An analytical solution to the discrete ordinates approximation of the adjoint to the multigroup transport equation in one-dimensional slab geometry is developed in this work, in order to be used in source estimation problems. The solution is firstly tested in a source-detector problem, where explicit expressions are derived to approximate the absorption rate of particles of internal detectors. Noisy data generated from readings of internal detectors were then used, along with the adjoint formulation, in an iterative process to solve an energy-dependent inverse problem of source reconstruction in the cases of polynomials and piecewise constant sources. The approach is shown to be fast and accurate.

在这项工作中，开发了一种对一维平板几何中的多组输运方程的伴随离散坐标近似的解析解，以便用于源估计问题。该解决方案首先在源探测器问题中进行了测试，其中导出了明确的表达式以近似内部探测器粒子的吸收率。然后，在迭代过程中使用从内部检测器的读数生成的噪声数据以及伴随公式，来解决多项式和分段常数源情况下源重构的能量相关逆问题。该方法被证明是快速而准确的。