RECURSIVE PHASE RETRIEVAL USING BOUNDARY-CONDITIONS

The phase-retrieval problem for discrete multidimensional fields is investigated. In particular, a recursive procedure is developed for reconstructing a signal from the modulus of its Fourier transform. The information necessary to begin the recursion is the boundary values of the signal. Although it is not always possible to determine these boundary values from Fourier modulus data only, if the sequence has a region of support with a certain geometry then these boundary values can be determined. These geometries represent a generalization of the conditions for off-axis holography.