Baran A J, Havemann S
Meteorological Research Flight, Y46 Building, Defence Evaluation and Research Agency, Farnborough, Hampshire GU14 0LX, England.
Appl Opt. 2000 Oct 20;39(30):5560-8. doi: 10.1364/ao.39.005560.
The applicability of various approximations for computing the absorption efficiency and single-scattering albedo of a randomly oriented hexagonal column is tested versus electromagnetic theory. To calculate the absorption efficiency and single-scattering albedo of the hexagonal column from electromagnetic theory we used a generalization to the separation-of-variables method, which enables continuous calculation of optical properties up to size parameters of 86. We found that the asymptotic absorption efficiency is independent of particle shape, and that, as the size parameter increases, the hexagonal column tends to its asymptotic absorption value more quickly than Mie theory. The asymptotic absorption limit of the hexagonal column is calculated accurately (to within 1%) and rapidly by use of the complex-angular-momentum approximation, indicating that this approximation could be used to calculate the absorption limit of nonspherical particles. The equal-volume sphere best approximates the hexagonal column single-scattering albedo at a strongly absorbing wavelength (e.g., 11.9 microm for an ice particle). However, in the resonance region (e.g., 80 microm for an ice particle) Mie theory fails to approximate the single-scattering albedo of the hexagonal column, but as the size parameter exceeds 10 the error in the sphere approximation reduces to within 2%. At 80-microm wavelength there is a characteristic ripple structure superimposed on the hexagonal column absorption efficiency solutions between size parameters from approximately 1 to 4. The ripple structure is indicative of surface-wave interference and is similar to the sphere but less pronounced on the hexagonal column. We investigated the applicability of ray tracing for calculating the single-scattering albedo at absorbing wavelengths relevant to remote sensing of ice particles in the atmosphere and found it to be within 4% for size parameters between 3 and 42 at 3.7-microm wavelength. At mid-infrared wavelengths (e.g., 8.5 and 11.9 microm) ray tracing is within 5% of electromagnetic theory for size parameters exceeding 10. We also tested the Bryant and Latimer absorption approximation to anomalous diffraction theory by using the separation-of-variables method.
针对随机取向的六边形柱体，测试了各种用于计算吸收效率和单次散射反照率的近似方法与电磁理论的契合度。为了依据电磁理论计算六边形柱体的吸收效率和单次散射反照率，我们采用了对变量分离法的推广，该方法能够连续计算直至尺寸参数为86时的光学特性。我们发现，渐近吸收效率与粒子形状无关，并且随着尺寸参数的增加，六边形柱体比米氏理论更快地趋近其渐近吸收值。利用复角动量近似法能够精确（误差在1%以内）且快速地计算六边形柱体的渐近吸收极限，这表明该近似法可用于计算非球形粒子的吸收极限。在强吸收波长（例如，冰粒子为11.9微米）下，等体积球体最能近似六边形柱体的单次散射反照率。然而，在共振区域（例如，冰粒子为80微米），米氏理论无法近似六边形柱体的单次散射反照率，但当尺寸参数超过10时，球体近似法的误差降至2%以内。在80微米波长下，在尺寸参数约为1至4之间的六边形柱体吸收效率解上叠加有特征性的波纹结构。该波纹结构表明存在表面波干涉，与球体类似，但在六边形柱体上不太明显。我们研究了光线追踪法在计算与大气中冰粒子遥感相关的吸收波长下的单次散射反照率时的适用性，发现在3.7微米波长下，尺寸参数在3至42之间时，其误差在4%以内。在中红外波长（例如，8.5和11.9微米）下，对于尺寸参数超过10的情况，光线追踪法与电磁理论的误差在5%以内。我们还通过变量分离法测试了布莱恩特和拉蒂默对异常衍射理论的吸收近似法。
