ABSTRACT

We study the inverse problem in Optical Tomography of determining the optical properties of a medium $\mathrm{\Omega }\subset {\mathbb{R}}^n$, with $n\ge 3$, under the so-called diffusion approximation. We consider the time-harmonic case where Ω is probed with an input field that is modulated with a fixed harmonic frequency $\omega =k/c$, where c is the speed of light and k is the wave number. We prove a result of Lipschitz stability of the absorption coefficient ${\mu }_a$ at the boundary $\mathrm{\partial }\mathrm{\Omega }$ in terms of the measurements in the case when the scattering coefficient ${\mu }_s$ is assumed to be known and k belongs to certain intervals depending on some a-priori bounds on ${\mu }_a$, ${\mu }_s$.

中文翻译：

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时谐漫反射光学层析成像边界处的 Lipschitz 稳定性

摘要

我们研究光学断层扫描中确定介质光学特性的逆问题$\mathrm{\Omega }\subset {\mathbb{R}}^n$， 和$n\ge 3$，在所谓的扩散近似下。我们考虑时谐情况，其中 Ω 用固定谐波频率调制的输入场进行探测$\omega =ķ/C$，其中c是光速，k是波数。我们证明了吸收系数的 Lipschitz 稳定性的结果 ${\mu }_{\mathrm{一个}}$在边界$\mathrm{\partial }\mathrm{\Omega }$在散射系数的情况下的测量 ${\mu }_s$假设是已知的，并且k属于某些区间，取决于一些先验边界${\mu }_{\mathrm{一个}}$,${\mu }_s$.