Bayesian inference of anisotropic 2D small-angle scattering from sparse measurement

Area of Science:

• Materials Science
• Neutron Scattering Physics
• Computational Physics

Background:

• Two-dimensional small-angle scattering (2D SAS) is crucial for analyzing material structures.
• Current methods struggle with sparse, noisy, or incomplete 2D SAS data.
• Reconstructing accurate patterns is essential for quantitative structural analysis.

Purpose of the Study:

• To present a novel Bayesian inference framework for reconstructing 2D SAS patterns.
• To enable accurate pattern reconstruction from limited, noisy, or partially missing data.
• To enhance the applicability of 2D SAS techniques under challenging experimental conditions.

Main Methods:

• A Bayesian inference framework combining a symmetry-aware angular basis.
• Radial Gaussian process priors for training-free interpolation and denoising.
• Computational benchmarks and experimental validations on various materials.

Main Results:

• Reliable recovery of isotropic and anisotropic features from severely reduced data.
• Improved fidelity and resolution compared to raw 2D SAS measurements.
• Achieved comparable accuracy with up to 50-fold fewer detected neutrons.

Conclusions:

• The framework enables quantitative structural analysis under low-flux, time-limited, or single-shot conditions.
• Extends 2D SAS applicability to compact neutron sources.
• Facilitates the study of soft matter systems with transient structural changes.