Far-Field Diffraction Patterns of Single and Multiple Apertures Bounded by Arcs and Radii of Concentric Circles*†

Abstract

Some equations are derived for computing the form of the far-field diffraction pattern of an aperture bounded by arcs and radii of concentric circles whose dimensions are large compared with the wavelength of the incident radiant flux and over which the amplitude and phase are constant. These equations are derived in such a way that it is possible not only to compute the form of the far-field diffraction pattern of individual apertures bounded by arcs and radii of concentric circles, but also for combinations of such apertures over which the amplitudes and phases are constant but differ from aperture to aperture. With the aid of an IBM 7090 computer, these equations have been used to compute the forms of the far-field diffraction patterns of a 60° sector aperture, a semicircular aperture, and an aperture formed by arcs and radii from concentric circles, and three-dimensional models have been constructed to describe the radiant flux distribution. A start has also been made on the more complicated problem of multiple apertures by computing the form of the far-field diffraction pattern of two adjacent semicircular apertures, over which the amplitudes and phases are constant in the two apertures, but the amplitudes in the two apertures have been assumed to be equal and the phases different. Some corresponding photographed far-field diffraction patterns are also included for comparison purposes and to illustrate the wide variety possible.