Investigating the convergence properties of iterative ptychography for atomic-resolution low-dose imaging

TL;DR

This paper explores how the choice of update strengths in iterative electron ptychography affects convergence and accuracy at low electron doses, emphasizing the importance of parameter optimization for reliable atomic-resolution imaging.

Contribution

It demonstrates that smaller, carefully chosen update strengths are crucial for convergence and accuracy in low-dose ptychography, revealing critical thresholds that influence algorithm performance.

Findings

Optimal update strengths are smaller than traditionally used.

Convergence is achievable only with carefully tuned parameters.

Excessively small update strengths can trap algorithms in local minima.

Abstract

This study investigates the convergence properties of a collection of iterative electron ptychography methods, under low electron doses ($<$ 10$^3$ $e^-/A^2$) and gives particular attention to the impact of the user-defined update strengths. We demonstrate that carefully chosen values for this parameter, ideally smaller than those conventionally met in the literature, are essential for achieving accurate reconstructions of the projected electrostatic potential. Using a 4D dataset of a thin hybrid organic-inorganic formamidinium lead bromide (FAPbBr$_{3}$) sample, we show that convergence is in practice achievable only when the update strengths for both the object and probe are relatively small compared to what is found in literature. Additionally we demonstrate that under low electron doses, the reconstructions initial error increases when the update strength coefficients are reduced below a certain threshold emphasizing the existence of critical values beyond which the algorithms are trapped in local minima. These findings highlight the need for carefully optimized reconstruction parameters in iterative ptychography, especially when working with low electron doses, ensuring both effective convergence and correctness of the result.