Abstract

We compute and measure diffraction patterns of nested polygonal apertures. A nested polygonal aperture comprises concentric polygonal strips (alternating transparent and opaque) of decreasing size. The key to writing a simple closed-form solution lies in decomposing the polygon into elemental triangles having a gratinglike structure. We present results for the particular case of a regular pentagon; here the elemental building blocks are gratinglike segments. First, we compute the optical transform of these gratinglike segments. Then we combine them appropriately to arrive at a formula for the diffraction pattern of a nested pentagonal aperture. The solution is especially well suited for computer calculation, and we show the results of such a calculation. Examining the diffraction pattern over a wide dynamic range (70 dB down from the diffraction peak) reveals fascinating low-intensity features. The combined effect of the gratinglike structure and the segment edges produces double-nested pentagons in the diffraction pattern. These features have been observed and measured experimentally.

© 1988 Optical Society of America