Serrated Apertures: Statistical Diffraction Theory and Experiments

Author: Morris, George Michael

Year: 1979

Degree: Dissertation (Ph.D.)

Advisor: George, Nicholas A.

Committee Member: Unknown, Unknown

Option: Electrical Engineering

DOI: 10.7907/5ghb-zk17

Abstract

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 edges and gaps. 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. The serration causes a damping of the major spike in the edge transform and it leads to considerable scattering of the radiation. It is shown that edge statistics may be determined by processing the transform plane intensity measurements. Edge roughness (or standard deviation) is established from transform plane measurements along the central spike. For edges and gaps, intensity measurements of the spread of energy perpendicular to the central spike are Fourier transformed to determine the functional form for the correlation coefficient of the edge roughness. Two classes of serrated edges have been fabricated to verify the theory. One group is generated by plotting computer-generated number sets, with independently controlled roughness and correlation length, on microfiche. A metallic edge is then made from the film images using photo-etching techniques. These edges have been particularly useful in verifying the theory.

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