The theory of deep holograms

Abstract

A simple theory of the first-order properties of holograms in thick photographic emulsions is presented. Following a combination by Denisyuk of the basic method of wavefront recon­struction with Lippmann’s method of colour photography, such holograms are produced by the interference of an object wave with a coherent reference wave, falling on the emulsion from opposite sides. It is shown, by using the first Born approximation, that such deep holograms have three properties which distinguish them from two-dimensional or ‘plane’ holograms: (1) They have directional selectivity, that is to say the image will appear only if the hologram is illuminated in the reconstruction within a certain angular zone. (2) They have colour selectivity, that is to say they will reflect only within a certain narrow waveband close to the original wavelength. (3) The second wave, which is a disturbance in two-dimensional holograms is as good as completely suppressed. All three are of great practical value. It is shown that holograms which are produced by strongly diffused, wide-angle illumina­tion, and which have a random, noise-like appearance, contain the information in the form of the auto-correlation function of densities or scattering powers between different space-elements in the emulsion.