This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation in the Fourier domain between measurements of the scattered wave and reconstructions of the scattering potential. With this theorem at hand, Fourier coverages for different experimental setups are investigated taking into account parameters such as object orientation, direction of incidence and frequency of illumination. Allowing for simultaneous and discontinuous variation of these parameters, a general filtered backpropagation formula is derived resulting in an explicit approximation of the scattering potential for a large class of experimental setups.

翻译：本文研究以散射势表征的物体的衍射层析重建。我们建立了任意维度下傅里叶衍射定理的严格推广，在傅里叶域中给出了散射波测量值与散射势重建之间的精确关系。基于该定理，我们结合物体取向、入射方向及照明频率等参数，研究了不同实验配置下的傅里叶覆盖范围。通过允许这些参数同时且非连续变化，推导出通用的滤波反传播公式，从而为多种实验配置下的散射势提供了显式近似解。