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 shown 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 presented for serrated gaps and edges. Both space and wavelength dependences are included and solutions for cross correlations of electric field and intensity are obtained. These are valid for arbitrary roughness and correlation coefficient. Experiments are described contrasting the optical transforms of serrated and sharp edges. Good qualitative agreement is obtained with the theory. The serration causes a damping of the major spike in the edge transform and it leads to considerable scattering of the radiation.