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Multiple scattering spectra through fog particles in the ellipsoidal model

Dai Bing Yuan Yin-Nan Mei De-Qing Jiang Jun-Kang Dai Shan-Shan

Multiple scattering spectra through fog particles in the ellipsoidal model

Dai Bing, Yuan Yin-Nan, Mei De-Qing, Jiang Jun-Kang, Dai Shan-Shan
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  • 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.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 50976051), the Key Science and Technology Program of Ministry of Transport, China (Grant No. 2009-353-332-280), and the Key Science and Technology Innovation Program of the Transport Bureau of Jiangsu Province, China (Grant No. 10Y25).
    [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 物理学报 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]

  • [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 物理学报 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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  • Received Date:  16 June 2011
  • Accepted Date:  28 April 2012
  • Published Online:  20 April 2012

Multiple scattering spectra through fog particles in the ellipsoidal model

  • 1. School of Science, Nantong University, Nantong 226019, China;
  • 2. School of Mechanical Engineering, Nantong University, Nantong 226019, China;
  • 3. School of Automobile and Traffic Engineering, Jiangsu University, Zhenjiang 212013, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 50976051), the Key Science and Technology Program of Ministry of Transport, China (Grant No. 2009-353-332-280), and the Key Science and Technology Innovation Program of the Transport Bureau of Jiangsu Province, China (Grant No. 10Y25).

Abstract: 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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