Real-Time Complex Spatial Modulation

We may convolute two spatial distributions without photographic processing by square-law recording the sum of their diffraction patterns with a dynamic spatial sensor and Fourier transforming the result electronically. The coherently illuminated input distributions are spatially separated at the front focal plane of a spherical lens so that the spatial Fourier transforms are detected with a relative phase shift between the two transforms that are a linear function of the coordinates of the transform plane. The result is that the detection is sensitive to both amplitude and relative phase of the two Fourier transforms. This technique is used to operate directly on transparencies of interest and the result is displayed on a cathode-ray tube. Spatial distributions may be compared for differences or a distribution may be interrogated for images of a particular shape.