Abstract

An algorithm for correcting instrumental effects in polarization lidar studies is discussed. Cross-talk between the perpendicular and parallel polarization channels and imperfect polarization of the transmitted laser beam are taken into account. On the basis of the Mueller formalism it is shown that - with certain assumptions - the combined effects of imperfect polarization of the transmitted laser pulse, non-ideal properties of transmitter and receiver optics and cross-talk between parallel and perpendicular polarization channels can be described by a single parameter, which is essentially the overall system depolarization.

© 2000 Optical Society of America

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References

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  1. S. R. Pal and A. I. Carswell, “Polarization properties of lidar backscattering from clouds,” Appl. Opt. 12, 1530–1535 (1973)
    [Crossref] [PubMed]
  2. C. M. R. Platt, “Lidar observations of a mixed-phase altostratus cloud,” J. Appl. Meteorol.,  16, 339–345 (1977)
    [Crossref]
  3. K. Sassen, “Depolarization of laser light backscattered by artificial clouds,” J. Appl. Meteorol.,  13, 923–933 (1973)
    [Crossref]
  4. R. M. Schotland, R. M. Sassen, K. Stone, and R. J., “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol.,  10, 1011–1017 (1971)
    [Crossref]
  5. H. C. van de Hulst, “Light Scattering by Small Particles,” Dover Publications, New York(1957)
  6. D.R. Bates, “Rayleigh Scattering by Air,” Planet. Space Sci. 32, 785–790 (1984)
    [Crossref]
  7. A.T. Young, “Revised depolarization corrections for atmospheric extinction,” Appl. Opt. 19, 3427–3428 (1980)
    [Crossref] [PubMed]
  8. A.T. Young, “Rayleigh Scattering,” Appl. Opt. 20, 533–535 (1981)
    [Crossref] [PubMed]
  9. G. Beyerle, “Untersuchungen polarer stratosphärischer Aerosole vulkanischen Ursprungs und polarer stratosphärischer Wolken mit einem Mehrwellenlängen-Lidar auf Spitzbergen (79° N, 12° O),” Berichte zur Polarforschung 138/’94, Alfred-Wegener-Institut für Polar- und Meeresforschung, Bremerhaven (1994)
  10. M. Mishchenko and J. Hovenier, “Depolarization of light backscattered by randomly oriented non-spherical particles,” Optics Letters 20, 1356–1358 (1995)
    [Crossref] [PubMed]
  11. G. Baumgarten, “Erste Messungen des Bonner Rayleigh/Mie/Raman-Lidar auf Esrange, Schweden, zur Untersuchung von dynamisch induzierten polaren Stratosphärenwolken im Januar 1997,” Diploma thesis, IB-97-26 University of Bonn, Germany (1997)
  12. J. Biele, “Polare stratosphärische Wolken: Lidar-Beobachtungen, Charakterisierung von Entstehung und Entwicklung,” Berichte zur Polarforschung 03/’99, Alfred-Wegener-Institut für Polar- und Meeresforschung, Bremerhaven (1999)
  13. J. Biele, A. Tsias, B. P. Luo, K. S. Carslaw, R. Neuber, G. Beyerle, and Th. Peter, “Non-equilibrium co-existence of Solid and Liquid Particles in Arctic Stratospheric Clouds,” J. Geophy. Res. submitted (2000)

1995 (1)

M. Mishchenko and J. Hovenier, “Depolarization of light backscattered by randomly oriented non-spherical particles,” Optics Letters 20, 1356–1358 (1995)
[Crossref] [PubMed]

1984 (1)

D.R. Bates, “Rayleigh Scattering by Air,” Planet. Space Sci. 32, 785–790 (1984)
[Crossref]

1981 (1)

1980 (1)

1977 (1)

C. M. R. Platt, “Lidar observations of a mixed-phase altostratus cloud,” J. Appl. Meteorol.,  16, 339–345 (1977)
[Crossref]

1973 (2)

K. Sassen, “Depolarization of laser light backscattered by artificial clouds,” J. Appl. Meteorol.,  13, 923–933 (1973)
[Crossref]

S. R. Pal and A. I. Carswell, “Polarization properties of lidar backscattering from clouds,” Appl. Opt. 12, 1530–1535 (1973)
[Crossref] [PubMed]

1971 (1)

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

Bates, D.R.

D.R. Bates, “Rayleigh Scattering by Air,” Planet. Space Sci. 32, 785–790 (1984)
[Crossref]

Baumgarten, G.

G. Baumgarten, “Erste Messungen des Bonner Rayleigh/Mie/Raman-Lidar auf Esrange, Schweden, zur Untersuchung von dynamisch induzierten polaren Stratosphärenwolken im Januar 1997,” Diploma thesis, IB-97-26 University of Bonn, Germany (1997)

Beyerle, G.

G. Beyerle, “Untersuchungen polarer stratosphärischer Aerosole vulkanischen Ursprungs und polarer stratosphärischer Wolken mit einem Mehrwellenlängen-Lidar auf Spitzbergen (79° N, 12° O),” Berichte zur Polarforschung 138/’94, Alfred-Wegener-Institut für Polar- und Meeresforschung, Bremerhaven (1994)

J. Biele, A. Tsias, B. P. Luo, K. S. Carslaw, R. Neuber, G. Beyerle, and Th. Peter, “Non-equilibrium co-existence of Solid and Liquid Particles in Arctic Stratospheric Clouds,” J. Geophy. Res. submitted (2000)

Biele, J.

J. Biele, “Polare stratosphärische Wolken: Lidar-Beobachtungen, Charakterisierung von Entstehung und Entwicklung,” Berichte zur Polarforschung 03/’99, Alfred-Wegener-Institut für Polar- und Meeresforschung, Bremerhaven (1999)

J. Biele, A. Tsias, B. P. Luo, K. S. Carslaw, R. Neuber, G. Beyerle, and Th. Peter, “Non-equilibrium co-existence of Solid and Liquid Particles in Arctic Stratospheric Clouds,” J. Geophy. Res. submitted (2000)

Carslaw, K. S.

J. Biele, A. Tsias, B. P. Luo, K. S. Carslaw, R. Neuber, G. Beyerle, and Th. Peter, “Non-equilibrium co-existence of Solid and Liquid Particles in Arctic Stratospheric Clouds,” J. Geophy. Res. submitted (2000)

Carswell, A. I.

Hovenier, J.

M. Mishchenko and J. Hovenier, “Depolarization of light backscattered by randomly oriented non-spherical particles,” Optics Letters 20, 1356–1358 (1995)
[Crossref] [PubMed]

Luo, B. P.

J. Biele, A. Tsias, B. P. Luo, K. S. Carslaw, R. Neuber, G. Beyerle, and Th. Peter, “Non-equilibrium co-existence of Solid and Liquid Particles in Arctic Stratospheric Clouds,” J. Geophy. Res. submitted (2000)

Mishchenko, M.

M. Mishchenko and J. Hovenier, “Depolarization of light backscattered by randomly oriented non-spherical particles,” Optics Letters 20, 1356–1358 (1995)
[Crossref] [PubMed]

Neuber, R.

J. Biele, A. Tsias, B. P. Luo, K. S. Carslaw, R. Neuber, G. Beyerle, and Th. Peter, “Non-equilibrium co-existence of Solid and Liquid Particles in Arctic Stratospheric Clouds,” J. Geophy. Res. submitted (2000)

Pal, S. R.

Peter, Th.

J. Biele, A. Tsias, B. P. Luo, K. S. Carslaw, R. Neuber, G. Beyerle, and Th. Peter, “Non-equilibrium co-existence of Solid and Liquid Particles in Arctic Stratospheric Clouds,” J. Geophy. Res. submitted (2000)

Platt, C. M. R.

C. M. R. Platt, “Lidar observations of a mixed-phase altostratus cloud,” J. Appl. Meteorol.,  16, 339–345 (1977)
[Crossref]

R. J.,

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

Sassen, K.

K. Sassen, “Depolarization of laser light backscattered by artificial clouds,” J. Appl. Meteorol.,  13, 923–933 (1973)
[Crossref]

Sassen, R. M.

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

Schotland, R. M.

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

Stone, K.

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

Tsias, A.

J. Biele, A. Tsias, B. P. Luo, K. S. Carslaw, R. Neuber, G. Beyerle, and Th. Peter, “Non-equilibrium co-existence of Solid and Liquid Particles in Arctic Stratospheric Clouds,” J. Geophy. Res. submitted (2000)

van de Hulst, H. C.

H. C. van de Hulst, “Light Scattering by Small Particles,” Dover Publications, New York(1957)

Young, A.T.

Appl. Opt. (3)

J. Appl. Meteorol. (3)

C. M. R. Platt, “Lidar observations of a mixed-phase altostratus cloud,” J. Appl. Meteorol.,  16, 339–345 (1977)
[Crossref]

K. Sassen, “Depolarization of laser light backscattered by artificial clouds,” J. Appl. Meteorol.,  13, 923–933 (1973)
[Crossref]

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

Optics Letters (1)

M. Mishchenko and J. Hovenier, “Depolarization of light backscattered by randomly oriented non-spherical particles,” Optics Letters 20, 1356–1358 (1995)
[Crossref] [PubMed]

Planet. Space Sci. (1)

D.R. Bates, “Rayleigh Scattering by Air,” Planet. Space Sci. 32, 785–790 (1984)
[Crossref]

Other (5)

G. Beyerle, “Untersuchungen polarer stratosphärischer Aerosole vulkanischen Ursprungs und polarer stratosphärischer Wolken mit einem Mehrwellenlängen-Lidar auf Spitzbergen (79° N, 12° O),” Berichte zur Polarforschung 138/’94, Alfred-Wegener-Institut für Polar- und Meeresforschung, Bremerhaven (1994)

G. Baumgarten, “Erste Messungen des Bonner Rayleigh/Mie/Raman-Lidar auf Esrange, Schweden, zur Untersuchung von dynamisch induzierten polaren Stratosphärenwolken im Januar 1997,” Diploma thesis, IB-97-26 University of Bonn, Germany (1997)

J. Biele, “Polare stratosphärische Wolken: Lidar-Beobachtungen, Charakterisierung von Entstehung und Entwicklung,” Berichte zur Polarforschung 03/’99, Alfred-Wegener-Institut für Polar- und Meeresforschung, Bremerhaven (1999)

J. Biele, A. Tsias, B. P. Luo, K. S. Carslaw, R. Neuber, G. Beyerle, and Th. Peter, “Non-equilibrium co-existence of Solid and Liquid Particles in Arctic Stratospheric Clouds,” J. Geophy. Res. submitted (2000)

H. C. van de Hulst, “Light Scattering by Small Particles,” Dover Publications, New York(1957)

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Figures (1)

Fig. 1.
Fig. 1.

Quasi-linear correlation between Sm and Sm on 20 February 1997 in an almost purely liquid polar stratospheric cloud (PSC), illustrating the correction of instrumental cross-talk between the parallel and perpendicular channels. All circles: uncorrected raw data; red circles: selected raw data with δmA <0.015; filled red circles: raw data with a corrected S consistent with 1. Dashed line: linear relation corresponding to δ C=0.0217. Note that the uncertainty of a single data point ranges from 0.1 to 0.5 (a few errorbars are shown for reference)

Equations (44)

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I = E · E * + E · E *
Q = E · E * E · E *
U = E · E * + E · E *
V = 1 E · E * E · E * .
δ = i i ,
δ = I Q I + Q .
i = c β ( z ) T 2 ( z ) / z 2
s = β R + β A β R = 1 + β A β R .
S , , T = β , , T R + β , , T A β , , T R = 1 + β , , T A β , , T R
δ V = i i = β β = S S β R β R S S δ R
δ A = β A β A = S 1 S 1 β R β R = S 1 S 1 δ R
= ( 1 + δ R ) δ V S T ( 1 + δ V ) δ R ( 1 + δ R ) S T ( 1 + δ V ) .
F s ( 180 ) = β T ( 1 0 0 0 0 ( 1 δ V ) ( 1 + δ V ) 0 0 0 0 F 33 0 0 0 0 F 44 ) .
F p , = 1 2 ( 1 1 B 0 0 1 B 1 0 0 0 0 0 0 0 0 0 0 )
F p , = 1 2 ( 1 ( 1 B ) 0 0 ( 1 B ) 1 0 0 0 0 0 0 0 0 0 0 ) .
i [ 1 2 ( 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ) F s ( 1 1 0 0 ) ] 1 . component
= β T 2 ( 1 + 1 δ V 1 + δ V ) = 1 1 + δ V β T = β
i [ 1 2 ( 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ) F s ( 1 1 0 0 ) ] 1 . component
= β T 2 ( 1 1 δ V 1 + δ V ) = δ V 1 + δ V β T = β .
i m [ 1 2 ( 1 ( 1 B ) 0 0 ( 1 B ) 1 0 0 0 0 0 0 0 0 0 0 ) F s ( 1 1 α 0 0 ) ] 1 . component
= β T 2 ( 1 + 1 δ V 1 + δ V ( 1 α ) ( 1 B ) ) = β m
i m [ 1 2 ( 1 ( 1 B ) 0 0 ( 1 B ) 1 0 0 0 0 0 0 0 0 0 0 ) F s ( 1 1 α 0 0 ) ] 1 . component
β T 2 ( 1 1 δ V 1 + δ V ( 1 α ) ( 1 B ) ) = β m .
( 1 2 δ ˜ C ) ( 1 α ) ( 1 B )
( 1 2 δ C ) ( 1 α ) ( 1 B ) .
i m = ( 1 δ ˜ C ) i + δ ˜ C i
i m = δ C i + ( 1 δ C ) i
β m = ( 1 δ ˜ C ) β + δ ˜ C β
β m = δ C β + ( 1 δ C ) β .
β m β
β m = δ C β + ( 1 δ C ) β .
S m = β A , m + β R , m β R , m
= S δ C + S ( 1 δ C ) δ R δ C + ( 1 δ C ) δ R
S m = β A , m + β R , m β R , m
S .
S ( 1 + δ C δ R ) S m δ C δ R S m
S S m .
S m S δ C + δ R δ C + δ R
δ C δ C + δ R S m + δ R δ C + δ R
δ C = δ R ( S m 1 ) S m S m .
δ V = i i .
δ m V = k i m i m = k ( δ C + ( 1 δ C ) δ V )
δ V = δ m V δ C / δ R + ( 1 δ C ) 1 δ C δ C 1 δ C
δ m V ( δ C / δ R + 1 ) δ C .

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