title: Ray matrix analysis of the fast Fresnel transform with applications towards liquid crystal displays.
abstract: We reexamine a previously published algorithm for performing a fast Fresnel diffraction calculation that uses two Fourier transform operations and is computationally much faster than the conventional approach. We analyze this technique using a ray matrix analysis and find explicit expressions for the maximum and minimum distances over which this algorithm is accurate. These distances coincide with the experimental distances that are appropriate when patterns are encoded onto liquid crystal displays. We show two examples that confirm our ideas. We expect that these results will be very useful for computational comparison with experimental studies of a variety of diffraction phenomena.
authors.affiliation: Department of Physics, San Diego State University, San Diego, California 92182-1233, USA. jdavis@sciences.sdsu.edu
authors.forename: Jeffrey A
authors.initials: JA
authors.lastname: Davis
authors.forename: Don M
authors.initials: DM
authors.lastname: Cottrell