A broad class of imaging modalities involve the resolution of an inverse-scattering problem. Among them, three-dimensional optical diffraction tomography (ODT) comes with its own challenges. These include a limited range of views, a large size of the sample with respect to the illumination wavelength, and optical aberrations that are inherent to the system itself. In this work, we present an accurate and efficient implementation of the forward model. It relies on the exact (nonlinear) Lippmann-Schwinger equation. We address several crucial issues such as the discretization of the Green function, the computation of the far field, and the estimation of the incident field. We then deploy this model in a regularized variational-reconstruction framework and show on both simulated and real data that it leads to substantially better reconstructions than the approximate models that are traditionally used in ODT.

中文翻译：

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采用 Lippmann-Schwinger 模型的三维光学衍射断层扫描


一类广泛的成像模式涉及逆散射问题的解决。其中，三维光学衍射断层扫描（ODT）也面临着自身的挑战。这些包括有限的视野范围、相对于照明波长而言较大的样品尺寸以及系统本身固有的光学像差。在这项工作中，我们提出了前向模型的准确有效的实现。它依赖于精确的（非线性）Lippmann-Schwinger 方程。我们解决了几个关键问题，例如格林函数的离散化、远场的计算以及入射场的估计。然后，我们将该模型部署在正则化变分重建框架中，并在模拟数据和实际数据上表明，与 ODT 中传统使用的近似模型相比，该模型可以带来更好的重建效果。