X射线衍射扫描成像装置中光斑计算与验证

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

  • 摘要: 针对自主研发的X射线衍射扫描成像装置中光斑尺寸的精确计算需求,本文提出了基于点投影累加(point projection accumulation,PPA)的光斑计算算法。PPA算法通过面源离散化、狭缝三维几何投影及面积覆盖计数累加,计算光斑强度在探测器像素上的分布,并利用半高宽与平方加权质心法提取光斑尺寸与位置信息。基于蒙特卡罗模拟,分析了探测器像素尺寸、狭缝位置及探测器位置等参数对PPA算法准确性的影响,并通过实验验证了算法的有效性。由PPA算法与蒙特卡罗模拟结果对比可知,光斑中心定位精度可达5 μm,光斑尺寸变化趋势一致,最大相对误差小于3.85%。通过实验结合Tikhonov-Miller正则化方法求出探测器的系统响应函数,将其与PPA算法结果进行卷积并改进了PPA算法。改进结果与实验结果相比,光斑长度与宽度最大相对偏差分别为2.65%和1.54%。经验证,PPA算法具有较高计算精度,且计算速度较蒙特卡罗模拟速度提升3个数量级,可作为XRD扫描成像装置的光斑优化与系统设计的辅助工具,也可为类似光学结构的光斑计算提供参考。

     

    Abstract: 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.

     

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