Vectorial algorithm for the computation of light propagation equation based on Huygens' principle using the scalar theory of diffraction

摘要

In digital holography, computation of holograms is often reduced to calculations of fast Fourier transforms if the distance between the object plane and the hologram plane is large enough. Two classical approximations for solving this problem include a binomial series expansion of the distance and an elimination of the so-called inclination factor. We present here a vectorial algorithm which computes the discrete form of the light propagation equation obtained by the Huygens' principle for a bidimensional object. None of the approximations mentioned above have been used. This enables the computation of a diffraction pattern at any distance compatible with the scalar theory of diffraction. This vectorial algorithm has been implemented on workstations, on a Convex C-220 and on a Cray YMP computer. We focus our attention on the computing granularity of the problem and we present processing times and the associated performances for bidimensional images. Various holograms are computed and compared with those obtained by two traditional methods, namely, Fresnel transforms and the resolution of the rigorous scalar diffraction equation using discrete convolutions. We then consider the 3D case and modifications are proposed in order to parallelize this algorithm.