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X-ray diffraction tomography (XRDT) is an exciting imaging modality because of its capacity to combine volumetric imaging with material discrimination. Despite this fact, practical implementation of such systems to security workflows have been fraught with challenges due to real world" constraints” one of the most notable being a limitation on the total photon budget. This challenge is exacerbated given that one of the more pronounced trade-offs in XRDT system design is that between imaging performance and the quantity of relevant, scattered photons collected. Consequently, two approaches have emerged that operate at different ends of this trade-off continuum. At one extreme, direct tomography (DT) uses a high degree of collimation to realize robust resolution but suffers from low signal levels. At the other extreme, coded aperture XRDT (CA-XRDT) employs coded apertures which allow for detection of a substantially greater number of photons but at the cost of signal multiplexing and potentially less robustness to object extent. While these two systems differ only slightly in hardware (i.e. whether a collimator or coded aperture is used), a fair and fundamental comparison between the two is not straightforward and has never been performed. Furthermore, such an analysis is important for understanding the strengths and weaknesses of each system and thereby identifying an optimal architecture. In this paper, we first present our methodology to define the theoretical resolution of DT and CA-XRDT systems, focusing on the case of a pencil beam geometry. After using this approach to tweak system design in simulation such that both systems have the same theoretical average resolution, we then conduct a numerical investigation of the imaging performance of each system as a function of the measurement SNR and target object width for linear and area array detector geometries. We find in our particular simulation study that, while there are cases where both systems can identify and localize an object equally well, there are certain imaging scenarios where CA-XRDT outperforms DT and vice versa. In addition, we find that DT generally provides more information per photon than CA-XRDT but that there can be comparatively less information overall.
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