Parallel Associative Search by use of a Volume Holographic Memory*

Parallel Associative Search by use of a Volume Holographic Memory* Xiaochun Li', Fedor Dimov, William Phillips, Lambertus Hesselink, Robert McLeod' Department of Electrical Engineering, Stanford University, Stanford, CA 94305 'Siros Technologies, San Jose, CA 95134 +Email: xiaochun@kaos.stanford.edu Abstract Volume holographic memory can offer massively parallel associative search capability in addition to high capacity data storage. After holograms have been stored into a photosensitive material, an optical correlation of an input user query against all eo-locationally stored patterns can be made simultaneously, resulting in fast search speed. We describe a correlator based on a 90 degree geometry holographic data storage system using thick (-1 em) storage media, Two important parameters considered are the correlation error rate and minimum size of the search template. A minimum template area less than 0.05% relative to the whole image area has been demonstrated. Due to the strict Bragg selectivity of volume holograms in thick media, the correlator has very small sh$t invariance. Thus it lends itself best to the search of relational databases, where information can have a fixed position on the stored record. We describe a demonstration database application designed to make best use of the volume holographic correlator. 1. Introduction In a volume holographic memory, multiple holograms are stored in one common location in a thick, photosensitive optical material such as an iron-doped lithium niobate crystal. When the multiplexed holograms are illuminated with an object beam that bears a search data pattern, all of the reference beams are reconstructed simultaneously. The intensity of each reconstructed reference beam is proportional to the correlation of the search pattern and the data page previously recorded with that particular reference beam. The array of correlation signals may be captured by a correlation CCD camera, and used to retrieve the holograms that match the search pattern, providing an optical associative search capability for the volume holographic memory. Figure 1 shows the * This work was supported by Air Force Rome Laboratories, Contract No. F30602-97-C-0343, under a subcontract from Siros Technologies. basic geometry of a volume holographic associative search system based on this principle. Galvo mirror Y Reference Data CCD CCD Correlation lens Fig. 1 Optical layout of a volume holographic associative search system. U2 half wave plate. PBS: polarizing beam splitter. SLM: spatial light modulator. S: shutter, LN: lithium niobate storage medium. If each stored hologram (page) represents one data record of a database, the optical correlation process in essence simultaneously compares the input search key against the entire database. The high parallelism with which this operation is performed gives the volume holographic associative search system an inherent speed advantage over a conventional search, especially for the management of a large database. For examplell], for an unindexed conventional retrieve-from-disk-and-compare software-based database, a search over 1 million 1-Kbyte records would take -40s (assuming the speed is limited only by the hard disk readout rate, 25Mbyte/s). In comparison, with off-the-shelf video rate SLM and CCD camera, a holographic associative system could search the same database in -30ms-resulting in more than looox improvement. This paper describes the demonstration of an associative search system utilizing the configuration shown in Figure 1. The storage medium is a 1 cm x 1 cm x 2 cm irondoped lithium niobate crystal. The liquid crystal spatial 0-7695-0978-9/00 $10.00 0 2000 IEEE 78

light modulator (SLM) is a 1K x 1K array, with a pixel size of 15.6~15.6 pm2, and a video frame rate. It was made by IBM Yorktown under the HDSS consortium. A Dalsa CCD camera (also 1K x 1K with video frame rate) was used to capture the retrieved data.. The CCD pixel size is 12x12 p2. The imaging lens (Ll) was manufactured by Rochester Photonics, under the HDSS consortium, to image the SLM to the CCD with low distortion, through a 1 cm path length of lithium niobate storage medium. A Kodak Megaplus CCD camera with 1008~1018 pixels (pixel size: 9 x 9 pm2) was used to capture the correlation signal. The integration time of the Kodak CCD camera is adjustable, so it is adaptable to a wide range of correlation signal intensity levels. A General Scanning galvanometer mirror is utilized for reference beam steering. With the reference telescope, the reference beam incidence angle can be changed while keeping the incident position on the crystal fixed. 2 Noise sources and suppression In the holographic associative search system shown in Figure 1, the main noise comes from the vertical overlap of correlation spots. Figure 2 shows a schematic diagram of the output profile of the holographic correlation system. While imprinting a small query pattern on the object beam and illuminating the stored holograms, multiple correlation spots along the vertical direction are generated because of the limited vertical shift invariance of volume holograms. Those spots with vertical position q=o represent the correlation signal between the input search key image X and different stored images I,. Spots with vertical position q#o represent the correlation between each stored image I, and search key vertically shifted by q-pixels. For holograms comprising digital data, the shifted image is totally different from the unshifted, so the intensity of correlation spots with qdl is thoroughly independent of the intensity of spots with q=o. Because of the finite correlation spot size and limited vertical separation distance, vertically adjacent correlation spots partially overlap each other, thus generating correlation crosstalk noise. To minimize the effect of the correlation crosstalk noise, a data sample window around the center of each correlation spot was applied, as shown in Figure 2. The correlation signal intensity is calculated only within the sample window. When the height of the window was set to 5 CCD pixels, the minimum search key size was about 3% of the entire SLM page (1024x1024 pixels). When we set the window height to 1 or 2 CCD pixels, the minimum search key size was reduced to 0.2% of the SLM page, resulting in 15X improvement. The high-frequency contrast of the IBM TN-liquid crystal SLM used in the associative search testbed is less than 5, so OFF pixels still have a significant reflectivity. For a small search key, the light contributed by the OFF pixels around the search key window contributes substantial background level to the expected correlation signals. The smaller the search key, the more serious the background noise. When we used a physical mask to block the SLM background area, the minimum search key was further reduced to less than 0.05% of the SLM page. Fig. 2 Filled ellipses represent correlation spots. Dotted rectangles represent the data samplewindows. Reducing the height of the data sample windows minimizes correlation crosstalk noise. 3. Search key size requirement 8 ". 1 om 10000 100000 1000000 10000000 Match number (SLM pixels) Fig. 3 Measured correlation signal intensity as a function of the expected response (the number of SLM pixels in common between an input key pattern and the corresponding stored page). The change of the matching pixel number was achieved by changing the input search key size. The data shown in Figure 3 provides information about search key size required for the operation of the associative search system. We first recorded a hologram with a random data page. The probability of each pixel being ON or OFF is 0.5. The exposure time was controlled so that the diffraction efficiency was equal to that when 200 holograms were recorded sequentially. We then utilized query patterns of varying size to illuminate the stored hologram, and measured the correlation signal intensity. The experimental result is shown in Figure 3. 79

The horizontal axis represents the number of SLM pixels in common between the query pattern and the corresponding stored page. For digital images, this match number in fact represents the correlation (2D inner product) between the query key and the stored image. The vertical axis is the measured correlation signal intensity. As can be seen, the larger the match number, the larger the correlation intensity. The flat portion of the data corresponding to small match numbers arises from light scattered primarily from SLM OFF pixels as described previously. Figure 3 indicates that to be detectable against this scattered light level, the match number should be in the neighborhood of 30,000 pixels. This translates into a minimum search key size -47,000 pixels for the (8,11,7) modulation code we have typically used with this system. Table 1 shows the inferred minimum search key size for several other modulation codes. K A L N Table 1 Minimum search key size for several I modulation codes Msg I Chunk I Wt I Sparseness I Min. search 1 length m size b w w Ib key size 6 12 2 0.17 180,000 1 2 1 0.50 60.000 8 11 7 0.64 1 47,000 6 12 10 0.83 1 36,000 4. Search demonstration modulation code for the demonstration because it appears to have the optimum sparseness for our system [2], and it has the relatively high code rate of 0.73. Fig. 4 An example page from the demo database. Figure 5 shows the generated image from the data record shown in Figure 4. A mask, as shown in Figure 6, has been used to remove areas of poor image quality. Each input field has a fixed position in the image. For example, the address map is encoded at the bottom of the image; the picture is placed just above the address map, and the resume field is placed at the top of the image. The most important advantage of a volume holographic associative memory over other correlation methods is its very high search speed. However, due to the strict Bragg selectivity of volume holograms, volume holographic memory has no (or very small) shift invariance. Based on these characteristics, the most appropriate application area of a volume holographic memory is the management of a large relational database, where each data field has a fixed position. 4.1 Demonstration database We developed a database to demonstrate the parallel search ability of a volume holographic associative search system. The demonstration database is a simple relational database that contains personal information of many individuals. As shown in Figure 4, each data record of the demo database consists of the following 10 fields: first name, last name, date of birth, phone number, gender, features, address, resume, picture and address map. Data of those 10 fields is converted to a binary image by one specific modulation code. The generated image is imprinted on the object beam by the SLM (refer to Figure 1). The program interface shown in Figure 4 also contains the definition of modulation code parameters. We selected an (8, 11, 7) Fig. 5 Generated SLM image from the data record shown in Figure 4. The mask shown in Fig. 6 has been used to remove areas of poor image quality. Each database field has a fixed position in the image. A modulation code with message length m=8, chunk size 641, weight m7 is applied. The mask is generated based on the SNR distribution of images retrieved from the holographic data storage system. Figure 7 shows the variation of bit error rate 80

(BER) with pixel-usage (defined as the ratio of the number of used pixels to that of the total SLM pixels). When pixel-usage is reduced from 100% to 80%, bit error rate drops from 1.6% to 0.01%, more than 100 times improvement. Further reduction of the pixel-usage drops the bit error rate at a slower rate. Based on this experimental result, we set the pixel-usage of the mask file as shown in Figure 6 to 80%. Fig. 6 The mask used to remove areas of poor image quality. The mask is generated based on the SNR distribution of images retrieved from the holographic storage system. The useful (black) area occupies 80 percent of the entire SLM page (1024x1024 pixels in size). second datum represents the existence of the address map, the third represents the existence of the first name field, the fourth datum is the length (in byte) of the fist name, and so on. The header is placed in the central part of the encoded bitmap file. On decoding, the control software first examines the header. If the first name is found to be absent, for example, the program simply skips this field. Otherwise, it continues to fetch the length of the first name, decode the encoded data, and, fially get the value of the fist name field. Both the picture and the address map contained in each data record are uncompressed bitmap images, 128x128 pixels in size with 256-colors. To achieve reliable search performance, we found the number of SLM pixels assigned to each data field has to be at least around 50,000, which is about 5% of the entire SLM page. This relatively large search key size results from the low contrast of the SLM, which cannot be masked when running the demo application. For example, if the length of the fist name field is 20 characters, or 20 bytes. Using the (8, 11,7) modulation code, 20 bytes will be transferred to a block of 220 pixels. This means the first name field has to be repeated 227 times in the encoded bitmap file in order that a total number of approximate 50,000 pixels can be assigned to the first name field. All other fields, except the picture and address map, are also required to repeat many times in order to achieve reliable search performance. For the purpose of data safety, the header in the encoded bitmap file is forced to repeat 100 times. 4.2 Search demonstration 1 1.E-064 i 0 20 40 60 80 100 1 Pixel usage (%) I Fig. 7 Bit error rate (BER) versus pixel-usage. When pixel-usage is reduced from 100% to 80%, BER drops by 160 times. When pixel-usage is further reduced, BER drops at a slower rate. - In addition to the 10 fields as required by the demo database, the encoded bitmap file (Fig. 5) also contains a header. The header stores the basic information of the Fig. 8 An example search key image. The query input is Bill as the first name field and Male as the gender fie d. Ode (m=83 & ly yif=7) and the mask shown in Figm is 81

testbed. Each hologram represents one record from the demo database. The reference beam angles were chosen in such a way that each reference beam was focused onto a unique portion of the correlation camera. An experimentally verified exposure schedule was used to achieve a uniform diffraction efficiency distribution among the multiplexed holograms. The processing software converts the user query inputs into a search key binary bitmap file by using the same modulation code and encoding mask as used to generate previously the stored data pages. Shown in Figure 8 is an example search key bitmap file. Each search operation includes the following operations: imprinting the search key on the object beam and illuminating stored holograms; detection of the correlation signal, normalization by hologram strength, ranking of the correlation intensity, mapping of selected correlation spots to reference beam angles, address-based recall of the selected hologram, decoding of the retrieved data page, and finally, display of the search result on the computer monitor. The time taken in each processing step is shown in Table 2. The total recycle time is -10 seconds. Table 2 Time taken in each processing step ODeration Search key bitmap file generation in the host computer (Pentium 400). Copy the search key bitmap file to the SLM control computer via network. Display search key on SLM. Close reference beam shutter, open object beam shutter. Correlation signal readout. Correlation signal normalization, ranking and galvanometer steering ( E 200 holograms). Close object beam shutter, open reference beam shutter. Data caoture. I Time(s r I 0.02 2 1 3 0.1 < 0.001 3 0.1 Decoding and display. 1 0.8 I As can be seen, the switching of the slow mechanical shutters and copying the search key from the host computer to the SLM control computer via network occupies 80% of the recycle time. Displaying search key on the TN LC SLM takes 10% of the recycle time. These operations would not limit to the highest possible search speed of a second generation associative retrieval data system using advanced components. For instance, with acoustic optic beam steering, the switching time could be less than 1 ps. Several SLMs can achieve frame rates in excess of 1OOOfps. The Texas Instruments DMD SLM can switch pixels at a rate of more than 10,000 per second. Using dedicated coding and decoding electronics, data can be acquired and displayed in less than 1 msec. The fundamental limit to the search speed comes from the key generation and correlation signal processing (ranking and normalization). Currently these two steps take about 20 nis in our search experiment, corresponding to a limiting search speed for the current configuration of 10,000 pageslsec. After applying normalization to the correlation spot intensities, the processing software ranks all the correlation spots on the order of correlation intensity values. By default, the search program displays the fist search result (which corresponds to the largest correlation intensity) on the computer monitor. By pressing other control buttons such as NEXT and PREVIOUS, the user can review through all search results on the order of the matching level. The performance of the volume holographic associative memory was evaluated in a number of search demonstrations. When any one of the 10 database-fields was used as the query key, the expected records were consistently within the top 10 of the 200 search results. With a larger query key (for example, using the combination of the fust name and last name field as the query key) better search results were obtained. Figure 9 is a partial picture that we used as the query key. Eighty percent of the photo in the query key has been erased, but still returns the correct record. The retrieved record is virtually identical to the original record shown in Figure 4. Fig. 9 A partial picture as the query key. 80 percent of the data in the picture has been erased. The first search result is identical to that shown in Figure 4. Figure 10 shows the distribution of bit error rate (BER) among the 200 holograms. The bit error rate was obtained by comparing the decoded output data from the retrieved bitmap image with its corresponding original data. It is defined as the ratio of the number of error bits (only in the picture and address map fields) to that of the total bits in the picture and address map fields. No error-correction code was used. The average raw bit error rate is 0.12%. 82

. 50 100 150 200 Hologram number Fig. 10 Bit error rate distribution among the 200 holograms. 5. Conclusion We have demonstrated parallel search of a volume holographic memory using a multimedia relational database as a demonstration application. The primary advantage of this approach arises from the inherent parallelism of holographic memory, which opens the possibility to achieve search speeds considerably faster than software approaches. Associative search capability is relatively easily incorporated into holographic data storage systems, providing the added capability to perform rapid hardware-based searches of massive amounts of stored data. 6. References [l] G.W. Burr, S. Kobras, H. Hanssen, H. Coufal, Contentaddressable data storage by use of volume holograms, Appl. Opt., Vo1.38,.No.32, 1999, pp. 6779-6784. [2] Xiaochun Li, William Phillips, Fedor Dimov, Low-cost optical search of digital holographic storage systems, Final report to Air Force Rome Laboratories. Contract No. F30602-97-C-0343. Oct., 2000. 83