Diffraction tomography is an inverse scattering technique used to reconstruct the spatial distribution of the material properties of a weakly scattering object. The object is exposed to radiation, typically light or ultrasound, and the scattered waves induced from different incident field angles are recorded. In conventional diffraction tomography, the incident wave is assumed to be a monochromatic plane wave, an unrealistic simplification in practical imaging scenarios. In this article, we extend conventional diffraction tomography by introducing the concept of customized illumination scenarios, with a pronounced emphasis on imaging with focused beams. We present a new forward model that incorporates a generalized incident field and extends the classical Fourier diffraction theorem to the use of this incident field. This yields a new two-step reconstruction process which we comprehensively evaluate through numerical experiments.

翻译：衍射断层成像是一种逆散射技术，用于重建弱散射物体材料特性的空间分布。该方法将物体暴露于辐射（通常为光或超声）中，并记录不同入射场角度激发的散射波。传统衍射断层成像假设入射波为单色平面波，这在实际成像场景中是一种不现实的简化。本文通过引入定制化照明场景的概念扩展了传统衍射断层成像，并重点强调聚焦光束成像。我们提出了一个新的前向模型，该模型整合了广义入射场，并将经典傅里叶衍射定理推广至该入射场的适用场景。由此衍生出一种新的两步重建过程，并通过数值实验对其进行了全面评估。