The effect of vignetting on the impulse response of coherent optical processors

Passive linear electronic filtering systems are often assumed to be characterized by time-invariant impulse responses. It is shown that due to vignetting, their optical analog, the general coherent optical Fourier processor, is represented by a function analogous to a time-varying response. Hence, the usual convolution integral cannot be applied to it. Limits are also given on the maximum size of the input functions with respect to the aperture of the Fourier-transforming lenses. For "band-limited" Fourier filter functions, the impulse response becomes analogous to being time invariant for input sizes within specified bounds. These bounds represent a tradeoff between input size and bandwidth.