Quantitative tissue information, like the light scattering properties, is considered as a key player in the detection of cancerous cells in medical diagnosis. A promising method to obtain these data is optical coherence tomography (OCT). In this article, we will therefore discuss the refractive index reconstruction from OCT data, employing a Gaussian beam based forward model. We consider in particular samples with a layered structure, meaning that the refractive index as a function of depth is well approximated by a piece-wise constant function. For the reconstruction, we present a layer-by-layer method where in every step the refractive index is obtained via a discretized least squares minimization. For an approximated form of the minimization problem, we present an existence and uniqueness result. The applicability of the proposed method is then verified by reconstructing refractive indices of layered media from both simulated and experimental OCT data.

翻译：定量组织信息（如光散射特性）在医学诊断中被视为检测癌细胞的关键因素。获取这些数据的一种有前景的方法是光学相干断层扫描（OCT）。因此，本文将讨论基于高斯光束正向模型的OCT数据折射率重建。我们特别考虑具有层状结构的样本，这意味着作为深度函数的折射率可以通过分段常数函数很好地近似。对于重建问题，我们提出了一种逐层方法，其中每一步均通过离散化最小二乘最小化来获取折射率。针对该最小化问题的近似形式，我们给出了存在唯一性结果。随后，通过从模拟和实验OCT数据中重建层状介质的折射率，验证了所提方法的适用性。