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

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.