Differentiation and integration of images in different channels using one acousto-optic filter

We report a theoretical and experimental investigation of two-dimensional Fourier processing of an image using two channels when the image is differentiated in one channel and integrated in the other. Both operations are carried out by one acousto-optical (AO) spatial frequency filter operating in the AO diffraction regime in two symmetrical Bragg orders. The transfer functions of the channels are analyzed and differentiation and integration operations are demonstrated. The results are confirmed experimentally through optical Fourier processing of an image formed by radiation at a wavelength of 0.63 μm. An AO cell made of TeO₂, operating at a sound frequency of 44 MHz, is used as a spatial frequency filter.