Focal plane invariant algorithm for digital reconstruction of holograms recorded in the near diffraction zone

For digital reconstruction of holograms recorded in near diffraction zone, Discrete Fresnel is used as a discrete model of wave propagation. In applications where reconstruction of holograms in many observation planes is required, conventional implementation of Discrete Fresnel Transform reconstructs images of the object plane sections that are shifted with respect to each other depending on plane distance from the hologram plane. In the paper, a novel representation of Discrete Fresnel Transform, Focal Plane Invariant Discrete Fresnel Transform is suggested and illustrated which secures reconstruction of images automatically aligned with respect to the same optical axis. The transform invariance allows to substantially reduce computation burden whenever only a relatively small portion of the reconstructed wave front has to be analyzed and to ease analysis of the reconstructed wave front as a function of distance to the object.