Optical correlation of spatial-frequency-shifted images in a photorefractive BSO correlator

The optical cross correlation of an image with another image that was spatial-frequency shifted in one dimension was demonstrated in a photorefractive VanderLugt correlator. The first image was stored as a Fourier-transform hologram in a photorefractive Bi12SiO20 crystal (BSO) and was successively correlated with different spatial-frequency-shifted versions of a second image. We implemented the spatial-frequency shift by rotating a galvanometer mirror in an image plane, causing the Fourier transform to be shifted laterally in the BSO. We verified that the resulting operation in the BSO was an accurate complex multiplication of the shifted and the stored Fourier transforms. As many as 20 successive readouts were conducted without measurable erasure of the stored hologram. The dynamic range, saturation behavior, and other performance parameters were measured and are discussed.