Holographic Optical Data Storage Do,an A. Timu_:in and John D. Downie Historical Introduction paper, predicting bit storage densities on the order of I/Z 3 with source wavelength ,,1.- a fantastic capacity Although the basic idea may be traced back to the of nearly I TB/cm _for visible light! The science and earlier X-ray diffraction studies of Sir W. L. Bragg, engineering of such a storage paradigm was heavily the holographic method as we know it was invented pursued thereafter, resulting in many novel hologram by D. Gabor in 1948 as a two-step lensless imaging multiplexing techniques for dense data storage, as technique to enhance the resolution of electron mi- well as important advances in holographic recording croscopy, for which he received the 1971 Nobel Prize materials. Ultimately, however, the lack of such ena- in physics. The distinctive feature of holography is bling technologies as compact laser sources and high- the recording of the object phase variations that carry performance optical data I/O devices dampened the the depth information, which is lost in conventional hopes for the development of a commercial product. phot4bg,j'aphy where only the intensity (= squared am- After a period of relative dormancy, successful appli- plitude) distribution of an object is captured. Since cations of holography in other arenas sparked a re- all photosensitive media necessarily respond to the newed interest in holographic data storage in the late intensity incident upon them, an ingenious way had 1980s and the early 1990s. Currently, with most of to be found to convert object phase into intensity the critical optoelectronic device technologies in variations, and Gabor achieved this by introducing a place and the quest for an ideal holographic recording coherent reference wave along with the object wave medium intensified, holography is once again consid- during exposure. Gabor's in-line recording scheme, ered as one of several future data storage paradigms however, required the object in question to be largely that may answer our constantly growing need for transmissive, and could provide only marginal image higher-capacity and faster-access memories. quality due to unwanted terms simultaneously recon- structed along with the desired wavefront. Further Holographic Principles handicapped by the lack of a strong coherent light source, optical holography thus seemed fated to re- We show the basic recording and reconstruction ar- main just another scientific curiosity, until the field rangements for off-axis holography in Figure I, as- was revolutionized in the early 1960s by some major suming that the object whose hologram (meaning breakthroughs: the proposition (A. L. Schawlow and "whole record") we wish to make is available in the C. H. Townes) and demonstration (T. H. Maiman) of form of a transparency. Here coherent light from a the laser principle, the introduction of off-axis holo- laser source is collimated to produce a unit-amplitude graphy (E. Leith and J. Upatnieks), and the invention plane wave normally incident on the object, while at of volume holography (Y. N. Denisyuk). Conse- the same time a portion of this plane wave is inter- quently, the remainder of that decade saw an expo- cepted by a prism to produce a spatial carrier refer- nential growth in research on theory, practice, and ence wave (Fig. la). A distance L behind the object applications of holography. Today, holography not is a photosensitive recording medium, which we shall only boasts a wide variety of scientific and technical simply refer to as "film" for convenience. The object applications (e.g., holographic interferometry for transparency diffracts, or scatters, the illuminating strain, vibration, and flow analysis, microscopy and plane wave, producing across the film plane a com- high-resolution imagery, imaging through distorting plex-amplitude field distribution media, optical interconnects, holographic optical elements, optical neural networks, three-dimensional O(x,y) =]O(x, y)le ''_°_'''. displays, data storage, etc.), but has become a promi- nent art, advertising, and security medium as well. The evolution of holographic optical memories The offset-reference plane wave, meanwhile, is inci- has followed a path not altogether different from dent on the film at an angle 0 with the z axis, and can holography itself, with several cycles of alternating be expressed mathematically as interest over the pastfour decades. P. J.van Heerden is widely credited for being the first to elucidate the R(x,y) =e_'°', principles behind holographic data storage in a 1963 Collimation Prism optics ,Laser --_ _-- ,-_" L )1 A Object Recording transparency medium (a) hologram recording x z _/'_ Observer wave _ \'_ _ Virtual _I .'..'," a image }._...._ L (b) hologram reconstruction Figure ! Basic holography - the recording and reconstruction steps for a thin hologram where k= 2tr/A. is the wave number, and _.denotes where (bias) t_ and (slope) fl_ are (real) constants the source wavelength. These mutually coherent characteristic of the film and the exposure time 1:. If object and reference waves interfere inside the (thin) this hologram is now illuminated at normal incidence film, creating the (2-D) intensity distribution by a plane wave of amplitude A (Fig. lb), then the transmitted field immediately behind the hologram =I"+o1='14+1=°1+ plane is found quite simply to be =1 +lOl= +2JO[cos(ksinOy-argO). U(x,y) = Atu(x,y) = + .1o=l Note that the last term of this interference pattern isa standing wave (or "fringe") whose amplitude and + A/3_O'e _''"°_' + A[3,0e -'*'"e:'. phase are modulated by those of the object wave; object phase information has thus been successfully The first two terms here are the transmitted plane converted to intensity variations inside thefilm. wave and an ambiguity field, both of which propagate Within the linear exposure regime of the photo- along the z axis, while the last two terms are encoded graphic medium, the amplitude transmittance of the on complex-exponential carrier waves and therefore developed 1iIm (i.e., the hologram) becomes propagate away from the z axis. Specifically, we see that the third term is (up to a constant factor) the t,,(x,y) = t, +.13,l(x,y), complex conjugate of the original object wave, which forms a real (pseudoscopic) image of the object as lightfromthe hologram converges in space at a dis- more economical fashion; Fresnel holograms provide tance L behind the hologram and at an angle 0 with a convenient design compromise between these two the : axis. Finally, the fourth term is a reconstruction conflicting requirements. Another advantage of Fou- of the original object wavefront, and forms a virtual rier and Fresnel holograms is the distributed (or re- (orthoscopic) image of the object as an observer sees dundant) nature of the information storage method light from the hologram appear to diverge away from that provides robustness against damage: localized a location a distance L in front of the hologram and at detects and degradations in the hologram do not lead an angle -0 with the .- axis. For faithful reconstruc- to a total loss of recorded information, but merely tion of the object, it is clearly necessary that these reduce the signal strength in the retrieved images. individual terms separate in space as they propagate away from the hologram. One can readily show, with Volume Holograms the help of Fourier analysis, that this will indeed be guaranteed if the carrier angle is chosen to satisfy So far we have discussed thin holograms operating in 0 > arcsin(3BZ), where B is the (spatial) bandwidth the Raman-Nath diffraction regime whose influence of the object along the y axis. We thus see that the on incident optical waves can simply be characterized presence of a suitably chosen spatial carrier reference by a multiplicative amplitude transmittance function, wave during the recording step is what facilitates the as we did above. Although images can clearly be succ,.essful subsequent reconstruction of the object stored in and retrieved from such holograms, the true from it6 hologram - an essential feature missing from potential of holographic data storage can be realized Gabor's original in-line holography concept and was only when one considers utilizing the third dimension later introduced by Leith and Upatnieks. of the recording medium. A grating whose thickness Under a unit-amplitude normally incident plane- significantly exceeds the fundamental fringe period wave illumination, the relationship between the (pos- recorded in it is said to operate in the Bragg diffrac- sibly complex-valued) object amplitude transmittance tion regime, where the extended volume of the me- to(_,rl) and the recording object wave O(x,y) can dium serves to suppress (or "filter out") all but the be expressed in the form of a linear superposition as first diffraction order in reconstruction. The physics of volume diffraction thus endows the grating with a selectivity property that can be exploited to store data m O(x,y)= f f K(x,y;_,rl)to(_,rl)d_drl, in a multiplexed fashion: many holograms can be stored within the same physical volume and then re- trieved independently thanks to a unique addressing where K(x,y;_,rl) denotes the propagation kernel scheme, thus greatly enhancing the overall storage between the object and film planes, and is called the capacity of such amedium. point-spread function (or the impulse response) of the To illustrate the salient features of volume grat- intervening optical system. Depending on the par- ings, we consider the basic arrangement shown in ticular form of K, one can therefore speak of different Figure 2. (Refraction at the air-medium interfaces, types of holograms. For instance, if the film falls though neglected for clarity in this diagram, is fully within the near-field (Fresnel) diffraction region of accounted for in the following analysis.) Two unit- the object transparency, then the setup of Fig. la re- amplitude plane waves of common wavelength ;I.(in cords what is termed a Fresnel hologram. Now, if a air) are incident on the same side of a photosensitive medium of thickness d, making angles 4-0 (in air) thin positive lens of focal length f = _L is inserted with the surface normal (Fig. 2a). (This arrangement halfway between the object and film planes, the cor- records a transmission hologram, whereas incidence responding recording is called a Fourier hologram, from opposite sides of the medium forms a reflection since the object wave incident on the film in this case hologram.) For simplicity, the medium is assumed to is the (2-D) spatial Fourier transform of the object be transparent (at _) with an initial refractive index amplitude transmittance. Finally, if a lens with focal n_and a maximum optically induced refractive*index length f =_L is used instead, then an (inverted) change An=,=. The two waves playing the roles of image of the object is formed at the film plane, with the result appropriately called an image hologram. object and reference here may be identified by their 4 Fourier holograms provide an excellent mis- wave vectors {ko,kR} = k(T-_rsin0+_ zcos0), and alignment tolerance and make the most efficient use the (3-D) intensity pattern formed by their interfer- of the hologram space-bandwidth product (i.e., they ence inside the recording medium is then simply use a minimal hologram area to record the object information), while image holograms utilize the dy- namic range of the recording medium in a much 3 Reference " / _ d -_,. Recording wave y_// i...:....,':,,.-.,,"" medium Object__/'/!;: ;-:_i:'_ "-,,..3Interference wave'. " " pattern xO--_ z wy (a) hologram recording Index fringes Playback First-order _FqL_ wave diffracted \ wave 2O Transmitted wave ,'tO (b) hologram reconstruction L 0.8 0.6 o(,_e) -3 -2 -1 0 1 2 3 ,_e/e (c) grating angularselectivity Figure 2 Volume holograph2 - elements ofathick zinusoidal phase diffraction grating .ere_o. _,- _oisc,.,d==g.,.t,n,g,e.o,a..ndi. tothex-z plane: _'a=ar2ksinO). Wenote from the perpendiculartotheintensityfrihges (e.g.,parallel¢o recording wave-vectordiagram that thefringe period they axis inFig.2a, withthe fringes planesparallel is A= 2x/lk_ l= _/2sinO. 4 The refractive-index distribution inside the me- which is the case of object wave reconstructing the dium (0 _ ..-_ d) resulting from this exposure is then reference wave, as well as for # = _+.(,'r- 0) (i.e., from right to left in Fig. 2b) corresponding to the cases of conjugate object wave reconstructing the conjugate reference wave and vice versa. It should be evident, even from this simplistic assuming an infinite lateral extent. Note that no_enA description, that as the scattering of the playback in general, as the constant background intensity in- wave starts giving rise to the original object wave evitably uses up part of the available dynamic range inside the medium, this wave itself gets scattered by during exposure. Also, one typically tries to maintain the grating, coupling its energy back into the play- n_<< An,._ to assure operation in the linear exposure back wave. There is, in fact, a steady exchange of regime and to utilize the material dynamic range eco- energy (or "multiple reflections") between these two nomically for multiplexed hologram recording. (The waves as they co-propagate through the grating - a ratio n_/n o is called the modulation transfer func- process known as two-wave mixing. Therefore, the tion, and represents the spatial frequency response of diffraction efficiency 17of the grating, defined as the the recording medium at frequency I/A.) The tran- ratio of the first-order diffracted power to the incident sition between the Raman-Nath and Bragg diffrac- power, may be expected to depend on the optical tion _'e,gimes may be roughly characterized by the interaction distance n_d/cosO in a periodic fashion, paramder Q =-;_d/noA z : a sinusoidal grating is said and a complete power transfer between the two to be thin ifQ _<I; otherwise it is considered thick. waves (i.e., r/= 1) should be feasible. In addition, we To reconstruct the object wave, let us now illu- may expect a Bragg-mismatched playback wave to minate the grating with a unit-amplitude plane play- lose some of its power to higher-order grating modes back wave at the recording wavelength ,t.and at an (with wave vectors k-,-- ka - nkc;, n ..... -2, -1, 2, angle _ (Fig. 2b); that is, the playback wave vector is 3.... ), yielding only a partial reconstruction (i.e., '('e = k(d rsin ¢_+ cizcos _). We can develop an intui- r7< 1). This problem of power loss to higher orders is also encountered with gratings that are nonuniform tive understanding of the volume diffraction process (i.e., decaying in modulation into the depth of the by thinking of the recorded fringe planes as partially medium) due to the ever-present absorption, or non- reflecting mirrors. (This is literally the case with sinusoidal (i.e., over- and under-exposed at their ex- photographic film, where silver platelets are formed trema, or "saturated" and "cut off") due to the typi- at locations of high exposure upon development.) cally nonlinear recording dynamics of the material. These partially reflecting mirrors transmit part of the This intuitive picture of volume diffraction was playback wave along its direction of incidence, while substantiated formally in a seminal paper published deflecting the remaining part along an angle -¢_ with by H. Kogelnik in 1969, where an approximate yet the z axis, in accordance with the law of reflection. highly satisfactory coupled-wave approach was de- Now, for these reflected waves to interfere construc- veloped to solve the scalar Helmholt'. equation tively and recreate the original object wave, the opti- VzU(7)+kZnZ(F)U(F)=O for the total optical field cal path-length (or phase) difference between reflec- U inside the grating. Kogelnik's analysis shows that tions from adjacent fringe planes must be precisely the diffraction efficiency of a thick sinusoidal phase one wavelength (or its integer multiples). Simple grating can be expressed as trigonometry reveals that this requirement will be met if the playback angle satisfies the condition r/= sin2 tP,J I+.f2a , __ rcn_d .O-_ sin 20 zaO, ;t 1+ .05 Acos 0' n_ sin¢:_"7",=sin0 _ ¢a:0. where dO is the angular detuning of the playback Here Ca is referred to as the Bragg angle, and this wave from the Bragg angle O. The dependence of r/ particular playback wave, designated as /_8, is said to on A0 is plotted in Fig. 2c, where we firstly observe a be Bragg-matched to the grating. Evidently, the broad main lobe: essentially, the finite size (in our playback wave is scattered by the grating in such a case thickness) of the medium has the net effect of way that the diffracted wave vector satisfies spreading the grating angular (/_-space) spectrum ko = ka-/_a, thus closing the reconstruction wave- into a range of wave vectors centered at /_u. One can vector diagram (conservation of momentum). Note therefore visualize a cloud of grating vectors around that the Bragg condition is also satisfied for ¢=-0, the tip of /_c;in /_ space (position-momentum un- 5 certainty), the consequence being that the Bragg con- tributions. Yet another method that has been studied dition can now be (at least partially) satisfied by a vigorousl,, in recent years is shift muhiplexing, where range of playback waves k_, _:/_, that may not be a highly divergent spherical beam is used as refer- perfectly Bragg-matched to the grating (Fig. 2b). We ence, and detuning is achieved by slight lateral secondly note the appearance of the so-called Bragg translation of the medium. Depending on the afford- nulls, the first of which occurs for a AO value of ap- able level of system complexity, any one or a combi- proximately O =A./2dsin O" there is a discrete set of nation of these and other (e.g., speckle, fractal, peris- trophic, etc0 multiplexing techniques may be used. roughly equally spaced reconstruction angles at which no grating diffraction is observed. This sug- gests the possibility of recording many holograms Storage Materials within the same physical volume by using reference waves at angles (or "addresses") 0o± nO, n = 0, I, 2, As can be inferred from the foregoing discussion, the characteristics of the recording material are of para- .... around some nominal center angle 80 - a scheme mount importance for volume holographic applica- known as angular multiplexing. Since each holo- tions. A list of ideal physical attributes for a holo- gram sits at a Bragg null with respect to all the other graphic storage medium may include the following: holograms, it should thus be possible to reconstruct individual holograms without any interference from Recording mechanism - a large dynamic range the bd2ers. In practice, of course, recorded object of optically induced, and preferably optically patterns have some spatial structure (representing the erasable, refractive-index change (e.g., An,,,= _= information being stored) with a corresponding 10-3 to 10-"), negligible absorption; spread in their angular spectra, and therefore some cross talk between retrieved patterns is inevitable. Sensitivity- responsive to (widely and cheaply available) red wavelengths, an appreciable holo- As the angular bandwidth O of a thick grating is graphic writing sensitivity (e.g., on the order of inversely proportional to its width, it would seem that 10-z cm3.1')requiring low recording powers; the thicker the medium can be made, the higher the attainable storage density becomes, and in fact stor- Optical quality - suitable for casting in the form of thick slabs with large surface areas (i.e., a age of several thousand angle-multiplexed holograms thick disk), high resolution (e.g., up to 5000 cy- has been routinely demonstrated in recent experi- cles/ram), negligible scattering; ments. The ultimate physical limit on the storage density of a medium therefore comes from its finite Stability- retain recorded data indefinitely over a wide range of ambient (temperature, humidity, dynamic range: each recorded hologram uses up a etc.) conditions, show low fatigue over many certain portion of the total available refractive-index (e.g., millions of) write-read-erase cycles; change, and once the entire range is exhausted, no Volatili_" - a (simple) physical means of"fixing" more holograms can be recorded even if the spatial the recorded holograms so that they are _lot bandwidth of the medium would allow it. (For a large number N of multiplexed holograms, the aver- weakened (or erased) by subsequent recording and read-out beams; age diffraction efficiency per hologram has been Self-processing- no need for processing or de- found empirically to scale as 1/N z.) It may also be veloping of any kind (e.g., chemical, thermal, worthwhile to note here that in multiplexed record- magnetic, UV, IR, etc.) before or after recording; ing, holograms far apart in recording order experi- and last but not least, ence notably different exposure conditions due to the Cost - material readily and cheaply available or changing optical properties of the medium. It is manufacturable. therefore imperative that an optimal exposure sched- ule be formulated for the particular storage material Although photographic silver-halide emulsions being used to obtain equal diffraction efficieneies for have been the work horse of traditional holography, all of the N holograms. they fail to meet many of these requirements, and a Finally, mention should also be made of other host of more suitable materials has been found and multiplexing schemes that can achieve similarly developed for holographic storage. None of the can- dense holographic storage. For instance, the kind of didate holographic storage media considered so far, Bragg detuning described above can alsobe achieved however, has been able to fulfill all the requirements, by holding the reference angle fixed and instead and instead of a single "magical" material, an arsenal changing the wavelength - a scheme referred to as of possible materials, each with a unique set of wavelength multiplexing. In an alternative technique strengths and weaknesses has emerged. Among these known asphase-code multiplexing, reference waves are photopo!ymer films (available from DuPont and are chosen from a setof orthogonal (2-D) phase dis- 6 Polaroid), photorefractive crystals such as iron-doped • optics for routing and imaging the wavefields lithium-niobate (Fe:LiNbOj), and photochromic films within the system, along with other components such as those made from dichromated gelatin and the tbr performing data multiplexing; and finally light-harvesting protein BacterioRhodopsin. For a • a storage medium within which holograms may given type of memory to be developed, it is thus be written by altering the optical properties of likely that a sufficiently suitable material can be the material through some physical process. found among this collection, and the storage system can then be designed to compensate for the short- A page-oriented holographic optical memory ar- comings of the material to the extent possible. chitecture featuring these components is depicted in The key point of departure between different Figure 3, which is the 90"-geometry commonly used holographic materials is the nature of the physical with photorefractive crystals to achieve maximum recording process, which largely determines most of angular selectivity. A pair of high-quality lenses the other properties of the storage medium. For in- forms a 4-fimaging system that matches the pixels of stance, in an impurity-doped electro-optic oxide like a (2-D) SLM to those of a CCD camera or a CMOS Fe:LiNbO3, an inhomogeneous space-charge distri- detector array, and the crystal is placed at the Fourier bution is created inside the medium via the diffusion plane of this setup. During recording, data is com- of electron-hole pairs excited by the illuminating posed as a binary or gray-level image on the SLM intensity, and the associated electric field then locally and subsequently impressed on a collimated object moc_tes the refractive index of the medium via the beam, whose Fourier transform is then formed inside linear electro-optic effect. In a photochromic me- the crystal by lens L_. At the same time, a plane ref- dium like a BR film, meanwhile, the incident inten- erence wave is introduced from the side of the crystal sity creates a spatially varying volume population at a unique angle designated for that data page, thus difference between the two stable states of the mole- recording a Fourier hologram inside the crystal. cule, which leads directly to an absorption modula- During retrieval, this page is addressed at the same tion that is necessarily accompanied by a refractive- reference angle and the diffracted field is (inverse) index change through the Kramers-Kronig relation Fourier-transformed by lens L,, thus forming the (statement of causality). Both of these materials are image of the original data page on the detector. Due optically erasable and hence suitable for use in a to the high angular selectivity of the medium, many Re_.Writable memory design (despite their low sensi- pages can be multiplexed within the crystal volume tivity); however, this very property also leads to and randomly accessed by use of the appropriate volatility, requiring often complex engineering solu- addressing reference beams. This page-oriented data tions (e.g., two-photon gated recording, thermal or storage scheme also facilitates parallel data transfer, electrical fixing, etc.) for data persistence. On the thus enabling potentially very. high read-out rates. other hand, refractive-index changes can also be in- The design of a holographic data storage system duced in (organic) photopolymers by polymerizing a starts with the specification of a raw Bit-Error Rate monomer with visible illumination. Since these ma_ based on a target user BER and an affordable Error- terials typically offer a considerably larger dynamic Correction Coding scheme of choice: typically, an range, they are definitely a more attractive option for acceptable BER of 10-t2 can be delivered to the user a Write-Once Read-Many type of memory where with a reasonable ECC overhead ira raw BER of 10..4 their irreversibility and low sensitivity are of little can be attained at the detector. This, in turn, concerti. translates into a minimum Signal-to-Noise Ratio that must be achieved by the system at its output. Among System Architectures the numerous and inter-related factors determining the SNR are source wavelength and power, medium The components that comprise a typical holographic dynamic range, thickness, diffraction efficiency, and optical data storage system are scattering, inter-page and inter-pixel cross talk determined by the number of multiplexed pages, * a coherent source (array) or collection of sources number of bits per page, and the imaging system that provide object, reference, and reconstruction point-spread function, detector integration time and waves, and possibly another source for erasure; electrical noise, and other detrimental influences such • a .$.patial Light Modulator for preparing the (bi- as misalignments and nonuniformities. nary or multi-level) data to be stored as 2-D im- Due to the difficulties involved in working with ages (or "pages"); photoreffactive crystals and the pressures placed on • a detector (array) and subsequent electronics for the research community to produce a commercially data read-out, post-detection signal processing, viable technology, increasing attention has also been and error correction; paid to a holographic disk paradigm. Such a system 7 u Lj Recording medium L2 (photorefractive crystal) Page composer Addressing beams Read-out electronics (spatial light modulator) (fan of reference waves) (CMOS detector array) Figure 3 The standard holographic optical data storage system architecture may employ a thick photorefractive organic-polymer nical University in 1989 and Texas Tech University disk with a spiral single- or multi-track data format in 1991 and 1994, respectively. His current research (much like the familiar CD/DVD technology) that is interests are in holographic optical data storage (par- accessed holographically by shift, speckle, or phase- ticularly with bacteriorhodopsin films), near-field code multiplexing. In recent years, teams at univer- optics, quantum optoelectronics, and quantum infor- sities (California Institute of Technology, Stanford mation processing. University), government and industry research labo- ratories (IBM Almaden Research Center, Lucent John D, Downie is aresearch scientist in the Optical Technologies - Bell Laboratories, NASA), and small Network Research Department at Coming, Inc., Sul- companies (Siros Technologies, Holoplex, Inc.) have livan Park Science and Technology Center, Coming, been actively pursuing the optical head, media, and NY. He received a B.S. in Optics from the Univer- system design for commercial WORM and RW holo- sity of Rochester in 1985 and a Ph.D. in Electrical graphic optical data storage products. The present Engineering from Stanford University in 1989. He goal is to manufacture asystem capable of astorage has worked at both NASA Ames Research Center capacity of about 50 GB, with roughly 100-ms re- and Lawrence Livermore National Laboratory before cording and 100-1ss read-o,.,t times per (I-MB) page, joining Coming in 1999. His current research is which may fulfill the market need for a memory that centered on optical communications, optical network is cheaper than silicon DRAM while offering faster architectures, and optical network performance access than magnetic storage. monitoring. There is a rapidly increasing demand for high- capacity and fast-access data storage in virtually all Further Reading avenues of human endeavor from medicine and edu- cation to business and communications, from multi- • J.F. Heanue, M. C. Bashaw, and L. Hesselink, media and entertainment to military and space, With "Volume holographic storage and retrieval of the development of suitable architectures and materi- digital data," Science 265, 749-752 (1994). als, and the cost-effective availability of enabling • J.W. Goodman, Introduction to Fourier Optics, technologies, holographic storage is well positioned 2nded. (McGraw-Hill, New York, 1996). to satisfy this need in the near future. • P. Hariharan, Optical Holography - Principles, Techniques, and Applications, 2rid ed. (Cam- Authors bridge University Press,Cambridge, UK, 1996). • R.J. Collier, C. B. Burckhardt, and L. H. Lin, Do_,an A. Timui;in is a research scientist in the In- Optical Holography (Academic Press, New formation Physics Group at NASA Ames Research York, i971). Center, Moffett Field, CA, where he has been since • G.T. Sincerbox, ed., Selected Papers on Holo- 1995. He received the B.S., M.S., and Ph.D. degrees graphic Storage (SPIE Mileston© Series, Vol. in Electrical Engineering from the Middle East Tech- MS05, Bellingham, WA, 1994). 8