Representation-related errors in binary digital holograms: a unified analysis

Images reconstructed from binary digital holograms are degraded by errors due to the binary representation of the complex-valued object spectrum and by errors due to computational and plotter limitations. In this paper, representation-related errors are analyzed in terms of false images that appear in the desired reconstruction order and in adjacent diffraction orders. It is shown that the false images are strongly dependent on the manner in which the object spectrum is sampled and on the mapping from spectral sample to binary transmittance. Three categories of digital holograms are distinguished: those that sample the object spectrum at the center of each hologram cell; those that sample at the center of each aperture; and those that sample at each resolvable spot. In going from the first to the third category, the reconstruction is successively less degraded by false images. For the third category, there are no false images in the desired reconstruction order and only one false image in each adjacent order. The two methods in this category differ only in the suppression of these false images.