Yura H T, Thrane L, Andersen P E
Electronics and Photonics Laboratory, The Aerospace Corporation, Los Angeles, California 90009, USA.
J Opt Soc Am A Opt Image Sci Vis. 2000 Dec;17(12):2464-74. doi: 10.1364/josaa.17.002464.
Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens-Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s >> 1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens-Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.
在傍轴近似下，针对随机介质中的漫反射和小角度散射，推导了维格纳相空间分布函数的闭式解。该解基于光场的扩展惠更斯 - 菲涅尔原理，此原理在研究波通过随机介质的传播中被广泛应用。结果具有普遍性，适用于任意小角度体积散射函数以及任意（实）ABCD光学系统。此外，它们在单次散射和多次散射区域均有效。讨论了维格纳相空间分布函数的一些一般特征，并在光学深度s >> 1的渐近极限下，针对各种类型的散射函数获得了解析结果。特别地，给出了光学相干断层扫描（OCT）系统的明确结果。在此基础上，提出了一种基于维格纳相空间分布的动量宽度测量来创建OCT图像的新方法，并讨论了其相对于传统OCT图像的优势。由于之前所有关于维格纳函数的已发表研究都是在透射几何结构中进行的，需要注意的是，扩展惠更斯 - 菲涅尔原理和ABCD矩阵形式体系可成功用于描述这种几何结构（在傍轴近似内）。因此，为了完整性，我们在附录中给出了ABCD傍轴光学系统中维格纳相空间分布函数在通过随机介质直接传播时的一般闭式解，并且在第二个附录中考虑了吸收效应。
