A general solution for two-dimensional volume holograms

Abstract

We inv estigate the problem in which a volume hologram is produced by two waves of arbitrary amplitude and phase distribution (the only restriction being that they must obey the rules of geometrical optics), and the developed hologram is illuminated by one of the waves having the same phase distribution but not necessarily the same amplitude distribution. Coupled partial differential equations are derived and solved in the form of an infinite series valid for both transmission and reflection holograms. For transmission holograms a simple approximate solution is given for the amplitude of the reconstructed wave in the immediate vicinity of the input surface.