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.

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References

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  1. Pal, S. R. and Carswell, A. I., "Polarization properties of lidar backscattering from clouds," Appl. Opt. 12, 1530-1535 (1973)
    [CrossRef] [PubMed]
  2. Platt, C. M. R., "Lidar observations of a mixed-phase altostratus cloud," J. Appl. Meteorol. 16, 339-345 (1977).
    [CrossRef]
  3. Sassen, K., "Depolarization of laser light backscattered by arti_cial clouds," J. Appl. Meteorol. 13, 923-933 (1973).
    [CrossRef]
  4. R. M. Schotland, R. M., Sassen, K., and Stone, R. J., "Observations by lidar of linear depolariz- ation 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. Bates, D.R., "Rayleigh Scattering by Air," Planet. Space Sci. 32, 785-790 (1984)
    [CrossRef]
  7. Young, A.T., "Revised depolarization corrections for atmospheric extinction," Appl. Opt. 19, 3427-3428 (1980)
    [CrossRef] [PubMed]
  8. Young, A.T., "Rayleigh Scattering," Appl. Opt. 20, 533-535 (1981).
    [CrossRef] [PubMed]
  9. Beyerle, G., "Untersuchungen polarer stratospharischer Aerosole vulkanischen Ursprungs und polarer stratosph�arischer Wolken mit einem Mehrwellenlangen-Lidar auf Spitzbergen (79 N, 12 O)," Berichte zur Polarforschung 138/'94, Alfred-Wegener-Institut fur Polar- und Meeresforschung, Bremerhaven (1994).
  10. Mishchenko, M., Hovenier, J., "Depolarization of light backscattered by randomly oriented nonspherical particles," Optics Letters 20, 1356-1358 (1995)
    [CrossRef] [PubMed]
  11. Baumgarten, G., "Erste Messungen des Bonner Rayleigh/Mie/Raman-Lidar auf Esrange, Schweden, zur Untersuchung von dynamisch induzierten polaren Stratosph�arenwolken im Januar 1997," Diploma thesis, IB-97-26 University of Bonn, Germany (1997).
  12. Biele, J., "Polare stratospharische Wolken: Lidar-Beobachtungen, Charakterisierung von Entstehung und Entwicklung," Berichte zur Polarforschung 03/'99, Alfred-Wegener-Institut fur Polarund Meeresforschung, Bremerhaven (1999).
  13. Biele, J., A. Tsias, B. P. Luo, K. S. Carslaw, R. Neuber, G. Beyerle, Th. Peter, "Non-equilibrium co-existence of Solid and Liquid Particles in Arctic Stratospheric Clouds," J. Geophy. Res. submitted (2000).

Other (13)

Pal, S. R. and Carswell, A. I., "Polarization properties of lidar backscattering from clouds," Appl. Opt. 12, 1530-1535 (1973)
[CrossRef] [PubMed]

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

Sassen, K., "Depolarization of laser light backscattered by arti_cial clouds," J. Appl. Meteorol. 13, 923-933 (1973).
[CrossRef]

R. M. Schotland, R. M., Sassen, K., and Stone, R. J., "Observations by lidar of linear depolariz- ation ratios by hydrometeors," J. Appl. Meteorol. 10, 1011-1017 (1971)
[CrossRef]

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

Bates, D.R., "Rayleigh Scattering by Air," Planet. Space Sci. 32, 785-790 (1984)
[CrossRef]

Young, A.T., "Revised depolarization corrections for atmospheric extinction," Appl. Opt. 19, 3427-3428 (1980)
[CrossRef] [PubMed]

Young, A.T., "Rayleigh Scattering," Appl. Opt. 20, 533-535 (1981).
[CrossRef] [PubMed]

Beyerle, G., "Untersuchungen polarer stratospharischer Aerosole vulkanischen Ursprungs und polarer stratosph�arischer Wolken mit einem Mehrwellenlangen-Lidar auf Spitzbergen (79 N, 12 O)," Berichte zur Polarforschung 138/'94, Alfred-Wegener-Institut fur Polar- und Meeresforschung, Bremerhaven (1994).

Mishchenko, M., Hovenier, J., "Depolarization of light backscattered by randomly oriented nonspherical particles," Optics Letters 20, 1356-1358 (1995)
[CrossRef] [PubMed]

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

Biele, J., "Polare stratospharische Wolken: Lidar-Beobachtungen, Charakterisierung von Entstehung und Entwicklung," Berichte zur Polarforschung 03/'99, Alfred-Wegener-Institut fur Polarund Meeresforschung, Bremerhaven (1999).

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

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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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