Uniqueness results for the phase-retrieval problem for radial functions

Abstract

A representation theorem for band-limited functions of several variables whose moduli are radial is stated. The proof of this theorem, which is based on techniques from Fourier analysis and the theory of analytic functions of several variables, is outlined in the Appendix. Several uniqueness results concerning the phase-retrieval problem that follow from the representation theorem are derived. References that relate the phase-retrieval problem to the problem of wave-front reconstruction in optics and image reconstruction in speckle interferometry are cited.