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arXiv · 2604.05989

The 2D approximation quickly breaks down in reflection ptychography

Sander Senhorst·Stefan Witte·Wim Coene
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Abstract

Ptychographic reconstructions in reflection geometries are commonly interpreted with the same two-dimensional thin-sample model used in transmission, yet the validity of this approximation has not been established. We develop a three-dimensional weak-scattering description of reflection ptychography and derive explicit thickness criteria for when a two-dimensional model remains accurate. Because the sampled axial spatial frequency range is dominated by the rotation of the Ewald sphere rather than its curvature, reflection geometries impose far stricter thin-sample conditions than transmission geometries. The allowable thickness is reduced by one to two orders of magnitude for a representative extreme ultraviolet geometry, depending on the tolerance for appearance of artifacts. Simulations verify that conventional two-dimensional reconstructions may exhibit the thickness-dependent artifacts as predicted by the theory, with particularly strong distortions near specular Bragg minima. We further show that incorporating the correct depth-dependent propagation into the forward model resolves these distortions and enables recovery of sample thickness. These results establish practical validity limits for two-dimensional reflection ptychography and identify a path toward quantitative depth-sensitive reconstructions at all geometries.

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Sander Senhorst, Stefan Witte, Wim Coene. 2026-04-07. The 2D approximation quickly breaks down in reflection ptychography. https://doi.org/10.1364/oe.601179

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