DIFFRACTION BY SERRATED APERTURES

Diffraction of monochromatic light by rough apertures is analyzed. Correlation functions are derived for the electric field and for the intensity in the optical transform plane. The expectations calculated are over an ensemble of edges; their roughness is described in terms of a second-order density and associated characteristic function. It is found that in-plane roughness causes a speckle pattern. The analytical details are markedly different from the more usual case in which speckle is caused by longitudinal phase delay across an extended aperture. Detailed solutions are given for serrated gaps and edges.