Holography in a Random Spatially Inhomogeneous Medium

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Abstract
The Huygens-Fresnel principle, extended to a medium that exhibits a random spatial variation in the index of refraction, is used to calculate the resulting fringe patterns in the Fresnel-Fraunhofer and point-reference Fourier-transform methods of holography. The resolution limits pertaining to these two methods are derived. In the Fresnel-Fraunhofer method, the effect of the medium is a lateral reduction in the size of the hologram that leads to a corresponding loss of resolution. In the point-reference Fourier-transform method, on the other hand, the medium does not limit the lateral extent of the hologram but gives a uniform reduction in amplitude to the resulting fringe pattern. Thus in the latter method, resolution is not degraded; but the medium does limit the size of objects that can form holograms. Numerical results pertaining to underwater holography are given.