Abstract

Light backscattering by randomly oriented hexagonal ice crystals of cirrus clouds is considered within the framework of the physical-optics approximation. The fine angular structure of all elements of the Mueller matrix in the vicinity of the exact backward direction is first calculated and discussed. In particular, an approximate equation for the differential scattering cross section is obtained. Its simple spectral dependence is discussed. Also, a hollow of the linear depolarization ratio around the exact backward direction inherent to the long hexagonal columns is revealed.

© 2013 Optical Society of America

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References

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  1. K. Sassen and S. Benson, J. Atmos. Sci. 58, 2103 (2001).
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    [CrossRef]
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2013 (1)

2011 (1)

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

2009 (1)

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

2008 (1)

2007 (1)

2006 (1)

K. Sato and H. Okamoto, J. Geophys. Res. 111, D22213 (2006).
[CrossRef]

2005 (1)

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, Opt. Eng. 44, 071208 (2005).
[CrossRef]

2003 (1)

2002 (1)

2001 (1)

K. Sassen and S. Benson, J. Atmos. Sci. 58, 2103 (2001).
[CrossRef]

Baum, B. A.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

Benson, S.

K. Sassen and S. Benson, J. Atmos. Sci. 58, 2103 (2001).
[CrossRef]

Bi, L.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

Borovoi, A.

Borovoi, A. G.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, Opt. Eng. 44, 071208 (2005).
[CrossRef]

A. G. Borovoi and I. A. Grishin, J. Opt. Soc. Am. A 20, 2071 (2003).
[CrossRef]

Brock, R. S.

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

Chepfer, H.

Delaval, A.

Flamant, P. H.

Flittner, D.

Grishin, I. A.

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

Hu, Y.

Hu, Y. X.

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

Huang, J.

Hunt, B.

Kattawar, G. W.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

Konoshonkin, A.

Kuehn, R.

Kustova, N.

Kustova, N. V.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, Opt. Eng. 44, 071208 (2005).
[CrossRef]

Ledanois, G.

Lin, B.

Liu, Z.

Lu, J. Q.

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

McCormick, M. P.

Mishchenko, M. I.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

Noel, V.

Okamoto, H.

K. Sato and H. Okamoto, J. Geophys. Res. 111, D22213 (2006).
[CrossRef]

Oppel, U. G.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, Opt. Eng. 44, 071208 (2005).
[CrossRef]

Powell, K.

Rodier, S.

Sassen, K.

K. Sassen and S. Benson, J. Atmos. Sci. 58, 2103 (2001).
[CrossRef]

Sato, K.

K. Sato and H. Okamoto, J. Geophys. Res. 111, D22213 (2006).
[CrossRef]

Tao, Z.

Travis, L. D.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

Trepte, C.

Vaughan, M.

Vaughan, M. A.

Winker, D.

Winker, D. M.

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

Wu, D.

Yang, P.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

Y. Hu, M. Vaughan, Z. Liu, B. Lin, P. Yang, D. Flittner, B. Hunt, R. Kuehn, J. Huang, D. Wu, S. Rodier, K. Powell, C. Trepte, and D. Winker, Opt. Express 15, 5327 (2007).
[CrossRef]

Appl. Opt. (2)

J. Atmos. Sci. (1)

K. Sassen and S. Benson, J. Atmos. Sci. 58, 2103 (2001).
[CrossRef]

J. Geophys. Res. (2)

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

K. Sato and H. Okamoto, J. Geophys. Res. 111, D22213 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, J. Quant. Spectrosc. Radiat. Transfer 112, 1492 (2011).
[CrossRef]

Opt. Eng. (1)

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, Opt. Eng. 44, 071208 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (1)

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Plane-parallel beams leaving a hexagonal crystal: (a) specular and relative beams; (b), (d) straight and (c) skew corner-reflection beams.

Fig. 2.
Fig. 2.

Differential scattering cross section for the corner-reflection beams at different aspect ratios. In (a), the scaling factor of a2 is used.

Fig. 3.
Fig. 3.

Polarization elements of the Mueller matrix in the neighborhood of the backward direction for a long hexagonal column (a=2)

Fig. 4.
Fig. 4.

Linear depolarization ratio at backscattering for hexagonal ice columns and plates. The dashed line is the limiting curve for the long columns (a1)

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

M(θ)=σ(θ)(1m12(θ)00m12(θ)m22(θ)0000m33(θ)m34(θ)00m34(θ)m44(θ)),
Mr(θ)=12π02πL(φ)M(θ)L(φ)dφ=σ(θ)(10000μ22(θ)0000μ22(θ)0000m44(θ)),
δL(θ)=[1μ22(θ)]/[1+μ22(θ)].
σ(θ|λ,h,D)=D3λ103F(t,a)σ0F(t,a),
F(t,a)={a2φ(at)ata1,f(t)ata1,
σspec(θ)=S16πR(θ/2),
σ(λ)=A+B/λ,

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