Far-Field Diffraction and Boresight Error Properties of a Two-Dimensional Wedge*†

Abstract

An optical diffraction theory has been developed which can be used to predict the forms of the far-field diffraction patterns and boresight error effects of a two-dimensional wedge made from two semi-infinite plane parallel plates. The solution is strictly an optical one, since the wavelength has been assumed to be small compared with the dimensions of the rectangular diffracting aperture, and also because the rectangular diffracting aperture is assumed to lie in the “near-field” of the wedge. In tracing the directly transmitted and all the multiply internally reflected wave fronts through the wedge to the plane of the diffracting aperture, amplitude losses due to reflection and absorption, phase changes due to increases in optical path, and changes in width of the various wave fronts are all evaluated in the plane of the diffracting aperture. When once the amplitude and phase distributions are known in the plane of the diffracting aperture, the Kirchhoff integrals are readily written and integrated. The UNIVAC computer can then be used to evaluate the forms of the far-field diffraction patterns characteristic of the wedge and diffracting aperture. These far-field diffraction patterns are in general non-symmetric and have forms which are functions of the plane of polarization of the incident electric vector and nine other variables. For arbitrary values of the variables, the forms of these far-field diffraction patterns cannot be understood in terms of conventional plane parallel plate theory, but in certain limiting cases plane parallel plate theory is useful. Boresight error curves have been evaluated as functions of many of the variables, and the magnitudes and signs of these errors are in agreement with the previously computed diffraction patterns. “Qualitative” checks on the theory have also been made by comparing the calculated forms of the far-field diffraction patterns for a particular glass wedge with those which were photographed experimentally. All of the calculated changes in form of these far-field diffraction patterns have been observed experimentally, and there is good reason to believe that a quantitative check might also be possible under more favorable experimental conditions.