Color-reflection holography: theory and experiment

Color-reflection holography: theory andexperiment

Paul M. Hubel and Laszlo Solymar

We present a theoretical and experimental analysis of color-reflection holography. Full parallaxthree-dimensional color images are obtained by the superposition of wavelength-selective reflectionholograms recorded at eight combinations of three laser wavelengths. The test object used was a set ofeight Munsell color chips recommended by the Commission Internationale de l'Eclairage (CIE) for

color-rendering analysis. The spectral power distributions of all the holographic images are measuredusing a telespectroradiometer and corresponding points are calculated and plotted on a color diagram. Theholograms are modeled by a combination of sinc functions for the diffracted replay signal and anempirically determined function for the replay scatter noise. A new definition of signal-to-noise ratio forcolor holograms is described. The model is matched to a spectral power distribution by choosing values forrelative diffraction efficiencies, bandwidth, signal-to-noise ratio, and wavelength shift components. Onespectral power distribution having been matched, theoretical predictions of the remaining colors in theholographic images are obtained. The predictions mapped on the CIE 1976 diagram are shown to agreewith experimental results: the average distance between theoretical and experimental points on the CIEdiagram for all eight Munsell chips on all eight holograms is 0.0001 CIE 1976 chromaticity diagram unit;the discrepancy of the average gamut area between theoretical and experimental points on the CIEdiagrams was < 10%. Good agreement between theory and experiment having been shown, a synthesis ofholographic color reproduction at any combination of wavelengths predicts optimum recording wave-lengths of 460, 530, and 615 nm for typical replay by a color-reflection hologram.

Key words: Holography, color, display holography, reflection holography, color reproduction, colorrendering, color gamut, modeling of color holograms.

I. Introduction

This paper is a detailed analysis of the calorimetricproperties of color-reflection holograms. We presenttheoretical and experimental research on color imag-ing obtained by the superposition of three wavelength-selective reflection holograms.

The first attempt to analyze color holograms wasmade by Noguchi,' who recorded reflection hologramsof two-dimensional transparent objects in contactwith a holographic plate. When compensation wasmade for noise, extremely good color reproductionwas obtained with a large gamut of color. Transmis-sive objects, however, are capable of giving more

When the research was performed the authors were with theHolography Group, Department of Engineering Science, Univer-sity of Oxford, Parks Road, Oxford OX1 3PJ, UK. P. M. Hubel isnow with the Spatial Imaging Group, the Media Laboratory,Massachusetts Institute of Technology, E15-416, Cambridge, Mas-sachusetts 02139.

Received 4 February 1991.0003-6935/91/294190-14$05.00/0.Mcl991

saturated colors than are reflective objects; a three-dimensional transmissive color object could only besomething like a stained glass window. Also, when anobject is in contact with the plate, the process avoidsany interaction among different parts of the objectbeam.

True or natural color holography of reflective three-dimensional objects was first reported by Upatniekset al.2 and Lin and LoBianco3 and was accomplishedby the incoherent superposition of three holograms.Kubota et al.' improved the efficiency and the noiseof color holograms by using dichromated gelatinsensitized to red with Methylene Blue dye. The lowsensitivity and the difficult processing of this tech-nique led Hariharan7 to develop a two-layer sand-wiched silver halide method that uses two separateAgfa plates, one sensitized at blue-green and theother sensitized at red. Hariharan also improvedimage luminance by using a one-step limited-aper-ture image plane geometry (along with the two typesof silver halide). In Hariharan's research, the choiceof laser wavelengths and the spatial frequency re-

4190 APPLIED OPTICS / Vol. 30, No. 29 / 10 October 1991

sponse of the recording material in blue limited therange of color reproduction.

Sobolev and Serov5 and Kubota and Ose9 both useda hybrid process combining dichromated gelatin inone layer for the blue and green components andsilver halide in a second layer for the red component.This method overcame the 'low sensitivity and thedifficult procedure involved in using Methylene Bluesensitization for the red exposure and gained the highresolution and the low scatter found in blue and greendichromated gelatin holograms. In 1986 Kubotal'reached what is probably still the state of the art insignal-to-noise ratio and color saturation by using thehybrid technique with improved silver halide process-ing." Kubota's hologram, called "Dojo," is an excep-tional example of what holography can achieve.

The choice of laser wavelengths used in Kubota'sresearch still results in color reproduction of only alimited range of colors. Dichromated gelatin process-ing procedures require high-power lasers and humid-ity controlled laboratory conditions to achieve consis-tent results. Quantitative information concerningcolor reproduction by holograms is still limited.

Further improvements on Hariharan's 7 two-layersilver halide technique were made by Hubel andWard,'2 using Ilford emulsions that have better re-sponse in blue and using an improved choice of laserwavelengths.'3 The choice of laser wavelengths wasfound to be critical for achieving true color for acomplete range of colors.

The theory of color reproduction by holograms hasscarcely been touched. Many presumptions that 'ho-lography can produce better color reproduction thantelevision, etc.' have been based on little theoreticalor practical knowledge. The lack of analysis in thisarea has indeed caused much confusion and misunder-standing.

To our knowledge, the work of Komar et al.""'5 hasbeen the only major attempt at solving the manycolorimetric problems involved in holography. Theirresearch applies theories of color rendering to anidealized holographic reproduction, where the diffrac-tion from the hologram at replay is assumed to beidentical to the object beam at recording. Relatedresearch by Thornton'7 on color rendering of fluores-cent lights lends itself to holography but falls short ofan adequate explanation.

In this paper we describe a method for producingtrue color-reflection holograms in silver halide byusing multiple wavelength recording. The experimen-tal study concerns recording color-reflection holo-grams in a sandwiched layer of two Ilford emulsions.A theoretical model is presented and shown to agreewith experimental results when they are matched toone surface color. The theory is then used to synthe-size holographic color reproduction over a large rangeof wavelengths and noise levels.

II. Experiment

The basic principle of incoherent superposition ofthree holograms recorded at red, green, and blue laser

wavelengths'8 in a reflection geometry with fixedobjects and reference angles was used to recordcolor-reflection holograms. Separate object illumina-tions were used to control accurately the intensity ofthe reference and object beams. Image color wasproduced by the wavelength-selective nature of thethree-volume holograms on replay in white light.(The wavelength selectivity is similar to Lippmann'scolor photography, 9 but the type of color reproduc-tion is more closely related to that described byMaxwell.2 0 ) To eliminate color distortion and colormisregistration caused by image distortions,2 2 theon-Bragg wavelength and the angle were made equalto the recording wavelength and angle.

The techniques described above were used to createvirtual image color holograms of real objects. Our aimwas to produce a full parallax three-dimensionalimage that gave the same perceived color as the objectat every viewing angle. The methods described herecan be applied to projection holograms made fromthree masters recorded at the appropriate wave-lengths.

The decision to use Ilford film followed from adetailed comparison of silver halide emulsions forcolor holography.2 Two films recorded separately andlaminated together after processing were used (asother authors have done with plates7 ). One film(Ilford SP672T) recorded both the green and the bluegratings, and the other (Ilford SP673T) recorded thered grating, all in sequential exposures. Initial testswith a special Ilford panchromatic emulsion showedpromising results (true color holograms of reflectiveobjects with a complete range of colors were achieved)but the signal-to-noise ratio is still inferior to thatobtained by the sandwiched technique.

A. Basic Configuration

Figure 1 is a diagram of the basic setup for recordingcolor-reflection holograms. The three lasers werearranged so that different combinations of wave-lengths could easily be used at recording. The refer-ence beam diverged onto the hologram plane from anoverhead tower; this overhead reference allowed twobeams to be used for object illumination, one fromeach side of the plate. The distance between the

primary,mirrors

mIrro rswmounted ontranlatlonstages

I 4 1 Ar- LASER @4) 58, 488, 514, 529 shutters

W E KrLASERC>47nm

3 - HeNe=LASER633nmbs spatial

5 / >^w ~~~~~~~~~~~~~filters14so overhead | / ~~~~film g

beam spltte 6( - 11

beam splitter object:secdary sellmirrors so h gas

Fig. 1. Basic setup for recording color-reflection holograms.

10 October 1991 / Vol. 30, No. 29 / APPLIED OPTICS 4191

I.

pinhole and the hologram plane was 1.5 m. The beamratio (reference:object) was set to approximately 3:1for all experiments and not varied.

The 150 tilt geometry recommended by Ward et al.2 3

for recording reflection holograms was used to reduceimage blurring caused by dispersion under white-light replay. This geometry is important for colorreproduction because it gives superior registration ofthe color components and sharper edges in the image.

Ar', Kr', and He-Ne lasers were used for all thecolor test object holograms, which are comparedbelow with theoretical results. The configuration ofthe lasers is illustrated in Fig. 1. The mirror thatreflected the Ar' laser light was a stationary broad-band dielectric mirror that reflected blue and green.For the Kr' and He-Ne lasers, red-reflecting dielec-tric mirrors were used upon translation stages, asshown in Fig. 1. In all exposures the blue beam wasadjusted and exposed first (so that the laser modecould be checked before the plate was positioned inthe plate holder). Subsequently the Ar' laser waschanged to green and exposed, and finally one of thetranslating red mirrors was shifted into position andthe red exposure was made in a separate film.

B. Test ObjectsTo prove that a technique for color reproduction issuccessful, it is necessary to choose objects that canboth be analyzed scientifically and demonstrate (sub-jectively) that the process works. We used a set ofMunsell colored papers for the scientific tests andseveral different-colored three-dimensional objects(such as a mug of colored pencils'3 ) for the subjectivetests. The Munsell object comprised a two-dimen-sional Mondrian of 22 colored chips. (Initial experi-ments were conducted with an array of 46 Munsellchips.) These chips were actual swatch cards made atthe Munsell factory in Baltimore, Maryland. TheMondrian array included a pure white chip, a blackchip, two gray chips, and the set of eight chipsrecommended by the 1973 CIE Commission on ColorRendering.24 25 The eight color-rendering chips aresurprisingly unsaturated, but their points on a CIEdiagram are evenly spaced, giving a good representa-tion of color.26

One important limitation of holography is that itcannot record fluorescence. Many dyed and plasticobjects (most children's toys, e.g., Lego) achieve theirbright, saturated colors by fluorescence. Since thelight that is fluorescing is incoherent, it cannot berecorded on the hologram. As a result, objects illumi-nated under white light or laser light will not look thesame as their holograms. Fluorescence also affectsradiometer readings at recording making it difficultto adjust the exposure energy and beam ratio; it mayalso fog the plate.

C. Recording and Processing

The holograms discussed in this section were re-corded to support theoretical investigations. By record-ing holograms of a suitable test object at different sets

of wavelengths, we sought to obtain a strong founda-tion of experimental data affording a thorough com-parison with theoretical predictions.

Color-reflection holograms of the Munsell Mon-drian object were recorded at the eight combinationsof wavelengths listed in Table I. The blue and greenexposures were made in one layer of Ilford SP672T,and the red holograms were recorded in one layer ofIlford SP673T. Unfortunately, the latter emulsion isavailable in consistent form only on a triacetate filmbase. The exposure times were calculated from thepower levels measured, and energy levels were variedto adjust the color balance of the holograms.

The film was positioned in the recording plane by athin layer of index-matching liquid that, throughcapillary action, holds the film tight against a piece ofglass. For the Mondrian test holograms, the z position(perpendicular to the hologram plane) was not ad-justed to compensate for the film thickness, becausethe small error in alignment caused by displacementwould not have any effect on the color measurements(assuming that color measurements are taken nearthe center of each Munsell chip to avoid edge effectsand that the colors of the individual chips are uni-form).

The processing procedure used was a variation onCW-P1, which was used by Cooke and Ward" anddescribed in a past communication.'2 This methoduses the tanning developer pyrogallol, which leaves acharacteristic brown stain in the emulsion. The stainis useful in display holograms for absorption ofundiffracted light, which would otherwise be scat-tered at replay. The factors of diffraction efficiency,wavelength holding control, and signal-to-noise levelgave indications that this was one of the best process-ing schemes for color-reflection holography. No at-tempt was made to improve the processing proce-dure-which was used as a tool to investigate thecolor characteristics of reflection holography.

D. Replay and Measurement

Because the blue and green components were re-corded in one layer and the red component wasrecorded in another, the red hologram was mountedbehind the blue-green hologram. In this arrange-ment, both the illumination and the diffraction of thered hologram were attenuated by the blue-greenhologram. This attenuation was acceptable (except

Table 1. Eight Sets of Recording Wavelengths Used for RecordingHolograms of the Munsell Mondrian Test Object

Hologram Type Xl (nm) X2 (nm) X, (nm)

a 458 514 633b 458 514 647c 458 529 633d 458 529 647e 488 514 633f 488 514 647g 488 529 633h 488 529 647


for the resultant noise level) because the red holo-gram, having been recorded in its own layer, was ofhigher diffraction efficiency and brightness then ei-ther the blue or the green hologram. This configura-tion gave relative efficiencies in the range needed tobalance the components by adjustment of exposureenergies.

A standard 250-W tungsten slide projector wasused for the white-light replay illumination source forall measurements (of both holograms and test sur-faces). In a light source selected for display hologra-phy, the illumination should have a uniform distribu-tion over the area of the hologram, the diameter ofthe source should be small, and the intensity shouldbe high. The slide projector used in these experimentsis one of the best types of source for illuminatingholograms.23 This particular source is similar to CIEstandard source A and CIE standard illuminant C. Allcomparisons and calculations in this study were madewith this particular slide projector source.

The holograms were positioned upon a 150 tiltmount and reconstructed with a 450 overhead refer-ence source. This geometry was the same as atrecording and was used to reduce the effects ofdispersion blurring.23

All holograms were measured by using the telespec-troradiometer apparatus shown in Fig. 2 (built our-selves). We focused a telescope spot meter onto theimage plane by looking through an eyepiece andthrough the various points on the hologram. Thediffracted light from the hologram was collected bythe telescope and fed into a fiber-optic bundle. A lensplaced at the other end of the fiber bundle focused thelight on the input slit of a spectrometer.

We scanned the spectral power distributions (therelative spectral power distribution of the light com-ing from the hologram-the illumination source re-flected and diffracted by the hologram) between 380and 730 nm at 1-nm intervals by positioning thetelescope left, right, up, and down to measure all theMunsell chip images. The telescope was mounted in aplane parallel to the plane of the image and remainedfocused on the two-dimensional Mondrian image.Because the white image was always brightest, therange of the spectrometer was adjusted so that thepeak value gave the maximum voltage from the

Fig. 2. Telespectroradiometer apparatus used to measure relativediffraction efficiency of image holograms.

photomultiplier. (This adjustment normalizes thescans to this value-between 0.9 and 1.0 V.) Therange of the spectrometer was kept constant, but theother image colors in each hologram were scanned.All scans measured include the efficiency of thetelespectroradiometer system (optics, monochroma-tor, and detector), but this will not affect relativecomparisons. Wavelength scans of each image colorwere made through different areas on the hologram;the high expansion of the reference beam at recordingensured that differences of color through the dif-ferent parts of the plate were small.

E. Experimental Results

Figure 3 shows one of the wavelength scans taken ofthe Mondrian hologram. This sample is a white areaof the image. The chemical processing was controlledso that the center wavelengths were almost exactlythe same as at recording. The bandwidth of thediffraction and the level of background scatter noisewere typical for a reflection hologram recorded in a6-p1m silver halide emulsion.

The wavelength scans (spectral power distribu-tions) of various areas of the images were used to plotcolor points on the 1976 CIE Uniform Scales Chroma-ticity (USC) diagram. The necessary calculationswere made with a computer program that incorpo-rates some basic colorimetry.27 The same measure-ments were taken of the original object under thewhite-light source that was used to reconstruct theholograms.

IlI. Modeling of Signal and Noise

In Section II we described how we measured thereplay spectrum, that is, the amount of power as afunction of wavelength reflected by a particular areain the holographic image. Because the hologram wasrecorded by three monochromatic sources, we mea-sured three corresponding peaks in the replay spec-trum, as shown in Fig. 3. There is, of course, replayscatter noise appearing as a broad spectrum tailing offtoward blue and red.

00-

400 450 500 550 600 650 700wavelength, nm

Fig. 3. Relative spectral power distribution of a white image on athree-color hologram.


The question now arises how we could match themeasured curve of Fig. 3. No rigorous theories areavailable to tell us how the reflected power shouldvary in such a complicated grating as that in a displayhologram. Our philosophy was to try the simplestformula that is likely to lead to a reasonable approxi-mation. The simplest physical configuration that isrelevant to our case is a low-efficiency uniform reflec-tion grating.28 The wavelength response for perpendic-ularly incident beams (the angles of incidence in ourcase are 30° and 150, but that would make littledifference) is as follows:

sin xsinc(x) = x |

,rr(X - X)BXX,

where

B = 2 od ' (2)

d is the thickness of the emulsion and n is theaverage index of refraction. The function is unity atthe center wavelength X, and its first zero occurs at

AX = - = BXX, B, (3)

where B is a constant for each hologram that dictatesthe bandwidth.

Let us see now how well Eq. (1) describes themeasured bandwidth. Taking d = 6 pm and no = 1.6,we obtain AX = 10.9 nm at the blue wavelength of 458nm, AX = 14.6 nm at the green wavelength of 529 nm,and AX = 20.9 nm at the red wavelength of 633 nm. Itis difficult to determine the bandwidth from Fig. 3,but it may be clearly seen that we have a reasonableapproximation.

In practice, the grating is not of uniform amplitude,and it is likely that both the grating spacing and theaverage index of refraction vary a little with depth.Hence, strictly speaking, Eq. (1) is not applicable atall. It is certainly possible further to refine thetheory,28 29 but that it is not our aim in this paper. Wewish to find a simple approximate description of thereplay spectrum valid for all the chips, a descriptionthat we can use as a tool to evaluate all our experimen-tal results. The theory will enable us to attempt asynthesis, that is, to make some predictions concern-ing the optimum choice of recording wavelengths. Weshall, therefore, abandon the relationship between Band our other quantities [as expressed by Eq. (2)] andtake B as an independent parameter. (Unfortunately,it is difficult, if not impossible, to measure the gratingthickness accurately-particularly when the emul-sion is soft and contains an antistress layer.) We shall,however, retain the sinc function because, as will beshown below, it provides a good match with experi-mental results. Our universal function for the ithchip, which we expect to describe the intensity replayspectra of all the chips (since we describe intensity the

sinc function is squared), is then chosen in thefollowing form:

3

Di(X) = E(X) I , sinc(xi),jow '= BjXX '

(4)

wherej = 1, 2, and 3 refer to the blue, green, and redcomponents, respectively. nij is the relative diffractionefficiency corresponding to the image of the ithsurface in the jth wavelength component, XCJ is thecenter wavelength (not necessarily the same as therecording wavelength) of the jth component, andE(A) is the spectrum of the replay light source. Notethat Bj is now an independent bandwidth parameterthat is experimentally determined and depends on thecharacteristics of the emulsion layer that contains the

jth grating component.Next, we need to find some functional description

of the noise. There are basically two kinds of noise,recorded noise gratings and replay scatter. Noisegratings are recorded by the interference between thereference beam and the scatter of the reference beamby the silver halide crystals.30 3' Fortunately, theeffects of noise gratings in display holograms canusually be avoided by slight geometrical alterationsbecause noise gratings are extremely sensitive toreplay angle. Replay scatter, however, is common indisplay holograms, particularly when western silverhalide emulsions and rehalogenating bleaching areused. At replay, the undiffracted components of thewhite-light illumination are scattered by the crystalsin the processed emulsion.

Replay scatter noise depends on processing; someprocessing methods give higher levels of scatter thanothers, depending on how the chemistry affects theemulsion layer. Because it is so important that colorholograms replay close to their recording wave-lengths,2' the types of processing that can be used arelimited to those that do not change the emulsionthickness. As a result, the procedure of using a fixingagent that removes undeveloped silver halide grains(which would decrease noise but also shrink thelayer) is avoided.

The noise measured experimentally in the replayspectrum always appeared to be of the same shape,giving rise to the hope that we can describe it by afairly simple function valid for all our holograms-although the magnitude of the noise would of coursevary from hologram to hologram. The polynomialfunction fitted to the observed noise [observed whenreplayed by the light source E(A)] was taken in thefollowing form:

E(X)N(X) = 1.1 - 8.3

x 10-3 X + 2.3 x 10-5 X2 - 2.9 x 10-1 X3+ 1.3 x 10-11 4, (5)

where is given in nanometers. This form hasalready included a normalization, namely, our func-tion obeys the relationship

f E(WN(My(X) dh = 1, (6)


where y() is the y-tristimulus function that accountsfor the luminous efficiency of the eye.27 To describethe noise observed, we obviously need one more freeparameter. The replay spectrum, including both sig-nal and noise, will therefore take the form

Di(X) = E(X) [i qu sinc'(xj) + - N(X)], (7)

where r is a constant to be related to the signal-to-noise ratio of the hologram.

The signal-to-noise ratio has been defined by Hari-haran2 as

SNR = Il -12 (8)

where I, is the intensity at the brightest point on theimage and I2 is the intensity at the darkest point onthe image. A definition of signal-to-noise ratio moreappropriate for color holography would replace I, bythe total power of the brightest (usually white) and I2by the total power of the darkest (black) chips. Henceour definition is

R D(\)y(X) d - f D,(X)y(X) dX

J D,(X)y(X) dX

where D(X) is the brightest spectral distribution(usually a white chip) and Db(X) is the black spectraldistribution. Further simplification may be achievedby assuming that the i = b chip is perfectly black andgives only noise contribution so that Db(A) may bewritten as

N(X)Db(X) =- (10)

Substituting D.(X) and Db(A) into Eq. (9) and consid-ering Eq. (6), we obtain

3SNR = r E(X) 2 'qj sinc'(xj)y(X) d. (11)

J=l

Because the i = w chip is the brightest chip (usuallywhite), it follows that

Ri < r. (15)

We are now in a position to match a measured replayspectrum such as that of the purple chip shown inFig. 4. The choices of

11 pl = 0.12, flp = 0.13, llp = 0.25,

B = B2 = 0.065, B = 0.075, R, = 1.5,

AX,1 = -1 nm, AX,2 = -2 nm, AX,3 = +10 nm (16)

indeed lead to good accuracy [in this case E(X) is thespectroradiometer measurement of the slide projec-tor source]. Note that the subscript p refers to thepurple chip and that AXC, is the difference between therecording wavelength and the experimentally foundpeak replay wavelength. Because a sandwich of twodifferent materials was used in the experiments, it isnot surprising that the bandwidth-hologram emul-sion parameter, B, differs slightly between the blue-green and the red components. The red bandwidthparameter was found to be 15% larger than theblue-green bandwidth parameter.

We have to mention here that, although the normal-izations defined by Eqs. (6) and (12) are the mostsuitable ones for mathematical simplicity, they wouldlead to rather odd values on the vertical scale. Weadopted a normalization based on the measuredresults, which, for convenience, were presented on a0-1 vertical scale. The normalization makes, of course,no difference since the color mapped to the CIEdiagram depends only on the spectral distribution,which is determined by the relative efficiencies and onthe relative values of signal to noise.

IV. Relationships among the Replay Spectra of theVarious Chips

Having chosen the relative diffraction efficiencies,bandwidth levels, hologram signal-to-noise level, and

Until now the magnitudes of the diffraction effi-ciencies, 'qb, have been arbitrary. It is only theirrelative values that are determined by the hologram.If we now introduce the further normalization so that

3

f E(A) q .. j sinc(xj)y(X) d = 1, (12)

then, by definition,

SNR = r, (13)

0.7

0.6

a)` 0.5

0)- 0.4

aN'0.3

o 0.2r_

which we define as the hologram signal-to-noise ratio,a figure describing a property of the hologram. Wemay also define a signal-to-noise ratio for each chip bythe relation

0.10

0400 450 500 550 600

wavelength, nm

Ri = r f E(X) 2 n sinc2 (xj)y(X) dX.J=1

(14) Fig. 4. Model matched to the purple chip spectral power distribu-tion of the type c hologram.


650 700-

shifting components, we have modeled the spectralpower distribution of one holographic chip image byfour simple functions (the sinc2 and noise functions).Using the parameters determined by the matchedsurface, we can make theoretical predictions of thecolors of the other surfaces in the same holographicimage based solely on the original surface reflectancesof the object chips at the recording wavelengths. Foreach hologram, all image points are assumed to havethe same noise level, bandwidths, and shifting compo-nents.

A. Linearity

The last factor that could affect color reproduction bya color hologram is the relationship between objectbrightness and image brightness.2" 6 2 When a mono-chromatic display hologram is recorded, the strengthof the signal beam varies with position on the object.At replay, the hologram reproduces this variation ofbrightness in the image by way of a variation in theefficiencies of the component gratings. The plot inFig. 5 shows a linear relationship between theamounts of light radiating from the various positionson the object and the corresponding positions on theimage. Because initial results indicate that this rela-tionship is linear, it will not affect the color reproduc-tion capabilities of the hologram. If this relationshipwere not linear, it would have a considerable effect onthe color reproduction. (One might expect this effectto come from some material characteristic.)

B. Surface Reflectances

To obtain the spectral power distributions of theremainder of the surfaces in the holographic image,one must first obtain the spectral surface reflectancedistribution of the surfaces. The spectral power distri-bution of each surface is measured under our stan-dard slide projector source, and then the distributionof the source is divided out (the source data aremeasured with the same spectroradiometer so thespectral efficiency of the device is also divided out).

C

.Ea0 6m E

0 s 50 E C

' a0 .'

0) 8

g,2 0-=1

(d 0

Fig. 5.

11099.

The surface reflectance distribution of the ith chip,Si(X), is thus obtained. (This is a continuous functionover the entire visible spectrum.)

The results from subsection IV.A support the as-sumption that for each component hologram thediffraction efficiencies from various positions of theholographic image are linearly related to the amountof laser light reflected by the corresponding positionson the original object. The ratio of the diffractionefficiency of the image of the ith chip, ij over that ofthe matched chip, lmjX is equal to the ratio of thecorresponding surface reflectances. That is,

(17)

C. Predicted Replay Colors

Figure 6 plots three theoretical predictions of thespectral power distributions for the red-purple, blue-green, and orange chips in the holographic image andthe corresponding measurements made from thehologram made with the 458-, 529-, 633-nm (type c)wavelength combination. Using a computer program,we mapped the spectral power distributions to pointson the 1976 CIE USC diagram. Figure 6(d) illustratesthe theoretical prediction of the eight Munsell chipscompared with the measured results. The predictedcolors of the eight Munsell chips are in good agree-ment with the colors measured from the hologram.[Again, the replay source E(A) used in the calculationsis measured from the projector source, so both theo-retical and experimental points include the distribu-tion of this source and the efficiency of the telespectro-radiometer device.]

V. Comparison between Theory and Experiment

A. Eight Recording Wavelength Combinations

The purple chip spectral power distributions from alleight types of hologram are shown in Fig. 7 along withthe matched model for each hologram. Figure 8shows the corresponding set of eight octagons mea-sured from each hologram and the theoretical predic-tions generated as in Section IV.

B. Accuracy of the Theory

The chromaticity coordinates of two sets of colors(such as the theoretical predictions and experimentalmeasurements in each of the eight sets in Fig. 8) canbe compared by the average vector length, L0, whichwe define as

La = -2 [(u', -U`s') + ('' -V8j=1

0 2 4 6 8relative power reflected off the object when

illuminated by the recording source

Linear relationship between object and image bi

(18)

where u and v1" are the coordinates of the ith chip ofone set of points and u 2 and v,'2 are the coordinates of

10 the ith chip of the other set of points, all plotted onthe 1976 CIE USC diagram for the eight Munsellcolor-rendering chips.

right- Average vector length can be used to make a directcomparison between the u' v' point positions of the


f w

I ij-si(xj) .114 S.(Xi)

I

L

I

. . I. . .I- - I

0.7

450 500 550 600wavelength, nm

(a)

0.6

_ 0.5a)

m 0.4

N 0.3

0.10

00650 700 400 450 500 550 600

wavelength, nm

(b)


(C)

650 700

0.6

0.56

0.52V'

0.48

0.44

0.4 . . I . I .. . I

0.1 0.14 0.18 0.22 0.26 0.3

(d)Fig. 6. Theoretical predictions compared with measured data for the spectral power distributions of (a) the red-purple chip image, (b) theblue-green chip image, and (c) the orange chip image; (d) theoretical prediction of the Munsell octagon (dashed lines) compared with themeasured octagon (solid lines).

theoretical and experimental colors, Le. For the exam-ple shown in Fig. 6, the value of Le is 2.1 x lo-'chromaticity coordinate (cc) units, which shows thatthe theory fits the experimental chromaticity dia-gram point position to within four decimal places.

A second measure of accuracy of the theory isgamut area differences. The gamut area of the Mun-sell octagon can be calculated as the area of theoctagon within the points on the CIE diagram corre-sponding to the eight Munsell chips.26 For the exam-ple in Fig. 6, the area of the experimental gamut is1.7 x 10-3 CC

2 , and the theoretical prediction is 1.9 x10-3 CC

2, giving a difference of 2.0 x 10-i CC

2. When

gamut area is considered with respect to the gamutarea of the reference octagon (the eight Munsell chipsilluminated by white light), the experimental gamutis 39%, and the theoretical prediction is 45%, giving adifference of 6.3% (of the reference octagon).

Figure 8 illustrates the degree to which the theoret-ical predictions fit the experimental data for all eightsets of recording wavelengths. The average of theaverage vector length (point position deviation) be-tween the theoretical and experimental u' v' point

positions, L, for all eight types of hologram recordedin Section IV, is 1.2 x 10-4 cc. The average of thegamut area difference between the theoretical andexperimental octagons for all eight holograms is 4.3 x

0-4 CC2

, which is 9.9% of the area of the referenceoctagon.

VI. Optimization of Recording Wavelengths

The holographic color theory matches the spectralpower distribution to one particular holographic im-age and predicts the colors of other images in thesame hologram. The aim now is to analyze the colorreproduction by holograms recorded at all possiblewavelengths. To achieve this comparison, one mustmake predictions for the spectral power distributionat any set of three recording wavelengths, that is,matched to one particular color. From this match wecan predict the other image colors and calculateaverage vector length and gamut area figures ofmerit. The central issue here is how to predict thespectral power distribution at other wavelengths-inparticular, how signal varies with noise.


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500 550 600 650 700wavelength, nm

0 L

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650 700

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wavelength, nm

(c) 458:5,


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0650 700 400




0.7

29:647 0.6

0.5

5.0.4

0.3

9 0.2

0.10

00650 700 400 450 500 550 600

wavelength, nm

Fig. 7. Points on these diagrams are the purple chip spectral power distributions measured from all eight types of hologram that wererecorded with the experimental configuration in Fig. 1. The lines are the theoretical model matched to this color image.


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400 450

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650 700

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:C........... ~~. . . ..

0.14 0.18 0.22 0.26U.

Fig. 8. Having matched one of the color chip images between theory and experiment, we can see how well the theory predicts the colors ofthe other images. The colors of the Munsell chip images measured experimentally (solid lines) compare well with the theoretical predictions(dashed lines).


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I

A. Relationship between Signal and Noise

In recording holographic images the aim is always tokeep total diffraction efficiency high and the amountof replay scatter noise low. It therefore makes practi-cal sense to assume some kind of quality relationshipbetween maximum diffraction efficiency and theamount of replay scatter noise. The magnitude of thenoise component in a holographic image can bedefined by a new term, a, called the noise level. Weassume, for the comparisons in this paper, that theratio of these two quantities is constant for a particu-lar experimental configuration, namely,

3

2 constant for all hologramsa 1 recorded with a particular (19)a experimental configuration,

where j are the maximum relative diffraction effi-ciencies in a particular hologram. The noise level, oa, isa property of the experimental configuration (materi-als, processing, etc.) and is assumed to have a con-stant relationship with the maximum available diffrac-tion efficiency for holograms recorded at allwavelengths. This assumption is supported below bythe experimental results from Section II.

The spectral power distribution from a holographicimage can now be defined in terms of the noise level:

3

Di(X) = E(X) bn [ail sinc'(xj)] + aE(X)N(X), (20)

and from the definition of the hologram signal-to-noise ratio, r, we can determine a relation in terms ofthe noise level, a:

signal responsenoise response

J E() > [Aql j sinc'(x)]y(X)dX

a f E(X)N(X)y(X)dX

The relationship between this noise level and thesum of the maximum diffraction efficiencies from allthe component holograms can now be calculated fromthe experimental results. If we fix the noise level atsay a = 0.0157 for all eight holograms, we cancalculate the magnitude of the relative diffractionefficiencies, qwj, which are related to a by the corre-sponding hologram signal-to-noise-ratio, r (for eachof the eight holograms in Section II). Fixing the noiselevel for the eight holograms makes practical sensebecause the developed density of each hologram waskept constant. (Experimentally, there is a relation-ship between density and replay scatter for this typeof processing similar to that analyzed by Hariha-ran.") The average of the sums of the maximumdiffraction efficiencies, imax,tota1,avg) is 1.00. The stan-dard deviation of these values between the eightholograms is 0.23, and when the two extreme holo-grams are omitted (those with the highest and lowestr) the standard deviation falls to 0.091.

To obtain the condition of Eq. (19), we thereforekeep the maximum total diffraction efficiency con-stant as we vary wavelength. Thus we assume that

Thax,total = 'flwl + 1w2 + q1w3 = 1 (22)

for all wavelength combinations.The assumption of this simple relationship be-

tween "imaxtotal and a implies that for a given techniquethere is a total amount of modulation (availablediffraction efficiency), with respect to the backgroundnoise level, that must be shared among the threecomponent holograms. This assumption will dependon characteristics of the material and the processing.The relationship considered here is the simplest andmakes practical sense when one is considering silverhalide materials processed with the techniques usedfor this study. A more complex relationship may existfor other materials (such as dichromated gelatin,where saturation at 100% diffraction efficiencies canbe obtained for more than one component), but theserelationships should not have a great effect on the endresults and so are left for future work.

The holographic color theory is now normalized tothe physical constraints of the holographic media.Thus the hologram signal-to-noise ratio obtainablefor a particular experimental configuration will varywith the recording wavelengths: because our defini-tion of signal-to-noise ratio includes y(X), recordingwavelengths that are closer to the peak of y(X) willhave higher signal-to-noise ratios than those fartheraway.

Another advantage of this normalization is thatcomparisons between holograms recorded at differentwavelengths are now also dependent on the replaysource (because the same source is used for thecomparisons at different wavelengths). The shape ofthe source spectral power distribution will determineat what wavelengths the efficiency of the hologram isused most effectively, for example, for a tungstensource-like the one used in our measurements-gratings near the center of the spectrum will diffractmore light than those at the extremities [if the totaldiffraction efficiency is fixed as in Eq. (22)].

B. Balancing Components to White

Using the holographic color theory we can predict thecolor of the holographic images at any combination ofthree wavelengths. To make comparisons amongdifferent sets of wavelengths we must balance thethree components to a particular color. We balancedthe relative 'wi values to achieve a standard whitepoint on the CIE diagram (as was done by Thornton 7

by using monochromatic sources). The white refer-ence point used is the same as the coordinates of ourslide projector.

The balancing calculation was achieved by using aNewton-Raphson routine incorporating the color cal-culations for mapping between the spectral power


distributions generated by Eq. (20) and the CIEdiagram and under the constraint of Eq. (22).

The holograms compared in Section V (recorded intwo Ilford emulsions and processed as described inSection II) were found to have average values of B, =B2 = 0.065 for the blue and green components andB, = 0.075 for the red component and an averagenoise level of a avg = 0.0157. When these values arefixed, the color rendering (average vector length) andgamut area dependencies as functions of the record-ing wavelengths can be calculated.

A computer program was used to scan through alarge number of combinations of blue, green, and redwavelengths (in 1-nm intervals between the ranges of420-480, 500-560, and 580-660 nm for the blue,green, and red components, respectively-288,000combinations). For each set of wavelengths the spec-tral power distribution of a typical color hologram of awhite surface illuminated by the standard slide projec-tor light source, E(X), was calculated to match thewhite reference point [the point on the CIE diagramcorresponding to E(X)]. Each calculation requiredseveral iterations of the Newton-Raphson routine todetermine the relative diffraction efficiencies, From the calculated responses of the holographicimages at each wavelength combination, the averagevector length and color octagon gamut area werecalculated for the eight color-rendering Munsell chips.

C. Average Vector Length Synthesis

The wavelength combination in Table II gave the leastaverage vector length [B, = B2 = 0.065, B, = 0.075,a = 0.0157, illuminated and matched to E(X)].

Figure 9 shows the dependence of average vectorlength on wavelength. Two of the optimum wave-length components were held constant, while thethird was varied. Again, at each combination theholographic color theory was used to generate aspectral power distribution that was matched to thechromaticity of the reference white point.

D. Gamut Area Synthesis

The wavelength combination in Table III gave thelargest gamut area. The resulting gamut area was3.5 x 10-' cc2, which is 80% of the reference octagon(the eight chips illuminated by our standard projectorlight source). Figure 10 shows the dependence ofgamut area on wavelength, again with one wave-length varied while the other two are held constant.

E. Discussion of Results

The most noticeable aspect of these results is how thetwo figures of merit give similar optimum wavelength

Table II. Optimum Recording Wavelengths Determined by Minimizationof Average Vector Lengths for a Typical Hologram'

Optimum Wavelengths Xl X2 X,

Minimum average vector length = 0.00851 cc 464 527 606

pB1 = B2 = 0.065, B, = 0.075, and a = 0.0157.

0.05

o0.04

0.03

0C) 0.02

CZ

CZ

0 . . . . J . . . .400 450 500 550 600 650 700

wavelength of varying component, nm

Fig. 9. Dependence of the average vector length on wavelength.The wavelength, X, of one spectral color is varied, while that of eachof the other two is held at one of 464, 527, or 606 nm.

combinations. Thornton2 6 postulated that color ren-dering and gamut size were directly related, but,when the theory of the no-bandwidth, no-noise case(similar to his calculations) is used, the two figuresgave different results-especially for the red compo-nent. Nevertheless, the results given here narrow thechoice of optimum wavelengths alleviating the needfor some type of trade-off between the two figures ofmerit.

When Figs. 9 and 10 are compared with the corre-sponding no-bandwidth, no-noise curves (an equiva-lent to the average vector length curves were calcu-lated by Thornton 7 ), there are some importantdifferences.

Figure 11 shows the average vector length curve ofFig. 9 plotted together with a no-noise, no-bandwidthcalculation (similar to Thornton's results) on thesame scale. The red curve, in particular, has broad-ened and become more forgiving, especially at higherred wavelengths. From Fig. 11 we can conclude that acolor-reflection hologram recorded with 464, 527, and633 or 647 nm (point ( or (©) actually gives moreaccurate color point reproduction than that obtainedby the laser illumination alone (point ® or (0).

When gamut area is considered, however, the ef-fects of the holographic process are not so favorable.Figure 12 plots no-noise, no-bandwidth gamut areacurves along with Fig. 10. This comparison shows thereduction in gamut area resulting from the desatura-tion of the holographic process. Although in theexample above the accuracy of the holographic images

Table Ill. Optimum Recording Wavelengths Determined byMaximization of Gamut Area for a Typical Hologram'

Optimum Wavelengths X, X, X,

Maximum gamut area = 80.15% of ref. octagon 456 532 624

aB = B = 0.065, B = 0.075, and a = 0.0157.


450 500 550 600 650wavelength of varying component, nm

0.0043 200

0.0032

8

0.0022 (a

ECa

0.0011 0)

0.0700

a

cto 1600

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ts 120 _0

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400

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I I I I I

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450 500 550 600 650wavelength of varying component, nm

0.00650to

0.0043 2

.cm

0.0022

_ 0.0700

Fig. 10. Dependence of gamut area on wavelength. The wave-length, , of one spectral color is varied, while that of each of theother two is held at either 456, 532, or 624 nm.

may be higher than that of the laser illumination, theholographic octagon is smaller than the referenceoctagon, whereas the laser illumination octagon islarger than the reference octagon. This discrepancy isillustrated in Fig. 13; the inner hologram octagon(dashed lines) is closer in distance to the referenceoctagon (solid lines) than the laser illumination octa-gon (dotted lines) but has a much smaller gamut.These comparisons of average vector length andgamut area show how misleading one measure couldbe when considered on its own.

Vil. Conclusion

We have studied the properties of color reproductionby white-light illuminated reflection holograms byrecording a set of eight Munsell color chips in silverhalide emulsions, using eight combinations of record-ing wavelengths. The spectral distribution of each

Fig. 12. Dependence of gamut area on wavelength, as in Fig. 10(solid curves), plotted alongside the no-bandwidth, no-noise curves(dashed curves).

0.6

0.55

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0.45

0.4

A . .

A

A

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0)CDa)

a)

a)

a)Ce

0.04

0.03

0.02

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0* ........400 450 500 550 600 650 700

wavelength of varying component, nm

Fig. 11. Dependence of average vector length on wavelength, as inFig. 8(a) (solid curves), plotted alongside the no-bandwidth, no-noise curves similar to those calculated by Thornton (dashedcurves).

Fig. 13 Octagons comparing the holographic image (dashed lines)and the laser illumination (dotted lines) with the reference octagon(solid lines).

image was measured and modeled by a sine functionand by an empirically determined polynomial repre-senting noise. Good agreement was found betweenthe theoretically predicted and experimentally mea-sured image colors by plotting the respective pointson the 1976 CIE diagram. Finally, the theory wasused to search for the set of wavelengths that opti-mize color reproduction. The optimum recordingwavelengths were found to be 460, 530, and 615 nm.

We thank Andrew Ward for experimental adviceand Mark Neil for help with computing. We alsothank the Science and Engineering Research Council,UK, for support of this research. Paul Hubel thanksthe Rowland Foundation and the Rowland Institutefor Science.

Address all correspondence to P. M. Hubel.


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Color-reflection holography: theory and experiment

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