Abstract

Almost all of the depolarization papers in the lidar literature employ a physically inappropriate notation and they use a definition of the depolarization ratio that is not linear in the quantity of interest. This depolarization lidar legacy is misleading and confusing. In particular, subscripts meaning parallel and perpendicular do not apply to atmospheric parameters, such as the volume backscatter coefficient, because (for linear polarization) the two components of the backscattered light are polarized in the transmitted sense and completely unpolarized; the unpolarized component is not “perpendicular.” An analysis of lidar depolarization measurements with a particle scattering matrix recently provided in the literature yields algorithms for retrieving the depolarization parameter from either linear or circular depolarization lidar measurements. The analysis, notation, and definitions recommended here harmonize lidar depolarization analysis with radiative transfer theory, particle scattering theory, and standard polarization measurement techniques.

© 2008 Optical Society of America

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References

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  1. K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848-1866 (1991).
    [CrossRef]
  2. K. Sassen, “Polarization in Lidar,” in Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer, 2005), pp. 19-42.
  3. T. Murayama, “Ground-based network observation of Asian dust events of April 1988 in east Asia,” J. Geophys. Res. 106, 18345-18359 (2001).
    [CrossRef]
  4. L. R. Poole, G. S. Kent, M. P. McCormick, and W. H. Hunt, “Dual-polarization airborne lidar for observations of polar stratospheric cloud evolution,” Geophys. Res. Lett. 17, 389-392 (1990).
    [CrossRef]
  5. Y. Hu, D. Winker, P. Yang, B. Baum, L. Poole, and L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: A multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569-579 (2001).
  6. R. M. Schotland, K. Sassen, and R. Stone, “Observations by lidar of linear depolarization ratios for hydrometeors,” J. Appl. Meteorol. 10, 1011-1017 (1971).
  7. L. J. Battan, Radar Meteorology (University of Chicago Press, 1959).
  8. S. R. Pal and A. I. Carswell, “Polarization properties of lidar backscattering from clouds,” Appl. Opt. 12, 1530-1535 (1973).
  9. R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley, 1984).
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    [CrossRef]
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    [CrossRef]
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  13. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  14. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  15. E. Hecht, Optics (Addison-Wesley, 1990).
  16. E. Collett, “Field Guide to Polarization,” in SPIE Field Guides, J. E. Greivenkamp, ed. (SPIE, 2005), Vol. FG05.
  17. C. J. Flynn, A. Mendoza, Y. Zheng, and S. Mathur, “Novel polarization-sensitive micropulse lidar measurement technique,” Opt. Express 15, 2785-2790 (2007).
    [CrossRef]
  18. A. Gross, M. J. Post, and F. F. Hall, Jr., “Depolarization, backscatter, and attenuation of CO2 lidar by cirrus clouds,” Appl. Opt. 23, 2518-2522 (1984).
  19. M. I. Mishchenko and J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20, 1356-1358 (1995).
  20. M. Del Guasta, E. Vallar, O. Riviere, F. Castagnoli, V. Venturi, and M. Morandi, “Use of polarimetric lidar for the study of oriented ice plates in clouds,” Appl. Opt. 45, 4878-4887(2006).
    [CrossRef]
  21. 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, 5327-5332 (2007).
    [CrossRef]
  22. E. W. Eloranta, “High spectral resolution lidar,” in Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer, 2005), pp. 143-163.
  23. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).
  24. P. Yang, H. Wei, G. W. Kattawar, Y. X. Hu, D. M. Winker, C. A. Hostetler, and B. A. Baum, “Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase,” Appl. Opt. 42, 4389-4395 (2003).
    [CrossRef]
  25. J. M. Alvarez, M. A. Vaughan, C. A. Hostetler, W. H. Hunt, and D. M. Winker, “Calibration technique for polarization-sensitive lidars,” J. Atmos. Ocean. Technol. 23, 683-699 (2006).
  26. H. Adachi, T. Shibata, Y. Iwasaka, and M. Fujiwara, “Calibration method for the lidar-observed stratospheric depolarization ratio in the presence of liquid aerosol particles,” Appl. Opt. 40, 6587-6595 (2001).
    [CrossRef]

2007 (2)

2006 (2)

J. M. Alvarez, M. A. Vaughan, C. A. Hostetler, W. H. Hunt, and D. M. Winker, “Calibration technique for polarization-sensitive lidars,” J. Atmos. Ocean. Technol. 23, 683-699 (2006).

M. Del Guasta, E. Vallar, O. Riviere, F. Castagnoli, V. Venturi, and M. Morandi, “Use of polarimetric lidar for the study of oriented ice plates in clouds,” Appl. Opt. 45, 4878-4887(2006).
[CrossRef]

2003 (1)

2001 (3)

H. Adachi, T. Shibata, Y. Iwasaka, and M. Fujiwara, “Calibration method for the lidar-observed stratospheric depolarization ratio in the presence of liquid aerosol particles,” Appl. Opt. 40, 6587-6595 (2001).
[CrossRef]

T. Murayama, “Ground-based network observation of Asian dust events of April 1988 in east Asia,” J. Geophys. Res. 106, 18345-18359 (2001).
[CrossRef]

Y. Hu, D. Winker, P. Yang, B. Baum, L. Poole, and L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: A multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569-579 (2001).

2000 (1)

1999 (1)

1998 (1)

1995 (1)

1991 (1)

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848-1866 (1991).
[CrossRef]

1990 (1)

L. R. Poole, G. S. Kent, M. P. McCormick, and W. H. Hunt, “Dual-polarization airborne lidar for observations of polar stratospheric cloud evolution,” Geophys. Res. Lett. 17, 389-392 (1990).
[CrossRef]

1984 (1)

1973 (1)

1971 (1)

R. M. Schotland, K. Sassen, and R. Stone, “Observations by lidar of linear depolarization ratios for hydrometeors,” J. Appl. Meteorol. 10, 1011-1017 (1971).

Adachi, H.

Adriani, A.

Alvarez, J. M.

J. M. Alvarez, M. A. Vaughan, C. A. Hostetler, W. H. Hunt, and D. M. Winker, “Calibration technique for polarization-sensitive lidars,” J. Atmos. Ocean. Technol. 23, 683-699 (2006).

Battan, L. J.

L. J. Battan, Radar Meteorology (University of Chicago Press, 1959).

Baum, B.

Y. Hu, D. Winker, P. Yang, B. Baum, L. Poole, and L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: A multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569-579 (2001).

Baum, B. A.

Baumgarten, G.

Beyerle, G.

Biele, J.

Cairo, F.

Carswell, A. I.

Castagnoli, F.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Collett, E.

E. Collett, “Field Guide to Polarization,” in SPIE Field Guides, J. E. Greivenkamp, ed. (SPIE, 2005), Vol. FG05.

Del Guasta, M.

Di Donfrancesco, G.

Eloranta, E. W.

E. W. Eloranta, “High spectral resolution lidar,” in Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer, 2005), pp. 143-163.

Fierli, F.

Flittner, D.

Flynn, C. J.

Fujiwara, M.

Gobbi, G. P.

Gross, A.

Hall, F. F.

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 1990).

Hostetler, C. A.

J. M. Alvarez, M. A. Vaughan, C. A. Hostetler, W. H. Hunt, and D. M. Winker, “Calibration technique for polarization-sensitive lidars,” J. Atmos. Ocean. Technol. 23, 683-699 (2006).

P. Yang, H. Wei, G. W. Kattawar, Y. X. Hu, D. M. Winker, C. A. Hostetler, and B. A. Baum, “Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase,” Appl. Opt. 42, 4389-4395 (2003).
[CrossRef]

Hovenier, J. W.

Hu, Y.

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, 5327-5332 (2007).
[CrossRef]

Y. Hu, D. Winker, P. Yang, B. Baum, L. Poole, and L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: A multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569-579 (2001).

Hu, Y. X.

Huang, J.

Hunt, B.

Hunt, W. H.

J. M. Alvarez, M. A. Vaughan, C. A. Hostetler, W. H. Hunt, and D. M. Winker, “Calibration technique for polarization-sensitive lidars,” J. Atmos. Ocean. Technol. 23, 683-699 (2006).

L. R. Poole, G. S. Kent, M. P. McCormick, and W. H. Hunt, “Dual-polarization airborne lidar for observations of polar stratospheric cloud evolution,” Geophys. Res. Lett. 17, 389-392 (1990).
[CrossRef]

Iwasaka, Y.

Kattawar, G. W.

Kent, G. S.

L. R. Poole, G. S. Kent, M. P. McCormick, and W. H. Hunt, “Dual-polarization airborne lidar for observations of polar stratospheric cloud evolution,” Geophys. Res. Lett. 17, 389-392 (1990).
[CrossRef]

Kuehn, R.

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

Lin, B.

Liu, Z.

Mathur, S.

McCormick, M. P.

L. R. Poole, G. S. Kent, M. P. McCormick, and W. H. Hunt, “Dual-polarization airborne lidar for observations of polar stratospheric cloud evolution,” Geophys. Res. Lett. 17, 389-392 (1990).
[CrossRef]

Measures, R. M.

R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley, 1984).

Mendoza, A.

Mishchenko, M. I.

M. I. Mishchenko and J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20, 1356-1358 (1995).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

Morandi, M.

Murayama, T.

T. Murayama, “Ground-based network observation of Asian dust events of April 1988 in east Asia,” J. Geophys. Res. 106, 18345-18359 (2001).
[CrossRef]

Pal, S. R.

Poole, L.

Y. Hu, D. Winker, P. Yang, B. Baum, L. Poole, and L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: A multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569-579 (2001).

Poole, L. R.

L. R. Poole, G. S. Kent, M. P. McCormick, and W. H. Hunt, “Dual-polarization airborne lidar for observations of polar stratospheric cloud evolution,” Geophys. Res. Lett. 17, 389-392 (1990).
[CrossRef]

Post, M. J.

Powell, K.

Pulvirenti, L.

Riviere, O.

Rodier, S.

Sassen, K.

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848-1866 (1991).
[CrossRef]

R. M. Schotland, K. Sassen, and R. Stone, “Observations by lidar of linear depolarization ratios for hydrometeors,” J. Appl. Meteorol. 10, 1011-1017 (1971).

K. Sassen, “Polarization in Lidar,” in Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer, 2005), pp. 19-42.

Schotland, R. M.

R. M. Schotland, K. Sassen, and R. Stone, “Observations by lidar of linear depolarization ratios for hydrometeors,” J. Appl. Meteorol. 10, 1011-1017 (1971).

Shibata, T.

Stone, R.

R. M. Schotland, K. Sassen, and R. Stone, “Observations by lidar of linear depolarization ratios for hydrometeors,” J. Appl. Meteorol. 10, 1011-1017 (1971).

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

Trepte, C.

Vallar, E.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Vann, L.

Y. Hu, D. Winker, P. Yang, B. Baum, L. Poole, and L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: A multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569-579 (2001).

Vaughan, M.

Vaughan, M. A.

J. M. Alvarez, M. A. Vaughan, C. A. Hostetler, W. H. Hunt, and D. M. Winker, “Calibration technique for polarization-sensitive lidars,” J. Atmos. Ocean. Technol. 23, 683-699 (2006).

Venturi, V.

Wei, H.

Winker, D.

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, 5327-5332 (2007).
[CrossRef]

Y. Hu, D. Winker, P. Yang, B. Baum, L. Poole, and L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: A multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569-579 (2001).

Winker, D. M.

J. M. Alvarez, M. A. Vaughan, C. A. Hostetler, W. H. Hunt, and D. M. Winker, “Calibration technique for polarization-sensitive lidars,” J. Atmos. Ocean. Technol. 23, 683-699 (2006).

P. Yang, H. Wei, G. W. Kattawar, Y. X. Hu, D. M. Winker, C. A. Hostetler, and B. A. Baum, “Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase,” Appl. Opt. 42, 4389-4395 (2003).
[CrossRef]

Wu, D.

Yang, P.

Zheng, Y.

Appl. Opt. (7)

Bull. Am. Meteorol. Soc. (1)

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848-1866 (1991).
[CrossRef]

Geophys. Res. Lett. (1)

L. R. Poole, G. S. Kent, M. P. McCormick, and W. H. Hunt, “Dual-polarization airborne lidar for observations of polar stratospheric cloud evolution,” Geophys. Res. Lett. 17, 389-392 (1990).
[CrossRef]

J. Appl. Meteorol. (1)

R. M. Schotland, K. Sassen, and R. Stone, “Observations by lidar of linear depolarization ratios for hydrometeors,” J. Appl. Meteorol. 10, 1011-1017 (1971).

J. Atmos. Ocean. Technol. (1)

J. M. Alvarez, M. A. Vaughan, C. A. Hostetler, W. H. Hunt, and D. M. Winker, “Calibration technique for polarization-sensitive lidars,” J. Atmos. Ocean. Technol. 23, 683-699 (2006).

J. Geophys. Res. (1)

T. Murayama, “Ground-based network observation of Asian dust events of April 1988 in east Asia,” J. Geophys. Res. 106, 18345-18359 (2001).
[CrossRef]

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

Y. Hu, D. Winker, P. Yang, B. Baum, L. Poole, and L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: A multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569-579 (2001).

Opt. Express (3)

Opt. Lett. (1)

Other (9)

K. Sassen, “Polarization in Lidar,” in Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer, 2005), pp. 19-42.

L. J. Battan, Radar Meteorology (University of Chicago Press, 1959).

R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley, 1984).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

E. Hecht, Optics (Addison-Wesley, 1990).

E. Collett, “Field Guide to Polarization,” in SPIE Field Guides, J. E. Greivenkamp, ed. (SPIE, 2005), Vol. FG05.

E. W. Eloranta, “High spectral resolution lidar,” in Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer, 2005), pp. 143-163.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

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Figures (3)

Fig. 1
Fig. 1

Schematic illustration of a linear lidar depolarization measurement. The transmitted polarization is linear along the x axis (horizontal, in this figure). The received power is analyzed in two receiver channels with linear polarization analyzers oriented horizontally (parallel) and vertically (perpendicular). The powers emerging from the analyzers are converted to signals by detectors. For single scattering by spheres, all of the received power is in the parallel receiver channel.

Fig. 2
Fig. 2

Legacy depolarization ratio δ as defined in Eq. (2) has a range of 0–1 but it is not linear in the quantity of interest, which is the parameter d in the matrix defined in Eq. (7).

Fig. 3
Fig. 3

Schematic illustration of a circular lidar depolarization measurement. The transmitted polarization is linear at + 45 ° and it passes through a quarter-wave plate with the fast axis vertical to form RHC. The received power passes through quarter-wave plates with the fast axes vertical and the linear analyzers at + 45 ° and 45 ° . The powers emerging from the analyzers are converted to signals by detectors. The signal from the + 45 ° analyzer is called copolar and the signal from the 45 ° analyzer is called cross-polar. For single scattering by spheres, all of the received power is in the copolar receiver channel.

Equations (28)

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

P r | | ( Z ) = P T | | A r h 8 π Z 2 β | | ( Z ) exp ( 2 τ | | ) ,
P r ( Z ) = P T | | A r h 8 π Z 2 β ( Z ) exp [ ( τ | | + τ ) ] ,
δ = P r / P r | | .
δ ( Z ) = β ( Z ) β | | ( Z ) exp ( τ | | τ ) .
δ ( Z ) = β ( Z ) β | | ( Z ) .
M = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] .
F = [ a 1 0 0 0 0 a 2 0 0 0 0 a 2 0 0 0 0 a 1 2 a 2 ] .
M atm = [ 1 0 0 0 0 1 d 0 0 0 0 d 1 0 0 0 0 2 d 1 ] ,
1 2 [ 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ] [ 1 0 0 0 0 1 d 0 0 0 0 d 1 0 0 0 0 2 d 1 ] [ 1 1 0 0 ] = [ 1 d / 2 1 d / 2 0 0 ] .
[ 1 d / 2 1 d / 2 0 0 ] = ( 1 d ) [ 1 1 0 0 ] + ( d / 2 ) [ 1 1 0 0 ] .
1 2 [ 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ] [ 1 0 0 0 0 1 d 0 0 0 0 d 1 0 0 0 0 2 d 1 ] [ 1 1 0 0 ] = ( d / 2 ) [ 1 1 0 0 ] .
S | | ( I pol + 1 2 I unpol ) ,
S 1 2 I unpol ,
d = 2 S S | | + S .
1 d = S | | S S | | + S .
d = 2 δ 1 + δ .
1 d = 1 δ 1 + δ .
1 A S = ( 1 + δ 1 δ ) 2
A S = ( 1 d ) 2 ,
1 2 [ 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 ] [ 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 ] [ 1 0 0 0 0 1 d 0 0 0 0 d 1 0 0 0 0 2 d 1 ] [ 1 0 0 1 ] = ( 1 d ) [ 1 0 1 0 ] .
1 2 [ 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 ] [ 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 ] [ 1 0 0 0 0 1 d 0 0 0 0 d 1 0 0 0 0 2 d 1 ] [ 1 0 0 1 ] = d [ 1 0 1 0 ] .
d = S S | | + S ,
F 22 / F 11 = 1 2 ( 1 F 44 / F 11 ) .
P ( R ) = P 0 C A R 2 ( c τ 2 ) β ( R ) exp ( 2 0 R α ( r ) d r ) ,
P | | ( R ) = P 0 C | | A R 2 ( c τ 2 ) f | | ( d ) β ( R ) exp ( 2 0 R α ( r ) d r ) ,
P ( R ) = P 0 C A R 2 ( c τ 2 ) f ( d ) β ( R ) exp ( 2 0 R α ( r ) d r ) .
f | | ( d ) = ( 1 d / 2 ) ,
f ( d ) = ( d / 2 ) .

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