Partially Coherent Ptychography by Gradient Decomposition of the Probe

TL;DR

This paper introduces GDP, a novel method for partially coherent ptychography that models the illumination as a superposition of coherent light convolved with a separable kernel, improving image reconstruction under less ideal conditions.

Contribution

The paper proposes the Gradient Decomposition of the Probe (GDP) model and an efficient GDP-ADMM algorithm for better handling partial coherence in ptychography.

Findings

GDP-ADMM effectively reconstructs images with Gaussian and binary kernels.

Method performs well even with large kernel-to-beam width ratios.

Reconstruction quality remains high with increased acquisition spacing.

Abstract

Coherent ptychographic imaging experiments often discard over 99.9 % of the flux from a light source to define the coherence of an illumination. Even when coherent flux is sufficient, the stability required during an exposure is another important limiting factor. Partial coherence analysis can considerably reduce these limitations. A partially coherent illumination can often be written as the superposition of a single coherent illumination convolved with a separable translational kernel. In this paper we propose the Gradient Decomposition of the Probe (GDP), a model that exploits translational kernel separability, coupling the variances of the kernel with the transverse coherence. We describe an efficient first-order splitting algorithm GDP-ADMM to solve the proposed nonlinear optimization problem. Numerical experiments demonstrate the effectiveness of the proposed method with Gaussian and binary kernel functions in fly-scan measurements. Remarkably, GDP-ADMM produces satisfactory results even when the ratio between kernel width and beam size is more than one, or when the distance between successive acquisitions is twice as large as the beam width.