由微焦斑X射线源和高分辨率平板探测器构成的X射线显微CT系统可以对小样品的内部结构进行微米级的无损分析，在生命科学、材料科学等领域具有广阔的应用前景。显微CT系统是通过旋转样品进而采集不同角度下的投影数据来完成样品内部结构的重建。对于在CT重建过程中使用投影矩阵的迭代重建算法而言，改进现有的投影矩阵模型并建立新的模型有助于进一步提高算法的重建图像质量和计算效率，从而推进迭代重建算法在显微CT系统的理论与应用研究。

本文使用微焦斑（小于20 μm）X射线源、高精度旋转台和X射线平板探测器构建了一套桌面型X射线显微CT系统。基于此系统，提出了一种适用于小锥角（<4°）投影的面积积分模型联合代数重建算法（Simultaneous algebraic reconstruction technique, SART），通过获取的苍蝇样品投影数据，重建了苍蝇样品的CT图像，证明了对该显微CT系统的有效性。数值模拟和实验结果均表明，与常用的线积分模型SART算法相比，提出的算法可以有效地减少CT重建图像中的伪影。

针对投影矩阵计算量大导致的重建时间过长限制迭代重建算法在显微CT系统推广应用这一问题，本文提出了一种不同径向宽度同心环的极坐标像素模型，利用该模型的旋转对称性和各同心环间距不同的特性，建立了一种快速计算投影矩阵的方法。数值模拟和实验结果表明，在不同参数设置条件下，该方法比Siddon算法和一种基于截距快速计算投影矩阵算法的重建时间缩短了2~3倍。

基于该显微CT系统，本文还提出了一种采用对比度增强X射线显微CT技术表征单毛细管内部三维形貌的方法。该方法可以重构单毛细管的内部整体形貌，进而可以计算其各处内径（500~600 μm）及圆度数值。对比表明，显微CT技术获取的单毛细管内径结果与激光测径仪的测量结果吻合，证明了提出方法的有效性。与常用的激光测径仪法相比，提出的表征方法具有获取单毛细管三维几何参数的优势。基于显微CT技术获取的离散内径数据，本文对其进行三次样条插值处理以获得单毛细管内管壁的曲线方程，使用光线追迹法仿真模拟了存在内径误差的单毛细管的光学性能。为了进一步完善单毛细管的常见缺陷模型，建立了具有横截面椭圆变形和中心线变形的单毛细管数学模型，并使用光线追迹法对存在这些缺陷的单毛细管光学性能进行了模拟。X射线光学系统对单毛细管的轮廓精度有着严格的要求，上述单毛细管表征工作有助于为下一步将单毛细管应用于显微CT系统以提高其系统光学性能打下基础。

The X-ray micro-CT system composed of a micro-spot X-ray source and a high-resolution flat panel detector can be used to analyze the internal structure of small samples in micron scale. It has broad application prospects in life science, material science and other fields. The micro-CT system achieves the CT reconstruction by rotating the sample and collecting projection data at different angles. For the iterative reconstruction algorithm using projection matrix in CT reconstruction, improving the existing projection matrix model and establishing a new model can further improve the image quality and computational efficiency of the algorithm, thus promoting the theoretical and application research of iterative reconstruction algorithm in micro-CT system.

In this paper, a desktop X-ray micro-CT system was constructed by using the micro-spot (less than 20 μm) X-ray source, a high-precision rotating stage and the X-ray flat-panel detector. Based on this system, a simultaneous algebraic reconstruction technique (SART) algorithm for area integral model for small cone angle (<4°) projection was proposed. Through the projection data of the fly sample, the CT images of the fly sample were reconstructed, which proves the effectiveness for the micro-CT system. In addition, both numerical simulation and experimental results have shown that the proposed algorithm can effectively reduce the artifacts in CT reconstruction images compared with the SART algorithm for line integral model.

Due to long reconstruction time that results from high computation cost of the system matrix, it is difficult to popularize and apply the iterative reconstruction algorithm in micro-CT system. In this paper, a polar-coordinate pixel model with concentric annuluses of different radial widths was established. Taking advantage of the rotational symmetry of this model and the different spacing between the concentric annuluses, a fast method for calculating the projection matrix was proposed. Both numerical simulation and experimental results have shown that, under the conditions of different parameter settings, the reconstruction time of the proposed method was 2~3 times shorter than that of both the Siddon algorithm and the algorithm based on the intercept to quickly calculate the projection matrix.

Based on this micro-CT system, a contrast-enhanced X-ray micro-CT technology was also proposed to characterize the three-dimensional morphology of the monocapillary. This method can reconstruct the overall internal morphology of the monocapillary, and then calculate its inner diameters (500 ~ 600 μm) and roundness. The comparison has shown that the inner diameters of the monocapillary obtained by micro-CT technology are in good agreement with those measured by laser caliper, which proves the effectiveness of the proposed method. Compared with the commonly used laser caliper method, the proposed characterization method has the advantage of obtaining three-dimensional geometric parameters of the monocapillary. Based on the discrete inner diameter data obtained by micro-CT technology, cubic spline interpolation was used to obtain the curve equation of the inner wall of the monocapillary. The optical performance of the monocapillary with inner diameter errors was simulated by ray-tracing method. In order to improve the defect models of the monocapillary, the mathematical models of the monocapillary with elliptic cross-section deformation and centerline deformation were established, respectively. The optical properties of the monocapillary with these imperfections were simulated by ray-tracing method. Since the X-ray optical system has strict requirements for the profile accuracy of the monocapillary, the above characterization work can help to lay a foundation for the next step to apply the monocapillary to micro-CT system to improve the optical performance of the system.