Lock James A, Laven Philip
Department of Physics, Cleveland State University, Cleveland, Ohio 44115, USA.
J Opt Soc Am A Opt Image Sci Vis. 2012 Aug 1;29(8):1489-97. doi: 10.1364/JOSAA.29.001489.
Although scattering of light by a coated sphere is much more complicated than scattering by a homogeneous sphere, each of the partial wave amplitudes for scattering of a plane wave by a coated sphere can be expanded in a Debye series. The Debye series can then be rearranged in terms of the various reflections that each partial wave undergoes inside the coated sphere. For a given number of internal reflections, it is found that many different Debye terms produce the same scattered intensity as a function of scattering angle. This is called path degeneracy. In addition, some of the ray trajectories are repeats of those occurring for a smaller number of internal reflections in the sense that they produce identical time delays as a function of scattering angle. These repeated paths, however, have a different intensity as a function of scattering angle than their predecessors. The degenerate paths and repeated paths considerably simplify the interpretation of scattering within the coated sphere, thus making it possible to catalog the contributions of the various paths.
尽管涂层球体对光的散射比均匀球体对光的散射要复杂得多，但平面波被涂层球体散射的每个分波振幅都可以展开为德拜级数。然后，德拜级数可以根据每个分波在涂层球体内经历的各种反射进行重新排列。对于给定数量的内部反射，发现许多不同的德拜项作为散射角的函数产生相同的散射强度。这被称为路径简并。此外，一些光线轨迹是内部反射次数较少时出现的轨迹的重复，因为它们作为散射角的函数产生相同的时间延迟。然而，这些重复路径作为散射角的函数，其强度与之前的路径不同。简并路径和重复路径大大简化了涂层球体内散射的解释，从而使得对各种路径的贡献进行分类成为可能。
