Abstract A novel integral equation method based on radiation distribution factor (RDFIEM) is developed for solving radiation transfer equation (RTE) to obtain radiation intensity signal in a small solid angle on a small point, which is effectively applied to reconstruct the three-dimensional (3D) temperature distribution in an absorbing, emitting and scattering medium. The spatial distribution of radiation intensity inside the medium can be derived by the reverse Monte Carlo method based on the radiation distribution factor (RDF), and source term distribution can be obtained by integration of RDFs. Consequently, according to the idea of integral equation method (IEM), the boundary exit radiation intensity with respect to the RDF and temperature can be deduced. It is worth noting that the RDF is only related to the geometry and radiation properties of the medium, which can be calculated only once to make RDFIEM be more efficient. Meanwhile, the error caused by the random number of RMC can be reduced by integrating the RDFs. As a consequence, the RDFIEM is particularly suitable for temperature field reconstruction. The directional radiation intensity signals obtained by charge-coupled device (CCD) camera are used as the known information to reconstruct the temperature distribution, the effects of CCD combinations, detection directions, optical thickness, boundary conditions, scattering type and scattering albedo, measurement and coefficient errors on the implementation of RDFIEM have been examined. The least square QR decomposition (LSQR) algorithm is introduced to solve the 3D temperature reconstruction problem. The results show that the temperature field can be reconstructed accurately and efficiently.

中文翻译：

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基于RDFIEM的参与介质三维逆辐射问题的有效求解

摘要 提出一种基于辐射分布因子(RDFIEM)的积分方程法求解辐射传递方程(RTE)，得到小点上小立体角的辐射强度信号，有效地应用于三维( 3D) 吸收、发射和散射介质中的温度分布。介质内部辐射强度的空间分布可以通过基于辐射分布因子(RDF)的逆蒙特卡罗方法得到，源项分布可以通过RDF的积分得到。因此，根据积分方程法(IEM)的思想，可以推导出相对于RDF和温度的边界出射辐射强度。值得注意的是，RDF 只与介质的几何形状和辐射特性有关，只需计算一次即可使 RDFIEM 更加高效。同时，通过对 RDF 进行积分，可以减少 RMC 随机数引起的误差。因此，RDFIEM 特别适用于温度场重建。以电荷耦合器件（CCD）相机获得的定向辐射强度信号作为已知信息重构温度分布、CCD组合的影响、探测方向、光学厚度、边界条件、散射类型和散射反照率、测量和对 RDFIEM 实施的系数误差进行了检查。引入最小二乘 QR 分解 (LSQR) 算法来解决 3D 温度重建问题。结果表明，温度场可以准确有效地重建。