论文标题
吸收和散射培养基中线性各向异性辐射源的逆源问题
An inverse source problem for linearly anisotropic radiative sources in absorbing and scattering medium
论文作者
论文摘要
我们在二维吸收和散射培养基中考虑，这是固定辐射转运中的逆源问题，其中源是线性各向异性的。该培养基具有各向异性散射特性，该特性既不容易忽略，也不足够大，可以保持扩散近似。假定已知培养基的衰减和散射特性。为了在角变量中散射有限傅立叶含量的内核，我们展示了如何从边界测量中恢复各向异性辐射源。该方法基于与$ A分析图相关的类似Beltrami的方程式的Cauchy问题。作为一个应用程序，我们确定来自两个不同来源的数据的必要条件，可以彼此误解。
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.
