Reconstructed images from volume holograms in the Fraunhofer approximation: Analysis by a new spherical-wave expansion

Abstract

The “circular plane-wave” expansion of a spherical wave is newly proposed, and the reconstructed images from volume holograms are studied analytically by applying this method to the expansion of the object wave. The analysis is performed on the weakly coupled amplitude holograms in the Fraunhofer approximation. Both the amplitude and phase of the reconstructed waves are modulated, except the case of exact reconstruction, and are determined by recording and reconstruction parameters and the hologram thickness. The amplitude modulation by the volume hologram of a semitransparent object causes the space-variant or the space-invariant bandpass filtering effect by the spherical-wave or the plane-wave illumination of the object, respectively. The phase modulation causes aberrations and becomes small for a hologram having the large thickness.