Abstract

We investigate the quality of image correlation produced by a photorefractive crystal, where the forward pump contains one image and the probe contains the other. The nonlinear Kukhtarev equations, which describe four-wave mixing in a photorefractive crystal, are solved in the steady state, assuming only one grating and the effects of diffraction. We linearize the set of equations by making the assumptions that the pump beams are undepleted and that the backward pump is uniform and much larger than the forward pump. The resulting equations are solved using perturbation techniques. The conjugate image is found to be a bilinear functional of the forward-pump images, separately. These linear transformations include spread in the transverse plane, which results from the diffraction of both the pump and probe beams. Since the crystal is placed in the Fourier plane of the system, a bilinear transformation, instead of correlation, is performed.

© 1991 Optical Society of America