Abstract

The problem of phase retrieval is to reconstruct a function, f(x),from the modulus, |F(u)|, of its Fourier transform, This is equivalent to reconstructing the phase of F(u) from |F(u)| or to reconstructing f(x) from its autocorrelation function, which is given by the in verse Fourier transform of |F(u)|². This problem arises in many fields, including astronomy, x-ray crystallography, wavefront sensing, pupil function determination, electron microscopy, and particle scattering. In this paper the function, f, is assumed to be a square-integrable, one-dimensional, complex-valued function. If f has disconnected compact support contained in the union of a sequence of intervals satisfying a certain separation condition, then it can be shown that f is almost always essentially the only solution with support contained in the union of those intervals. This holds no matter how many non-real zeroes F has.

© 1983 Optical Society of America