Abstract

The phase retrieval from Fourier magnitude problem has traditionally been considered from the viewpoint of the analytic properties of Fourier transforms of finite support object distributions, [1]. It is well known that intrinsic phase ambiguities arise if the product representation of the Fourier transform has one or more non-self conjugate factors. In one dimension there can be an infinity of such factors but in two or more the exact number is difficult to ascertain. Recently there has been a trend towards considering object distributions comprising a set of discrete points,[2]. For several applications, e.g. astronomy, this is not unreasonable. This model has the great advantage that one can adopt a discrete Fourier transform representation for the Fourier data or, equivalently, a z-transform representation leading to a finite degree polynomial model. Such a model can be generally assumed to lead to a unique relationship between Fourier magnitude and phase [3] and has given confidence to the use of iterative methods which had been observed to succeed in the recovering Fourier phase from magnitude or vice-versa,[4].

© 1986 Optical Society of America