An adaptive constraint algorithm for image understanding of digitally reconstructed in-line holograms

Accurate quantitative decoding of inline holograms can be achieved by A/D sampling of the hologram followed by digital reconstruction. Using a standard reconstruction technique, the resulting image bandwidth is limited by the size of the hologram. In addition, the phase ambiguity inherent in magnitude-only hologram recording yields an out-of-focus conjugate artifact called the twin image. Both limited bandwidth and twin image restrict the available resolution well below the theoretical diffraction limit. An algorithm is presented that addresses both problems by iteratively combining phase retrieval and spectrum continuation to produce estimates of the phase of the recorded hologram, and both magnitude and phase of the hologram beyond its physical recorded boundaries. Since algorithms based on spectral continuation are sensitive to the constraints imposed on the extent of the objects being imaged, a method for selecting these constraints adaptively, which greatly accelerates convergence of the algorithm, was developed. Examples demonstrate the degree of improvement in resolution with phase retrieval only. The algorithm suggests the possibility of superresolution holography, in which the diffraction limit is exceeded.