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为了解决天空偏振光模式的描述问题，从经典的瑞利散射模型出发，考虑大气粒子尤其是气溶胶粒子的多次散射特性，构建了一种天空偏振光模式的解析模型. 首先分析大气分子的瑞利散射，并结合Perez光强分布模型描述光强分布，而后考虑二次散射因素，分析不同尺度不同组分典型粒子的散射相位函数，根据其角度分布特征，解决二次散射积分的求解问题，最终得到本模型. 仿真实验表明，与瑞利散射模型相比，本模型能够解决实际天空中存在的中性点的描述问题. 与晴朗天气下不同时刻实际测量结果之间的对比进一步说明，本模型不仅可以定性地描述实际天空中偏振光模式的角度变化趋势、中性点以及对称性等重要特征，而且具体数值与实际分布之间的符合程度要优于单次散射模型，其中偏振度的相似度最高可以达到75%左右.To solve the issues in the modeling of skylight polarization, we build a new analytical model of skylight polarization patterns, which is based on the classic Rayleigh scattering and takes into consideration the multiple scattering properties of atmospheric particles, especially the aerosol. In this paper, we first build the model by the combination of single Rayleigh scattering and classic Perez sky models. Then we analyze the influence of secondary scattering by solving scattering phase function of different particle sizes and components of aerosol in OPAC data. Finally, the integral function for secondary scattering is simplified with the preferences of scattering phase function in forward direction. Compared with the Rayleigh model, our model can depict the existence of neutral points in the sky. The comparisons between our model and the measured results of clear sky further validate that the model not only exhibits characters of measured skylight polarization, such as the variation tendency, neutral points and the pattern symmetry, but also consists with the acquired values than the single scattering model; for example, the degree of similarity of polarization can be up to 75%.
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Keywords:
- polarized light /
- multiple scattering /
- analytical model /
- neutral point
[1] Kinsell L C 1988 A. Deepak Pub
[2] Können G P 1985 CUP Archive
[3] Horváth G, Varjú D 2004 Springer
[4] Horváth G, Wehner R 1999 Journal of Comparative Physiology A 184 1
[5] Lambrinos D, Möller R, Labhart T, Pfeifer R, Wehner R 2000 Robotics and Autonomous Systems 30 39
[6] Yan L, Guan G X, Cheng J B, Wu T X, Shao X 2009 Acta Scientiarum Naturalium Universitatis Pekinensis. 45 616 (in Chinese) [晏磊, 关桂霞, 陈家斌, 吴太夏, 邵轩 2009 北京大学学报(自然科学版) 45 616]
[7] Pust N J 2007 Ph. D. Dissertation (Montana State University Bozeman)
[8] Cheng T H, Gu X F, Cheng L F, Yu T, Tian G L 2008 Acta Phys. Sin. 57 5323 (in Chinese) [程天海, 顾行发, 陈良富, 余涛, 田国良 2008 57 5323]
[9] Jian X H, Zhang C M, Zhu B H, Zhao B C, Du J 2008 Acta Phys. Sin. 57 7565 (in Chinese) [简小华, 张淳民, 祝宝辉, 赵葆常, 杜娟 2008 57 7565]
[10] Han Y, Wang T J, Rao R Z, Wang Y J 2008 Acta Phys. Sin. 57 7396 (in Chinese) [韩永, 王体健, 饶瑞中, 王英俭 2008 57 7396]
[11] Wang L, Xu Zh H, Feng H J, Wang Y J 2008 Acta Phys. Sin. 57 2694 (in Chinese)[王凌, 徐之海, 冯华君 2008 57 2694]
[12] Wang Yue, Wu Qun, Wu Yu-Ming, He Xun-Jun, Li-Le-Wei 2012 Chin. Phys. B 21 014212
[13] Ji Xiao-Ling, Pu Zheng-Cai 2010 Chin. Phys. B 19 029201
[14] Chandrasekhar S 1960 Courier Dover Publications
[15] Zhai P W 2006 Ph. D. Dissertation (Texas A&M University)
[16] Hansen J E, Travis L D 1974 Space Science Reviews 16 527
[17] Sun Bin, Wang Han, Sun Xiao-Bing, Hong Jin, Zhang Yun-Jie 2012 Chin. Phys. B 21 129501
[18] Berry M V, Dennis M R, Lee L R 2004 New Journal of Physics 6 162
[19] Tilstra LG, Schutgens NAJ, Stammes P 2003 KNMI
[20] Wilkie A, Ulbricht C, Tobler RF, Zotti G, Purgathofer W 2004 Rendering Techniques 2 387
[21] Perez R, Seals R, Michalsky J 1993 Solar Energy 50 235
[22] Hess M, Koepke P, Schult I 1998 Bulletin of the American Meteorological Society 79 831
[23] Huang Y B, Huang H L, Hang Y, Rao R Z 2007 Journal of Atmospheric and Environmental Optics 2 423 (in Chinese) [黄印博, 黄红莲, 韩永, 饶瑞中 2007 大气与环境光学学报 2 423]
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[1] Kinsell L C 1988 A. Deepak Pub
[2] Können G P 1985 CUP Archive
[3] Horváth G, Varjú D 2004 Springer
[4] Horváth G, Wehner R 1999 Journal of Comparative Physiology A 184 1
[5] Lambrinos D, Möller R, Labhart T, Pfeifer R, Wehner R 2000 Robotics and Autonomous Systems 30 39
[6] Yan L, Guan G X, Cheng J B, Wu T X, Shao X 2009 Acta Scientiarum Naturalium Universitatis Pekinensis. 45 616 (in Chinese) [晏磊, 关桂霞, 陈家斌, 吴太夏, 邵轩 2009 北京大学学报(自然科学版) 45 616]
[7] Pust N J 2007 Ph. D. Dissertation (Montana State University Bozeman)
[8] Cheng T H, Gu X F, Cheng L F, Yu T, Tian G L 2008 Acta Phys. Sin. 57 5323 (in Chinese) [程天海, 顾行发, 陈良富, 余涛, 田国良 2008 57 5323]
[9] Jian X H, Zhang C M, Zhu B H, Zhao B C, Du J 2008 Acta Phys. Sin. 57 7565 (in Chinese) [简小华, 张淳民, 祝宝辉, 赵葆常, 杜娟 2008 57 7565]
[10] Han Y, Wang T J, Rao R Z, Wang Y J 2008 Acta Phys. Sin. 57 7396 (in Chinese) [韩永, 王体健, 饶瑞中, 王英俭 2008 57 7396]
[11] Wang L, Xu Zh H, Feng H J, Wang Y J 2008 Acta Phys. Sin. 57 2694 (in Chinese)[王凌, 徐之海, 冯华君 2008 57 2694]
[12] Wang Yue, Wu Qun, Wu Yu-Ming, He Xun-Jun, Li-Le-Wei 2012 Chin. Phys. B 21 014212
[13] Ji Xiao-Ling, Pu Zheng-Cai 2010 Chin. Phys. B 19 029201
[14] Chandrasekhar S 1960 Courier Dover Publications
[15] Zhai P W 2006 Ph. D. Dissertation (Texas A&M University)
[16] Hansen J E, Travis L D 1974 Space Science Reviews 16 527
[17] Sun Bin, Wang Han, Sun Xiao-Bing, Hong Jin, Zhang Yun-Jie 2012 Chin. Phys. B 21 129501
[18] Berry M V, Dennis M R, Lee L R 2004 New Journal of Physics 6 162
[19] Tilstra LG, Schutgens NAJ, Stammes P 2003 KNMI
[20] Wilkie A, Ulbricht C, Tobler RF, Zotti G, Purgathofer W 2004 Rendering Techniques 2 387
[21] Perez R, Seals R, Michalsky J 1993 Solar Energy 50 235
[22] Hess M, Koepke P, Schult I 1998 Bulletin of the American Meteorological Society 79 831
[23] Huang Y B, Huang H L, Hang Y, Rao R Z 2007 Journal of Atmospheric and Environmental Optics 2 423 (in Chinese) [黄印博, 黄红莲, 韩永, 饶瑞中 2007 大气与环境光学学报 2 423]
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