The Phase-space Interpretation of Self-imaging and the Phase Retrieval Problem

摘要

The problem of recovering the complex amplitude of optical signals from intensity measurements is studied in the context of phase-space optics. Special attention is given to periodic wavefronts subject to the self-imaging phenomenon. It is shown that for the case of bandlimited periodic signals perfect phase-retrieval can be achieved by recording the intensity in a finite set of fractional Talbot planes. This corresponds to a rigorous discrete formulation of phase-space tomograpy. Approximations inherent to the numerical implementation of phase-space tomography can be interpreted as a consequence of deviating from the ideal case of a periodic bandlimited signal, rather than as the byproduct of discretization.