We propose and demonstrate experimentally a method for utilizing a dynamic phase-encoded photorefractive memory to realize parallel optical addition, subtraction, and inversion operations of stored images. The phase-encoded holographic memory is realized in photorefractive BaTiO(3), storing eight images using Walsh-Hadamard binary phase codes and an incremental recording procedure. By subsampling the set of reference beams during the recall operation, the selectivity of the phase address is decreased, allowing one to combine images in such a way that different linear combination of the images can be realized at the output of the memory.

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1 Introduction In the context of optical information processing great interest is focused on the development of systems for optical data storage. Photorefractive materials are widely used in the schemes which have been proposed in this domain. They offer the possibility to easily obtain thick phase holograms with great diffraction efficiency. Volume holography allows the multiplexing of a great number of holograms within the medium by using the Bragg selectivity of the gratings to independently address the images. Several methods to realize multiplexing have been widely discussed during the last years: In the angular multiplexing technique the angle of the reference beam is varied from one image to the next, while in wavelength multiplexing the wavelength of the laser is the variable parameter to obtain independently addressable holographic gratings. The phase encoding method has been pro posed as a third possibility (Ref. 1): Here a set of reference beams are incident on the medium under a discrete angular spec trum as in the case of angular multiplexing, but the beams are not switched in suc cession but illuminate the medium conti- nouslV. The variable parameters which make up the address of a single image are the phase relations between the reference beams as we will describe in Chap. 2. Hence a phase modulator is needed which allows to adjust the relative phases of the set of ref erence waves. A sketch of a possible setup is shown in Fig. 1. An expanded beam is used in the signal arm of the holographic configuration Fig. 1 to create the respective image wave by illumination of a spatial light modulator or simply a series of diapositives. In the reference arm it is incident on a computer generated hologram to create a focus array in the Fourier plane. Here the p' ase modulator is placed which is a special purpose liquid crystal display, capable of independently inducing a phase shift.at each of the spots of the focus array. The beams are recombined in the medium where they interfere with the signal wave. In the our case the medium is a photorefractive BaTiO 3 crystal oriented for optimum holographic efficiency. With this setup alignmeit problems and speed limitations due to mechanical adjustment as occuring in the case of conventional angular multiplexing are overcome as well as technological complications associated with wavelength multiplexing.

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