Abstract

Recently, an empirical relationship between the layer integrated backscattered light and the layer accumulated depolarization ratio has been established for linear polarization for the case of water droplet clouds. This is a powerful relation, allowing calibration of space lidar and correction of the lidar signal for multiple scattering effects. The relationship is strongly based on Monte Carlo simulations with some experimental evidence. We support the empirical relationship with strong experimental data and then show experimentally and via second order scattering theoretical calculations that a modified relationship can be obtained for circular polarization. Also, we demonstrate that other empirical relationships exist between the layer accumulated linear and circular depolarization ratios and the layer integrated backscattered light for submicrometer particles and nonspherical particles.

© 2009 Optical Society of America

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  1. Y. Hu, Z. Liu, D. Winker, M. Vaughan, V. Noel, L. Bissonnette, G. Roy, and M. McGill, “Simple relation between lidar multiple scattering and depolarization for water clouds,” Opt. Lett. 31, 1809-1811 (2006).
    [CrossRef] [PubMed]
  2. Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.
  3. Y. Hu, M. Vaughan, Z. Liu, B. Lin, D. Flittner, B. Hunt, R. Kuehn, J. Huang, D. Wu, S. Rodier, K. Powell, C. R. Trepte, and D. Winker, “The depolarization-attenuated backscatter relation: CALIPSO lidar measurements versus theory,” Opt. Express 15, 5327-5332 (2007).
    [CrossRef] [PubMed]
  4. D. P. Donovan, “The use of circular polarization in space-based lidar systems: consideration for the earth CARE lidar,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.
  5. Y.-X. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transfer 79-80, 757-764(2003).
    [CrossRef]
  6. M. Del Guasta, “Use of polarimetric lidar for the study of oriented ice plates in clouds,” Appl. Opt. 45, 4878-4887 (2006).
    [CrossRef] [PubMed]
  7. C. J. Flynn, A. Memdoza, Y. Zheng, and S. Mathur, “Novel polarization-sensitive micropulse lidar measurement techniques,” Opt. Express 15, 2785-2790 (2007).
    [CrossRef] [PubMed]
  8. K. Sassen, “Polarization in lidar,” in Lidar : Range-Resolved Optical Remote Sensing of the Atmosphere, Springer Series in Optical Sciences, C. Weikamp, ed. (Springer, 2005).
  9. G. Roy and N. Roy, “Relation between circular and linear depolarization ratios under multiple scattering conditions,” Appl. Opt. 47, 6563-6579 (2008).
    [CrossRef] [PubMed]
  10. N. Roy and G. Roy, “Influence of multiple scattering on lidar depolarization measurements with an ICCD camera,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.
  11. N. Roy and G. Roy, “Standoff determination of the particle size and concentration of small optical depth clouds based on double scattering measurements; validation with calibrated target plates and limitations of the technique for daytime and night time measurements,” Appl. Opt. 47, 4235-4252(2008).
    [CrossRef] [PubMed]
  12. L. R. Bissonnette, “Lidar and multiple scattering,” in Lidar : Range-Resolved Optical Remote Sensing of the Atmosphere, Springer Series in Optical Sciences, C. Weikamp, ed. (Springer, 2005).
  13. G. G. Gimmestad, “Reexamination of depolarization in lidar measurements,” Appl. Opt. 47, 3795-3802 (2008).
    [CrossRef] [PubMed]

2008

2007

2006

2003

Y.-X. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transfer 79-80, 757-764(2003).
[CrossRef]

Bissonnette, L.

Y. Hu, Z. Liu, D. Winker, M. Vaughan, V. Noel, L. Bissonnette, G. Roy, and M. McGill, “Simple relation between lidar multiple scattering and depolarization for water clouds,” Opt. Lett. 31, 1809-1811 (2006).
[CrossRef] [PubMed]

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.

Bissonnette, L. R.

L. R. Bissonnette, “Lidar and multiple scattering,” in Lidar : Range-Resolved Optical Remote Sensing of the Atmosphere, Springer Series in Optical Sciences, C. Weikamp, ed. (Springer, 2005).

Del Guasta, M.

Donovan, D. P.

D. P. Donovan, “The use of circular polarization in space-based lidar systems: consideration for the earth CARE lidar,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.

Flittner, D.

Flynn, C. J.

Gibson, G.

Y.-X. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transfer 79-80, 757-764(2003).
[CrossRef]

Gimmestad, G. G.

Hostetler, C.

Y.-X. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transfer 79-80, 757-764(2003).
[CrossRef]

Hu, Y.

Hu, Y.-X.

Y.-X. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transfer 79-80, 757-764(2003).
[CrossRef]

Huang, J.

Hunt, B.

Kuehn, R.

Lin, B.

Y. Hu, M. Vaughan, Z. Liu, B. Lin, D. Flittner, B. Hunt, R. Kuehn, J. Huang, D. Wu, S. Rodier, K. Powell, C. R. Trepte, and D. Winker, “The depolarization-attenuated backscatter relation: CALIPSO lidar measurements versus theory,” Opt. Express 15, 5327-5332 (2007).
[CrossRef] [PubMed]

Y.-X. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transfer 79-80, 757-764(2003).
[CrossRef]

Liu, Z.

Mathur, S.

McGill, M.

Y. Hu, Z. Liu, D. Winker, M. Vaughan, V. Noel, L. Bissonnette, G. Roy, and M. McGill, “Simple relation between lidar multiple scattering and depolarization for water clouds,” Opt. Lett. 31, 1809-1811 (2006).
[CrossRef] [PubMed]

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.

Memdoza, A.

Noel, V.

Y. Hu, Z. Liu, D. Winker, M. Vaughan, V. Noel, L. Bissonnette, G. Roy, and M. McGill, “Simple relation between lidar multiple scattering and depolarization for water clouds,” Opt. Lett. 31, 1809-1811 (2006).
[CrossRef] [PubMed]

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.

Powell, K.

Rodier, S.

Roy, G.

G. Roy and N. Roy, “Relation between circular and linear depolarization ratios under multiple scattering conditions,” Appl. Opt. 47, 6563-6579 (2008).
[CrossRef] [PubMed]

N. Roy and G. Roy, “Standoff determination of the particle size and concentration of small optical depth clouds based on double scattering measurements; validation with calibrated target plates and limitations of the technique for daytime and night time measurements,” Appl. Opt. 47, 4235-4252(2008).
[CrossRef] [PubMed]

Y. Hu, Z. Liu, D. Winker, M. Vaughan, V. Noel, L. Bissonnette, G. Roy, and M. McGill, “Simple relation between lidar multiple scattering and depolarization for water clouds,” Opt. Lett. 31, 1809-1811 (2006).
[CrossRef] [PubMed]

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.

N. Roy and G. Roy, “Influence of multiple scattering on lidar depolarization measurements with an ICCD camera,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.

Roy, N.

Sassen, K.

K. Sassen, “Polarization in lidar,” in Lidar : Range-Resolved Optical Remote Sensing of the Atmosphere, Springer Series in Optical Sciences, C. Weikamp, ed. (Springer, 2005).

Trepte, C. R.

Y. Hu, M. Vaughan, Z. Liu, B. Lin, D. Flittner, B. Hunt, R. Kuehn, J. Huang, D. Wu, S. Rodier, K. Powell, C. R. Trepte, and D. Winker, “The depolarization-attenuated backscatter relation: CALIPSO lidar measurements versus theory,” Opt. Express 15, 5327-5332 (2007).
[CrossRef] [PubMed]

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.

Vaughan, M.

Vaughan, M. A.

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.

Winker, D.

Winker, D. M.

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.

Wu, D.

Yang, P.

Y.-X. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transfer 79-80, 757-764(2003).
[CrossRef]

Zheng, Y.

Appl. Opt.

J. Quant. Spectrosc. Radiat. Transfer

Y.-X. Hu, P. Yang, B. Lin, G. Gibson, and C. Hostetler, “Discriminating between spherical and non-spherical scatterers with lidar using circular polarization: a theoretical study,” J. Quant. Spectrosc. Radiat. Transfer 79-80, 757-764(2003).
[CrossRef]

Opt. Express

Opt. Lett.

Other

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.

D. P. Donovan, “The use of circular polarization in space-based lidar systems: consideration for the earth CARE lidar,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.

K. Sassen, “Polarization in lidar,” in Lidar : Range-Resolved Optical Remote Sensing of the Atmosphere, Springer Series in Optical Sciences, C. Weikamp, ed. (Springer, 2005).

N. Roy and G. Roy, “Influence of multiple scattering on lidar depolarization measurements with an ICCD camera,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24--28 July 2006.

L. R. Bissonnette, “Lidar and multiple scattering,” in Lidar : Range-Resolved Optical Remote Sensing of the Atmosphere, Springer Series in Optical Sciences, C. Weikamp, ed. (Springer, 2005).

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Figures (16)

Fig. 1
Fig. 1

Calculated layer-integrated signals as a function of the accumulated linear and circular depolarization ratios, δ acc , lin ( z , θ ) and δ acc , cir ( z , θ ) . The single-scattering component I s ( z ) is obtained through extrapolation at δ equals zero. The calculations were performed using a second order scattering model on a 10 μm water droplet cloud with an extinction coefficient of 0.02 and 0.1 m 1 . The clouds ranged from 105 m to 127 m and the calculations were performed for penetration depths of 2, 5.5, 9, 12.5, and 16 m . Each point on the curve is for a specific FOV. O.D. represents optical depth.

Fig. 2
Fig. 2

Single scattering fraction A s ( θ ) as a function of the accumulated linear and circular depolarization ratios, δ acc , lin ( z , θ ) and δ acc , cir ( z , θ ) . A s ( θ ) = ( I s ( z ) ) / ( I T ( z , θ ) ) . I s ( z ) is obtained from the extrapolated curves of Fig. 1.

Fig. 3
Fig. 3

MFOV lidar measurements with an ICCD camera. Two measurement methods are displayed: the variable gate width at the top and the fixed gate width technique at the bottom. The parameter t i corresponds to the camera delay before acquisition. The parameter Δ T corresponds to the camera gate width or depth of acquisition. The images correspond to a measurement obtained on a water droplet cloud at the beginning of the cloud (Cell 2) with the dual channel polarization ICCD lidar for linear polarization illumination.

Fig. 4
Fig. 4

(Top) Illustration of two unwanted scattering processes contributing to an increase of the secondary polarization signal: off-axis laser beam energy returning into the lidar after double scattering ( a 1 and a 2 ) at depolarization occurring when the distance from cloud to lidar is short and the size of the collecting optics must be taken into account (scattering b 1 ). (Bottom) Light paths c and d illustrate, respectively, second order and third order scattering processes that we are interested in measuring.

Fig. 5
Fig. 5

Derivation of the single-scattering component I s ( z ) from MFOV lidar observations through extrapolation. The measured layer integrated energy is plotted for five penetration depths as a function of the accumulated linear depolarization ratios for a water droplets experiment. The cloud begins at 105 m , and the optical depths (O.D) are obtained from an independent measurement made with a transmissometer along the aerosol chamber (homogenous aerosol dispersion inside the aerosol chamber is assumed).

Fig. 6
Fig. 6

Same as for Fig. 5 except the measurements are for a circular polarization illumination.

Fig. 7
Fig. 7

Measured accumulated single scattering factor, A s , as a function of the accumulated linear and circular depolarization ratios, δ acc , lin ( z , θ ) and δ acc , cir ( z , θ ) , for a water droplets clouds. A s ( θ ) = ( I s ( z ) ) / ( I T ( z , θ ) ) . I s ( z ) is obtained from Figs. 5, 6. The different penetration depths are represented with a different symbols, and the letters L and C represent the linear and circular polarization measurement.

Fig. 8
Fig. 8

Derivation of the single-scattering component I s ( z ) from MFOV lidar observations through extrapolation. The measured layer integrated energy is plotted as a function of the accumulated linear depolarization ratios for a fog oil droplets experiment. The cloud beginning at 105 m and the optical depths (O.D) are obtained from an independent measurement made with a transmissometer along the aerosol chamber (homogenous aerosol dispersion inside the aerosol chamber is assumed).

Fig. 9
Fig. 9

Measured accumulated single scattering factor, A s , as a function of the accumulated linear depolarization ratios, δ acc , lin ( z , θ ) , for fog oil droplet clouds. A s ( θ ) = ( I s ( z ) ) / ( I T ( z , θ ) ) . I s ( z ) is obtained from Fig. 8.

Fig. 10
Fig. 10

Same as for Fig. 9 except the measurements are for circular polarization illumination. A s ( θ ) = ( I s ( z ) ) / ( I T ( z , θ ) ) . I s ( z ) is obtained from a figure similar to Fig. 8 but is not shown.

Fig. 11
Fig. 11

Calculated accumulated single scattering factor, A s , as a function of the accumulated linear depolarization ratios for fog oil. The calculation was performed using a second order scattering model on 0.28 μm fog oil cloud with extinction coefficients of 0.02 and 0.1 m 1 . The cloud distance was 105 m , and, as previously, five penetration depths ranging from 2 m to 16 m were considered.

Fig. 12
Fig. 12

Same as for Fig. 11 except the calculations were performed for circular polarization illumination.

Fig. 13
Fig. 13

Measured accumulated single scattering factor, A s , as a function of the accumulated linear and circular depolarization ratios, δ acc , lin ( z , θ ) and δ acc , cir ( z , θ ) , for glass bead clouds. A s ( θ ) = ( I s ( z ) ) / ( I T ( z , θ ) ) . I s ( z ) is obtained by extrapolation as before.

Fig. 14
Fig. 14

Measured accumulated single scattering factor, A s , as a function of the accumulated linear and circular depolarization ratios, δ acc , lin ( z , θ ) and δ acc , cir ( z , θ ) , for Arizona road dust. A s ( θ ) = ( I s ( z ) ) / ( I T ( z , θ ) ) . I s ( z ) is obtained by extrapolation as before.

Fig. 15
Fig. 15

(a) Measured accumulated single scattering factor, A s , as a function of accumulated polarization parameter d acc ( θ , z ) for water cloud measurements. Both linear and circular depolarization measurements superpose well and follow a Gimmestand proposed relationship. (b) Measured accumulated single scattering factor, A s , as a function of accumulated polarization parameter d acc ( θ , z ) for fog oil cloud measurements. Both linear and circular depolarization measurements superpose well but follow a new relationship. (c) Measured accumulated single scattering factor, A s , as a function of integrated polarization parameter d acc ( θ , z ) for glass bead cloud measurements. Both linear and circular depolarization measurements superpose well but follow a new relationship. (d) Measured accumulated single scattering factor, A s , as a function of integrated polarization parameter d acc ( θ , z ) for ARD clouds measurements. Linear and circular depolarization measurements do not superpose well. The divergence is most likely caused by improper correction of the laser beam profile.

Fig. 16
Fig. 16

A s 1 versus ( d Init + d acc ) for the four materials studied. Only the data obtained from linear polarization were used.

Tables (2)

Tables Icon

Table 1 Characteristics of the Aerosols

Tables Icon

Table 2 Generalized Hu Relationships for Linear and Circular Polarization Illumination and for the Depolarization Parameter d for the Four Materials Studied

Equations (25)

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A s I s ( z ) I T ( z ) ,
I s ( z ) = z a z ( P / / s ( z ) + P s ( z ) ) z 2 d z ,
I T ( z , θ ) = z a z ( P / / T ( z , θ ) + P T ( z , θ ) ) z 2 d z .
δ acc , lin ( z , θ ) = z a z P T ( z , θ ) z 2 d z z a z P / / T ( z , θ ) z 2 d z ,
A s ( θ ) I s ( z ) I T ( z , θ ) = ( 1 δ acc , lin ( z , θ ) 1 + δ acc , lin ( z , θ ) ) 2 .
δ acc , cir ( z , θ ) = 2 δ acc , lin ( z , θ ) 1 δ acc , lin ( z , θ ) .
A s ( z , θ ) I s ( z ) I T ( z , θ ) = ( 1 δ acc , lin ( z , θ ) 1 + δ acc , lin ( z , θ ) ) 2 = ( 1 1 + δ acc , cir ( z , θ ) ) 2 .
I T ( z ) = z a z ( P T ( z , θ ) P T ( z , θ = 1.3 mrad ) ) z 2 d z ,
I T / / ( z ) = z a z P T / / ( z , θ ) F ( θ ) x 2 d z .
( 1 1.061 δ acc , lin ( z , θ ) 1 + 1.061 δ acc , lin ( z , θ ) ) 2 ,
( 1 1 + 1.137 δ acc , cir ( z , θ ) ) 2 .
A s = ( 1 δ acc , lin 1 + 3.83 δ acc , lin ) 2 .
A s = ( 1 1 + 2.7 δ acc , cir ) 2 .
A s = ( 1 1 + 2.42 δ acc , cir ) 2 .
A s = ( 1 δ L 1 + 2.89 δ L ) 2 ,
A s = ( 1 1 + 2.18 δ C ) 2 .
A s = ( 1 1 + 1.95 δ acc , cir ) 2 .
A s = ( 1 δ acc , lin 1 + 0.82 δ acc , lin ) 2 .
A s = 1 δ acc , cir 1 + δ acc , cir .
A s = ( 1 1 + 0.91 δ acc , cir ) 2 .
M atm = ( 1 0 0 0 0 1 d 0 0 0 0 d 1 0 0 0 0 2 d 1 ) .
d = 2 δ lin 1 + δ lin = δ cir 1 + δ cir .
A S ( θ ) = ( 1 d acc ( z , θ ) ) 2 ,
d acc ( z , θ ) = 2 δ acc , lin ( z , θ ) 1 + δ acc , lin ( z , θ ) = δ acc , cir ( z , θ ) 1 + δ acc , cir ( z , θ ) .
δ acc , cir ( z , θ ) = 2 δ acc , cir ( z , θ ) 1 δ acc , cir ( z , θ ) ,

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