Spatial filtering in optics

Starting with the formulation of H. H. Hopkins for the image forming properties of an optical system in terms of a coherence factor over the object plane, the two extreme cases of complete coherence and incoherence are considered. The incoherent case is treated briefly as a low-pass spatial frequency filter. In the case of coherent illumination, it is shown that the optical analog of such well-known electrical concepts as equalization [17], edge-sharpening, and the detection of periodic and isolated signals in the presence of noise can be carried out with relative ease. A detailed theoretical treatment of the problem together with illustrations emphasizes the analogy between optical and electrical filtering.