Spatial fidelity of photorefractive image correlators

The set of equations describing photorefractive four-wave mixing of image-bearing beams has been solved in the presence of diffraction using a perturbation analysis assuming a strong uniform backward pump and a weak conjugate. To first order, it was found that the conjugate image is bilinearly related to the forward-pump and probe images. By using a Green's function approach, an analytical expression for the bilinear kernel was derived. This kernel, which governs the bandwidth of the conjugation system, is a function of the material parameters, the beam angles, and the crystal length. When a conjugator is used to determine the correlation between two images, the result was found to be a distorted version of the correlation image. This distortion was reduced when the image with the smallest extent was chosen as the forward-pump image.< >