Reliability of associative data search in phase encoded volume holographic storage systems G. Berger, M. Stumpe, W. Horn, C. Denz Institut f¨ ur Angewandte Physik Westf¨ alische Wilhelms-Universit¨ at M¨ unster Corrensstr. 2-4, 48149 M¨ unster, Germany Email: gberger@uni-muenster.de Abstract—We investigate the characteristics of correlation sig- nals obtained during content addressing under different realistic conditions. For two cases, either addressing with defective data or storing similar data sets, we present for the first time a theoretical approach and experimental results when employing phase-code multiplexing. I. I NTRODUCTION Volume holographic data storage has been thoroughly inves- tigated during the last decade and demonstrated its potential to become one of the next generation storage technologies (e.g. [1]). Its promising features are mainly achieved by exploiting the Bragg condition, which allows superposition of many holograms in one location of the storage media by varying the wavelength or angles of incident of the writing beams. Several superimposing techniques have been proposed, which are combinations or variations of these basic methods and spatial multiplexing (e.g. [2], [3], [4], [5]). Orthogonal phase- code multiplexing is a variant of pure angular multiplexing, in which a discrete number of reference beams are incident on the media from different angles. By means of a spatial light modulator the phase of each of these beams is individually controlled. Between successive recordings, the phases are specifically altered. In order to retrieve a particular data set, the appropriate phases have to be readjusted. Due to the use of orthogonal sets of phase shifts, particular data sets are reconstructed without crosstalk. This technique offers several advantages [6]. Most notably it avoids moving components in the storage setup and provides a signal-to-noise ratio that is two orders of magnitude higher than the case of pure angular multiplexing [7]. Moreover, the special characteristics of orthogonal phase encoding offer the opportunity to perform optical arithmetic operations, i.e. addition, subtraction and inversion, and to implement highly secure address-based data encryption techniques [8], [9]. However, the steadily enormous growing storage demands also require effective database search routines, especially in high capacity systems, in which conventional data search becomes inconveniently slow. Volume holographic storage sys- tems provide an efficient parallel search method by allowing content-addressed readout based on optical correlation. This technique has been demonstrated in systems based on angular or phase-code multiplexing [10], [11]. Here we investigate the impact of real conditions on the received correlation signals. We discuss two cases in which either the stored data possess various degrees of similarity or the storage media is addressed with defective data pages. Finally the results will be compared to the case when angular multiplexing is employed. II. CONTENT ADDRESSING IN VOLUME HOLOGRAPHIC STORAGE SYSTEMS During the storage process actually the Fourier transforma- tions of data pages, represented by a 2-D amplitude modulator in the signal arm, are recorded and superimposed in one location of the storage media, Fig. 1a. In order to perform associative recall, the media is addressed with some data page D ′ , Fig. 1b. This page is correlated in the Fourier R D -1 =F {S} (a) R D’ -1 =F {S } ’ 2 3 4 1 X X X X (b) L2 Fig. 1. Volume holographic data storage and retrieval: (a) Recording process; (b) Content addressing yielding correlation signals domain with all previously recorded pages. If the input page equals a specific stored data page, an exact facsimile of the reference wave, used to store that page, is reconstructed. The pure correlation signal can be accomplished by performing an inverse Fourier transformation, cf. lens L2 in Fig. 1b. The resulting correlation signal, whose actual appearance depends on the used multipllexing technique, can be computed by applying the convolution theorem [11]. In the case of phase-code multiplexing, when storing the i- th of N data sets with the reference wave j (bearing the phase shifts Φ ij ), the correlation signal is given by [11] R ∝ N  i=1 N  j=1 ( δ(x j ) ⊗  e iΦij · (D i * D ′ ) ) , (1) where ⊗ and * stand for the convolution and correlation re- spectively. Due to the inverse Fourier transformation the plane