Resolution analysis of a volumetric coded aperture X-ray diffraction imaging system

BACKGROUND: A coded aperture X-ray diffraction (XRD) imaging system can measure the X-ray diffraction form factor from an object in three dimensions -X, Y and Z (depth), broadening the potential application of this technology. However, to optimize XRD systems for specific applications, it is critical to understand how to predict and quantify system performance for each use case. OBJECTIVE: The purpose of this work is to present and validate 3D spatial resolution models for XRD imaging systems with a detector-side coded aperture. METHODS: A fan beam coded aperture XRD system was used to scan 3D printed resolution phantoms placed at various locations throughout the system's field of view. The multiplexed scatter data were reconstructed using a model-based iterative reconstruction algorithm, and the resulting volumetric images were evaluated using multiple resolution criteria to compare against the known phantom resolution. We considered the full width at half max and Sparrow criterion as measures of the resolution and compared our results against analytical resolution models from the literature as well as a new theory for predicting the system resolution based on geometric arguments. RESULTS: We show that our experimental measurements are bounded by the multitude of theoretical resolution predictions, which accurately predict the observed trends and order of magnitude of the spatial and form factor resolutions. However, we find that the expected and observed resolution can vary by approximately a factor of two depending on the choice of metric and model considered. We observe depth resolutions of 7-16 mm and transverse resolutions of 0.6-2 mm for objects throughout the field of view. Furthermore, we observe tradeoffs between the spatial resolution and XRD form factor resolution as a function of sample location. CONCLUSION: The theories evaluated in this study provide a useful framework for estimating the 3D spatial resolution of a detector side coded aperture XRD imaging system. The assumptions and simplifications required by these theories can impact the overall accuracy of describing a particular system, but they also can add to the generalizability of their predictions. Furthermore, understanding the implications of the assumptions behind each theory can help predict performance, as shown by our data's placement between the conservative and idealized theories, and better guide future systems for optimized designs.