SEPTEM BER, 1941 VOLUME 31

Studies on the Characteristic Curve of Photographic PapersFRANZ AND ANNIE URBACH

Department of Physics, University of Rochester, Rochester, New York(Received July 29, 1941)

I. REFLECTION AND TRANSMISSION

IN this paper the term "reflection curve" willbe used for the characteristic curve of photo-

graphic papers obtained by measuring thediffusely reflected light. The reflection density Dbeing defined, as usual, by

D = -log A,

A meaning the albedo of the paper (the albedoof an unexposed developed and fixed sample willbe taken as unity).

The term "transmission curve" will be usedfor the H and D curve obtained with transmittedlight, the transmission being defined, as usual, by

S= -log T,where T means the transparency (the trans-parency of an unexposed developed and fixedsample is taken as unity). Some details concern-ing the apertures and angles of incidence andreflection are indicated in Fig. 1.

The relation between transmission and re-flection has been investigated repeatedly.

As far as we know the first formula was givenby Mees, Nutting, and Jones'

D = log 1/[(1 - C) T2+ C], C being a constant. (1)

The first measurements were made by F. F.Renwick2 who criticized sharply formula (1) andwho presented another formula in a verythorough investigation with Channon and Storr.3Renwick's formula accounts for the diffuse re-flection of the silver deposit and for the "inter-reflections." An analogous derivation, differingbut formally from Renwick's, has been givenmore recently by Neugebauer. 4

In applying his results to actual photographicmaterial, however, Renwick made use of some

1 Jones, Nutting, and Mees, Phot. J. 38, 342 (1914).2 F. F. Renwick, Eders Jahrbuch (1912), p. 106; Phot.

J. 37, 127 (1913).3Channon, Renwick, and Storr, Phot. J. 42, 121, 140

(1918).4 H. E. F. Neugebauer, Zeits. f. tech. Physik 18, 137

(1937).

approximations with the effect that the form ofhis final results differs from (1) virtually onlyin the meaning of the constants. AlthoughRenwick's formula represents also only a veryrough approximation, it will be sufficient for ourfurther purposes to derive an analogous formula.We thereby introduce from the very beginningthe factors which Renwick neglected.

Let T be the transparency of the layer, R thereflection power of its silver deposit. Then, ifinterreflections are disregarded, the albedo of thepaper coated with the layer will be

A = Tn+R, (2)

where n depends essentially upon the angles ofincidence.

The disregard for the interreflections is jus-tified if there is no optical contact between theemulsion layer and the reflecting paper. If sucha contact is established, however, the totalreflection at the interface between gelatin andair of a large part of the light diffusely reflectedby the paper support plays an important role.For densities larger than 0.2 this effect can beaccounted for sufficiently by properly adjustingthe value of n.

The behavior of D at low densities and theexact interpretation of n-which seems distinctlylower at low densities, especially if opticalcontact is established between the support andthe emulsion layer-present interesting butrather complicated problems which we do notintend to treat here. R itself in formula (2),

L

S

FIG. 1. Measuring device. L-light source. Dependenton the position of the screen sc the barrier layer photo-cellP measures either the light reflected diffusely by thesample s or the light transmitted by s and reflected on Pby the mirror M.

581

J. . S. A.

FRANZ AND ANNIE URBACH

+t

0 , 109 eopOs.

FIG. 2. Influence of silver-reflection. 0 Transmissiondensities; + reflection densities. II calculated accordingto formula (2) from curve I and the values of R whichwere measured separately.

however, obviously depends on T. Let dz be thenumber of grains in an infinitesimal thin layerof the coating; let z be the number of grainsbetween this layer and the surface; let T(z)represent the transparency of this same part ofthe coating; then the thin layer contributes to R:

dR= pT(`) dz, (2.1)

p being a constant which characterizes thereflecting power of the grains. Disregarding oncemore the interreflections we put T(z) = e- andby integration of (2.1)

R=(e/p)[I-exp (-enZ)], (2.2)

where Z means the total number of grains percm2 of emulsion and exp (-enZ) means thetransparency of the whole layer. Let e/p=Ro bea constant, dependent only upon properties ofthe individual silver grain. We rewrite

R=Ro(l-Tn)and by combining this with (2) we get

A =Ro+(l -Ro)Tnand

D = -log [Ro+ (1-Ro) X 10-nq].

In this deduction the light diffusely reflected bythe surface of the layer is not accounted for; itplays no role in most of the following con-siderations.

In Renwick's equation the mass of the silverdeposit is used instead of s. In checking hisequation, Renwick replaces the mass by thedensity as measured between opal glasses. Hejustifies this by referring to previous measure-ments.' These data, however, are in very pooragreement with Renwick's own statement.Moreover, according to our derivation, themeasuring of the transmission densities has to becarried out under the same circumstances as thereflection density measurements. These, however,cannot easily be carried out with completelydiffused light. We present, therefore, the resultsof some measurements of our own before furtherusing Eq. (4). They were made with the simpledevice shown in Fig. 1.* We checked our deri-vation step by step. First formula (2) was testedby using a paper emulsion coated on glass. Itsreflection was measured with a white papersupport (result A) and without any support, i.e.,with a "blackbody" behind the layer (result R);at the same time the transparency (T) wasmeasured. Figure 2 shows that the simple relation(2) is sufficiently exact within the limits men-tioned above.

Then relation (3) which relates the reflectionof the scattering silver deposit to its transmissiondensity was checked by comparing the R and Tvalues. Figure 3 shows the results.

FIG. 3. Silver-reflection R asa function oftransmissiondensity. Theline correspondsto formula (3).

DFIG. 4. Reflection

density as a func-tion of transmissiondensity. The linecorresponds to for-mula (4.1).

(3)

(4)

With n= 2 this corresponds exactly to Eq. (1).

5 F. F. Renwick, Phot. J. 37, 203 (1913).* Of course, the obvious corrections due to the imper-

fections of such an arrangement were made.

582

CHARACTERISTIC CURVE OF PHOTOGRAPHIC PAPERS

Finally Eq. (4) was checked by using a com-mercial photographic paper with even and thinsupport (Fig. 4). Equation (4) satisfactorilyrepresents the experiments within the limits oferror. Some more series were made with virtuallythe same results.

II. THE INFLECTION POINT AND ARULE OF RENWICK'S

The properties of an emulsion are usuallyjudged by its H and D curve obtained withtransmitted light: the transmission curve. TheEq. (4.1) shows in which way the characteristiccurve of a paper (the reflection curve) is deter-mined by the transmission curve of the emulsionon one hand, and on the other hand by thespecial conditions under which it is used,especially by the reflecting power of the silverdeposit; the magnitudes s and D in (4.1) are tobe read as functions of the log of exposure.

It is of some interest to see what conditionsthe transmission curve has to fulfill in order toyield certain properties of the paper curve. Inorder to obtain, e.g., a straight line portion in thepaper curve (which may or may not be of anyappreciable length) the transmission curve ob-viously has to be bent upward (convex towardthe log E axis) in order to compensate for theeffect of the silver reflection. Mathematically,this is easily shown by deriving from Eq. (4) theequation of the transmission curve which wouldyield a straight line reflection curve. Using thedefinitions

dDL=logE, G=-,dL

where E means the exposure, andbe constant, we find from (4)

ds/dL= G/n(l -R0 10-G

as the differential equation of saidcurve. With G= 1 and proper adjuintegration constant, the solution cas

1- 1-Ros=- log

n 10-L-R,

The graph Fig. 5 shows this curvesion curve as closely as possible res

ds

3 of this diagram would be required in order tomake a paper with a long straight line portion.'

The transmission curve of such a paper wouldhave two approximately straight line portions,the one at low densities, the other at the inflec-tion point. It is obvious that such a paper couldbe made, e.g., by a mixture of two differentemulsions: one, with a small toe and a ratherlong straight line portion, would have to be usedin such a quantity as to yield only a relatively

DCs)

l-o lo3 et'O.

FIG. 5. The transmission curve corresponding to astraight line reflection curve. In order to obtain a straightline reflection curve (1) a transmission curve of the form(3) would be required. (2) shows the transmission curvewhich would yield curve (1) if no silver reflection occurred.The difference between (2) and (3) illustrates the influenceof the silver reflection.

-, (5) low F and possibly a low maximum density; thedL other, much less sensitive emulsion should have

assuming G to a very high r and a very distinct "toe."Whichever the form of the paper curve may

be, obviously the transmission curve must beL) (6) convex toward the log E axis at least up to theI transmission point which corresponds to the inflection pointstment of the of the reflection curve (which practically repre-,an be written sents a short straight line portion). The inflection

point of the transmission curve, therefore, willbe situated beyond this point. Since the inflection

(6.1) * In this connection it is interesting to note that thestraight line portion has virtually been abandoned in theEastman Kodak papers, as Jones has recently stated. In view

A transmis- of the results obtained, however, e.g., with the chromategelatin processes, papers of this type might still be of

ambling curve considerable interest for some purposes.

583

go=

FRANZ AND ANNIE URBACH

point of the paper curve is situated at rather highdensities with all papers which are in practicaluse, by far the largest part, if not the whole, ofthe characteristic curve of the paper will cor-respond to the "toe" of the transmission curve.This has been stated long ago as an empiricalrule by Renwick: "The gradation of silverprinting papers is due to the under-exposureperiod of their emulsions." 6

Though the gradient of the transmission curvein most of the cases shows some increase beyondthe inflection point of the paper curve, as hasjust been pointed out, this increase ordinarilywill not be made very large, since it would haveno strong effect upon the behavior of the papercurve in the important shoulder region; in thisregion no practically obtainable steepness of thetransmission curve is able to make up for theincreasing effect of the silver reflection.

III. THE "SHOULDER" OF THE REFLECTION

CURVE AND A RULE OF JONES'S

In his thorough investigation of the contrastof printing papers Jones7 gave as a by-product athumb-rule concerning the upper part of thereflection curve; the density Db at the upperpoint b, where G=0.2, is situated about 0.02below the maximum density:

Dmax-Db=A 0.02. (7)

The figures in this purely empirical rule seemto be purely accidental. The facts which werediscussed in the preceding part make possible,however, some approximate general statementsconcerning the so-called shoulder region. Usingthe definition (5) we get from (4)

Ro/A = 1- G/ng. (4.2)

At the "critical" point b the log Ro/Ab means thedifference Dmax-Db. Since Ro/Ab is certainlynot far from unity, we find

A = 0.43Gb/ngb- (4.3)

Of course, we generally do not know the valueof g corresponding to the point b; but we doknow that in almost every practical case it willnot be far from the G that corresponds to the

6 F. F. Renwick, Phot. J. 37, 127 (1913).'L. A. Jones, J. Frank. Inst. Z02, 177 (1926); 203, 111

(1927); 204, 41 (1927).

FIG. 6. "The up-per limitingpoint." Distance

/ 0° of the upper limit-a / ing point from the

o maximum densityas a function of r.

.02- -o … The points areaverage values

o from Jones's work.The dotted linerepresents Jones's

(.0 y/r rule, the solid lineformula (8).

inflection point of the paper curve, though pre-sumably a little larger. Thus we may-as a firstapproximation-write

ng=r/( -Ro/A*), (4.4)

where r means the maximum value of G and A*the albedo at the inflection point (or rather atthe upper end of the straight line portion).Since, as we mentioned already, the inflectionpoint is usually not far from the shoulder, thevalue Ro/A* is mostly of the order of ", and, as avery rough approximation, we may put ng = 2F,keeping in mind that this represents rather alower limit. Thus we get

A = 0.43Gb/2r - 0.04/r. (8)

With 37 types of papers investigated by Jones,the average value of F is about 1.7 ; so the averagevalue of A should be near A-0.025.

This is virtually the rule of Jones. We shouldexpect, however, that this value might be rathertoo large. In fact, the average from Jones's datais about 0.015. In any case, our considerationsenable us to understand well the order of mag-nitude of Jones's constant.

Formula (8), however, suggests a modificationof that rule. While Jones states one approximatevalue of A, whatever the constants of the emul-sion might be, our equation indicates that thepoint b should be nearer the maximum densitywith emulsions of more contrast.

The material of Jones enables us to check therelation (8) although only very roughly,* byplotting the available values (or average values)of Gmax against the corresponding A: The result,represented by Fig. 6, seems to show that themodification of Jones's rule, suggested by the

theory, means a distinct improvement.

* The values of A are given but roughly and the valuesof Gmx fluctuate widely with constant A.

584

CHARACTERISTIC CURVE OF PHOTOGRAPHIC PAPERS

The critical point b, discussed above, is im-portant for the definition of an approximativemeasure of contrast as will be shown in thefollowing part.

IV. THE MEASURE OF CONTRAST

Numerous attempts have been made to definea measure for the contrast of papers in a waymeeting the practical requirements. In theauthors' opinion, however, none of these attemptsis better based on psycho-physiological con-siderations and none better checked by practicaltests than the measure given by Jones in hisclassical paper.'

Recently Boutenbal 8 compared virtually alldefinitions given by different authors with a veryextended material of practical tests, using variouscommercial papers. He finds five of the formulae-including that of Jones- to be in very goodagreement with his statistical data. Three ofthem, however, are the average gradients orexposure scales in a range, the upper limit ofwhich is given by Dmax-0.1. If these measureswere generally accepted, it would be very easyto produce papers of "high contrast," simply bymeans providing for a very low value Dinax. (Thiscriticism is, to a certain extent, analogous toJones's well-known argument against the DINsensitivity measure.) The fourth measure, theone proposed by Reinders and Boutenbal, is theexposure scale between D=0.25 and D=0.9. Itis, however, obviously not desirable to make thejudgment of contrast quite independent from thehighlights and the deep shadows. Only the factthat all the papers used by Boutenbal had ratherwell-balanced characteristic curves, preventeddisagreement of this measure with the judgingof the prints.

Jones' formula, the fifth, being in good agree-ment with Boutenbal's test, is in no way met bythat kind of criticism. It belongs, however, tothose which, in Mr. Boutenbal's opinion, "requiretoo great an amount of work for determining thecontrast value." In fact, the determining of thecontrast value according to Jones's rigorousdefinition involves an enormous amount of work.It will be shown below how this difficulty can beovercome, owing to some approximate relations

I C. Boutenbal, Phot. J. 78, 76 (1938).

between the magnitudes involved. The measureof contrast according to Jones is: the product ofthe numbers of just perceptible differences in-cluded in the density scale, by the averagenumber of just perceptible differences per unitdifference in log E. This means, practically, theproduct of the density scale by the averagegradient of the paper, within that part of thecharacteristic curve that is actually used inmaking pictures. The determination of theactually used part of the scale, however, as wellas that of the average gradient within givenlimits, is a very complicated procedure, if it isto be made in accordance with the strict require-ments of Jones's psycho-physiological consider-ations.

Jones has shown that, in order to find theactually used part of the density curve, a sta-tistical method is necessary, using several testnegatives, a series of copies, and the opinion ofseveral experts. The limiting points and theranges of exposure and density determined inthis way are widely different from those fixedby any simple rule, like the postulate that G = 0.2.

The determination of the average gradient,according to Jones, has to be made with respectto equal increments of densities, not, as usually,with respect to equal increments of log exposure.Jones has shown that this correct G(D) differswidely from G(L).

Keeping in view, however, the S-like shape ofthe H and D curves and the location of thelimiting points at its "toe" and its "shoulder,"it is easy to see that a shifting of the limitingpoints influences the density scale and the G(D)values by the same order of magnitude but in theopposite direction. Although the postulate G = 0.2for the limiting points yields quite wrong valuesof the density scales as well as of the averagegradient, the product of these values is affectedbut little by these errors. This statement can besubstantiated by data from Jones's original paper,where all the values discussed here are to befound. Moreover, a remark in a more recentpublication 9 of Jones and Morrison shows thatthe Kodak Laboratories use practically thelimiting points G = 0.2 with quite satisfactoryresults.

I L. A. Jones, J. Frank. Inst. 228, 445, 605, 755 (1939).

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FRANZ AND ANNIE URBACH

I.O

/

/

/ /

aA

.

./

/ 0

cc,

I/

/

/

lo Issn 1.5

FIG. 7. Comparison of the values of contrast according toformula (9) with Jones's values (logarithmic scales).

There remains, however, the difficulty of cal-culating correctly G(D). This requires unusuallyexact determination of the H and D curve andits graphical differentiation (or a special equip-ment) and then some computation and graphicalintegration. In spite of some interesting simpli-fications found by Jones, quite a lot of workremains. This might be avoided in the followingway: If G(D) is replaced by the usual averagegradient (L) with respect to equal incrementsof logE-which is simply the quotient of thedensity scale over the exposure scale-it isobvious that much more stress is laid on the flatparts of the transmission curve than on thevalue G(D). Just the opposite error would bemade by replacing (D) simply by the maximumvalue of the gradient, r. This suggests the replace-ment of (D) by a mean value of both, e.g.,(r XG(L)) . Using Jones's data, this was found tobe feasible. Thus, on the basis of our considera-tions, we are led to try the following formula asan approximation for Jones's measure of contrast.

c = (r/x)is 1(9)where o is the density scale, X the logarithmicexposure scale, both between the points whereG=0.2. The value of contrast according to thisformula can be read from any H and D curvewith reasonable accuracy. The major source oferror is involved in the determination of thelimiting points where G=0.2. It was, however,mentioned already as a basis of the deduction of

this formula that a shift in the limiting pointdoes not matter very much. We formulate thisnow by differentiation of formula (9); takinginto account that, at the points in question,do=0.2dX, we get

dc/c = 2 X (0.6/0(L) - 1)dX/X. (9.1)

Using Jones's data for G(L) it is found that therelative error in the determination of the contrastdue to the error in the limiting points is on theaverage only of the relative error of X (evenin the most unfavorable case found in Jones'material this error does not exceed that of ).

Figure 7 shows the contrast as determined byformula (9) as a function of the contrastevaluated according to Jones's strict definition.The sequence of Jones's 37 types of papers withrespect to their contrast is practically the samewith both measures. The correlation coefficientis found to be 0.997, the few differences in therank order are of no significance at all.

In only three cases does the change of Cnecessary to make both orders identical seem toexceed the limits of error, and in no case does itexceed 4 percent of the total range covered bythe C values. In order to appreciate this agree-ment, let Jones's measures be compared with thatrepresented by (L). In this case the maximumchange of C necessary to "restore the order" isabout 25 percent. If the contrast values aregrouped, as usual, into 5 or 6 classes, this errorexceeds the whole range of at least one of them.With the measure given by formula (9) thiscould happen only if 25 or more classes of con-trast were to be established.

It may be mentioned that formula (9) givesnot only the same rank order as Jones's measure,but can be regarded as a good numerical approx-imation, as shown by the dotted line in Fig. 7.Jones has proposed, more recently, the use of thelogarithm of his measure as a characteristic ofcontrast. This can be done, of course, with ourapproximation with practically equivalent re-sults. The authors would consider the possibilityof using the square root of C for the samepurpose. This is suggested by the fact that,according to Jones's definition, his measure con-tains a product of two reciprocal values of leastperceptible differences. Any monotonically in-creasing function of a measure of the kind in

586

CENTRAL NOTATIONS FOR ISCC-NBS COLOR NAMES

question may be chosen to fit best the practicalneed for conveniently spaced values. The essen-tial meaning of such a formula, however, is notexpressed by those values, but by the rank orderit establishes for its objects, which is not affectedby such numerical changes.

Formula (9), which we propose as a practicalbasis for the rating of contrast, uses just thosemagnitudes which many authors have felt to beall-important for the same purpose. While these

SEPTEMBER, 1941

magnitudes have already been combined in dif-ferent simple ways, we propose a combinationwhich seems, at first glance, rather odd, but whichis justified, however, by its close relation toJones's definition of contrast. While formula (9)is thus founded on Jones's psycho-physiologicalconsiderations and his comprehensive empiricalmaterial, and supported also by Boutenbal'sstatistical investigations, its evaluation seems tobe simple enough to encourage its practical use.

J. 0. S. A. VOLUME 31

Central Notations for ISCC-NBS Color Names

DOROTHY NICKERSON,' Agricultural Marketing Servce, U. S. Department of Agriculture, Washington, D. C.

AND

SIDNEY M. NEWHALL,2 Psychology Department, Johns Hopkins University, Baltimore, Maryland

(Received July 14, 1941)

THE problem of developing color designa-tions "sufficiently standardized to be ac-

ceptable and usable by science, sufficiently broadto be used by science, art, and industry, andsufficiently commonplace to be understood, atleast in a general way, by the whole public"was presented to the Inter-Society Color Councilat its first meeting in 1931 by the Revision Com-mittee of the U. S. Pharmacopoeia.

A report in 1933 (1)' of the Council's Com-mittee on Measurement and Specification, I. H.Godlove, Chairman, provided the basis whichwas followed in developing what is now knownas the ISCC-NBS4 System of Color Designation.Setting boundaries for these color names provedto be the greatest problem, but in 1939 the workwas completed at the National Bureau of Stand-ards with the aid of the American PharmaceuticalAssociation and the U. S. Pharmacopoeial Re-vision Committee who for this purpose jointlysupported a research associateship at the Na-tional Bureau of Standards. The Inter-SocietyColor Council in 1939 formally approved by

I Color Technologist, and Chairman of the ISCC com-mittee to obtain central notations for ISCC-NBS names.

2 Member of committee.3Italic numbers in parentheses refer to literature cited,

p. 591.4 Initials are for Inter-Society Color Council-National

Bureau of Standards.

letter ballot' and recommended to the U. S.Pharmacopoeial Revision Committee the methodas described in a report by Judd and Kelly (2).Delegates from the Optical Society of Americawere active in cooperating with those from othermember bodies and with individual members indeveloping this method.

The method adopted is simple in principle.The terms light, medium, and dark designatedecreasing degrees of lightness, the adverb

TABLE I. Abbreviations for use with ISCC-NBS system ofdesignating colors

NOUN FORM ADJECTIVE FORMOF HUE OF HUE ADJECTIVE MODIFIERS

Pk pink pk pinkish It lightR red r reddish dk darko orange o orange wk weak

Br brown br brownish str strongY yellow y yellowish mod moderate01 olive ol olive med mediumG green g greenish viv vividB blue b bluishP purple p purplish

Wh white ADVERB MODIFIERGr grayBk black v very

I Out of 27 votes received (33 possible), 26 were foradoption. Except for one association, and one ballotmarked "not voting," there were at least two affirmativevotes (out of a possible 3) from each association representedin the Council at the time the vote was taken. There wereno negative votes.

587