吸收和散射介质中线性各向异性辐射源的源反问题
An inverse source problem for linearly anisotropic radiative sources in absorbing and scattering medium
摘要：
考虑二维吸收散射介质中稳态辐射输运的源反问题，其中源是线性各向异性的。该介质具有各向异性散射特性，既不能忽略，也不能大到足以使扩散近似成立。假设介质的衰减和散射特性是已知的。对于角变量中有限傅立叶含量的散射核，我们展示了如何从边界测量中恢复各向异性辐射源。该方法是基于柯西问题的Beltrami型方程与$A$ -解析映射。作为应用，我们确定了来自两个不同来源的数据被误认为彼此的充要条件。
英文摘要：
We consider in a two dimensional absorbing and scattering medium, an inverse source problem in the stationary radiative transport, where the source is linearly anisotropic. The medium has an anisotropic scattering property that is neither negligible nor large enough for the diffusion approximation to hold. The attenuating and scattering properties of the medium are assumed known. For scattering kernels of finite Fourier content in the angular variable, we show how to recover the anisotropic radiative sources from boundary measurements. The approach is based on the Cauchy problem for a Beltrami-like equation associated with $A$-analytic maps. As an application, we determine necessary and sufficient conditions for the data coming from two different sources to be mistaken for each other.
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