Theory of reconstruction of volume holograms of speckle fields

The diffraction of light in the interior of a hologram recorded using a speckle field is considered. A quantitative calculation is made of the effects produced by a spatial resonance of a speckle field with inhomogeneities of a medium that reproduce the field intensity profile. It is shown that, contrary to the established view, the Kogelnik model of coupled plane waves gives quantitatively correct results for the diffraction efficiency even in the case of speckle-field holograms. Introduction of a speckle structure into recording beams shifts the spectral-angular selectivity curve, but does not change its profile in the case of phase holograms, whereas in the case of holograms with an amplitude component in the grating it alters additionally the maximum of this curve. Under normal conditions these effects are small and they become significant only when the holographic grating amplitude is less than or of the order of the total amplitude of the perturbations recorded in the hologram medium.