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由于雾滴的非球形、多重散射特性以及几何光学效应,光通过实际雾场的散射问题成为一个研究难点. 建立了近于实际的椭球雾滴模型,考虑光的衍射、透射及反射特性后,利用辐射传播方程得到了在不同的雾滴大小分布 及不同的雾滴形状分布下通过雾场的多重散射光强公式.在两种特例下与已有的结果较为相符,说明了方法的可靠性. 计算表明:与随机取向的非球形颗粒场的散射谱呈圆形特征不同,通过椭球形雾滴场的散射谱呈椭圆特征, 不同方位角的散射光强角分布有所差异,雾滴的形状因子越接近于1,差异越小;与单散射不同, 散射谱中的条纹随光学厚度增大逐步消失;对于不同大小分布及不同形状分布的雾滴场, 在不同方位角及不同观察角的散射光强随光学厚度的增加总是先增大再减小,光强的极大值位置在 = 1.03.0 范围内.计算同时还表明,由于多数情况下实际雾场的雾滴大小偏差较大, 因而通过雾场的散射谱将呈现以中央亮斑为中心向四周弥散的图样.Because of the properties of non-sphericity and multiple scattering of fog particles and the effects of geometrical optics, the light scattering through fog has become a difficult problem. In this paper, we establish an ellipsoidal model of fog particles. On the basis of radiative-transfer equation and with the consideration of the effects of geometrical optics, we obtain a formula of calculating multiple light scattering intensity through the fog particles with different sizes and different shape distributions. Our results are in agreement with the earlier results in two special cases, which verifies that our method is reliable. The calculations show that scattering spectra through the ellipsoidal fog particles present elliptical feature, which is different from circular feature for random orientation non-spherical particles. At the different orientation angles the angular distributions of the light intensity are different, and this difference becomes smaller with the shape ratio approaching to 1. The stripes of the scattering spectra progressively disappear with the increase of optical thickness, which is different from the case of single-scattering. At different orientation angles and observation angles, the scattering intensities always first increase then decrease with the increase of optical thickness for the fog particles of the different size distributions and different shape ratio distributions, and a maximal intensity occurs at =1.03.0. The calculations also indicate that the scattering spectra of actual fog particles present the turbid pattern around the central light speckle because of wide size distribution in many cases.
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Keywords:
- multiple light scattering /
- fog particles /
- ellipsoid /
- light spectrum
[1] Awan M S, Nebulo R, Capsoni C, Horvath L C, Muhammad S S, Nadeem F, Khan M S, Leitgeb E 2011 Int. J. Satell. Commun. Networking 29 97
[2] Du Y C, Yang L, Zhang X F, Wu M M 2010 Spectrosc. Spect. Anal. 30 2632 (in Chinese) [杜永成, 杨立, 张修峰, 吴猛猛 2010 光谱学与光谱分析 30 2632]
[3] Fischer K W, Witiw M R, Eisenberg E 2008 Atmos. Res. 87 252
[4] Li S J, Jiang W A 2010 J. Civil Aviation Univ. China 28(6) 1 (in Chinese) [李素娟, 蒋维安 2010 中国民航大学学报 28(6) 1]
[5] Zege E P, Kokhanovsky A A 1994 Appl. Opt. 33 6547
[6] Kokhanovsky A A, Weichert R 2001 Appl. Opt. 40 1507
[7] Kokhanovsky A A, Weichert R, Heuer M, Witt W 2001 Appl. Opt. 40 2595
[8] Flock S T, Patterson M S, Wilson B C 1989 IEEE Trans. Biomed. Eng. 36 1162
[9] Ye Y X, Fan D Y 2007 Acta Opt. Sin. 27 951 (in Chinese) [叶云霞, 范滇元 2007 光学学报 27 951]
[10] Dai B, Luo X D, Wang Y W 2009 Acta Phys. Sin. 58 3864 (in Chinese) [戴兵, 罗向东, 王亚伟 2009 58 3864]
[11] Han Y P, Du Y G 2006 Acta Opt. Sin. 26 630 (in Chinese) [韩一平, 杜云刚 2006 光学学报 26 630]
[12] Hulst H C 1981 Light Scattering by Small Particles (New York: Dover) p25
[13] Paramonov L E 1995 J. Opt. Soc. Am. A 12 2698
[14] Chen T W 1995 Opt. Commun. 114 199
[15] Hirleman E D 1991 Appl. Opt. 30 4832
[16] Zhao Z W, Wu Z S, Shen G D, Lin L K 2002 J. Infrared Millim. Waves 21 95 (in Chinese) [赵振维, 吴振森, 沈广德, 林乐科 2002 红外与毫米波学报 21 95]
[17] Kahnerta F M, Stamnesa J J, Stamnesb K 2002 J. Quant. Spectrosc. Radiat. Transfer 74 167
[18] Schnablegger H, Glatter O 1995 Appl. Opt. 34 3489
[19] Tang S Q, Bai L, Wu Z S, Xie P H, Wang S M 2010 J. Atmos. Environ. Opt. 5 112 (in Chinese) [汤双庆, 白璐, 吴振森, 谢品华, 汪世美 2010 大气与环境光学学报 5 112]
[20] Dai B 2003 College Phys. 22(3) 5 (in Chinese) [戴兵 2003 大学物理 22(3) 5]
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[1] Awan M S, Nebulo R, Capsoni C, Horvath L C, Muhammad S S, Nadeem F, Khan M S, Leitgeb E 2011 Int. J. Satell. Commun. Networking 29 97
[2] Du Y C, Yang L, Zhang X F, Wu M M 2010 Spectrosc. Spect. Anal. 30 2632 (in Chinese) [杜永成, 杨立, 张修峰, 吴猛猛 2010 光谱学与光谱分析 30 2632]
[3] Fischer K W, Witiw M R, Eisenberg E 2008 Atmos. Res. 87 252
[4] Li S J, Jiang W A 2010 J. Civil Aviation Univ. China 28(6) 1 (in Chinese) [李素娟, 蒋维安 2010 中国民航大学学报 28(6) 1]
[5] Zege E P, Kokhanovsky A A 1994 Appl. Opt. 33 6547
[6] Kokhanovsky A A, Weichert R 2001 Appl. Opt. 40 1507
[7] Kokhanovsky A A, Weichert R, Heuer M, Witt W 2001 Appl. Opt. 40 2595
[8] Flock S T, Patterson M S, Wilson B C 1989 IEEE Trans. Biomed. Eng. 36 1162
[9] Ye Y X, Fan D Y 2007 Acta Opt. Sin. 27 951 (in Chinese) [叶云霞, 范滇元 2007 光学学报 27 951]
[10] Dai B, Luo X D, Wang Y W 2009 Acta Phys. Sin. 58 3864 (in Chinese) [戴兵, 罗向东, 王亚伟 2009 58 3864]
[11] Han Y P, Du Y G 2006 Acta Opt. Sin. 26 630 (in Chinese) [韩一平, 杜云刚 2006 光学学报 26 630]
[12] Hulst H C 1981 Light Scattering by Small Particles (New York: Dover) p25
[13] Paramonov L E 1995 J. Opt. Soc. Am. A 12 2698
[14] Chen T W 1995 Opt. Commun. 114 199
[15] Hirleman E D 1991 Appl. Opt. 30 4832
[16] Zhao Z W, Wu Z S, Shen G D, Lin L K 2002 J. Infrared Millim. Waves 21 95 (in Chinese) [赵振维, 吴振森, 沈广德, 林乐科 2002 红外与毫米波学报 21 95]
[17] Kahnerta F M, Stamnesa J J, Stamnesb K 2002 J. Quant. Spectrosc. Radiat. Transfer 74 167
[18] Schnablegger H, Glatter O 1995 Appl. Opt. 34 3489
[19] Tang S Q, Bai L, Wu Z S, Xie P H, Wang S M 2010 J. Atmos. Environ. Opt. 5 112 (in Chinese) [汤双庆, 白璐, 吴振森, 谢品华, 汪世美 2010 大气与环境光学学报 5 112]
[20] Dai B 2003 College Phys. 22(3) 5 (in Chinese) [戴兵 2003 大学物理 22(3) 5]
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