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.
JOHN T. WINTHROP and C. R. WORTHINGTON, "Convolution Formulation of Fresnel Diffraction," J. Opt. Soc. Am. 56, 588-591 (1966)