Holograms made with diffused illumination have some interesting properties. As shown by Leith and Upatnieks, this hologram technique involves both the dispersion of each resolution element and an increase of the signal bandwidth by a convolution of the spatial-frequency spectrum of the object with the noise-like diffused illumination. This paper presents a quantitative treatment of this phenomenon. Expressions are derived for the spread of the hologram. The results show that this spread is increased with diffuse illumination by an amount corresponding to the product of the mean-square value of the phase of the diffuse illumination and its spatial-frequency bandwidth. It is assumed that the light emerging from the diffusing element is a wavefront with a random phase.
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