Optical Image Synthesis (Complex Amplitude Addition and Subtraction) in Real Time by a Diffraction-Grating Interferometric Method

A coherent processing system for obtaining complex addition of two or more patterns in real time is described. In this system, a sinusoidal diffraction grating is used in the spatial-frequency plane. The input patterns to be added are displayed symmetrically about the optical axis in the object plane. The complex amplitude addition appears in th zero-order location in the output plane. Complex amplitude subtraction may be obtained by adding a 180° phase plate behind one of the input patterns. Displacing the sinusoidal diffraction grating by half a line pitch is also shown to change the performance of the system from addition to subtraction for two input functions, without the need for a phase plate. Experimental verification of the performance is presented. Analysis of the system for two input patterns is first given, then extended to the complex addition of multiple inputs.