color correction in color printing^1

8
A. C. HARDY AND F. L. WURZBURG. JR. related in the following manner a=I-21'. (6) The aperture shown in Fig. 5 was designed to satisfy this relationship. This program was interrupted by the war at a time when we had made only a few printing plates by this method. Our tests have shown that faithful tone reproduction is easily achieved in the photographic images; but it should be men- tioned that the etching of printing plates is, in JOURNAL OF THE OPTICAL SOCIETY OF AMERICA general, a non-linear process. This non-linearity can be compensated, of course, by making appro- priate modifications in the shape of the aperture used to vary the width of the dots and spaces. As might be expected, four-color reproductions having this quasi single-line pattern did not exhibit the moire that is characteristic of con- ventional process printing. It will be shown in the following paper that full color correction can be automatically introduced during the scanning operation. VOLUME 38, NUMBER 4 APRIL, 1948 Color Correction in Color Printing' ARTHUR C. HARDY liassachusetts Institute of Technology, Camnbridge, Massachusetts AND F. L. WURZBURG, JR. Intercheinical Corporation, New York, New York (Received December 22, 1947) In a three-color print, the color of any area that is large in comparison with the size of the dots of the structured image can be regarded as an additive mixture of eight colors: the unprinted paper stock; the cyan, magenta, and yellow of the individual ink dots; the red, green, and blue that result when ink dots overlap in pairs; and the black that results when all three ink dots overlap. Since the ex- tent of overlapping is determined by the sizes of the dots, the color of the additive mixture can be expressed by three equations. The straightforward attack on the problem of color reproduction is to solve these fundamental equations for the required dot sizes on the assumption that, in every area, the tristimulus values of the reproduction should be equal to those of the original. This has not been accom- plished hitherto, because it involves solving three simul- taneous equations of third degree, each containing eight T HE preceding paper 2 has described a scan- ning machine that converts a continuous- tone photographic image into the structured type of image that is required by many printing processes. One purpose of this paper is to show how full color correction in either a three-color ' Extension of paper presented at the October, 1946 meeting of the O.S.A. 2 A. C. Hardy and F. L. Wurzburg, Jr., J. Opt. Soc. Am. 16, 295 (1948). terms. However, a relatively simple electronic equation- solving network has been constructed which solves these equations with ample precision in 0.001 second. By using this network in connection with a scanning machine of the type described in the preceding paper, full color correction is achieved. A corresponding set of equations can be written for the additive mixture produced in four-color printing, wherein the fourth color is black. Since the three equations now contain four unknowns, an additional condition must be imposed. From the standpoint of the printing require- ments, it is desirable that at least one of the color dots be absent, or of some predetermined minimal size, in every region of the reproduction. An extension of the principles embodied in the electronic network mentioned above imposes this condition and yields a continuous solution to the three fourth-degree equations. or a four-color process can be automatically introduced during the scanning operation. STATEMENT OF THE PROBLEM The starting point in any method of color printing is the making of three color-separation negatives, so-called. These are ordinarily made by photographing the subject (which may be a color photograph, an artist's sketch, or a scene 300

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Page 1: Color Correction in Color Printing^1

A. C. HARDY AND F. L. WURZBURG. JR.

related in the following manner

a=I-21'. (6)

The aperture shown in Fig. 5 was designed tosatisfy this relationship.

This program was interrupted by the war at atime when we had made only a few printingplates by this method. Our tests have shown thatfaithful tone reproduction is easily achieved inthe photographic images; but it should be men-tioned that the etching of printing plates is, in

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

general, a non-linear process. This non-linearitycan be compensated, of course, by making appro-priate modifications in the shape of the apertureused to vary the width of the dots and spaces. Asmight be expected, four-color reproductionshaving this quasi single-line pattern did notexhibit the moire that is characteristic of con-ventional process printing. It will be shown in thefollowing paper that full color correction can beautomatically introduced during the scanningoperation.

VOLUME 38, NUMBER 4 APRIL, 1948

Color Correction in Color Printing'

ARTHUR C. HARDY

liassachusetts Institute of Technology, Camnbridge, Massachusetts

AND

F. L. WURZBURG, JR.

Intercheinical Corporation, New York, New York

(Received December 22, 1947)

In a three-color print, the color of any area that is largein comparison with the size of the dots of the structuredimage can be regarded as an additive mixture of eight

colors: the unprinted paper stock; the cyan, magenta, andyellow of the individual ink dots; the red, green, and bluethat result when ink dots overlap in pairs; and the blackthat results when all three ink dots overlap. Since the ex-tent of overlapping is determined by the sizes of the dots,the color of the additive mixture can be expressed by threeequations. The straightforward attack on the problem ofcolor reproduction is to solve these fundamental equationsfor the required dot sizes on the assumption that, in everyarea, the tristimulus values of the reproduction should beequal to those of the original. This has not been accom-plished hitherto, because it involves solving three simul-taneous equations of third degree, each containing eight

T HE preceding paper2 has described a scan-ning machine that converts a continuous-

tone photographic image into the structuredtype of image that is required by many printingprocesses. One purpose of this paper is to showhow full color correction in either a three-color

' Extension of paper presented at the October, 1946meeting of the O.S.A.

2 A. C. Hardy and F. L. Wurzburg, Jr., J. Opt. Soc. Am.16, 295 (1948).

terms. However, a relatively simple electronic equation-solving network has been constructed which solves theseequations with ample precision in 0.001 second. By usingthis network in connection with a scanning machine of thetype described in the preceding paper, full color correctionis achieved. A corresponding set of equations can be writtenfor the additive mixture produced in four-color printing,wherein the fourth color is black. Since the three equationsnow contain four unknowns, an additional condition mustbe imposed. From the standpoint of the printing require-ments, it is desirable that at least one of the color dots beabsent, or of some predetermined minimal size, in everyregion of the reproduction. An extension of the principlesembodied in the electronic network mentioned aboveimposes this condition and yields a continuous solution tothe three fourth-degree equations.

or a four-color process can be automaticallyintroduced during the scanning operation.

STATEMENT OF THE PROBLEM

The starting point in any method of colorprinting is the making of three color-separationnegatives, so-called. These are ordinarily madeby photographing the subject (which may be acolor photograph, an artist's sketch, or a scene

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COLOR PRINTING

in nature) through a red filter, a green filter,and a blue filter. Regardless of the subsequentprocedures, these color-separation negatives mustproperly evaluate the color' of every elementalarea of the subject. Photographic positives madefrom these negatives will then represent the tri-stimulus values of every elemental area of thesubject; and the representation will be linear ifthe photographic operations fulfill the usual re-quirements of faithful tone reproduction in mono-chrome (i.e., reproduce a gray scale correctly).If three such positives are scanned simultaneouslyin proper register on a three-platen scanningmachine like that represented schematically inFig. 1, the three photo-tube currents will indicatethe tristimulus values of the subject as each ele-mental area is scanned in sequence. The problemis to use this intelligence to produce color-cor-

rected structured images from which printingplates can be made by standard procedures,without resort to hand correction at any stage.

DOT RATIOS IN THREE-COLOR PRINTING

The fundamental problem set forth in thepreceding section may be restated more preciselyas follows. Let the tristimulus values of anelemental area of the subject be represented insome colorimetric system by R, G, and B. If thephotographic positives on the scanning machinehave been properly prepared, the three photo-tube currents may likewise be represented (inappropriate units) by R, Gs and B. Then, if thetristimulus values of the corresponding area inthe reproduction are represented by R', G',and B', the color reproduction will be perfect if

FIG. 1. Schematic representation of a scanning machine adapted for scanning three photographic positives simul-taneously. The three positives A are attached to circular platens in the proper register. The platens are clamped to acarriage whose motions are identical with those described in connection with Fig. 2 of the preceding paper. Three scanningbeams produce photo-tube signals which are fed to computing channels in relay rack B whose output signals controlthe dot-producing circuit in relay rack C. The output signal from the latter actuates a light valve in the recording headD producing an intermittent exposure that results in recording a structured image on an unexposed photographic plateclamped to the fourth platen. The circular platens are rotated through an appropriate angle after each recording.

3 Since there may be areas of the subject which are unlike in spectral composition but nevertheless appear to the eye tobe of the same color, it is evident that the color-separation negatives must evaluate these areas in the same manner asdoes the human eye. In other words, the gammas of the three emulsions must be independent of wave-length within thespectral range transmitted by each filter and the spectral sensitivity curves of the three filter-emulsion combinationsmust correspond to the color-mixture curves of a normal observer for some set of basic stimuli. In the cycle of opera-tions to be described below, these are the only requirements that need be imposed on the filter-emulsion combinationsused in making the color-separation negatives. In other words, the spectral sensitivities of the filter-emulsion combina-tions are quite independent of the colors of the printing inks.

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A. C. HARDY AND F. L. WURZBURG, JR.

TABLE I.

Color Symbol Fractional Area

White w (I-c)(l-rn)(1-y)Cyan c c(1-m)(1-y)Magenta 7mt 171(1-C)(1-y)Yellow y y(l-c)(1- ni)Red my my(l -C)Green cy cy(1 - 1)Blue CM 1 -( -y)

Black cilly ciny

R'=R, G'=G, and B'=B for every elementalarea of the reproduction.

When printing from structured images, thetristimulus values R', G' and B' of any elementalarea of the reproduction are controlled by thesizes of the printed dots that lie within this area.In three-color printing each elemental area con-tains only eight colors: the unprinted paperstock; the cyan, magenta, and yellow of theindividual ink dots; the red, green, and blue thatresult when ink dots overlap in pairs; and theblack that results when all three ink dots overlap.Practices vary widely with respect to the orderin which the three inks are printed; but, sincethe theory to be developed here is applicable toany sequence, the alphabetical order (cyan,magenta, yellow) will be assumed. The dot ratiosin any elemental area of the structured imageswill be represented by m, c, and y, respectively.

A sheet of white paper that has received onlythe cyan impreession will have dots of cyan inkcovering a fraction c of each elemental area;whereas a fractional area (1-c) will remain un-printed. When the magenta impression is super-imposed, the magenta dots will overlap the cyandots in a fractional area cm, and will fall on whitepaper in a fractional area m(1 - c), by virtue ofthe effectively random distribution of the dots.By the same reasoning, the fractional areas ofthe cyan dots and of the white paper remainingafter the second impression are, respectively,c(1-im and (I-c)(1--m). When this reasoningis extended to include the third impression, thefractional areas occupied by the eight colors arefound to be as given in Table 1. The sum of thesefractional areas is unity, of course.

In some colorimetric system, let the tristimulusvalues of the white paper be represented byR., G, and B.. Similarly, let the tristimulus

values of the other seven colors be representedby R, G, and B with appropriate subscripts fromcolumn 2 of Table I. Then, in terms- of theseconstants, the tristimulus values R', G', and B'of the additive mixture of the eight colors withinany elemental area are

R'= (l-c)(l-m)(+-y)R ( R+c(1-m) (1-y)R+m(1-c) (1-y)R,+y(l - c) (1 -m)R+my(1 -c)Ry+cy(1 -m)R,+cm( -y)Rcm

+cmyRcmy, (la)

+c(l-m)(1-y)G,+m(1-c)(1-y)G,,,+y(l-c)(l-m)Gy+my(-c)GBmy+cy(1 - m)Gc+cm( -y)Gcm

+cmyG,,m,, (lb)

B'= (-c)(l-m)(l-y)B,,+c(l-m) (1-y)B,+m(l-c) (1-y)B.,+y(l-c) (1-m)By+my(l-c)Bmy+ cy (1-) B,+ cm (- y) B

+cmyBcmY. (c)

It is obvious that these equations will accuratelydescribe the color of the mixture of the eightcomponents under ideal printing conditions; andNeugebauer,4 who first published these equations,has shown that they apply in practice. Theequations are therefore useful in predicting thecolor gamut that can be achieved with a givenset of inks; but the primary purpose of thispaper is to show how these equations provide abasis for automatic color correction.

It has been stated previously that perfect colorreproduction will result when R' = R, G' = G, andB'=B for every elemental area. This assumptionof perfect reproduction can be introduced intothe above equations by merely substituting R,G, and B for R', G', and B'. Then, if the newequations could be made explicit for c, m, and y,the proper dot ratios would be known in terms ofthe color of the subject and the constant colorsof the eight components of the reproduction. Thefollowing section will describe a method by whichvalues of c, m, and y which satisfy these equationscan be determined and recorded as dots onstructured images at a rate of more than onethousand dots per second.

4 Neugebauer, Zeits. f. tech. Physik 36, 22 (1937).

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SOLUTION OF THE NEUGEBAUER EQUATIONS

It will be conducive to a better understandingof the method of solving the Neugebauer equa-tions if numerical values are substituted for theconstants, as has been done in Eqs. (2) for a setof high quality process inks and a typical printingroutine. These constants were determined bystandard procedures, the spectrophotometriccharacteristics of the eight colors being deter-mined with a sheet of white paper as the whitestandard. These spectrophotometric data werethen used to compute the tristimulus values ofthe eight colors, assuming Illuminant C and thestandard observer. 5 On this basis,6 the tristimulusvalues of the white paper are 1.000, 1.000, 1.000;those of the cyan ink are 0.146, 0.197, 0.613, etc.

R=R'= 1.000(1-c)(1-m)(1-y)+0.146c(1 -m)(1 -y)+0.442m (I -c) (1-y)+0.857y(1-c)(1 -m)+0.398my(1 -c) +0.064cy(1-m)

+0.033cm(1-y) +0.023cmy, (2a)

G=G'= 1.000(1-c)(1-m)(1-y)+0.197c(1-m)(1-y)+0.219m(1-c) (1-y)+0. 9 8 0y(1-c)(1-m)+0.206my(1-c) +0.196cy(1-m)

+0.014cm(1-y) +0.019cmy, (2b)

B=B'= 1.000(1-c)(1-m)(1-y)+0.613c(1-m)(1-y)+0.185m(1 -c) (1 -y)+0.1 4 8y(I -c)(1 -im)+0.012my(1 - c) +0.103cy(1 - m)

+0.120cm(1-y) +0.016cmy. (2c)

It will be evident from inspection of the aboveequations that, if they were solved explicitly forc, m, and y by analytical procedures, the resultingexpressions would contain terms of ninth degree.

American Standards Association, "Specification anddescription of color," Z44-1942.

6 The assumption of standard colorimetric procedures ismade in the interest of clarity of presentation, inasmuch asthe meaning of tristimulus values in the I.C.I. system isnow widely understood. By adopting this colorimetricsystem, however, freedom of selection of filter-emulsioncombinations for the color-separation negatives is restrictedto a single set; namely, a set whose spectral sensitivitycurves correspond to the mixture curves for the basicstimuli of the I.C.I. system.

Doubting that such an analytical approachwould be profitable, we7 undertook to devise ameans for handling the equations without makingthem explicit for c, m, and y. In view, of thenumber of solutions required (one for each dotin the reproduction), it appeared that onlyelectronic circuits could be made to operate withsufficient rapidity. The underlying principles in-volved in solving the equations electronicallywill be outlined here.

Imagine three electrical networks so con-structed that, when supplied with input signalsc, m, and y, their output signals will be R', G',and B', respectively. In other words, let eachnetwork perform the algebraic operations indi-cated by one of the equations. Imagine alsothree vacuum tubes whose plate currents provideinput signals c, m, and y to these networks. Theproblem is then to adjust the values of thesethree plate currents until the output signals R',G', and B' are equal, respectively, to the photo-tube signals R G, and B. In general, R', forexample, will not be equal to R, but the disparitybetween R' and R can be used to control thegrid of the vacuum tube whose plate currentis c in such a manner as to tend always to reducethe disparity. Then, if the disparity between G'and G is used to control m, and the disparitybetween B' and B is used to control y, all threedisparities can be reduced simultaneously. Byintroducing sufficient gain into these feed-backcircuits, the three disparities can be made sub-stantially zero. Under these conditions, the platecurrents c, m, and y of the three vacuum tubesrepresent the required solutions of the equations.These currents can then be used, one at a time,to control the dot-producing circuit described inthe preceding paper.

THE SCANNING MACHINE

In 1937, we published a paper8 which indi-cated the nature of the corrections that arenecessary in additive methods of color repro-duction and showed that the same corrections

7 Edward C. Dench took part in this development andis a co-author of the following paper which describes ingreater detail the means devised for achieving color cor-rection in both three- and four-color printing.

8 A. C. Hardy and F. L. Wurzburg, Jr., "The theory ofthree-color reproduction," J. Opt. Soc. Am. 27, 227 (1937).

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TABLE II.

Color Symbol Fractional area

White w (1-c)(1-mIn)(l-y)(l-nt)Cyan c c(1-m)(1-y)(1- )Magenta in n(1 -c)(1 -y)(I -it)Yellow y y( -c) (1-min) (1-n)Red ly my(1-c)(1-n)Green cy cy(1-?m)(I-n)Blue cO Cm (1 -y)(1- )Black cmry cy(l -n)Black n (1-c)(I-in)(1-y)nBlack ci c( 1-min) ( -y)nBlack itn in(l -C)(1 -y)nBlack yn y( 1-c) ( 1-m)nBlack Inyn iny(l -c)nBlack cyn cy(1-m)nBlackO cOn c((l-y)nBlack cnmyn cmyn

would suffice in subtractive methods if idealizeddyes or inks could be used. Earlier in that year,we had started the construction of a three-platen scanning machine to determine the ade-quacy of this relatively simple type of colorcorrection for letter-press printing. After makinga number of color reproductions, it was concludedthat color corrections of a higher order arenecessary, even when using the best of availableinks. We therefore undertook to solve theNeugebauer equations, which hold for any setof inks; but it was not until just prior to the warthat the equation-solving networks were incor-porated with the scanning machine. Tests showedthat these networks performed with sufficientrapidity and accuracy, and this was borne out bymaking three-color reproductions with full colorcorrection. For reasons discussed below, a fourthcomputing channel was then added to adapt themachine to the so-called four-color processes.

FOUR-COLOR PRINTING

One of the inherent disadvantages of three-color printing is the loss of detail that ensueswhen the three impressions are out of register.In four-color printing, the additional black im-pression carries much of the detail and makesthe registration less critical. For this and otherreasons, relatively little three-color printing isbeing done today.

An extension of the reasoning that led to thedevelopment of Eqs. (1) shows that an elementalarea of a four-color reproduction contains six-teen components, just double the number of a

three-color reproduction. These components arelisted in Table II, wherein the dot ratio of thefourth structured image is represented by n. Itwill be noticed that, since nine of the sixteencomponents are listed as black, their fractionalareas may be added together on the assumptionthat the tristimulus values of all black areas aresubstantially the same. When this is done, thefraction of each elemental area of the reproduc-tion occupied by black becomes cmy(1-n)+n.The Neugebauer equations for a typical four-color process then become

R=R'= 1.000(-c) (1-m)(1-y) (1-n)+0.146c(1 -m) (1 -y) ( -n)+0.442m(1 -c) (1 -y) ( -n)+0. 8 5 7y(l -c) (1-m) (1-n)+0.398my(1 -c) (1-n)+0.064cy(1-m) (1-n)+0.033cm(1 -y) ( -n)

+0.023cmy(1 - n) +0.023n,

G= G'= 1.000(1-c)(1-m)(1-y)(1-n)+0.197c(-m)(1 -y)(1-n)+0.219m(1 -c)(1-y)(1 -n)+0. 9 8 0y(l -c)(1 -m)(1 -n)+0.206my(1 - c) (1-n)+0.196cy(1-m) (1-n)+0.014cm(1-y) (1-n)

+0.019cmy(1 -n) +0.019n,

B =B'= 1.000(1-c)(1-m)(1-y)(1-n)+0.613c(1 -m) (1-y)(1 -n)+0.185m(1 -c) (1 -y) (1 -n)+0.148y(l -c) (1 -m)(1 -n)

+0.012my(1-c)(1 -n)+0.103cy(1 -m) (1-n)+0.120cm(1 -y) (1-n)

+0.016cmy(1 -n) +0.016n.

(3a)

(3b)

(3c)

The'solution of these equations presents a newproblem because the three equations containfour unknown quantities, c, m, y, and n. If n isassumed to be zero, the equations take the formof Eqs. (2) for the three-color case. At theopposite extreme, the maximum value of n isdetermined by the fact that c, m, and y cannot benegative. From the standpoint of good printingpractice, the maximum amount of black inkshould be used; and it was found that this canbe accomplished in the following manner.

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Let the equation-solving networks describedpreviously with reference to Eqs. (2) be modifiedso as to compute values of R', G', and B' inaccordance with Eqs. (3) when supplied withinput signals c, m, y, and n. Let the control ofc, m, and y be the same as before. The networkswill then automatically solve for values of c, m,and y which satisfy Eqs. (3), provided the inputsignal n does not require c, m, or y to be less thanzero. Now let the grid of another vacuum tubebe controlled by whichever of the signals c, m,or y has the smallest value at any instant, andlet the plate current of this tube supply theinput signal n to the equation-solving networks.The n signal will then be just large enough toreduce at least one of the input signals c, m, or yto zero. This n signal is then used to controlthe dot-recording circuit during a fourth scanningoperation to produce the structured image fromwhich the black plate is made.

Four-color reproductions made by this methodare, from the standpoint of accuracy in therendition of color values, virtually indistinguish-able from a three-color reproduction made undercomparable conditions. However, the progressiveproofs are very unlike those to which the art isaccustomed, as might perhaps be expected. Inthe first place, if a gray scale is included with thesubject, it is not reproduced at all by the colorplates but only by the black plate. On the otherhand, a color chart containing the eight com-ponent colors is not reproduced by the blackplate, except for the black area, which is notreproduced by the color plates. The appearanceof the progressive proofs of a multicolored sub-ject is, in many ways, even more striking becauseof their lack of resemblance to those produced byconventional procedures. Most striking of all isthe appearance of a progressive proof that hasreceived the three-color impressions but not theblack impression. The radical difference betweenit and a three color print of the same subjectamply justifies the view that three-color and four-color processes are essentially different methodsof color reproduction.

THE TWO TYPES OF COLOR CORRECTION

It is of some theoretical interest to analyzeand classify the two types of color correctionthat are intermingled in Eqs. (1) which, for this

purpose, are more conveniently rewritten in thefollowing form:

R' = R,,-(R. - R,) c-(R.-R,,) m- (Rw-Ry)y+(Rw-Rm-R+Rm,)my+ (R.-R-R,+Rcy)cy+ (Rw-Rc-Rn+Rcm)cm- (Rw-Rc-Rm-Ry,+Rmy

+Rcy+Rcm-Rcmy)cmy, (4a)

G' = G- (Gw-G,)c- (Gw-Gm)m- (Gw-G y)y+(G. -Gm-G,+Gm)my+ (Gw - G- G,+Ge,)cy+ (G-Gc-Gm+Gcm)cm- (Gw-Gc-Gm-Gy+Gm,

+Gcy+Gcm-Gcny)cmy,

B'=Bw- (Bw-Bc)c- (Bw-Bm)m

-(Bw-By,)y+(Bw-B.m-Bv+Bmy)my+ (B, -Bc-B+Bc,)cy+ (Bw-Bc-Bm+Bcm)cm- (Bw-Bc-Bm-By+Bmy

+Bcy+Bcm-Bcm)cmy.

(4b)

(4c)

Color Correction of the First Type

The nature of the first type of color correctionwill be obvious when it is recognized that, evenwhen the separation negatives properly evaluatethe colors of the subject, they inevitably do soin terms of a set of primaries which are not thereproduction primaries of the system. In ourearlier paper,8 we outlined an experimental pro-cedure for identifying the reproduction primariesin any subtractive process, the mathematicalequivalent of which is as follows. In some areaof the reproduction, let the dot ratio c be reducedby an amount Ac without altering the values ofm or y. This reduction in the size of the cyandots will increase R' by an amount AR', G' byan amount AG', and B' by an amount AB', where

AR'= - (OR'/dc)Ac,AG'= - (OG'/Oc)Ac,AB'= - (aB'/ac)Ac.

Hence, the tristimulusivalues of the reproductionprimary controlled by the size of the cyan dot arerepresented by the negative values of the partialderivatives of Eqs. (4) with respect to c. Simi-larly, the tristimulus values of the primariescontrolled by the magenta dot and by the yellowdot can be found by partial differentiation of

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these equations with respect to m and withrespect to y.

Assume for the moment that the printingprocess uses ideal inks whose spectrophotometriccharacteristics show no gaps between their ab-sorption bands and no overlapping of theirabsorption bands. It is easily shown that, forsuch ideal inks, the coefficients of my, cy, cm,and cmy in Eqs. (4) are all identically zero.Hence, in this case, perfect reproduction willresult when

R =R'= R,- (R.-R,)c- (Rw-Rm)m-(R.-R 1,)y, (a)

G = G' = Gu,- (G,-GJ)c- (Gw-Gm)l-(G.-Gv)y, (5b)

B =B'=Bu- (B,-B,)c- (Bu,-Bm)m-(B.-B ,)y. (5c)

For these ideal inks, the tristimulus values of thereproduction primary controlled by the cyan dotare seen by partial differentiation to be

- (OR'/ac) = (R. - )-(aG'/d c) (G.- G),- (B'/ac) = (B,-B,).

Similarly, the tristimulus values of the otherprimaries are (R. - Rm), (G,- G-), (B.- Bm) and(R. - R ,), (G. - G,), (B. - B,), respectively. Inother words, the reproduction primaries of thissystem are represented by the coefficients of thec, m, and y terms in Eqs. (5).

Now, knowing what the reproduction primariesare, it is theoretically possible to simplify mattersby imposing a further restriction on the separa-tion negatives. Instead of requiring merely thatthe separation negatives properly evaluate thecolors of the subject in terms of any arbitraryset of basic stimuli, let the choice of filter-emulsion combinations be such as to evaluatethe colors of the subject directly in terms of theamounts of the three reproduction primaries.This could be effected by selecting filter-emulsion

combinations whose spectral sensitivity curvescorrespond to the color-mixture curves that anormal observer would obtain if he were to usethe reproduction primaries as his basic stimuli.Such separation negatives would require no colorcorrection of the first type; and it would bequite proper to make the cyan plate from the rednegative, the magenta plate from the greennegative, and the yellow plate from the bluenegative. Of course, if the reproduction primariesare real colors, the spectral sensitivities of thecorresponding filter-emulsion combinations mustbe negative at certain wave-lengths.

Equations (5) indicate how separation nega-tives, whose spectral sensitivities are everywherepositive, can be made to serve in the productionof a faithful result with a set of real reproductionprimaries. By making Eqs. (5) explicit for c, m,and y, it is found that c, for example, is not afunction of R alone but is, in fact, a function ofboth G and B as well. Those who are accustomedto thinking in clorimetric terms will recognizethat these equations represent the well-knownlinear transformation by which data expressedin terms of one colorimetric system are trans-lated into corresponding data in another system.It is evident, therefore, that the second, third,and fourth terms in Eqs. (4) effect color correc-tions of the first type which, as our earlierpaper indicated, must be made even in additiveprocesses.

Color Correction of the Second Type

Our earlier paper introduced the concept ofstable primaries to describe the result of usingideal dyes or inks in a subtractive process. Withreference to the present analysis, partial differ-entiation of Eqs. (4) indicates just how unstablethe primaries are when physically realizable inksare used. Thus, the primary controlled by thecyan dot has tristimulus values as follows:

- (OR'/Oc) = (R,-R,) - (R. -R.- R+R 0 , )y- (Rw-Rc-Rm±Rcm)m+ (Rw-RcRm-R +Rmy +Roy +Rcm-Rcmy)my,

- (OG'/ac) = (G. -G) - (G. -G,-GG+G ,,)y- (Gw-Gc-Gm+Gcm)m+ (G. - G, G. - Gy +Gmy+Gc1y+Gcm - Gcmy)my,

- (OB'/ac) = (Bw,-B) - (Bw,-B-B , +B 0 , )y- (Bw-Be-Bw+Bcm)m+ (B.-Be-B,,-By+Bmy+Bcy+Bcm-Bcm1,)my.

(6a)

(6b)

(6c)

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COLOR PRINTING

As was indicated above, the coefficients of they, m, and my terms are found to be zero whenideal inks are assumed, and the tristimulus valuesof this primary are therefore constant. Whennon-ideal inks are used, the coefficients of theseterms make allowance for the overlapping of theabsorption bands of the three inks. It should benoted that the two types of color correction arecompletely intermingled in Eqs. (1), which, be-cause of their symmetry, are better adapted forsolution by electronic means.

COLOR CORRECTION IN FOUR-COLOR PROCESSES

It has been seen that, as a practical expedient,a four-color process can often be regarded ashaving nine components instead of sixteen. In-deed, if the black ink is black enough, the coeffi-cients of all the terms involving n as a multipliercan be assumed to be zero. Let this assumptionbe made in the interest of gaining some insightinto the nature of the color corrections in thistype of process.

Inspection of Eqs. (3) will show that, with thisassumption, the equations are exactly like thoseof the three-color case (Eqs. (2)), except for thecommon factor (1 -n). Hence, the right-handsides of Eqs. (3) become identical with those ofEqs. (2) when multiplied by 1/(1-n). Now,consider the physical significance of multiplyingR, G, and B by this quantity 1/(1-n), whosenumerical value is always equal to or greaterthan unity. Imagine a subject that is to bereproduced by a four-color process, and imagineanother subject like the first, except that thetristimuluA values of every elemental area of thesecond are 1/(1-n) times those of the first.This modified subject will be more luminousthan the original, but everywhere of the samechromaticity. Indeed, on the assumption thatcmy =0, the luminance of every elemental areawill be increased until it is equal to the maximum

luminance attainable at this chromaticity by thegiven set of colored inks, used in pairs. Thismodified subject represents the appearance thatthe four-color reproduction should have beforethe final black impression is made.

The literature pertaining to the art of four-color printing contains many erroneous state-ments concerning the amount of dot-size reduc-tion required in the color plates of a four-colorset. The straightforward method of determiningthe amount of reduction required would be tosolve the Neugebauer equations for values ofc, m, and y in the three-color case and then tosolve them again in the four-color case, makinguse of the additional fact that cmy=0. A com-parison of the results would then indicate theamount of reduction required in any area ofthe subject whose tristimulus values are R, G,and B. The fact that these algebraic operationsare too formidable to be considered seriouslyneed not deter us from the conclusion that thereare no simple rules by which a set of three-colorplates can be converted for use in a four-colorprocess.

MULTICOLOR PROCESSES

The electronic methods that have been de-veloped for solving the Neugebauer equationshave proved so satisfactory that extension toprocesses using more than four colors shouldinvolve no real difficulties. Of course, there willalways be only three fundamental equations,but they can be supplemented by the impositionof additional conditions, as -was done in thetreatment of the four-color case.

It is of interest in this connection to noteagain that, regardless of the number of im-pressions, the inks may be selected solely on thebasis of their color gamut. Their colors need notbe cyan, magenta, and yellow; nor is it requiredthat they be transparent. The way is thereforeopened for entirely new printing processes.

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