RAINBOWS - MIE COMPUTATIONS AND THE AIRY APPROXIMATION

作     者：WANG, RT VANDEHULST, HC 

作者机构：INST SPACE SCI & TECHNOLSPACE ASTRON LAB1810 NW 6TH STGAINESVILLEFL 32609 UNIV FLORIDASPACE ASTRON LABGAINESVILLEFL 32609 LEIDEN OBSERV2300 RA LEIDENNETHERLANDS 

出 版 物：《APPLIED OPTICS》 (Appl. Opt.)

年 卷 期：1991年第30卷第1期

页      面：106-117页

核心收录：

学科分类：070207[理学-光学] 07[理学] 08[工学] 0803[工学-光学工程] 0702[理学-物理学] 

主　　题：Computation methods Geometric optics Light scattering Mie theory Rainbows Refractive index 

摘      要：Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to 6 mm. We present a method for evaluating the Mie coefficients from the ratios between Riccati-Bessel and Neumann functions of successive order. We probe the applicability of the Airy approximation, which we generalize to rainbows of arbitrary p (number of internal reflections = p - 1), by comparing the Mie and Airy intensity patterns. Millimeter size water drops show a match in all details, including the position and intensity of the supernumerary maxima and the polarization. A fairly good match is still seen for drops of 0.1 mm. A small spread in sizes helps to smooth out irrelevant detail. The dark band between the rainbows is used to test more subtle features. We conclude that this band contains not only externally reflected light (p = 0) but also a sizable contribution from the p = 6 and p = 7 rainbows, which shift rapidly with wavelength. The higher the refractive index, the closer both theories agree on the first primary rainbow (p = 2) peak for drop diameters as small as 0.02 mm. This may be useful in supporting experimental work.