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Significance X-ray photon correlation spectroscopy (XPCS) is a powerful technique that can probe a broad range of space and time scales and will become increasingly powerful due to coming advancements in coherence. Assessing translational and rotational diffusion is a key quantity in analyzing material structures and dynamics, with applications across molecular biology, drug discovery, and materials science. While methods for estimating translational diffusion coefficients from XPCS data are well-developed, there are no algorithms for measuring the rotational diffusion. Here, we present a mathematical formulation and algorithm based on angular-temporal cross-correlations for extracting this rotational information, providing tools for data analysis of XPCS. Although we focus on XPCS, the proposed method can be applied to other experimental techniques due to its generality.

Cross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficients