THEORY OF HOLOGRAPHY

Abstract

Computation of the amplitudes of the diffracted fields which are produced when a reflection hologram or a thick transmission hologram is illuminated requires that the 3-dimensional nature of the hologram be accounted for. A general analytical method is formulated for computing the diffracted fields in terms of the initial exposing field, the film characteristics, and the illumination field, taking into account the entire emulsion volume. This method, which is applicable to both transmission and reflection holograms, involves characterizing the emulsion volume by the volume density of scattering particles, with the diffracted field being found by coherently summing the scattered waves, neglecting multiple scattering. The initial exposing field and the illumination field are expressed in the form of a sum of plane or quasi-plane waves, and the diffracted field is expressed as a sum of waves, each of which is found by solving a variation of the same basic problem. This problem consists of computing the directions, amplitudes, and phases of the first-order diffracted waves produced when a 3-dimensional array of scattering particles having a sinusoidal density distribution is illuminated by a plane wave. The solution of this problem is considered, with the directions and phases of the diffracted fields being computed for both transmission and reflection holograms. The amplitudes are computed for the case of transmission holograms and the analytical expressions are evaluated numerically for a number of particular cases to determine the effect of varying different parameters on the amplitudes of the diffracted waves. The results are compared with experimental data obtained by making a careful study of different holographic diffraction gratings. The results of the analytical method described above are compared with the results of the method whereby the hologram is characterized by the transmittance, and it is shown that with respect to the computation of the directions and phases of the diffracted waves, the two methods are equivalent for the case of transmission holograms. The case where the reference beam is composed of a series of waves (ghost imaging) is considered using both of the above methods, and the translational sensitivity and background noise which arise in this case are investigated. An experiment dealing with translational sensitivity was carried out and the experimental results were found to be in good agreement with the theory. The duplication of holograms is considered and the duplication process is described in terms of making a hologram of a hologram, rather than in terms of making a contact print. Experimental results are presented to support this point of view and the effects of varying the characteristics of the illumination wave are described. The duplication of both transmission and reflection holograms is dealt with and a simple method for duplicating reflection holograms is proposed and discussed.