We introduce a local signal decomposition method for the analysis of three-dimensional (3D) diffraction fields involving curved surfaces. We decompose a given field on a two-dimensional curved surface into a sum of properly shifted and modulated Gaussian-shaped elementary signals. Then we write the 3D diffraction field as a sum of Gaussian beams, each of which corresponds to a modulated Gaussian window function on the curved surface. The Gaussian beams are propagated according to a derived approximate expression that is based on the Rayleigh–Sommerfeld diffraction model. We assume that the given curved surface is smooth enough that the Gaussian window functions on it can be treated as written on planar patches. For the surfaces that satisfy this assumption, the simulation results show that the proposed method produces quite accurate 3D field solutions.
© 2012 Optical Society of America
Fourier Optics and Signal Processing
Original Manuscript: March 9, 2012
Manuscript Accepted: April 26, 2012
Published: June 29, 2012
Erdem Şahin and Levent Onural, "Scalar diffraction field calculation from curved surfaces via Gaussian beam decomposition," J. Opt. Soc. Am. A 29, 1459-1469 (2012)