Resolution enhancement by extrapolation of coherent diffraction images: A quantitative study on the limits and a numerical study of non-binary and phase objects

TL;DR

This paper investigates the potential of post-extrapolation of coherent diffraction images to surpass traditional resolution limits in coherent diffractive imaging, demonstrating theoretical and numerical feasibility for non-binary and phase objects.

Contribution

It provides a quantitative analysis of resolution enhancement via diffraction pattern extrapolation using iterative phase retrieval, highlighting the limits and optimal procedures.

Findings

Diffraction patterns can be unambiguously extrapolated from partial data.

The extrapolated signal ratio is linearly proportional to the oversampling ratio.

Iterative phase retrieval methods have defined limits for effective extrapolation.

Abstract

In coherent diffractive imaging (CDI) the resolution of the reconstructed object is limited by the numerical aperture of the experimental setup. We present here a theoretical and numerical study for achieving super-resolution by post-extrapolation of coherent diffraction images, such as diffraction patterns or holograms. We demonstrate that a diffraction pattern can unambiguously be extrapolated from only a fraction of the entire pattern and that the ratio of the extrapolated signal to the originally available signal is linearly proportional to the oversampling ratio. While there could be in principle other methods to achieve extrapolation, we devote our discussion to employing iterative phase retrieval methods and demonstrate their limits. We present two numerical studies; namely the extrapolation of diffraction patterns of non-binary and that of phase objects together with a discussion of the optimal extrapolation procedure.