2D approximation quickly breaks down in reflection ptychography

Area of Science:

• Coherent X-ray Diffraction Imaging
• Materials Science
• Surface Analysis

Background:

• Ptychographic reconstructions in reflection geometries typically employ a 2D thin-sample model, analogous to transmission geometries.
• The validity and limitations of this 2D approximation in reflection ptychography have not been rigorously established.

Purpose of the Study:

• To develop a 3D weak-scattering theory for reflection ptychography.
• To derive explicit criteria for the accuracy of 2D models in reflection geometries.
• To investigate the impact of sample thickness on reconstruction fidelity and explore depth-sensitive imaging.

Main Methods:

• Development of a 3D weak-scattering theoretical framework for reflection ptychography.
• Derivation of thickness criteria based on Ewald sphere geometry and spatial frequency sampling.
• Computational simulations to verify theoretical predictions and assess artifact formation.
• Implementation of depth-dependent propagation in the forward model for improved reconstructions.

Main Results:

• Reflection geometries impose significantly stricter thin-sample conditions compared to transmission geometries, reducing allowable thickness by 1-2 orders of magnitude.
• Simulations confirm that 2D reconstructions exhibit thickness-dependent artifacts, particularly near specular Bragg minima.
• Incorporating depth-dependent propagation into the forward model successfully resolves artifacts and enables sample thickness recovery.

Conclusions:

• The study establishes practical validity limits for the commonly used 2D thin-sample approximation in reflection ptychography.
• A path towards quantitative, depth-sensitive reflection ptychography is identified by accounting for 3D propagation effects.
• These findings are crucial for accurate surface and thin-film analysis using ptychographic techniques.