Reconstruction of missing information in diffraction patterns and holograms by iterative phase retrieval

TL;DR

This paper demonstrates that iterative phase retrieval can successfully reconstruct objects from diffraction patterns or holograms even with missing data, depending on the oversampling ratio and distribution of missing values.

Contribution

It introduces a method to recover objects from incomplete diffraction data, quantifying the maximum missing data allowable based on oversampling ratio and distribution.

Findings

Up to 5% missing data can be recovered at s=8.

Maximum missing pixels depend on oversampling ratio s.

Random distribution of missing data is crucial for successful reconstruction.

Abstract

It is demonstrated that an object distribution can be successfully retrieved from its diffraction pattern or hologram, even if some of the measured intensity samples are missing. The maximum allowable number of missing values depends on the linear oversampling ratio s, where the higher the value of s, the more intensity samples can be missing. For a real-valued object, the ratio of missing pixels to the total number of pixels should not exceed (1 - 2/s^2) or (1 - 1/s^2) in the acquired diffraction pattern or hologram, respectively. For example, even 5% of the measured intensity values at an oversampling ratio of s = 8 are sufficient to simultaneously retrieve the object distribution and the missing intensity values. It is important that the missing intensity values should not be concentrated in the centre, but should be randomly distributed over the acquired diffraction pattern.