Calculation and Verification of Spot in X-ray Diffraction Mapping Device

In the self-developed X-ray diffraction mapping (XRD mapping) device, an L-shaped tungsten slit collimator was used to maintain structural compactness and cost-effectiveness, and keep the Bragg angle of about 10°. The size of the spot on the sample directly affects the quality of the XRD mapping image: An overly large spot reduces spatial resolution, while an excessively small spot reduces photon intensity and thus imaging efficiency. This paper proposed the point projection accumulation (PPA) algorithm to address this issue in X-ray spot collimation systems that use a rectangular slit. The PPA algorithm discretized the actual focal spot of the X-ray tube into multiple point sources. The rectangular projection areas formed on the area array detector were calculated separately based on the position of each point source and the geometric parameters of the slit collimator. The intensity distribution of the spot on the detector was obtained by accumulating the counts covered by each area of the detector. Finally, the spot size and position information were extracted using the full width at half maximum (FWHM) and square-weighted centroid methods. The accuracy and applicability of the PPA algorithm were verified using Geant4 Monte Carlo simulation. The influence of parameters such as detector pixel size, slit position, and detector position on the accuracy of the PPA algorithm was analyzed. Compared with the results of the Monte Carlo simulation, the spot centroid positioning accuracy can reach 5 μm. Consistent trends were exhibited in spot size variation and a maximum relative error of below 3.85% was shown. Furthermore, the PPA calculation takes only a few seconds, which is three orders of magnitude faster than the Monte Carlo simulation, which takes hours. To verify this further, an experimental verification platform was constructed. This includes a chromium target X-ray tube, a rectangular tungsten slit collimator and an area array detector. As the PPA calculation only considers physical geometric characteristics, and not the focal spot deviation of the X-ray tube or the experimental detector response, the results of the PPA calculation were deconvoluted with the experimental measurement data using the Tikhonov-Miller regularization method. This yielded the system response function of the imaging system. The system response function was used to correct the PPA algorithm results. Following the corrections, the maximum relative deviations in spot length and width compared to the experimental measurements are found to be 2.65% and 1.54%, respectively. Monte Carlo simulation and experimental verification demonstrate that the PPA algorithm is highly accurate and significantly more efficient than the Monte Carlo method. It can be used as an additional tool for optimizing spots and designing systems in XRD mapping devices. It can also be used to provide a reference for spot calculations in similar optical structures.