Abstract

It is shown that light backscattering by hexagonal ice crystals of cirrus clouds is formed within the physical-optics approximation by both diffraction and interference phenomena. Diffraction determines the angular width of the backscattering peak and interference produces the interference rings inside the peak. By use of a simple model for distortion of the pristine hexagonal shape, we show that the shape distortion leads to both oscillations of the scattering (Mueller) matrix within the backscattering peak and to a strong increase of the depolarization, color, and lidar ratios needed for interpretation of lidar signals.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  7. V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystals,” J. Atmos. Sci. 63(5), 1513–1525 (2006).
    [Crossref]
  8. Z. Ulanowski, E. Hesse, P. H. Kaye, and A. J. Baran, “Light scattering by complex ice-analogue crystals,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 382–392 (2006).
    [Crossref]
  9. A. J. Baran, “A review of the light scattering properties of cirrus,” J. Quant. Spectrosc. Radiat. Transf. 110(14-16), 1239–1260 (2009).
    [Crossref]
  10. B. H. Cole, P. Yang, B. A. Baum, J. Riedi, and L. C. Labonnote, “Ice particle habit and surface roughness derived from PARASOL polarization measurements,” Atmos. Chem. Phys. 14(7), 3739–3750 (2014).
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    [Crossref]
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    [Crossref]
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  14. K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part II: Microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58(15), 2103–2112 (2001).
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    [Crossref] [PubMed]
  17. H. M. Cho, P. Yang, G. W. Kattawar, S. L. Nasiri, Y. Hu, P. Minnis, C. Trepte, and D. Winker, “Depolarization ratio and attenuated backscatter for nine cloud types: analyses based on collocated CALIPSO lidar and MODIS measurements,” Opt. Express 16(6), 3931–3948 (2008).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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  22. K. Sassen, V. K. Kayetha, and J. Zhu, “Ice cloud depolarization for nadir and off-nadir CALIPSO measurements,” Geophys. Res. Lett. 39(20), L20805 (2012).
    [Crossref]
  23. M. Hayman, S. Spuler, and B. Morley, “Polarization lidar observations of backscatter phase matrices from oriented ice crystals and rain,” Opt. Express 22(14), 16976–16990 (2014).
    [Crossref] [PubMed]
  24. C. Zhou and P. Yang, “Backscattering peak of ice cloud particles,” Opt. Express 23(9), 11995–12003 (2015).
    [Crossref] [PubMed]
  25. A. Borovoi, I. Grishin, E. Naats, and U. Oppel, “Backscattering peak of hexagonal ice columns and plates,” Opt. Lett. 25(18), 1388–1390 (2000).
    [Crossref] [PubMed]
  26. A. Borovoi, A. Konoshonkin, and N. Kustova, “Backscattering by hexagonal ice crystals of cirrus clouds,” Opt. Lett. 38(15), 2881–2884 (2013).
    [Crossref] [PubMed]
  27. A. Borovoi, A. Konoshonkin, and N. Kustova, “Backscatter ratios for arbitrary oriented hexagonal ice crystals of cirrus clouds,” Opt. Lett. 39(19), 5788–5791 (2014).
    [Crossref] [PubMed]
  28. K. Sato and H. Okamoto, “Characterization of Ze and LDR of nonspherical and inhomogeneous ice particles for 45-GHz cloud lidar: Its implication to microphysical retrievals,” J. Geophys. Res. 111(D22), D22213 (2006).
    [Crossref]

2015 (1)

2014 (6)

M. Hayman, S. Spuler, and B. Morley, “Polarization lidar observations of backscatter phase matrices from oriented ice crystals and rain,” Opt. Express 22(14), 16976–16990 (2014).
[Crossref] [PubMed]

C. Liu, R. L. Panetta, and P. Yang, “The effective equivalence of geometric irregularity and surface roughness in determining particle single-scattering properties,” Opt. Express 22(19), 23620–23627 (2014).
[Crossref] [PubMed]

A. Borovoi, A. Konoshonkin, and N. Kustova, “Backscatter ratios for arbitrary oriented hexagonal ice crystals of cirrus clouds,” Opt. Lett. 39(19), 5788–5791 (2014).
[Crossref] [PubMed]

A. Borovoi, A. Konoshonkin, and N. Kustova, “The physical-optics approximation and its application to light backscattering by hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transf. 146, 181–189 (2014).
[Crossref]

B. H. Cole, P. Yang, B. A. Baum, J. Riedi, and L. C. Labonnote, “Ice particle habit and surface roughness derived from PARASOL polarization measurements,” Atmos. Chem. Phys. 14(7), 3739–3750 (2014).

L. Bi and P. Yang, “Accurate simulation of the optical properties of atmospheric ice crystals with the invariant imbedding T-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 138, 17–35 (2014).
[Crossref]

2013 (2)

C. Liu, R. L. Panetta, and P. Yang, “The effects of surface roughness on the scattering properties of hexagonal columns with sizes from the Rayleigh to the geometric optics regimes,” J. Quant. Spectrosc. Radiat. Transf. 129, 169–185 (2013).
[Crossref]

A. Borovoi, A. Konoshonkin, and N. Kustova, “Backscattering by hexagonal ice crystals of cirrus clouds,” Opt. Lett. 38(15), 2881–2884 (2013).
[Crossref] [PubMed]

2012 (2)

2011 (1)

2010 (1)

H. Okamoto, K. Sato, and Y. Hagihara, “Global analysis of ice microphysics from CloudSat and CALIPSO: Incorporation of specular reflection in lidar signals,” J. Geophys. Res. 115(D22), D22209 (2010).
[Crossref]

2009 (1)

A. J. Baran, “A review of the light scattering properties of cirrus,” J. Quant. Spectrosc. Radiat. Transf. 110(14-16), 1239–1260 (2009).
[Crossref]

2008 (3)

2007 (1)

2006 (3)

K. Sato and H. Okamoto, “Characterization of Ze and LDR of nonspherical and inhomogeneous ice particles for 45-GHz cloud lidar: Its implication to microphysical retrievals,” J. Geophys. Res. 111(D22), D22213 (2006).
[Crossref]

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystals,” J. Atmos. Sci. 63(5), 1513–1525 (2006).
[Crossref]

Z. Ulanowski, E. Hesse, P. H. Kaye, and A. J. Baran, “Light scattering by complex ice-analogue crystals,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 382–392 (2006).
[Crossref]

2005 (1)

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng. 44(7), 071208 (2005).
[Crossref]

2003 (1)

2002 (1)

2001 (1)

K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part II: Microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58(15), 2103–2112 (2001).
[Crossref]

2000 (1)

1996 (1)

A. Macke, J. Mueller, and E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53(19), 2813–2825 (1996).
[Crossref]

Baker, B.

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystals,” J. Atmos. Sci. 63(5), 1513–1525 (2006).
[Crossref]

Balin, Y. S.

Baran, A. J.

A. J. Baran, “A review of the light scattering properties of cirrus,” J. Quant. Spectrosc. Radiat. Transf. 110(14-16), 1239–1260 (2009).
[Crossref]

Z. Ulanowski, E. Hesse, P. H. Kaye, and A. J. Baran, “Light scattering by complex ice-analogue crystals,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 382–392 (2006).
[Crossref]

Baum, B. A.

B. H. Cole, P. Yang, B. A. Baum, J. Riedi, and L. C. Labonnote, “Ice particle habit and surface roughness derived from PARASOL polarization measurements,” Atmos. Chem. Phys. 14(7), 3739–3750 (2014).

Benson, S.

K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part II: Microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58(15), 2103–2112 (2001).
[Crossref]

Bi, L.

L. Bi and P. Yang, “Accurate simulation of the optical properties of atmospheric ice crystals with the invariant imbedding T-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 138, 17–35 (2014).
[Crossref]

J. C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, “Comparison between the pseudo-spectral time domain method and the discrete dipole approximation for light scattering simulations,” Opt. Express 20(15), 16763–16776 (2012).
[Crossref]

Borovoi, A.

Borovoi, A. G.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng. 44(7), 071208 (2005).
[Crossref]

A. G. Borovoi and I. A. Grishin, “Scattering matrices for large ice crystal particles,” J. Opt. Soc. Am. A 20(11), 2071–2080 (2003).
[Crossref] [PubMed]

Chen, W.-N.

Chiang, C.-W.

Cho, H. M.

Cole, B. H.

B. H. Cole, P. Yang, B. A. Baum, J. Riedi, and L. C. Labonnote, “Ice particle habit and surface roughness derived from PARASOL polarization measurements,” Atmos. Chem. Phys. 14(7), 3739–3750 (2014).

Flittner, D.

Gayet, J.-F.

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystals,” J. Atmos. Sci. 63(5), 1513–1525 (2006).
[Crossref]

Grishin, I.

Grishin, I. A.

Hagihara, Y.

H. Okamoto, K. Sato, and Y. Hagihara, “Global analysis of ice microphysics from CloudSat and CALIPSO: Incorporation of specular reflection in lidar signals,” J. Geophys. Res. 115(D22), D22209 (2010).
[Crossref]

Hayman, M.

Hess, M.

J. Reichardt, S. Reichardt, R.-F. Lin, M. Hess, T. J. McGee, and D. O. Starr, “Optical-microphysical cirrus model,” J. Geophys. Res. 113(D22), D22201 (2008).
[Crossref]

Hesse, E.

Z. Ulanowski, E. Hesse, P. H. Kaye, and A. J. Baran, “Light scattering by complex ice-analogue crystals,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 382–392 (2006).
[Crossref]

Hu, Y.

Huang, J.

Hunt, B.

Kattawar, G. W.

Kaul, B. V.

Kaye, P. H.

Z. Ulanowski, E. Hesse, P. H. Kaye, and A. J. Baran, “Light scattering by complex ice-analogue crystals,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 382–392 (2006).
[Crossref]

Kayetha, V. K.

K. Sassen, V. K. Kayetha, and J. Zhu, “Ice cloud depolarization for nadir and off-nadir CALIPSO measurements,” Geophys. Res. Lett. 39(20), L20805 (2012).
[Crossref]

Kokhanenko, G. P.

Konoshonkin, A.

Kuehn, R.

Kustova, N.

Kustova, N. V.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng. 44(7), 071208 (2005).
[Crossref]

Labonnote, L. C.

B. H. Cole, P. Yang, B. A. Baum, J. Riedi, and L. C. Labonnote, “Ice particle habit and surface roughness derived from PARASOL polarization measurements,” Atmos. Chem. Phys. 14(7), 3739–3750 (2014).

Lawson, P.

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystals,” J. Atmos. Sci. 63(5), 1513–1525 (2006).
[Crossref]

Lin, B.

Lin, R.-F.

J. Reichardt, S. Reichardt, R.-F. Lin, M. Hess, T. J. McGee, and D. O. Starr, “Optical-microphysical cirrus model,” J. Geophys. Res. 113(D22), D22201 (2008).
[Crossref]

Liu, C.

C. Liu, R. L. Panetta, and P. Yang, “The effective equivalence of geometric irregularity and surface roughness in determining particle single-scattering properties,” Opt. Express 22(19), 23620–23627 (2014).
[Crossref] [PubMed]

C. Liu, R. L. Panetta, and P. Yang, “The effects of surface roughness on the scattering properties of hexagonal columns with sizes from the Rayleigh to the geometric optics regimes,” J. Quant. Spectrosc. Radiat. Transf. 129, 169–185 (2013).
[Crossref]

Liu, J. C.

Liu, Z.

Macke, A.

A. Macke, J. Mueller, and E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53(19), 2813–2825 (1996).
[Crossref]

McCormick, M. P.

McGee, T. J.

J. Reichardt, S. Reichardt, R.-F. Lin, M. Hess, T. J. McGee, and D. O. Starr, “Optical-microphysical cirrus model,” J. Geophys. Res. 113(D22), D22201 (2008).
[Crossref]

Minnis, P.

Morley, B.

Mueller, J.

A. Macke, J. Mueller, and E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53(19), 2813–2825 (1996).
[Crossref]

Naats, E.

Nasiri, S. L.

Nee, J.-B.

Okamoto, H.

H. Okamoto, K. Sato, and Y. Hagihara, “Global analysis of ice microphysics from CloudSat and CALIPSO: Incorporation of specular reflection in lidar signals,” J. Geophys. Res. 115(D22), D22209 (2010).
[Crossref]

K. Sato and H. Okamoto, “Characterization of Ze and LDR of nonspherical and inhomogeneous ice particles for 45-GHz cloud lidar: Its implication to microphysical retrievals,” J. Geophys. Res. 111(D22), D22213 (2006).
[Crossref]

Oppel, U.

Oppel, U. G.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng. 44(7), 071208 (2005).
[Crossref]

Panetta, R. L.

Penner, I. E.

Powell, K.

Raschke, E.

A. Macke, J. Mueller, and E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53(19), 2813–2825 (1996).
[Crossref]

Reichardt, J.

J. Reichardt, S. Reichardt, R.-F. Lin, M. Hess, T. J. McGee, and D. O. Starr, “Optical-microphysical cirrus model,” J. Geophys. Res. 113(D22), D22201 (2008).
[Crossref]

Reichardt, S.

J. Reichardt, S. Reichardt, R.-F. Lin, M. Hess, T. J. McGee, and D. O. Starr, “Optical-microphysical cirrus model,” J. Geophys. Res. 113(D22), D22201 (2008).
[Crossref]

Riedi, J.

B. H. Cole, P. Yang, B. A. Baum, J. Riedi, and L. C. Labonnote, “Ice particle habit and surface roughness derived from PARASOL polarization measurements,” Atmos. Chem. Phys. 14(7), 3739–3750 (2014).

Rodier, S.

Sassen, K.

K. Sassen, V. K. Kayetha, and J. Zhu, “Ice cloud depolarization for nadir and off-nadir CALIPSO measurements,” Geophys. Res. Lett. 39(20), L20805 (2012).
[Crossref]

K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part II: Microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58(15), 2103–2112 (2001).
[Crossref]

Sato, K.

H. Okamoto, K. Sato, and Y. Hagihara, “Global analysis of ice microphysics from CloudSat and CALIPSO: Incorporation of specular reflection in lidar signals,” J. Geophys. Res. 115(D22), D22209 (2010).
[Crossref]

K. Sato and H. Okamoto, “Characterization of Ze and LDR of nonspherical and inhomogeneous ice particles for 45-GHz cloud lidar: Its implication to microphysical retrievals,” J. Geophys. Res. 111(D22), D22213 (2006).
[Crossref]

Shcherbakov, V.

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystals,” J. Atmos. Sci. 63(5), 1513–1525 (2006).
[Crossref]

Spuler, S.

Starr, D. O.

J. Reichardt, S. Reichardt, R.-F. Lin, M. Hess, T. J. McGee, and D. O. Starr, “Optical-microphysical cirrus model,” J. Geophys. Res. 113(D22), D22201 (2008).
[Crossref]

Tao, Z.

Trepte, C.

Ulanowski, Z.

Z. Ulanowski, E. Hesse, P. H. Kaye, and A. J. Baran, “Light scattering by complex ice-analogue crystals,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 382–392 (2006).
[Crossref]

Vaughan, M.

Vaughan, M. A.

Winker, D.

Wu, D.

Yang, P.

C. Zhou and P. Yang, “Backscattering peak of ice cloud particles,” Opt. Express 23(9), 11995–12003 (2015).
[Crossref] [PubMed]

C. Liu, R. L. Panetta, and P. Yang, “The effective equivalence of geometric irregularity and surface roughness in determining particle single-scattering properties,” Opt. Express 22(19), 23620–23627 (2014).
[Crossref] [PubMed]

B. H. Cole, P. Yang, B. A. Baum, J. Riedi, and L. C. Labonnote, “Ice particle habit and surface roughness derived from PARASOL polarization measurements,” Atmos. Chem. Phys. 14(7), 3739–3750 (2014).

L. Bi and P. Yang, “Accurate simulation of the optical properties of atmospheric ice crystals with the invariant imbedding T-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 138, 17–35 (2014).
[Crossref]

C. Liu, R. L. Panetta, and P. Yang, “The effects of surface roughness on the scattering properties of hexagonal columns with sizes from the Rayleigh to the geometric optics regimes,” J. Quant. Spectrosc. Radiat. Transf. 129, 169–185 (2013).
[Crossref]

J. C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, “Comparison between the pseudo-spectral time domain method and the discrete dipole approximation for light scattering simulations,” Opt. Express 20(15), 16763–16776 (2012).
[Crossref]

H. M. Cho, P. Yang, G. W. Kattawar, S. L. Nasiri, Y. Hu, P. Minnis, C. Trepte, and D. Winker, “Depolarization ratio and attenuated backscatter for nine cloud types: analyses based on collocated CALIPSO lidar and MODIS measurements,” Opt. Express 16(6), 3931–3948 (2008).
[Crossref] [PubMed]

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, “The depolarization - attenuated backscatter relation: CALIPSO lidar measurements vs. theory,” Opt. Express 15(9), 5327–5332 (2007).
[Crossref] [PubMed]

Yurkin, M. A.

Zhou, C.

Zhu, J.

K. Sassen, V. K. Kayetha, and J. Zhu, “Ice cloud depolarization for nadir and off-nadir CALIPSO measurements,” Geophys. Res. Lett. 39(20), L20805 (2012).
[Crossref]

Appl. Opt. (2)

Atmos. Chem. Phys. (1)

B. H. Cole, P. Yang, B. A. Baum, J. Riedi, and L. C. Labonnote, “Ice particle habit and surface roughness derived from PARASOL polarization measurements,” Atmos. Chem. Phys. 14(7), 3739–3750 (2014).

Geophys. Res. Lett. (1)

K. Sassen, V. K. Kayetha, and J. Zhu, “Ice cloud depolarization for nadir and off-nadir CALIPSO measurements,” Geophys. Res. Lett. 39(20), L20805 (2012).
[Crossref]

J. Atmos. Sci. (3)

K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part II: Microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58(15), 2103–2112 (2001).
[Crossref]

A. Macke, J. Mueller, and E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53(19), 2813–2825 (1996).
[Crossref]

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystals,” J. Atmos. Sci. 63(5), 1513–1525 (2006).
[Crossref]

J. Geophys. Res. (3)

J. Reichardt, S. Reichardt, R.-F. Lin, M. Hess, T. J. McGee, and D. O. Starr, “Optical-microphysical cirrus model,” J. Geophys. Res. 113(D22), D22201 (2008).
[Crossref]

H. Okamoto, K. Sato, and Y. Hagihara, “Global analysis of ice microphysics from CloudSat and CALIPSO: Incorporation of specular reflection in lidar signals,” J. Geophys. Res. 115(D22), D22209 (2010).
[Crossref]

K. Sato and H. Okamoto, “Characterization of Ze and LDR of nonspherical and inhomogeneous ice particles for 45-GHz cloud lidar: Its implication to microphysical retrievals,” J. Geophys. Res. 111(D22), D22213 (2006).
[Crossref]

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

J. Quant. Spectrosc. Radiat. Transf. (5)

Z. Ulanowski, E. Hesse, P. H. Kaye, and A. J. Baran, “Light scattering by complex ice-analogue crystals,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 382–392 (2006).
[Crossref]

A. J. Baran, “A review of the light scattering properties of cirrus,” J. Quant. Spectrosc. Radiat. Transf. 110(14-16), 1239–1260 (2009).
[Crossref]

L. Bi and P. Yang, “Accurate simulation of the optical properties of atmospheric ice crystals with the invariant imbedding T-matrix method,” J. Quant. Spectrosc. Radiat. Transf. 138, 17–35 (2014).
[Crossref]

C. Liu, R. L. Panetta, and P. Yang, “The effects of surface roughness on the scattering properties of hexagonal columns with sizes from the Rayleigh to the geometric optics regimes,” J. Quant. Spectrosc. Radiat. Transf. 129, 169–185 (2013).
[Crossref]

A. Borovoi, A. Konoshonkin, and N. Kustova, “The physical-optics approximation and its application to light backscattering by hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transf. 146, 181–189 (2014).
[Crossref]

Opt. Eng. (1)

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng. 44(7), 071208 (2005).
[Crossref]

Opt. Express (7)

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, “The depolarization - attenuated backscatter relation: CALIPSO lidar measurements vs. theory,” Opt. Express 15(9), 5327–5332 (2007).
[Crossref] [PubMed]

H. M. Cho, P. Yang, G. W. Kattawar, S. L. Nasiri, Y. Hu, P. Minnis, C. Trepte, and D. Winker, “Depolarization ratio and attenuated backscatter for nine cloud types: analyses based on collocated CALIPSO lidar and MODIS measurements,” Opt. Express 16(6), 3931–3948 (2008).
[Crossref] [PubMed]

C. Zhou and P. Yang, “Backscattering peak of ice cloud particles,” Opt. Express 23(9), 11995–12003 (2015).
[Crossref] [PubMed]

M. Hayman, S. Spuler, and B. Morley, “Polarization lidar observations of backscatter phase matrices from oriented ice crystals and rain,” Opt. Express 22(14), 16976–16990 (2014).
[Crossref] [PubMed]

C. Liu, R. L. Panetta, and P. Yang, “The effective equivalence of geometric irregularity and surface roughness in determining particle single-scattering properties,” Opt. Express 22(19), 23620–23627 (2014).
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Opt. Lett. (3)

Other (1)

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Figures (8)

Fig. 1
Fig. 1

Geometry of the irregular hexagonal column.

Fig. 2
Fig. 2

Skew (1-4) and straight (5-8) plane-parallel beams giving predominant contributions to backscatter. Their ray trajectories are shown in Fig. 2(b) and Figs. 2(c) and 2(d), respectively.

Fig. 3
Fig. 3

The differential scattering cross section of the skew beams 1-4 within the cone of 5° for the regular and irregular columns at λ = 0.532 μm . The left patterns correspond to the columns with the distortion angles: ξ = 0° (a); ξ = 0.2°(c); and ξ = 0.5°(e) at the fixed orientation ( β = 32.22 ° , γ = 0 ° ) while the patterns averaged over the rotation angle γ are shown to the right.

Fig. 4
Fig. 4

The same as Fig. 3 for the straight beams 5-6 where Figs. 4(a,b) and 4(c,d) correspond to the regular (ξ = 0°) and irregular (ξ = 0.5°) columns, respectively.

Fig. 5
Fig. 5

The differential scattering cross sections for the randomly oriented regular and irregular columns calculated in the geometric-optics (dashed) and physical-optics (solid) approximations.

Fig. 6
Fig. 6

The same as Fig. 5 for the skew beams 1-4 only.

Fig. 7
Fig. 7

Polarization elements of the Mueller matrix (a-c) and the linear depolarization ratio (d) for the regular and irregular columns. In Fig. 7(d), the dotted line corresponds to the geometric-optics approximation.

Fig. 8
Fig. 8

Backscattering cross sections (a) and the backscatter ratios (c-d) for the randomly oriented column versus its distortion angle calculated in the physical-optics approximation for two wavelengths of 0.532 µm (dashed) and 1.064 µm (solid).

Equations (10)

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M ( θ ) = σ ( θ ) ( 1 m 12 ( θ ) m 13 ( θ ) m 14 ( θ ) m 12 ( θ ) m 22 ( θ ) m 23 ( θ ) m 24 ( θ ) m 13 ( θ ) m 23 ( θ ) m 33 ( θ ) m 34 ( θ ) m 14 ( θ ) m 24 ( θ ) m 34 ( θ ) m 44 ( θ ) ) .
M ( 0 ) = σ ( 0 ) ( 1 0 0 m 14 ( 0 ) 0 m 22 ( 0 ) 0 0 0 0 m 22 ( 0 ) 0 m 14 ( 0 ) 0 0 1 2 m 22 ( 0 ) ) .
M r ( θ ) = 1 2 π 0 2 π L ( φ ) M ( θ ) L ( φ ) d φ = = σ ( θ ) ( 1 0 0 m 14 ( θ ) 0 μ 22 ( θ ) 0 0 0 0 μ 22 ( θ ) 0 m 14 ( θ ) 0 0 m 44 ( θ ) ) ,
δ l = σ ( 0 ) σ | | ( 0 ) , L = σ e σ ( 0 ) , χ = σ ( 0 , λ 1 ) σ ( 0 , λ 2 ) .
δ l = 1 m 22 ( 0 ) 1 + m 22 ( 0 ) .
δ l ( θ ) = 1 μ 22 ( θ ) 1 + μ 22 ( θ ) .
θ d i f λ / A ,
θ i n t λ / B ,
J 1 = J 2 = J 3 = J 4 = q ( 0 1 1 0 ) ,
M = M s k w + M s t r ( 5 , 6 ) + M s t r ( 7 , 8 ) .

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