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Theoretical and experimental results are presented for parallel EXCLUSIVE OR processing using thick Fourier holograms. The data pages used contained 1024 bits in a 32 × 32 format. A holographically stored data page is reconstructed together with an input data page that is imaged through the system. The amplitudes of the two wave fronts are adjusted to be equal, and their relative phase is adjusted to be 180°, thus producing the bit-by-bit EXCLUSIVE OR operation between the pages. Using an expanded reference beam for the geometrical configuration treated, it is calculated that the average dynamic range between a 0 and a 1 in the output power would be 17.4 dB. Experimentally, it is shown that excellent EXCLUSIVE OR results are obtainable. Photographs of these results are presented. An average dynamic range of 7.7 dB was measured, the decrease from the calculated value being primarily due to noise in the video method of detection used in the measurements. The probabilities of miss and false alarm and the total probability of error were also measured. The use of a small diameter reference beam, necessary in some applications, causes a large mismatch in the shapes of the two wave fronts, thus degrading the EXCLUSIVE OR results. It is shown theoretically and experimentally that using an aperture at the recording material produces partial compensation of the wave fronts, thus improving the EXCLUSIVE OR results.
© 1984 Optical Society of America
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