Conventional tomographic reconstruction algorithms assume that one has obtained pure projection images, involving no within-specimen diffraction effects nor multiple scattering. Advances in x-ray nanotomography are leading toward the violation of these assumptions, by combining the high penetration power of x-rays, which enables thick specimens to be imaged, with improved spatial resolution that decreases the depth of focus of the imaging system. We describe a reconstruction method where multiple scattering and diffraction effects in thick samples are modeled by multislice propagation and the 3D object function is retrieved through iterative optimization. We show that the same proposed method works for both full-field microscopy and for coherent scanning techniques like ptychography. Our implementation uses the optimization toolbox and the automatic differentiation capability of the open-source deep learning package TensorFlow, demonstrating a straightforward way to solve optimization problems in computational imaging with flexibility and portability.

传统的断层扫描重建算法假设获得了纯投影图像，不涉及样本内衍射效应，也不涉及多重散射。 X 射线纳米断层扫描技术的进步将 X 射线的高穿透力（使厚样本成像）与改进的空间分辨率（降低成像系统的焦深）相结合，导致这些假设被违反。我们描述了一种重建方法，其中通过多层传播对厚样本中的多重散射和衍射效应进行建模，并通过迭代优化检索 3D 目标函数。我们表明，所提出的相同方法适用于全视场显微镜和相干扫描技术（如叠层照相术）。我们的实现使用了优化工具箱和开源深度学习包 TensorFlow 的自动微分功能，展示了一种简单的方法来解决计算成像中的优化问题，具有灵活性和可移植性。