Fourier phasing with phase-uncertain mask

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.

References in corpus (2)

• Absolute Uniqueness of Phase Retrieval with Random Illumination
• Phase Retrieval with Random Phase Illumination

Cited by in corpus (12)

• Alternating Projection, Ptychographic Imaging and Phase Synchronization
• Coded Aperture Ptychography: Uniqueness and Reconstruction
• Phase Retrieval with One or Two Diffraction Patterns by Alternating Projection with Null Initialization
• Random phaseless sampling for causal signals in shift-invariant spaces: a zero distribution perspective
• Fourier Phase Retrieval with a Single Mask by Douglas-Rachford Algorithm
• Blind Ptychography: Uniqueness and Ambiguities
• Blind Ptychography by Douglas-Rachford Splitting
• Fixed Point Analysis of Douglas-Rachford Splitting for Ptychography and Phase Retrieval
• Total variation-based reconstruction and phase retrieval for diffraction tomography
• Fourier-Domain Fixed Point Algorithms with Coded Diffraction Patterns
• 3D Tomographic Phase Retrieval and Unwrapping
• Illumination strategies for intensity-only imaging