Optical Fourier Transformation of Area-Modulated Spatial Functions

A one-dimensional function may be represented spatially as an aperture in an opaque screen where the aperture's width is proportional to the function. When such an area-modulated screen is the input to a standard coherent optical fourier transformer, the amplitude of the light along one axis on the output plane is proportional to the fourier transform of the original function. Continuous and sampled area modulation for single and multichannel operation are discussed. Experimental agreement with the expected results is obtained. Hybrid configurations combining area and optical-density modulation are discussed.