Abstract

A convolution formulation of Fresnel diffraction is presented. The diffracted amplitude is expressed as a convolution in either direct or reciprocal space. Approximations involve the use of parabolic wavefronts and the omission of the obliquity factor. The formulation is readily applied to many optical phenomena.

A theory of Fresnel transforms is given. The Fresnel transforms are expressed as a convolution in either direct or reciprocal space. Two examples of their use are given.

© 1966 Optical Society of America

Fresnel-Transform Representation of Holograms and Hologram Classification*

John T. Winthrop and C. R. Worthington
J. Opt. Soc. Am. 56(10) 1362-1368 (1966)

Consistent Formulation of Kirchhoff’s Diffraction Theory*

E. W. Marchand and E. Wolf
J. Opt. Soc. Am. 56(12) 1712-1721 (1966)

Integral-Transform Formulation of Diffraction Theory*

George C. Sherman
J. Opt. Soc. Am. 57(12) 1490-1498 (1967)

Fresnel Diffraction of Light by Slits in Semitransparent Films

Joel A. Gwinn, John F. Kielkopf, and Paul M. Griffin
J. Opt. Soc. Am. 56(10) 1338-1344 (1966)

Huygens–Fresnel–Kirchhoff wave-front diffraction formulation: spherical waves

Hal G. Kraus
J. Opt. Soc. Am. A 6(8) 1196-1205 (1989)