is the luminance of the spectral componentand Bw is the luminance of the white component. Thisdefinition applies not only to monochromatic-plus-white-light combinations, but also to stimuli found toyield a color match to them. Given the excitation purityof a filtered light of given color for the 1931 CIEstandard observer, colorimetric purity for any actualobserver with normal color vision may be estimated bythe following formula':

Pc=Peyx/ys, (2)

where Pc is the excitation purity for the illuminantused, ys is the chromaticity coordinate of the filter forthat illuminant, and yx is the corresponding chroma-ticity coordinate of its dominant wavelength. Thisformula was employed to estimate the colorimetricpurities of all chromatic and chromatic-plus-whitestimuli utilized in these experiments.

Under many viewing and judgment conditions, thelight provided by the tungsten sources used here maybe perceived as possessing some hue. In the context ofthe present experiments, it was in fact defined as"white," and in no instance did any observer assign asaturation estimate greater than zero to the whitecomponent presented alone. In fact, a number of

16 Lamps for the scaling experiment were operated at approxi-mately 2800'K, those for the matching experiment at approxi-mately 2900'K. See G. R. Harrison, R. C. Lord, and J. R. Loof-bourow, Practical Spectroscopy (Prentice-Hall, Inc., EnglewoodCliffs, New Jersey, 1948), p. 174.

18 Y. LeGrand, Light, Colour and Vision (John Wiley & Sons,Inc., New York, 1957), p. 181.

68 mL

2.8

2.4

2.0

4.6

4.2

.8

.4

0

2.8

0 2.4

2.0

4.6

1.2

.8

.4

6.8 mL

40 HOMOCHROMATIC SCALES

FIG. 3. Median and range of saturation estimates of 18 observers.The functions drawn are least-squares linear fits of the medianestimates, and are characterized by the equations shown.

observers failed to perceive a relative saturation greaterthan zero even for stimuli of clorimetric purities ashigh as 0.2 (note for example Fig. 3 in which lowerlimits of the ratio estimates in the log-log plot cannotin some cases be shown). It should be emphasized thatin the scaling experiments, observers were required tomake estimates of saturation relative to standard stimuliwhich were moderately chromatic in appearance. Com-pared to these standard stimuli, the tungsten sourceitself appeared quite achromatic.

RESULTS AND DISCUSSION

Results of the magnitude estimation study for 40fields are summarized in Fig. 3, which shows the medianand range of estimates based on the group of 18 naiveobservers. All estimates were made by comparing thevariable test stimuli with a homochromatic standard ofcolorimetric purity equal to 0.4, where this standardwas assigned the number "100." Observers for bothmagnitude-estimation studies were allowed to reporteither numbers (e.g., "200") or ratios (e.g., "twice assaturated") to express the relative amount of chromaticcolor in each comparison stimulus.

A straight line on the log-log coordinates of Fig. 3and of subsequent figures describing magnitude estima-tion data indicates agreement with a power-lawprediction. The best-fitting straight line has beenderived by the method of least squares, and its equationis shown for each condition. The slope constant in eachequation represents the exponent of the power law forthat case. Note that for all conditions of this experi-ment, median estimates of saturation approximate apower-law form. There also appears to be some evidence

RED - RED

Rid - - std.. - --~t

Y. 2.30x + 2.77 Y *222 2.70

-L. -.8 -.4 -2 0 -4.0 -.8 -.6 -.4 -.2 0LOG C.P.

GREEN GREEN -

sd i _id

V L4.842 + 2.77 Y- .842 2.70

490 Vol. 53


that there is a systematic difference between saturationscales for this particular pair of red and green stimuli,with the green scale showing a consistently lowerexponent (i.e., the saturation of the green stimulusincreases less rapidly than that of the red, for similarvariations in colorimetric purity of the two stimuli), asmight be expected due to the higher saturation ofspectrum red.

Figures 4 and 5 summarize the findings of the magni-tude estimation study for 1.50 test fields. All estimateswere made by comparing the variable test stimuli witha standard of colorimetric purity equal to 0.5, wherethis standard was assigned the number "100." For theconditions of Fig. 4, comparison and standard were ofthe same dominant wavelength; for those shown inFig. 5, heterochromatic comparisons were made asindicated. Best-fitting straight lines derived by themethod of least squares are described by the equationsshown for each function. Median estimates of saturationonce again closely approximate power-law form: bothhomochromatic and heterochromatic comparisons yielda nearly linear result on the log-log plot. Note, however,from Fig. 4, that there is no evidence for difference inslope of the red and green scales at the 68-mL levelwhich corresponds to that of the earlier study, and thatthe difference in slope for the 680-mL condition is infact in the reverse direction.

Although heterochromatic comparisons, particularlyat the lower luminance level, appear to yield a power-law result with an exponent which is systematicallylower than that evidenced by homochromatic judg-ments, the results for red-vs-green comparisons andthose for the reverse case are virtually identical; there

2.8

2.4

2.0

1.6

.2

.8

.4

z0

2.8

CD 2.40

2.0

1.6

1.2

.8

.4

680 mL 68 mL

i,50 HOMOCHROMATIC SCALES

FIG. 4. Median and range of saturation estimates of 17 ob-servers. The functions drawn are least-squares linear fits of themedian estimates, and are characterized by the equations shown.

2.8

2.4

2.0

I.6

1.2

.8

.40

2.8

o 2.4

2.0

1.6

1.2

.8

.4

680 mL 68 mL

1.5° HETEROCHROMATIC SCALES

FIG. 5. Median and range of saturation estimates of 17 ob-servers. The functions drawn are least-squares linear fits of themedian estimates, and are characterized by the equations shown.

is no evidence from the data of heterochromaticestimates, Fig. 5, which would substantiate a syste-matic difference between scales for red and green lights.Although heterochromatic and homochromatic com-parisons were made by the same observers within asingle experimental session, most observers reportedestimates much more conservatively in the hetero-chromatic series, and were reluctant to assign extremevalues when making cross-color comparisons. It appearshighly probable that few observers were able to adopta stable ratio definition of saturation when forced toevaluate heterochromatic pairs.

It is clear from the complete ranges of estimates,shown in Figs. 3-5, that observers were generally ableto reproduce an ordinal scale of saturations, even whenstimuli were presented singly and could not be crosschecked with stimuli of the continuum other than thestandard. (Judgments greater than "100" were seldomgiven for stimuli below the standard; judgments lessthan "100" for stimuli of colorimetric purities higherthan the standard were similarly infrequent, even forthe heterochromatic comparisons.) Observers partici-pating in the magnitude estimation studies reportedvery little difficulty in assigning numbers which theyconsidered to be proportional to the relative amountsof color in comparison and standard stimuli when thesewere of the same dominant wavelength. Although it isunlikely that the specific instructions of the magnitude-estimation procedure would foster an interval definitionof saturation by the observer, there remains no inherentmeans of verifying the adoption of a ratio definition. Itmay be that a saturation scale based on quantitativeestimates by a naive observer possesses little more than

April 1963 491

RED RED -

G,. td. Dr. Wt.

Y 1.77X 2.40 Y 1,41 X + 2.44

-1.0 -.8 -.6 -.4 -.2 0 -.0 -.8 -.6 -.4 -.2 0

LOG C. RGREEN GREEN

R. i td. R, td,

Y LTOX + 2.22 V 1.502 4- 2.36

RED RED

Y O 1.80x 2.49 Y 1 .90 + 2.50

-1.o -8 -.6 -.4 -.2 0 -.o -.8 -.6 -.4 -.2 0LOG C.R

GREEN - GREEN -

- s d 2s td

Y .2.20 + 2.66 Y 1.90 + 2.63


W

I -

In

-LINEAR FIT RED SCALE/ (Least Squares)

-REFERENCE GREENSCALE (Slope arbitrary)

C.P. Difference (Hama- vsHetera-chromatic matchesfor the Standards shown)

LOG C.P. of STANDARD

FIG. 6. Prediction of the relative slopes of saturation scaleson the basis of heterochromatic vs homochromatic saturationmatches.

ordinal properties, and this is most certainly true whenthe estimates require the abstraction of saturation fromthe complex perception of colors which also differ indominant wavelength.

The results of the magnitude-estimation experimentsdiffer considerably from those reported by Galifret."1While the scales obtained by Galifret for a red surfacecolor exhibited power-law form, they were of consider-ably lower exponent than those reported here. It is byno means a novel finding that a subjective dimensionof color varies not only with its physical correlate, butwith other aspects, such as mode of appearance (e.g.,surface or illuminant mode; while for the dark-adaptedobserver the brightness scale has an exponent of about0.30, the similar scale for lightness exhibits an exponentnear 1.20).9 The practical definition of saturation mayalso be a critical factor contributing to lack of agreementin the two studies. Further, there is considerablevariability between saturation scales obtained forindividual observers in the present study, with theexponents of individual scales varying from as low as0.90 to about 2.90, and clearly encompassing the rangewithin which Galifret's median exponents lie. Althoughit is attempted by the use of a large group of observersto provide an adequate index of individual differencesand a stable median estimate of the saturation scale,individual differences cannot be ignored, and com-parison among conditions should ideally be made withthe same group of observers as their own control.Familiarization and context effects, however, mitigatestrongly against the use of the same observers for largenumbers of judgments on the same sensory continuum,when the method of magnitude estimation is employed.

Due to the high degree of variability inherent in thescales derived from magnitude estimations, it is un-likely that one could reliably establish differencesbetween scales for differing colors, even if these differ-ences do in fact exist. Quantitative estimates such asthose required by this procedure are relatively insensi-tive measures. Those who hold a conservative view ofpsychophysics would discount such measures in favorof the more critical judgments obtainable by procedureswhich require the observer to match stimuli, or to "nullout" differences between classes of stimuli which vary

along a specific physical continuum. 7 The latter typeof judgment cannot directly yield a subjective scale forthe dimension under consideration, but it may beapplied in investigating or verifying the parameters ofsuch a scale derived by ratio procedures.' 4 In the presentinvestigation, saturation matches for homochromaticand heterochromatic pairs of stimuli have been utilizedto predict the relative exponents of saturation scales forred and green light.

Assuming an arbitrary reference slope of 1.00 for thesubjective scale relating the log saturation of green(W65) light to log calorimetric purity, we may ask whatslope will a scale obtained under the same conditionsfor red (W29) exhibit? The application of matchingdata to this question is illustrated schematically inFig. 6. The clorimetric purity required for a homo-chromatic match in haploscopic view (see Fig. 1) isutilized as the reference baseline against which hetero-chromatic matches are evaluated. Plotted in thisillustration are the differences in median colorimetricpurity between homochromatic and heterochromaticmatches for each of a series of standards of specificcolorimetric purities. The use of the difference measurescompensates for possible sensitivity differences in thetwo eyes. Figure 7 summarizes these difference measuresfor each of two trained observers, under conditions inwhich each color was varied in turn to yield a saturationmatch with itself and with the second color. Bothobservers required relatively less green light in thechromatic-plus-white stimulus to equal a given satura-tion of red light at low clorimetric purities of thestandard, and relatively more green light at high

74 mL

RED ADJUSTED

0 JO / CK

-/

-4GREEN ADJUSTED

O Jo . CK

-12 -1.0 -8 -.6 -.4 -.2 -1.2 -1.0 -.8 -.6 -.4 -.2

LOG C.P. OF STANDARD

FIG. 7. Relative slopes of saturation scales for redand green stimuli of 1.50 subtense.

17 G. S. Brindley, Physiology of the Retina and Visual Pathway(Edward Arnold, Ltd., London, 1960).

492 Vol. 53


colorimetric purities of the standard. Stated anotherway, low-purity greens would appear more saturatedthan reds of the same purity; at an intermediate level(about 0.15 colorimetric purity) equal purity of thetwo colors implies equal saturation; high-purity greenswould appear less saturated than reds of the samepurity.

The experimental data of Fig. 7 have been fitted withstraight lines by using a least-squares technique whichminimizes horizontal deviations (since difference meas-ures are plotted as deviations in x, rather than y) fromthe arbitrary reference curve for green light. In allcases, the slope for the red function is greater than thatfor green, and the average ratio of red to green slopesis 1.55, with observer CLK showing some systematicdifferences between adjustments of red and of green.Although the absolute values of these slopes arearbitrary, their ratios may be compared directly to theratios of the power-law exponents for red and greensaturation scales obtained in the two earlier experi-ments. The ratio of power-law exponents for medianestimates under corresponding conditions in the 40magnitude estimation study was 1.28; for the 1.50 data,the ratio was 1.00.

One of the observers of the matching study (thesenior author) also participated in both scaling studies.Obtained ratios of red to green exponents for this singleobserver were: 1.20 for scales obtained by magnitudeestimation, 4 stimuli; 1.44 for scales obtained bymagnitude estimation, 1.50 stimuli; 1.56 and 1.53estimated from red and green judgments, respectively,in the matching study. For this observer, all three

procedures revealed consistent differences betweensaturation functions for red and green light. If anyconclusion at all may be drawn from the data of asingle observer, it is, in this case, that the observer maybest be used as his own control, and that the existenceof measurable differences between saturation magni-tudes may be obscured by the selection of medianmagnitude estimates as the quantitative measure ofperceived saturation.

The problem of definition of saturation remainscentral to the problem of scaling in this dimension.While observers may be capable of making ratio judg-ments when comparing equiluminant stimuli of thesame dominant wavelength, they may not be able toadhere to a ratio criterion when making comparisonsbetween differing hues. While the heterochromaticmatching procedure offers a more simple judgmentalsituation, it does not directly evaluate the form of thesaturation scale, and the application of heterochromaticmatching data involves the assumption of a particularscale form (in this case, power-law form). The data ofmagnitude estimations of saturation tend to verify apower-law form for this subjective scale withoutestablishing a definitive value for its exponent, ordifferentiating between scales for various dominantwavelengths. It is suggested by the data of the presentthree experiments that validation of scale informationbased on magnitude estimations requires additionalprocedures, such as saturation matching, and thatreliance on median magnitude estimates of saturationas indicators of the form and parameters of the scalemay be misleading.

493April 1963

Documents

Quantitative Estimates of Saturation