Abstract

Depolarization lidars are widely used to study clouds and aerosols because of their ability to discriminate between spherical particles and particles of irregular shape. Depolarization of cloud backscattered radiation can be caused also by multiple scattering events. One of the ways to gain information about particle parameters in the presence of strong multiple scattering is the measurement of radial and azimuthal dependence of the polarization patterns in the focal plane of receiver. We present an algorithm for the calculation of corresponding polarized patterns in the frame of double scattering approximation. Computations are performed for various receiver field of views, for different parameters of the scattering geometry, e.g., cloud base and sounding depth, as well as for different values of cloud particle size and refractive index. As the spatial distribution of cross-polarized radiation is of cross shape and rotated at 45° with respect to laser polarization, the use of a properly oriented cross-shaped mask in the receiver focal plane allows the removal of a significant portion of the depolarized component of the backscattered radiation produced by double scattering. This has been verified experimentally based on cloud depolarization measurements performed at different orientations of the cross-shaped mask. Results obtained from measurements are in agreement with model predictions.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. R. F. Cahalan, M. McGill, J. Kolasinski, T. Varnai, and K. Yetzer, "THOR--cloud thickness from offbeams lidar returns," J. Atmos. Ocean Technol. 22, 605-627 (2005).
    [CrossRef]
  2. L. R. Bissonnette and D. L. Hutt, "Multiply scattered aerosol lidar returns: inversion method and comparison with in situ measurements," Appl. Opt. 34, 6959-6975 (1995).
    [CrossRef] [PubMed]
  3. G. Roy, L. C. Bissonnette, C. Bastille, and G. Vallee, "Estimation of cloud droplet size density distribution from multiple-field-of-view lidar returns," Opt. Eng. 36, 3404-3415 (1997).
    [CrossRef]
  4. G. Roy, L. Bissonnette, C. Bastille, and G. Vallee, "Retrieval of droplet-size density distribution from multiple-field-of-view cross-polarized lidar signals: theory and experimental validation," Appl. Opt. 38, 5202-5211 (1999).
    [CrossRef]
  5. L. R. Bissonnette, G. Roy, and N. Roy, "Multiple-scattering-based lidar retrieval: method and results of cloud probing," Appl. Opt. 44, 5565-5581 (2005).
    [CrossRef] [PubMed]
  6. I. Veselovskii, M. Korenskii, V. Griaznov, D. N. Whiteman, M. McGill, G. Roy, and L. Bissonnette, "Information content of data measured with a multiple-field-of-view lidar," Appl. Opt. 45, 6839-6848 (2006).
    [CrossRef] [PubMed]
  7. A. I. Carswell and S. R. Pal, "Polarization anisotropy in lidar multiple scattering from clouds," Appl. Opt. 19, 4123-4126 (1980).
    [CrossRef] [PubMed]
  8. S. R. Pal and A. I. Carswell, "Polarization anisotropy in lidar multiple scattering from atmospheric clouds," Appl. Opt. 24, 3464-3471 (1985).
    [CrossRef] [PubMed]
  9. N. Roy, G. Roy, L. R. Bissonnette and J.-R. Simard, "Measurement of the azimuthal dependence of cross-polarized lidar returns and its relation to optical depth," Appl. Opt. 43, 2777-2785 (2004).
    [CrossRef] [PubMed]
  10. M. J. Rakovic and G. W. Kattawar, "Theoretical analysis of polarization patterns from incoherent backscattering of light," Appl. Opt. 37, 3333-3338 (1998).
    [CrossRef]
  11. F. B. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  12. I. Veselovskii, A. Kolgotin, D. Müller, and D. N. Whiteman, "Information content of multiwavelength lidar data with respect to microphysical particle properties derived from eigenvalue analysis," Appl. Opt. 44, 5292-5303 (2005).
    [CrossRef] [PubMed]
  13. I. Polonskii, E. Zege, and I. L. Katsev, "Lidar sounding of warm clouds and determination of their microstructure parameters," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 37, 624-632 (2001).
  14. A. Behrendt and T. Nakamura, "Calculation of the calibration constant of polarization lidar and its dependency on atmospheric temperature," Opt. Express 10, 805-817 (2002).
    [PubMed]
  15. E. W. Eloranta, "Practical model for the calculation of multiply scattered lidar returns," Appl. Opt. 37, 2464-2472 (1998).
    [CrossRef]

2006 (1)

2005 (3)

2004 (1)

2002 (1)

2001 (1)

I. Polonskii, E. Zege, and I. L. Katsev, "Lidar sounding of warm clouds and determination of their microstructure parameters," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 37, 624-632 (2001).

1999 (1)

1998 (2)

1997 (1)

G. Roy, L. C. Bissonnette, C. Bastille, and G. Vallee, "Estimation of cloud droplet size density distribution from multiple-field-of-view lidar returns," Opt. Eng. 36, 3404-3415 (1997).
[CrossRef]

1995 (1)

1985 (1)

1980 (1)

Appl. Opt. (10)

G. Roy, L. Bissonnette, C. Bastille, and G. Vallee, "Retrieval of droplet-size density distribution from multiple-field-of-view cross-polarized lidar signals: theory and experimental validation," Appl. Opt. 38, 5202-5211 (1999).
[CrossRef]

L. R. Bissonnette, G. Roy, and N. Roy, "Multiple-scattering-based lidar retrieval: method and results of cloud probing," Appl. Opt. 44, 5565-5581 (2005).
[CrossRef] [PubMed]

I. Veselovskii, M. Korenskii, V. Griaznov, D. N. Whiteman, M. McGill, G. Roy, and L. Bissonnette, "Information content of data measured with a multiple-field-of-view lidar," Appl. Opt. 45, 6839-6848 (2006).
[CrossRef] [PubMed]

A. I. Carswell and S. R. Pal, "Polarization anisotropy in lidar multiple scattering from clouds," Appl. Opt. 19, 4123-4126 (1980).
[CrossRef] [PubMed]

S. R. Pal and A. I. Carswell, "Polarization anisotropy in lidar multiple scattering from atmospheric clouds," Appl. Opt. 24, 3464-3471 (1985).
[CrossRef] [PubMed]

N. Roy, G. Roy, L. R. Bissonnette and J.-R. Simard, "Measurement of the azimuthal dependence of cross-polarized lidar returns and its relation to optical depth," Appl. Opt. 43, 2777-2785 (2004).
[CrossRef] [PubMed]

M. J. Rakovic and G. W. Kattawar, "Theoretical analysis of polarization patterns from incoherent backscattering of light," Appl. Opt. 37, 3333-3338 (1998).
[CrossRef]

L. R. Bissonnette and D. L. Hutt, "Multiply scattered aerosol lidar returns: inversion method and comparison with in situ measurements," Appl. Opt. 34, 6959-6975 (1995).
[CrossRef] [PubMed]

I. Veselovskii, A. Kolgotin, D. Müller, and D. N. Whiteman, "Information content of multiwavelength lidar data with respect to microphysical particle properties derived from eigenvalue analysis," Appl. Opt. 44, 5292-5303 (2005).
[CrossRef] [PubMed]

E. W. Eloranta, "Practical model for the calculation of multiply scattered lidar returns," Appl. Opt. 37, 2464-2472 (1998).
[CrossRef]

Izv. Acad. Sci. USSR Atmos. Oceanic Phys. (1)

I. Polonskii, E. Zege, and I. L. Katsev, "Lidar sounding of warm clouds and determination of their microstructure parameters," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 37, 624-632 (2001).

J. Atmos. Ocean Technol. (1)

R. F. Cahalan, M. McGill, J. Kolasinski, T. Varnai, and K. Yetzer, "THOR--cloud thickness from offbeams lidar returns," J. Atmos. Ocean Technol. 22, 605-627 (2005).
[CrossRef]

Opt. Eng. (1)

G. Roy, L. C. Bissonnette, C. Bastille, and G. Vallee, "Estimation of cloud droplet size density distribution from multiple-field-of-view lidar returns," Opt. Eng. 36, 3404-3415 (1997).
[CrossRef]

Opt. Express (1)

Other (1)

F. B. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Scattering geometry considered in the model.

Fig. 2
Fig. 2

Copolarized scattering patterns for PSDs with modal radius (a) 0.2 μ m , (b) 1 μ m , (c) 10 μ m , and (d) 50 μ m . Calculations are performed for z a = 500   m , Δ z = 50   m , and m = 1.33 . Laser polarization is oriented horizontally (along OX).

Fig. 3
Fig. 3

Total scattering patterns for PSDs with modal radius (a) 0.2 μ m , (b) 1 μ m , (c) 10 μ m , and (d) 50 μ m . Calculations are performed for z a = 500   m , Δ z = 50   m , and m = 1.33 . Laser polarization is oriented horizontally (along OX).

Fig. 4
Fig. 4

Cross-polarized pattern for r 0 = 10 μ m and m = 1.33 . Scattering geometry is the same as in Fig. 2.

Fig. 5
Fig. 5

Azimuthal distribution of copolarized return for r 0 = 1 μ m (solid curve, θ = 2 , 10   mrad ) and 10 μ m (dotted curve, θ = 0.2 , 1   mrad ). Computations are performed for m = 1.33 , z a = 500   m , and Δ z = 50   m . Dash-dotted curve corresponds to azimuthal distribution of cross-polarized return.

Fig. 6
Fig. 6

Copolarized patterns for refractive index (a) 1.5, (b) 1.6, and r 0 = 10 μ m . Scattering geometry is the same as in Fig. 2.

Fig. 7
Fig. 7

Azimuthal distributions of (a) E ( θ , φ ) and (b) depolarization ratio E ( θ , φ ) / E tot ( θ , φ ) for refractive indices m = 1.33 , 1.4, 1.5, and 1.6. Calculations are performed for r 0 = 10 μ m and θ = 1 mrad . Scattering geometry is the same as in Fig. 2.

Fig. 8
Fig. 8

Radial dependence of E ( θ , φ = 0 ) (solid) and E ( θ , φ = 45 ° ) (dash-dotted) on FOV. Computations are performed for z a = 1000   m , Δ z = 25 , 50, and 100   m ; r 0 = 10 μ m .

Fig. 9
Fig. 9

Azimuthal pattern of depolarization E ( θ , φ ) / E tot ( θ , φ ) for r 0 = 10 μ m . Calculations are performed for m = 1.33 , θ max = 5   mrad , z a = 500   m , and Δ z = 50   m . The shades of gray correspond to variation of depolarization in the 0–0.8 interval.

Fig. 10
Fig. 10

Multi-FOV measurements of particle depolarization, with FOV varied in the range 0.55 8.8   mrad with log-equidistant increments.

Fig. 11
Fig. 11

Depolarization ratio P ( θ ) / P ( θ ) of azimuthally integrated power for r 0 = 0.05 , 1, 4, and 10 μ m as a function of receiver FOV. Calculations are performed for m = 1.33 , λ = 0.355 μ m , z a = 500   m , and Δ z = 50   m .

Fig. 12
Fig. 12

Particle depolarization profiles measured with the cross-shaped mask oriented at 0° and 45° together with the particle backscattering coefficient.

Equations (33)

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

d P 2 d V 1 d ω 1 = β s M ( β ) R ( φ ) d P 1 d s 1 ,
R ( φ ) = | 1 0 0 0 0 cos   2 φ sin  2 φ 0 0 sin   2 φ cos   2 φ 0 0 0 0 1 |
d P 2 = β s M ( β ) R ( φ ) d P 0   exp [ α a z a α c ( z z a ) ] d ω 1 d z .
d P 3 = d P 2   exp ( α c v ) = β s   exp [ α a z a α c ( z z a ) α c v ] × M ( β ) R ( φ ) d P 0 d ω 1 d z ,
d P 4 d V 2 d ω 2 = β s M ( γ ) d P 3 d s 2   exp [ α c ( w z a cos   θ ) α a z a cos   θ ] ,
d P 4 = β s 2   exp ( 2 τ ) M ( γ ) M ( β ) R ( φ ) E 0 d s 0 d s 2 v 2 d ω 2 d z d v ,
τ = α a z a ( 1 + cos   θ cos   θ ) + α c [ R z a ( 1 + cos   θ cos   θ ) ] α a z a + α c ( R z a ) .
d P 4 = β s 2   exp ( 2 τ ) M ( γ ) M ( β ) R ( φ ) E 0 d s 0 × d s 2 v 2 d ω 2 d z d w .
d P 4 d s 2 d ω 2   cos   θ = β s 2   exp ( 2 τ ) M ( γ ) M ( β ) R ( φ ) E 0 d s 0 × d z d w v 2   cos   θ ,
d P 4 d s 3 d ω 2   cos   θ = β s 2   exp ( 2 τ ) M ( γ ) M ( β ) R ( φ ) E 0 d s 0 × d z d w v 2   cos   θ ,
d E = R ( φ ) d P 4 d s 3 = β s 2   exp ( 2 τ ) R ( φ ) M ( γ ) M ( β ) R ( φ ) × E 0 d s 0 d z d w v 2   sin   θ   cos   θ d θ d φ .
M ( γ ) = M [ ( π β ) + θ ] = M ( π β ) + d [ M ( π β ) ] d γ θ .
d E = β s 2 R ( φ ) [ M ( π β ) + θ · M ( π β ) ] M ( β ) R ( φ ) E 0 × exp ( 2 τ ) v 2 d s 0 d z d w   sin   θ   cos   θ d θ d φ .
  z R = sin   β θ 2 sin   β 2   cos   θ 2 , z β = R 2  cos   θ 2 sin   θ 2 sin 2 β 2 , w R = cos   β 2 cos   θ 2  cos   β θ 2 , w β = R   sin   θ 2 2  cos   θ 2 cos 2 ( β θ 2 ) .
z w β R = | z β z R w β w R | = R   sin   θ 2 2 sin 2 β 2   cos   θ 2 cos 2 ( β θ 2 ) .
d E = β s 2 R ( φ ) [ M ( π β ) + θ · M ( π β ) ] M ( β ) R ( φ ) E 0 × exp ( 2 τ ) R   cos   θ d s 0 d β d R d θ d φ ,
d E = β s 2 R ( φ ) [ M ( π β ) + θ · M ( π β ) ] M ( β ) R ( φ ) E 0 × exp ( 2 τ ) R d s 0 d β d R d θ d φ .
E = C M eff ( θ , φ , R ) E 00 ,
T = 1 2 | 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 | ,   T = 1 2 | 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 | .
E = C 2 | M 11 + M 21 + M 12 + M 22 M 11 + M 21 + M 12 + M 22 0 0 | ,  
E = C 2 | M 11 M 21 + M 12 M 22 M 11 + M 21 M 12 M 22 0 0 | .
E = C ( M 11 + M 21 + M 12 + M 22 ) / 2 ,
E = C ( M 11 M 21 + M 12 M 22 ) / 2 ,
M sca ( β ) = | a b 0 0 b c 0 0 0 0 d e 0 0 e f | .
M 11 = exp ( 2 τ ) R β min β max [ a ( π β ) a ( β ) + θ a ( π β ) a ( β ) + b ( π β ) b ( β ) + θ b ( π β ) b ( β ) ] d β ,
M 12 = exp ( 2 τ ) R   cos   2 φ β min β max [ a ( π β ) b ( β ) + θ a ( π β ) b ( β ) + b ( π β ) c ( β ) + θ b ( π β ) c ( β ) ] d β ,
M 21 = exp ( 2 τ ) R   cos   2 φ β min β max [ b ( π β ) a ( β ) + θ b ( π β ) a ( β ) + c ( π β ) b ( β ) + θ c ( π β ) b ( β ) ] d β ,
M 22 = exp ( 2 τ ) R { cos 2 2 φ β min β max [ b ( π β ) b ( β ) + θ b ( π β ) b ( β ) + c ( π β ) c ( β ) + θ c ( π β ) c ( β ) ] d β sin 2 2 φ β min β max [ d ( π β ) d ( β ) + θ d ( π β ) d ( β ) e ( π β ) e ( β ) θ e ( π β ) e ( β ) ] d β } .
E ( θ ) = C exp ( 2 τ ) 2 R β min β max d β { 3 π [ a ( π β ) a ( β ) + b ( π β ) b ( β ) + θ a ( π β ) a ( β ) + θ b ( π β ) b ( β ) ] π [ d ( π β ) d ( β ) e ( π β ) e ( β ) + θ d ( π β ) d ( β ) θ e ( π β ) e ( β ) ] } ,
E ( θ ) = C exp ( 2 τ ) 2 R β min β max d β { π [ a ( π β ) a ( β ) + b ( π β ) b ( β ) + θ a ( π β ) a ( β ) + θ b ( π β ) b ( β ) ] + π [ d ( π β ) d ( β ) e ( π β ) e ( β ) + θ d ( π β ) d ( β ) θ e ( π β ) e ( β ) ] } .
δ par ( z ) = β par ( z ) β par ( z ) = R ( z ) 1 R ( z ) 1 δ mol ( z ) ,
R ( z ) = β par ( z ) + β mol ( z ) β mol ( z ) ,
R ( z ) = β par ( z ) + β mol ( z ) β mol ( z )

Metrics