On Overlap Ratio in Defocused Electron Ptychography

TL;DR

This work analyzes how the overlap ratio between adjacent illuminated regions in defocused-probe 4D STEM affects electron ptychography (EP) reconstruction quality. It introduces a geometry-driven framework with recovery-agnostic redundancy metrics and a best-case EP scenario, alongside a Constrained PIE algorithm that leverages a phase-object constraint with a known probe. Through simulations, the study shows that a $40\%$ overlap yields stable, high-quality reconstructions comparable to higher overlaps, with problem difficulty depending on the object; this provides practical guidance for designing 4D STEM acquisitions to balance redundancy, resolution, and dose. The findings offer a principled approach to predict EP performance from scan geometry alone and inform experimental planning in EP applications to complex materials and biological specimens.

Abstract

Four-dimensional Scanning Transmission Electron Microscopy (4D STEM) with data acquired using a defocused electron probe is a promising tool for characterising complex biological specimens and materials through a phase retrieval process known as Electron Ptychography (EP). The efficacy of 4D STEM acquisition and the resulting quality of EP reconstruction depends on the overlap ratio of adjacent illuminated areas. This paper demonstrates how the overlap ratio impacts the data redundancy and the quality of the EP reconstruction. We define two quantities as a function of the overlap ratio that are independent of both the object and the EP algorithm. Subsequently, we evaluate an EP algorithm for varying overlap ratios using simulated 4D STEM datasets. Notably, a 40% or greater overlap ratio yields stable, high-quality reconstructions.

Figures (5)

• Figure 1: Defocused-probe 4D STEM. An electron probe scans a FoV over the object and a diffraction pattern per probe location is collected using a 2-D electron detector. Scanning all probe locations creates the 4-D dataset. Defocus and convergence semi-angle parameters are denoted, respectively, by $\Delta_f$ and $\alpha$ and are discussed in Sec. \ref{['sec:methods']}.
• Figure 2: Values of the quantities defined in Sec. \ref{['sec:recovery-agnostic']}. These values are independent from the recovery algorithm, illuminated object, and electron probe; and are derived only from the scan geometry, which in this paper follows a raster scan pattern.
• Figure 3: Ground truth images used for generating 4D STEM data. USAF-1951 (left) and rice (middle) images used for the object phase.
• Figure 4: Performance of CPIE and PIE reconstructions for phase object approximation. Efficient overlap ratio for stable reconstruction depends on the EP algorithm and structure of object. For both test images and for considered noise levels, a 40% overlap yields comparable reconstructions quality to that of 60% overlap via CPIE algorithm.
• Figure 5: Recovered object phase images via CPIE algorithm for different overlap ratios and mean SNRs.