Multicolor Imaging from Holograms Formedon Two-Dimensional Media

R. J. Collier and K. S. Pennington

Multicolor image reconstruction from holograms behaving as two-dimensional media suffer severely fromoverlap of the similarly structured crosstalk images unless special techniques are used in formation. Thispaper describes examples of two techniques which eliminate the crosstalk images. The first techniqueinvolves nonoverlapping spatial multiplexing and is illustrated by interlacing on the hologram the coloredimages of a mask placed in the reference beam. The second technique involves coding the reference beamso that each colored reference wave varies in a unique manner over the hologram plate. Photographs ofthe resulting multicolor reconstructions are shown.

1. Introduction

The problems related to reconstructing multicolorimages from holograms behaving as planar diffractiongratings or two-dimensional diffracting media have beenbriefly discussed by several authors. When such holo-grams are formed with light of more than one colorand then illuminated with the same colors, a number ofspurious and generally overlapping images are generatedin addition lo the true multicolor image. This is notthe case for holograms formed as volume diffractiongratings or three-dimensional diffracting media. Thedifference in response of the two grating types is madeevident by considering the grating equations:

d,sini + sino) = X (planar grating),

2d sini = X (volume grating).

The planar grating equation states that, for light of anywavelength (X less than twice the grating period d)incident at tay given angle i to the normal of the gratingplane, a diffracted output will always be observed atsome diffraction angle 0. The volume grating equa-tion states that the incident and diffracted light mustmake equal angles to the diffracting surfaces in thevolume and that for a given angle of incidence i lightof only one wavelength X will be significantly dif-fracted. In the case of volume holograms that areilluminated with light of the same wavelengths and

The authors are with Bell Telephone Laboratories, Inc., MurrayHill, New Jersey 07971.

Received 8 I)ecember 1966.This work was presented at the San Francisco meeting of the

Optical Society of America, 19-21 October 1966; [J. Opt. Soc.Am. 56, 1499 (966)].

direction as the reference beams used in their forma-tion, significant diffraction takes place only in thosedirections required to recreate the original subjectwave. Spurious outputs are suppressed by the filteringaction of the volume grating; consequently, volumeholograms have been found to be a practical means forobtaining multicolor holographic images. '2 On theother hand, if multicolor reconstruction is desired fromplanar holograms, the broadband response of theseholograms requires that special techniques be used information. To obtain full color representation of asubject it is necessary to form the hologram with theproper proportions of the primary colors red, green, andblue. Leith and Upatnieks3 have suggested usingseparate reference beam angles for the three colors inorder to avoid overlap of the spurious red, green, andblue images, while Mandel4 has suggested a single ref-erence beam which contains red, green, and bluecolors of specified wavelengths and which makes aspecified angle with the subject beam. It is thepurpose of this paper to describe examples of twoadditional techniques which allow multicolor recon-structions from planar holograms and to presentphotographs of the multicolor hologram images re-sulting from the application of these techniques. Themethods reported here allow hologram formation withreference-to-subject beam angles small enough forrecording on emulsions of resolution lower than that ofKodak 649F. We have obtained multicolor recon-structions from planar holograms formed on KodakS0-243 acetate-base film. The S0-243 emulsion isconsiderably lower in resolution than 649F but isseveral hundred times faster.

11. Illustration of the ProblemTo illustrate better the problems of multicolor imag-

ing from a planar hologram, consider formation of such

June 1967 / Vol. 6, No. 6 / APPLIED OPTICS 1091

Fig. 1. Aphotographof a two-color reconstruietion from a planarhologram formed on 640F emulsion illustrating severe overlappingof the one true and two crosstalk images. That there are threeimages present may be determined by observing the t hlree (list inet

edges near the top of the figure.

a hologram as a result of the interference of red andgreen subject light with a phase-related red and greenreference beam. The required light may be derivedfrom a helium-neon and an argon laser. Since the redlight is incoherent with respect to the green light, theinterference pattern recorded on the photographicemulsion can be regarded as two superimposed holo-grams or gratings: one formed with the red light andthe other with the green. Upon illumination of thehologram pair with the original reference beam, a trueimage resulting from red light diffracting from the grat-ing formed in red light and green light diffracting fromthe grating formed with green light will be observed.However, the red light will also diffract from thegrating formed in green light to give an erroneouslycolored, displaced crosstalk image. Displaced to theother side will be a similar crosstalk image caused bygreen light diffracting from the grating formed in redlight. Figure 1 is a photograph of the resulting over-lapping images reconstructed from a hologram formedwith red light at 6328 A and green light at 5145 A anda reference-to-subject beam angle of 150. The subjectwas a color transparency backed by a ground glassscreen so that the light emerging from the subject wasdiffuse. Red and green reference light were combinedinto a single beam which was then incident on 649Fphotographic emulsion. The completed hologram wasilluminated with the identical reference beam. Thesevere overlap of the red and green crosstalk imageson top of the true image was caused by the hologrambehaving as a planar recording. The red crosstalkimage resulting from red light diffracting from the

Fig. 2. An arrangement for interlacing red and green referencebeams at the hologram plate. The lens is positioned to focus the

mask onto the hologram plate. The mask pitch is 1.4 mm.

hologram formed with green light is magnified by theprocess, and the corresponding green crosstalk imageis demagiiified relative to the true image.

111. Nonoverlapping Spatial MultiplexingOne way to eliminate color crosstalk is to form the

hologram in such a way that the various colored i nterfer-ence patterns are not allowed to overlap on theemulsion. To reconstruct, the color illuminating lightmust be incident on the hologram in such a mannerthat any given color illuminates only that portion of thehologram which had been formed with the same color.That is to say, we can spatially multiplex in a nonover-lapping manner the several holograms corresponding tothe several colors used. There are a great many waysto achieve this objective. A simple concept would beto place a mask consisting of a series of thin red, green,and blue color filter strips over the hologram duringformation and to replace it again in register for re-construction of the multicolor image. Of course sucha filter arrangement offers the possibility of using whitelight for reconstruction of multicolor images. We

Fig. 3. A photograph of a two-color reconstruction from a planarhologram formed on 649F emulsion. Elimination of the twocrosstalk images indicates the success of the nonoverlapping

multiplex technique.

1092 APPLIED OPTICS / Vol. 6, No. 6 / June 1967

Fig. 4. An arrangement used to code a three-colored referencebeam. The three colors are mixed into a single beam before

passing through the diffusing screen coding plate.

have chosen as al example to demonstrate the tech-nique of nonoverlapping spatial multiplexing onewhich was relatively easy to implement. The experi-mental arrangement is shown in Fig. 2. In this experi-ment we have chosen to interlace the red and greenreference beams incident on the photographic plate bymeans of narrow transparent slits in an opaque plateand an arrangement of a beam splitter, color filters,mirrors, and a lens. The lens is positioned to image theslit mask on to the hologram plate. The combinationof beam splitter, color filters, and mirrors allows sepa-rate images of the mask to be formed in red and green,and a slight tilting of one of the mirrors effects the inter-lacing of the two images on the hologram. This par-ticular method can be used for three colors by additional

Fig. 5. A photograph of a three-color reconstruction from ahologram formed in 649F emulsion. Use of a coding plate sub-tending a rather small angle at the hologram plate results in

localized noise.

Fig. 6. A photograph of a three-color reconstruction from ahologram formed in 649F emulsion but with the coding platesubtending a large angle. As a result, the noise is spread over the

I image plane in a more uniform manner.

beam splitting, but the use of the simpler apparatus re-quired for two colors is sufficient to demonstrate theprinciple. In this case, we have chosen not to providefor nonoverlapping multiplexing of the subject beam,accepting the fact that red or green light from the sub-ject falling on regions of the hologram plate where nosuitable reference beam was present adds to the noiseof the developed emulsion. The color filter mask sug-gested earlier would, of course, cause an interlacing ofthe colors in both subject and reference beams. Figure3 is a photograph of the multicolor image reconstructedfrom a hologram formed on 649F emulsion -with thearrangement of Fig. 2. The completed hologram wasilluminated by the reference beam used to form itand was replaced in register with the interlaced coloredmask images. The reference-to-subject beam anglewas again 150. Comparison of Figs. 1 and 3 indicatesthe success of the technique in eliminating the crosstalkimages. A reconstruction was also obtained from ahologram formed in a similar manner on Kodak SO-243 acetate-base film. The quality of the reconstruc-tion was lower probably because of both stability pro-blems and the use of a reference-to-subject beam angleof 150 which is close to the resolution capability of SO-243. Nevertheless, the multicolor image obtained wasfree of crosstalk.

IV. Coding the Reference BeamThe second technique used to reduce the effects of

color crosstalk in planar hologram reconstruction ofmulticolor images involves the coding of the referencebeam. In this case the amplitude and phase of thereference wave are made to vary across the hologramplate in a significantly different manner for each of thecolors used to form the hologram. To reconstruct themulticolor image, the completed hologram must bereregistered in the position it occupied during formationand reilluminated with the identical reference beamused in the formation of the hologram. This technique

June 1967 / Vol. 6, No. 6 / APPLIED OPTICS 1093

of multicolor imaging can be compared with the generalconcept of ghost imaging predicted by Van Heerden5

and subsequently demonstrated in several ways.'- 9

If the reference wave amplitude and phase do vary overthe hologram plate in a complicated way, i.e., the com-plex reference wave is coded, reconstruction of thesubject beam can take place when the illuminatingwave varies in the same manner as the reference. Ifthis is not the case, the resulting set of incoherentphase relationships will tend to give a more or less uni-form noise output from the hologram. To demon-strate the application of the coded reference beam tech-nique to multicolor imaging we have chosen an examplewhich emphasizes the wavelength sensitivity of themethod. We have employed a ground glass screen toserve as the reference beam coding plate, althoughother devices, e.g., fiber optic arrays or ultrasonic cells,may prove to be more useful.

Figure 4, showing the configuration which we usedto perform the coded reference beam experiments,indicates that three colors of wavelengths 6328 A,5145 A, and 4880 A were combined into a single beamand then passed through the reference coding plate.We could have caused each color to pass through adifferent portion of the coding plate, but by allowingeach color to pass through the same portion of the cod-ing plate the wavelength dependence of the method isstressed. It is the wavelength dependence of the dis-persion 0 of the reference light in traversing the spacebetween the diffuse screen coding plate and the holo-gram plate that strongly contributes to the uniquenessof the reference wave pattern at the hologram for eachcolor. The complicated patterns impressed on thewavefronts of the several reference colors when passingthrough the diffuse screen are further scrambled by thedispersion process in a manner dependent on the wave-length so that each colored reference wave is uniquelycoded. In fact, when a hologram was formed with only5145 A light from an argon laser, the reference beampassing through a diffuse screen coding plate, an ex-cellent image was obtained by illuminating the holo-gram with the identical reference beam. However,when an output from the same argon laser, separatedby only 128 A from 5145 A, illuminated the hologramafter passing through the coding plate in an identicalmanner as the original reference, only a uniform noisewas observed. A further test of the sensitivity of thereconstruction process to the dispersion can be gaugedby the washing out of any image structure when a pieceof cellophane is inserted into the illuminating pathbetween coding plate and hologram.

A photograph of a three-color reconstruction madewith the arrangement of Fig. 4 is shown in Fig. 5. Thegreen-blue noise generated by blue and green lightinteracting with the grating formed with red light iseasily observable (the red noise on the opposite side ismore difficult to see). The geometry of the code plateplays a large part in determining the degree to whichthe noise affects the reconstruction. In this example,the active area of the diffuse screen was a circle of 1.2-cmdiam and located 43 cm from the hologram plate.

The noise is more uniformly distributed over the imagearea by increasing the solid angle subtended by the dif-fuse screen at the hologram. This is a desirablefeature, as is demonstrated in the photograph of thethree-color reconstruction (Fig. 6). For this case theactive area of the diffuse screen was a circle 2.5 cm indiam at a distance of 25 cm from the hologram plate.Here again, as in the case of the nonoverlapping spatialmultiplexing experiments, the subjects were colortransparencies backed with ground glass screens, andthe reference-to-subject beam angle was about 150.It is clear that a better geometry for the code platewould be to make it such that it occupies an annularregion about the subject. In the case where the sub-ject is three dimensional, a single beam could be usedto flood both the subject and an annular piece ofalumina surrounding the subject. The reflection fromthe alumina would act as the coded reference beam.

V. Further Discussion of the Coded ReferenceBeam

Spatial coding of holograms is not restricted to anyparticular hologram-forming geometry. However, theprocesses involved are more readily displayed byassuming that the hologram is formed in a geometrywhich produces a Fourier transform relation betweenthe hologram plane and the plane of the subject andcoded reference source.6'" If the amplitude of thesubject light, at the subject, is fo(x,y) and that of thecoded reference source, at the source is fr(X - xo,y),where xo denotes the offset of the center of gravity ofthe code plate from the center of the subject, then theamplitudes of these wavefronts at the hologram planeare given by the relations

Fo%7Z) = fffo(xy) expjltx + yl]dxdy

and

Fr(t,%-) exp(jixo) = fffr(x - x0 ,y) expjl4x + ny]dxdy.

The spatial radian frequencies t and 7 are inverselyproportional to the wavelength of the illuminatinglight.

The transmission of the hologram so formed is

[F0 + Fr expjtxol [Fo* + F,* exp(-jtxo)l,

the important term being

F0Q,-qX)Fr*Q,-q7) exp(-i~xo).

Illumination of the hologram with the coded beamFr/(t, y) expjtxo will give rise to a wavefront F7 '(,q)X F,* (S, V) X F o (e, a). The inverse Fourier trans-formation is applied to this wavefront to produce theimage and gives rise to a function [f,/(xy)*f7(xy) I®fo(xy), where * denotes a correlation operation andX denotes a convolution operation. When F7 is

identically F, and is a function having a large spatialbandwidth, the autocorrelation function is a sharplypeaked function, and the wavefront [fr(xy)* fr(xy)]®fo(x,y) will be a reconstruction of the original subjectwavefront fo(x,y) except for a loss in resolution. Theloss in resolution will be determined by the half-width

1094 APPLIED OPTICS / Vol. 6, No. 6 / June 1967

of the autocorrelation function. For a one-dimen-sional code with a spatial frequency spectrum which isflat and of random phase for -o/2 < < to/2 and zeroelsewhere, the autocorrelation function will be of theform sintox/tox. The half-width of the central maxi-mum is xi = r/to, indicating that a narrower auto-correlation function and a correspondingly greaterimage resolution will be obtained with greater spatialfrequency bandwidth. Similarly, if we consider atwo-dimensional code with a cylindrical spatial fre-quency spectrum of random phase, the autocorrelationfunction takes the form Ji(tox)/ox which has the sameform as the Abb6 point spread function and will like-

ise define the limits within which points can be re-solved in the image plane.

If, in attempting to reconstruct the hologram, wechange either the wavelength X or the spatial variationof the code fr(x - xo,y), then at the hologram planeF7 ' will not be the same as Fr. Since we consider thesefunctions to be large spatial bandwidth random func-tions, the cross-correlation [fr'(xy)*f,(x,y)] will be abroad random function, as will the function [f,'(x,y)*fr(x,y) ] Ofo(x,y). The latter will be spread out over theimage plane as a relatively uniform intensity noise.

VI. Concluding RemarksIt should be noted that, in each of the examples

chosen to demonstrate the application to multicolorimaging of the general techniques of nonoverlappingspatial multiplexing and reference beam coding,resolution or contrast was sacrificed to reduce crosstalk.Since the hologram generally contains more informationthan necessary, this trade-off will often be a desirable

one, e.g., in cases where color and texture are moreimportant for image recognition. The general tech-niques may be applied separately or in combination tothe problems of storing a multiplicity of monocolor aswell as multicolor holograms in thick as well as thinmedia. The desired image resolution and the signal-to-noise ratio will determine the best combination.Finally, these experiments emphasize the benefitsthat may be gained by placing information in both ofthe beams used to form a hologram.

We would like to acknowledge some helpful dis-cussions with H. W. Kogelnik.

References1. K. S. Pennington and L. H. Lin, Appl. Phys. Letters 7, 56

(1965).2. A. A. Friesem and R. J. Fedorowicz, Appl. Opt. 5, 1085

(1966).3. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 54, 1295

(1964).4. L. Mandel, J. Opt. Soc. Am. 55,1697 (1965).5. P. J. Van Heerden, Appl. Opt. 2, 387 (1963).6. G. W. Stroke, R. Restrick, A. Funkhouser, and D. Brumm,

Phys. Letters 18, 274 (1965).7. K. S. Pennington and R. J. Collier, Appl. Phys. Letters 8,

14 (1966).8. R. J. Collier and K. S. Pennington, Appl. Phys. Letters 8, 44

(1966).9. E. N. Leith, J. Upatnieks, A. Kozma, and N. Massey, Laser

Focus, p. 15, 1 November 1965.10. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123

(1962).11. A. VanderLugt, IEEE Trans. IT-10, 139 (1964).

G 33 ::0.:xg

This column is compiled partly from information sent in by APPLIED OPTICS Reporters in various centers of opticsacross the world, but the Editorial Consultant welcomes news from any source. It should be addressed to

P. R. WAKELING, W INC, 1500 Massachusetts Avenue N.W., Washington, D.C. 20005

A dove prism undergoes one of many in-process checks at theFairchild Space and Defense Systems' new facility.

Fairchild Space and Defense Systems has opened a new 4500sq. m plant on a less than two-hectare site in El Segundo, Cali-fornia. Considerations of diurnal temperature fluctuations,vibration, humidity variations, and soil structure led to a planwith the design and administration activities in the first storyand a lower floor 4.3 m below grade set aside for manufacturing,assembling and testing operations. All compressors, air con-ditioning equipment, etc., are housed in a separate building. Alltest areas have laminar-flow air conditioning which can be cutoff just prior to the moment of test to ensure that no air move-ment degrades lens performance. The photo on the left wastaken in one of the test facilities.

The SPIE Seminar-in-Depth on Underwater PhotoOpticsheld in Santa Barbara, California, on 10-11 October 1966 markedthe first time that the entire U.S. underwater photooptics com-munity ever gathered together at one time. Among the 282registrants were most of the workers from this country plus afew visitors from overseas, participating in a successful andworthwhile seminar in which the speakers provided clear andmeaningful discussions of the state of the art, including newdevelopments in their early research or development stages.

June 1967 / Vol. 6, No. 6 / APPLIED OPTICS 1095