Fourier phasing with phase-uncertain mask

TL;DR

This paper extends Fourier phase retrieval to cases with phase-uncertain masks, demonstrating uniqueness and developing algorithms capable of recovering both object and mask, even under noise and correlation conditions.

Contribution

It generalizes the uniqueness results to uncertain masks and introduces new algorithms for simultaneous object and mask recovery in Fourier phase retrieval.

Findings

Algorithms successfully recover object and mask within support.

Robustness demonstrated against noise and mask correlation.

Extended theoretical guarantees for phase-uncertain masks.

Abstract

Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to stagnate and produce wrong or inaccurate solutions. In this paper Fourier phase retrieval is carried out with the introduction of a randomly fabricated mask in measurement and reconstruction. Highly probable uniqueness of solution, up to a global phase, was previously proved with exact knowledge of the mask. Here the uniqueness result is extended to the case where only rough information about the mask's phases is assumed. The exponential probability bound for uniqueness is given in terms of the uncertainty-to-diversity ratio (UDR) of the unknown mask. New phasing algorithms alternating between the object update and the mask update are systematically tested and demonstrated to have the capability of recovering both the object and the mask (within the object support) simultaneously, consistent with the uniqueness result. Phasing with a phase-uncertain mask is shown to be robust with respect to the correlation in the mask as well as the Gaussian and Poisson noises.