Abstract

The Abbe transform is used to derive rigorous algebraic formulas for the wave function describing Fraunhofer diffraction at apertures in the form of arbitrary polygons. Two remarks bring the Abbe transform and the Abbe theorem into the context of the history of diffraction.

© 1982 Optical Society of America

Simple derivation of formulas for Fraunhofer diffraction at polygonal apertures from Maggi–Rubinowicz transformation

Salvatore Ganci
J. Opt. Soc. Am. A 1(5) 559-561 (1984)

Simple derivation of formulas for Fraunhofer diffraction at polygonal apertures: errata

Jiří Komrska
J. Opt. Soc. Am. 73(6) 864-864 (1983)

Fraunhofer diffraction at straight-edged apertures

Winifred Sillitto
J. Opt. Soc. Am. 69(5) 765-770 (1979)

Diffraction patterns of simple apertures

Richard C. Smith and James S. Marsh
J. Opt. Soc. Am. 64(6) 798-803 (1974)

Fresnel diffraction and fractal patterns from polygonal apertures

J. G. Huang, J. M. Christian, and G. S. McDonald
J. Opt. Soc. Am. A 23(11) 2768-2774 (2006)