Volume holography has generated widespread recentinterest as a possible next-generation storagetechnology.1–3 Since digital data are optically inputnd output as two-dimensional ~2-D! pages of bright
and dark pixels, and are stored throughout the vol-ume of a photosensitive storage medium, holographycan offer both fast parallel access and high storagedensity. An added feature is content addressabil-ity,4,5 implemented by correlation of an input datapage against all of the stored pages simultaneously.If each hologram represents a database record andthe input page encodes a user query, then the entirememory is searched in parallel—much faster than aconventional, software-based sequential search.Previous research has used data pages encoded tooptimize the sequential, address-based holographicreadout,5 which has tended to limit the fidelity of theparallel associative searches.6,7 Here we concen-trate on maximizing the performance of the parallelsearch operation through data encoding and simplepostprocessing. Two important steps toward animplementable content-addressable data-storagetechnology are made: We introduce novel encodingschemes for fuzzy database searches ~to find recordsthat are similar to a search argument!, and we
The authors are with the IBM Almaden Research Center, 650Harry Road, San Jose, California 95120. G Burr’s e-mail addressis [email protected].
Received 17 March 1999; revised manuscript received 3 August1999.
present the first, to our knowledge, demonstration ofhigh search fidelity ~using an all-holographic search-and-retrieve engine that operates on a small feature-space multimedia database!.
2. Holographic Data Storage and Correlation
Figure 1 shows the three modes of operation in aholographic data-storage system: storage, address-based retrieval, and content-addressable searching.For storage, two coherent laser beams illuminate thephotosensitive storage material @Fig. 1~a!#. The ob-ect beam, having passed through the pixelated spa-ial light modulator ~SLM!, contains the informationo be stored. Where this beam intersects the secondeference beam, a stationary interference pattern isormed, which modulates the optical properties of thetorage media ~such as index of refraction!.Once the hologram is recorded, either of the two
eams can be used to reconstruct a copy of the other,y diffraction of a small portion of the input power offhe stored interference pattern. For example, inddress-based retrieval @Fig. 1~b!#, the object beaman be reconstructed by illumination of the hologramith the original reference beam. Lenses image theixelated data page onto a matched array of detectorixels, where the bright and the dark pixels can beonverted back into binary data. When the holo-ram is stored throughout a thick storage material,hen Bragg diffraction causes the strength of the re-onstruction to be sensitive to changes in the angle ofhe reference beam. This Bragg mismatch is mostensitive to angle changes in the plane formed by thebject beam and the reference beam @Fig. 1~a!, theorizontal plane#. We can store and independentlyddress multiple data pages merely by steering the
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reference beam ~angle multiplexing!. As many as10,000 holograms have been superimposed in thesame ;1-cm3 volume in this way.8 In addition to
igh storage density, holographic data storage canlso provide fast parallel readout. Since each dataage can contain as many as 1 million pixels,9 a read-
out rate of 1000 pagesys leads to an output datastream of 1 Gbitys.
These same volume holograms, upon illuminationwith the object beam @Fig. 1~c!#, reconstruct all theangle-multiplexed reference beams that were used torecord data pages into the volume. The amount ofpower diffracted into each output beam is propor-tional to the correlation between the input data page~being displayed on the SLM!, and the stored datapage ~recorded with that particular reference beam!.
ach output beam can be focused onto a detectorrray to form a correlation peak. Because each ofhe system’s lenses performs a 2-D Fourier transformn spatial coordinates,10 the optical system is essen-
tially multiplying the Fourier transforms of the twodata pages and then taking the Fourier transform ofthis product. The role of the hologram is to hold thecomplex conjugate of the Fourier transform of thestored page for multiplication by the input data andto deflect the correlation output away from the brighttransmitted object beam. With a thin hologram it ispossible to obtain the entire 2-D correlation function,but only for a few stored pages. This procedure hasbeen used extensively for biometrics and target rec-ognition.11
With thick holograms, the Bragg-mismatch thatallows for angle multiplexing of multiple stored pagesalso reduces each hologram’s correlation output to anarrow, nearly vertical slice of the correlation func-tion. This slice includes the 2-D inner product ~thesimple overlap! between the input page being pre-sented to the system and the associated stored page.If the patterns that compose these pages correspondto the various data fields of a database, and if eachstored page represents a data record, then the opticalcorrelation process has just compared the entire da-tabase with the search argument simultaneously.This parallelism gives content-addressable holo-graphic data storage an inherent speed advantage
Fig. 1. Holographic data-storage system. ~a! Two coherent bephotosensitive material to record a hologram. ~b! Illuminating toriginal information-bearing beam for capture with a detector arreconstructs all the reference beams, computing in parallel the co
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over a conventional serial search, especially for largedatabases. For example, if an unindexed conven-tional retrieve-from-disk-and-compare software-based database is limited only by a sustained hard-disk readout rate ~25 Mbyteys!, a search over 1
illion 1-Kbyte records would take ;40 s. In com-arison, with off-the-shelf, video-rate SLM and CCDechnology, an appropriately designed holographicystem ~one in which the searching object beam illu-inates 1 million holograms simultaneously! could
search the same records in ;30 ms—a 12003 im-provement. Custom components could enable 1000or more parallel searches per second.
3. Data Encoding for Holographic Search
For this optical correlation process to represent adatabase search, the spatial patterns of bright ~ON!,pixels on the holographic data pages must somehowrepresent the digital data from fixed-length databasefields. For example, a 2-bit data field might be en-coded by four dedicated pixels within the SLM page.To find records for which this database field has aparticular value, one of these four pixels is turned ON
in the input page, thus reconstructing referencebeams only where the stored data page had this samepixel ON. A byte ~8 bits! of data might be encoded bycascading four of these 2-bit subfields. Alterna-tively, subfields might be organized specifically toencode letters and numbers5 instead of bytes. Whenonly a few matching bits are searched for, however,only a few of the SLM pixels are ON and the weaksignal is often overwhelmed by the background lightscatter or the detector’s thermal noise. In such acase data patterns must be encoded with blocks ofperhaps 10 3 10 pixels rather than with individual
ixels.The SLM is thus divided into separate regions,
ach dedicated to a particular fixed-length field of theatabase. Horizontally, these regions can be closelypaced, because Bragg mismatch will prevent inputixels from interacting with the stored pixels of dif-erent columns. However, the volume holographicorrelator is still shift invariant in the vertical direc-ion: Input pixels can and do interact with storedixels of different rows, resulting in strong, slightly
one carrying a spatial page of information, interfere within alogram with the reference beam reconstructs a weak copy of the
~c! Illuminating the hologram with a new page of informationtion between the search data and each of the stored pages.
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offset, and completely misleading correlation peaks.When several SLM pixel rows are left unused be-tween the encoded database fields, undesired corre-lation peaks can be sufficiently displaced ~within theoutput slice of the correlation function! to avoid crosstalk in the measurement of the desired correlationpeak ~the one that carries the 2-D inner product!.
The binary encoding technique described above im-plements an exact search through the database. Bythresholding of the detected optical signal ~essential-ly an analog quantity!, the matching records can beidentified. For example, during searching of a1-byte data field encoded in four subfields, the thresh-old must distinguish between a full match ~four offour blocks! and the closest near match ~three of four!.This becomes commensurately more difficult, how-ever, when many fields are being searched simulta-neously. When the threshold does not workcorrectly, completely unrelated records are identifiedas matches, because near matches between pixelblock patterns do not represent near matches in en-coded data value. For example, if one encodes thenumerical data value 128 in the above-mentioned1-byte data field, then near matches ~three of fourpixel blocks in common! will arise from records thatencode many disparate values ~including the datavalue 0!. Meanwhile, the neighboring data value of127 has no blocks in common and thus will not beconsidered. Gray codes can be used to guaranteethat neighboring data values retain similar encod-ings, but they do not prevent disparate values fromhaving equally similar encodings.
We developed a novel, to our knowledge, data-encoding method that allows for similarity or fuzzy12
searching, by encoding only similar data values intosimilar pixel block patterns. As shown in Fig. 2~a!,data values are encoded by the position of a block ofON pixels within a vertical track, creating a slider.For example, the data value 128 might be encoded asa pixel block of height hs, centered within a column of56 pixels. When data values near 128 are searched
Fig. 2. Data encoding for fuzzy searching. ~a! When a hologramis stored, a small block of SLM pixels are turned ON at someocation within a predefined rectangular portion ~slider track! of
the data page. ~b! For correlation readout an input query is en-coded as a similar block within the same track. ~c! Any offsetbetween the two blocks causes the brightness of the correlationpeak to decrease. By encoding data values with the center posi-tion of the pixel block, the holographic system can now measure thesimilarity between data records and the input query, thereby im-plementing fuzzy searching.
1
for, the partial overlap between the input slider block@Fig. 2~b!# and the stored slider block causes the re-sulting correlation peak to indicate the similarity be-tween the input query and the stored data.
Using our DEMON holographic storage demon-stration platform,13 we experimentally demonstratedthis fuzzy search encoding. To detect correlationpeaks, a CCD camera and lens were added in thereference beam downstream from the LiNbO3:Festorage material. Figure 2~c! shows a search of asingle fuzzy-encoded data field ~7 pixels wide 3 30pixels tall! as the input data value approaches andthen exceeds the stored value. The amplitude re-sponse ~the square root of measured power as a func-tion of the relative position of the input slider block!resembles a triangle function.14 The correlation ofdentical rectangles creates the triangle; the signalsdd in field amplitude yet are detected in intensity,hus the square root. Since this signal is measuredy the power falling on a small region of the correla-ion plane, only a few pixels of vertical shift invari-nce can contribute. In the center of the triangle,he signal added by shift invariance merely scales thelope of the triangle; at the edges of the triangle, soew pixels are involved that the correlator response isssentially unaffected by shift invariance. Thehoice of hs and hi—the vertical extent of the slider
blocks on the stored and the input pages—controlsthe detected signal power and the search range ~theheight and width of the response function!. Al-though hs is fixed when the holograms are stored, hican be changed on a search-by-search basis. Forfurther functionality, two slider blocks can be used toimplement an OR ~i.e., records with values ,16 or
240!.With this fuzzy-encoding technique the analog na-
ure of the optical output becomes an enabling fea-ure instead of a drawback. However, if the cost inLM pixels ~proportional to the maximum data val-e! is deemed too high, data fields could be made onlyartly fuzzy: fuzzy representation for the low-orderits and efficient exact coding for the more significantigits. For example, the data value 128 might havets top 4 bits encoded in binary, with a much smallerlider of only 16 pixels. This trades off search flex-bility for a more efficient use of the SLM area. Aolographically stored database might contain alend of fuzzy-, partly fuzzy-, and exact-coded dataelds, depending on the degree of similarity matchingequired.
4. Search Fidelity
The capacity ~both the number of stored records andthe amount of data per record! that such a holo-graphic content-addressable storage system canreach will depend on its reliability in the presence ofnoise. Because the optical correlation process is an-alog, low-overhead digital error correction is notavailable for the parallel search operation. Onemight duplicate every record in several different ho-lograms, but this would sharply reduce capacity. Amore attractive option is to use the optical parallel
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search engine as a front-end filter to a conventionalsequential search engine. This retains the speedand capacity benefits of the holographic content-addressable memory while reducing the bit-error-rate burden. For example, assume the search taskis to find the 10 best matches in a database of 1million records. If the holographic system actuallydelivers its 100 best matches to the conventional dig-ital search engine, then as long as the 10 best recordsare somewhere in this set, the optical system does notintroduce any error. At the same time the numberof records that the conventional search engine has tocheck is reduced 10,000 fold.
In addition to using the conventional search engineto relax the bit-error-rate constraints, we can makefurther improvements in signal-to-noise ratio. Asmentioned above, the optical detection will introducea background noise floor ~from scatter or thermal
Fig. 3. Three experimental search results from an all-holographvectors from the IBM QBIC image database.15 ~a! Four best imleftmost image. ~b! Measured correlation score ~ratio of the deterecords, as a function of the expected response ~the number of SLMbest images found when the color sliders for 20% white and 20% li~e! Four best images found when we search for the keyword “shcharacter. ~f ! Measured versus expected correlation score.
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noise! that sets a lower limit on acceptable signallevels. Unfortunately, the signal ~detected opticalenergy! decreases as we increase the number of su-perimposed volume holograms ~number of records!,
ecrease the optical readout time ~to increase searchpeed!, or decrease the number of pixels per searcheld ~for more data fields per record!. To study theserade-offs, a diffraction model has been developed forhe dependence of signal strength on the size andistribution of pixelated correlation patterns.14,16
This model shows that defocus of the correlator~placement of the storage material away from theback focal plane of the input lens! affects the accuracywith which the detected signals measure the 2-D in-ner product between the input and the stored datapatterns. We are currently exploring how these de-terministic variations will combine with the randomnoise to affect the system capacity and reliability.
arch-and-retrieve engine, operating on a database of 100 featurefound when the search query was the color feature vector for thesignal to the dark calibration value! for each of the 100 databasels in common between the input and each stored page!. ~c! Fourray were input. ~d! Measured versus expected correlation score.encoded into five characters with three nonbinary subfields per
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These deterministic signal variations can be re-duced by appropriate postprocessing of the detectedsignals or by preprocessing of the holograms. Thevariations are typically introduced by hologram-to-hologram fluctuations in diffraction efficiency or bynonuniform illumination across the SLM. Theformer can be calibrated for each reference beam anda scaling factor applied to detected signal values14;the latter can be corrected during hologram record-ing.17 A second calibration factor can be used to biasout the dark background signal.14 This dark signalomes from the finite contrast of the SLM device:uring a search with only a few ON pixels in the input
page, the remaining pixels are not completely OFF.Although each pixel transmits only a small amount oflight into the storage material, their diffracted con-tributions superimpose and can easily exceed the sig-nal from a few ON pixels. Subtracting a bias factorhelps but does not completely remove the problem,partly because of the deviation from the 2-D innerproduct described by our model14 and partly becausethe bias signal often uses up most of the detector’sdynamic range.
5. Experimental Demonstration
To demonstrate high-fidelity parallel searching of aholographic content-addressable memory, we storeda small multimedia database in the DEMON sys-tem.13 Each hologram represented one record froman IBM Query-by-Image-Content ~QBIC! database.15
In the QBIC system, searches are performed acrossfeature vectors previously extracted from the imagesrather than on the images themselves. Each recordincluded several alphanumeric fields ~such as imagedescription and image number! encoded for exactsearches and 64 fuzzy sliders containing the colorhistogram information ~percentage of each givencolor within the associated image!. To concentrateon low but nonzero color percentages, we ignored val-ues ,1%, truncated values .33%, and mapped thedomain 1–33% to a range of 100 pixels with a square-root nonlinearity. A separate portion of the SLMpage ~320 3 240 pixels!, pixel matched onto a CCD
etector for conventional address-based holographiceadout, was encoded with the binary GIF data forhe image thumbnail ~with a 6:8 modulation code13
and 7:11 Hamming error correction code!. Using anargon-ion laser at 514.5 nm, we recorded 100 holo-grams in an 8 mm 3 15 mm 3 15 mm LiNbO3 crystalin the 90° geometry,13 using a 62.5° span of referenceangles. These reference angles were mapped onto asecond CCD detector, and a 4 pixel wide 3 7 pixel tallbin was assigned empirically to each focused correla-tion peak. After recording, the portion of the SLMnot containing search data was blocked, leaving ap-proximately 100,000 SLM pixels. A single calibra-tion factor was then measured for each correlationbin by use of an input page with all pixels OFF.14
Each search, initiated by a user query, ran undercomputer control, including display of the appropri-ate patterns, detection of the correlation peaks ~av-eraging eight successive measurements to reduce
1
detector noise!, identification of the eight highest cor-elation scores, mapping of correlation bins to refer-nce beam angle, address-based recall of these eightolograms, decoding of the pixel-matched data pages,nd finally display of the GIF thumbnail images onhe computer monitor. Although the optical readoutccupied only 0.25 s, the software-based control andecoding on the 100-MHz Pentium computer slowedhe total search time, from search query to imageisplay, to ;5 s. Without the averaging, the entireptical search could be performed in a single camerarame ~0.016 s!. The object beam at the crystal con-ained approximately 20 nW for each SLM pixelurned ON ~intensity contrast ratio of 167:1!, whereashe readout reference beam contained ;100 mW.or simplicity in this initial proof-of-principle exper-
ment we chose to display the eight best imagesather than set a threshold.
To find images on the basis of color similarity, the4 sliders were used to input the color histogramnformation for the leftmost image in Fig. 3~a!; theolographic search process then output the otherhree images as the closest-matching images. Fig-re 3~b! quantifies the search fidelity. As expected,he leftmost image of Fig. 3~a! correlated stronglyith its own feature vector, but the system was alsoble to correctly identify the images with the highestross correlation These sliders could also be used toelect images by color distribution. In keeping withhe QBIC algorithm, sliders for similar colors werelso automatically added by the program, accordingo a color similarity matrix. For example, if the usersked for 30% red, the slider for 30% pink was alsonput. Figures 3~c! and 3~d! correspond to a searchor images containing 20% white and 20% light gray.lthough several images were ranked slightly higher
han they deserved ~red circle!, the system perfor-ance was impressive, considering that the back-
round dark signal level was twice as large as theesired signal. Note that 300 pixels corresponds to0.1% of the 640 3 480 SLM—in this experiment nottempt was made to optimize the number of SLMixels per character. In Figs. 3~e! and 3~f ! the al-hanumeric description field was used to search forhe keyword “shore.” Note that, because many char-cters are involved, both the expected and the mea-ured scores are large. However, we obtainedimilar results for exact search arguments as smalls a single character.
6. Conclusions
With the fuzzy-coding techniques and the signal-to-noise enhancements we have introduced, volume ho-lographic content-addressable data storage is anattractive method for rapidly searching vast data-bases with complex queries. Areas of current inves-tigation include implementing system architecturesthat support many thousands of simultaneously
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holograms in LiNbO :Fe,” in Digest on Conference on Lasers
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searched records and quantifying the tradeoffs be-tween capacity and reliability.
We thank J. Hafner for help with the QBIC imagesand feature vectors; M.-P. Bernal, H. Gunther, B.Lindsey, R. Macfarlane, J. Mamin, and R. Shelby fordiscussions; and G. Abstreiter for enabling S. Ko-bras’s thesis study at IBM Almaden.
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16. S. Kobras, G. W. Burr, H. Coufal, and G. Abstreiter are pre-paring a manuscript to be called “Optical correlation of digitaldata using volume holograms: diffraction analysis.”
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