Abstract

Lidars with multiple fields of view (MFOVs) are promising tools for gaining information on cloud particle size. We perform a study of the information content of MFOV lidar data with the use of eigenvalue analysis. The approach we have developed permits an understanding of the main features of MFOV lidars and provides a way to relate the accuracy of particle size estimation with the measurement uncertainty and the scattering geometry such as the cloud-base height and the lidar sounding depth. Second-order scattering computations are performed for an extended range of particle sizes and for a wide range of lidar fields of view (FOVs). The results obtained allow us to specify the areas of possible applications of these lidars in cloud studies. Comparison of results obtained with polarized and cross-polarized scattered components demonstrate that the cross-polarized signal should provide a more stable retrieval and is preferable when double scattering is highly dominant. Our analysis allows for the estimation of the optimal number of FOVs in the system and their angular distribution, so this work can be a useful tool for practical MFOV lidar design.

© 2006 Optical Society of America

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References

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  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, 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]
  7. E. W. Eloranta, "Practical model for the calculation of multiply scattered lidar returns," Appl. Opt. 37, 2464-2472 (1998).
    [CrossRef]
  8. P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "Monte Carlo calculations of lidar returns: procedure and results of Florence group," Appl. Phys. B 60, 325-329 (1995).
    [CrossRef]
  9. I. L. Katsev, E. P. Zege, A. S. Prikhach, and I. N. Polonsky, "Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems," J. Opt. Soc. Am. A 14, 1338-1346 (1997).
    [CrossRef]
  10. C. Weikamp, ed., Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, Springer Series in Optical Science (Springer-Verlag, 2005), Chap. 3.
  11. I. Polonskii, E. Zege, and I. L. Katsev, "Lidar sounding of warm clouds and determination of their microstructure parameters," Izv. Atmos. Oceanic Phys. 37, 624-632 (2001).
  12. F. B. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  13. S. Twomey, ed., Introduction to the Mathematics of Inversion in Remote Sensing and Direct Measurements (Elsevier, 1977).
  14. K. Sassen and H. Zhao, "Lidar multiple scattering in water droplet clouds: toward an improved treatment," Opt. Rev. 2, 394-400 (1995).
    [CrossRef]
  15. 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]
  16. E. W. Eloranta and P. Piironen, "Measurements of particle size in cirrus clouds with the high spectral resolution lidar," in Eighth International Workshop on Multiple Scattering Lidar Experiments, MUSCLE8, 98101, Quebec, Canada, (1996).
  17. D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
    [CrossRef]

2005 (3)

2004 (1)

2001 (1)

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

1999 (1)

1998 (1)

1997 (2)

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]

I. L. Katsev, E. P. Zege, A. S. Prikhach, and I. N. Polonsky, "Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems," J. Opt. Soc. Am. A 14, 1338-1346 (1997).
[CrossRef]

1995 (3)

K. Sassen and H. Zhao, "Lidar multiple scattering in water droplet clouds: toward an improved treatment," Opt. Rev. 2, 394-400 (1995).
[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]

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "Monte Carlo calculations of lidar returns: procedure and results of Florence group," Appl. Phys. B 60, 325-329 (1995).
[CrossRef]

Bastille, C.

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]

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]

Bissonnette, L.

Bissonnette, L. C.

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]

Bissonnette, L. R.

Bohren, F. B.

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

Bruscaglioni, P.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "Monte Carlo calculations of lidar returns: procedure and results of Florence group," Appl. Phys. B 60, 325-329 (1995).
[CrossRef]

Cadirola, M.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Cahalan, R. F.

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]

Demoz, B.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Eloranta, E.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Eloranta, E. W.

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

E. W. Eloranta and P. Piironen, "Measurements of particle size in cirrus clouds with the high spectral resolution lidar," in Eighth International Workshop on Multiple Scattering Lidar Experiments, MUSCLE8, 98101, Quebec, Canada, (1996).

Evans, K. D.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Feltz, W.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Gutman, S. I.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Huffman, D. R.

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

Hutt, D. L.

Ismaelli, A.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "Monte Carlo calculations of lidar returns: procedure and results of Florence group," Appl. Phys. B 60, 325-329 (1995).
[CrossRef]

Jedlovec, G. J.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Katsev, I. L.

I. L. Katsev, E. P. Zege, A. S. Prikhach, and I. N. Polonsky, "Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems," J. Opt. Soc. Am. A 14, 1338-1346 (1997).
[CrossRef]

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

Kolasinski, J.

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]

Kolgotin, A.

McGill, M.

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]

Melfi, S. H.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Müller, D.

Piironen, P.

E. W. Eloranta and P. Piironen, "Measurements of particle size in cirrus clouds with the high spectral resolution lidar," in Eighth International Workshop on Multiple Scattering Lidar Experiments, MUSCLE8, 98101, Quebec, Canada, (1996).

Polonskii, I.

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

Polonsky, I. N.

Prikhach, A. S.

Roy, G.

Roy, N.

Sassen, K.

K. Sassen and H. Zhao, "Lidar multiple scattering in water droplet clouds: toward an improved treatment," Opt. Rev. 2, 394-400 (1995).
[CrossRef]

Schmidlin, F. J.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Schwemmer, G. K.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Simard, J. R.

Starr, D. O'C.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Tobin, D.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Twomey, S.

S. Twomey, ed., Introduction to the Mathematics of Inversion in Remote Sensing and Direct Measurements (Elsevier, 1977).

Vallee, G.

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]

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]

Varnai, T.

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]

Veselovskii, I.

Weikamp, C.

C. Weikamp, ed., Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, Springer Series in Optical Science (Springer-Verlag, 2005), Chap. 3.

Whiteman, D. N.

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]

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Yetzer, K.

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]

Zaccanti, G.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "Monte Carlo calculations of lidar returns: procedure and results of Florence group," Appl. Phys. B 60, 325-329 (1995).
[CrossRef]

Zege, E.

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

Zege, E. P.

Zhao, H.

K. Sassen and H. Zhao, "Lidar multiple scattering in water droplet clouds: toward an improved treatment," Opt. Rev. 2, 394-400 (1995).
[CrossRef]

Appl. Opt. (6)

Appl. Phys. B (1)

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "Monte Carlo calculations of lidar returns: procedure and results of Florence group," Appl. Phys. B 60, 325-329 (1995).
[CrossRef]

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]

J. Geophys. Res. (1)

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

J. Opt. Soc. Am. A (1)

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. Rev. (1)

K. Sassen and H. Zhao, "Lidar multiple scattering in water droplet clouds: toward an improved treatment," Opt. Rev. 2, 394-400 (1995).
[CrossRef]

Other (5)

E. W. Eloranta and P. Piironen, "Measurements of particle size in cirrus clouds with the high spectral resolution lidar," in Eighth International Workshop on Multiple Scattering Lidar Experiments, MUSCLE8, 98101, Quebec, Canada, (1996).

C. Weikamp, ed., Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, Springer Series in Optical Science (Springer-Verlag, 2005), Chap. 3.

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

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

S. Twomey, ed., Introduction to the Mathematics of Inversion in Remote Sensing and Direct Measurements (Elsevier, 1977).

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Figures (16)

Fig. 1
Fig. 1

Geometry for the calculation of the scattered power at the entrance of a receiving telescope in the framework of a double-scattering approximation.

Fig. 2
Fig. 2

Angular distributions of scattered radiation power over the telescope FOV. Calculations are performed for a lognormal particle size distribution with a modal radius of r 0 = 5 , 10 , and 50 μm . The cloud base is at z a = 500 m ; the sounding depth is at Δ z = 50 m . Dashed–dotted curves show the results obtained with the Gaussian approximation of P ( r , β ) .

Fig. 3
Fig. 3

Dependence of the minimum eigenvalue on particle size. Calculations are performed for z a = 500 , 1000, 2000 m and Δ z = 50 m using (a) Gaussian approximation and (b) Mie formulas for the computation of P ( r , β ) . FOVs are in the interval θ min = 0.25 , θ max = 5 mrad .

Fig. 4
Fig. 4

Estimation of the accuracy of size retrieval with the use of MFOV lidar. The radius of the particles is varied as r 0 i = k r 0 i - 1 . Calculations are performed for k = 1.5 , 1.3, 1.2; z a = 500 m , Δ z = 50 m .

Fig. 5
Fig. 5

Illustration of the influence of the FOV range on the interval of particle sizes that can be retrieved. Calculations are performed for θ in the intervals 0.25 5 , 0.25 1 , 1 5 , and 0.1 10 mrad ; z a = 500 m , Δ z = 50 m .

Fig. 6
Fig. 6

Information content of MFOV lidar data for different intervals of θ: 0.25 5 , 0.25 10 , and 0.1 10 mrad . The dotted curve shows the results for the single value of Δ z .

Fig. 7
Fig. 7

Minimum eigenvalues calculated for 5, 8, and 15 FOVs distributed in the 0.25 5 mrad range with a log-equidistant law; z a = 1000 m , Δ z = 50 m .

Fig. 8
Fig. 8

Angular distribution of scattered radiation power for r 0 = 5 , 10 , and 50 μm when the phase function in the backward direction is calculated through Mie formulas. The cloud base is at z a = 500 m , and the sounding depth is at Δ z = 50 m . Dashed–dotted curves show the results for isotropic P ( r , β back ) .

Fig. 9
Fig. 9

Dependence of the minimum eigenvalue on particle size when the phase function in the backward direction P ( r , β back ) is isotropic (solid symbols) and calculated through Mie formulas (open symbols). z a = 500 m , Δ z = 50 m .

Fig. 10
Fig. 10

Angular distributions of the cross-polarized component s power (solid curves) for r 0 = 5 , 10 , and 20 μm . Dotted curves show the corresponding results for polarized components s . Distributions are normalized to keep θ min θ max s , ( θ ) d θ = 1 . z a = 1000 m , Δ z = 50 m .

Fig. 11
Fig. 11

Angular dependence of the depolarization δ l ( θ ) = s / s . Calculations are performed for lognormal particle size distributions with r 0 = 5 , 10, and 20 μm ; z a = 1000 m , Δ z = 50 m .

Fig. 12
Fig. 12

Comparison of the information content of the total (sum of both polarization components) and cross-polarized (perpendicular) lidar return. Calculations are performed for the interval 0.25 < θ < 5 mrad .

Fig. 13
Fig. 13

Dependence of the minimum eigenvalue on particle size for the parallel and cross-polarized components. Eight FOVs are log-equidistantly distributed over the 0.25 5 mrad range; z a = 1000 m , Δ z = 50 m .

Fig. 14
Fig. 14

Depolarization ratio S / S as a function of the FOV angle θ. Calculations are performed for z a = 500 , 1000, 2000 m and Δ z = 50 m through Mie formulas. Size distribution is lognormal with r 0 = 10 μm .

Fig. 15
Fig. 15

Depolarization ratio S / S as a function of the FOV angle θ. Calculations are performed for r 0 = 5 , 20, 10, 50 μm ; z a = 1000 m , Δ z = 50 m .

Fig. 16
Fig. 16

Maximum and minimum particle radii that can be estimated from MFOV lidar measurements as functions of parameter η = Δ z / z a for a measurement error δ < 10 % . Results are obtained for eight FOVs in the 0.25 5 mrad range and for cross-polarized backscatter.

Equations (4)

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S ( z c , Δθ ) = S 0 e - 2 α ( z c - z a ) 2 z c 2 z a z c 0 2 π β j β j + 1 [ α ( z ) P ( r , β ) ] × [ α ( z c ) P ( r , β back ) ] sin βdβdϕd z .
S ( z c , Δθ ) = S 0 * e - 2 α ( z c - z a ) z c 2 r min r max f ( r ) r 2 z a z b β j β j + 1 P ( r , β ) × [ α ( z c ) P ( r , β back ) ] sin βdβd z d r ,
S i = θ i - 1 θ i s ( θ ) .
δ ( r , z ) = P 2 ( r , β back ) cos 2 β back - 2 P 3 ( r , β back ) cos β back + P 1 ( r , β back ) 3 P 2 ( r , β back ) cos 2 β back + 2 P 3 ( r , β back ) cos β back + 3 P 1 ( r , β back ) ,

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