Abstract

Multiple-field-of-view (MFOV) secondary-polarization lidar signals are used to calculate the particle-size density distribution (PSD) at the base of a cloud. At the cloud base, multiple scattering is weak and single backscattering is predominant by many orders of magnitude. Because secondary polarization is a direct measure of multiple scattering, it is therefore advantageous to use secondary polarization. A mathematical relation among the PSD, the lidar fields of view, the scattering angles, and the angular depolarization is derived to facilitate use of secondary polarization. The model is supported by experimental MFOV lidar measurements carried out in a controlled environment, and its limitations and restrictions are discussed.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Roy, L. C. Bissonnette, C. Bastille, G. Vallée, “Estimation of cloud droplet size density distribution from multiple-field-of-view lidar returns,” Opt. Eng. 36, 3404–3415 (1997).
    [CrossRef]
  2. L. R. Bissonnette, “Multiple-scattering lidar equation,” Appl. Opt. 35, 6449–6465 (1996).
    [CrossRef] [PubMed]
  3. L. R. Bissonnette, D. L. Hutt, “Multiply scattered aerosol lidar returns: inversion method and comparison with in situ measurements,” Appl. Opt. 34, 6959–6975 (1995).
    [CrossRef] [PubMed]
  4. Y. Benayahu, A. Ben-David, S. Fastig, A. Cohen, “Cloud-droplet-size distribution from lidar multiple-scattering measurements,” Appl. Opt. 34, 1569–1578 (1995).
    [CrossRef] [PubMed]
  5. E. W. Eloranta, “Practical model for the calculation of multiply scattered lidar returns,” Appl. Opt. 37, 2464–2472 (1998).
    [CrossRef]
  6. E. W. Eloranta, “Calculation of doubly scattered lidar returns,” Ph.D. dissertation (University of Wisconsin, Madison, Wisc., 1972).
  7. C. M. R. Platt, “Lidar and radiometer observations of cirrus clouds,” J. Atmos. Sci. 30, 1191–1204 (1973).
    [CrossRef]
  8. R. J. Allen, C. M. R. Platt, “Lidar for multiple backscattering and depolarization observation,” Appl. Opt. 16, 3193–3199 (1977).
    [CrossRef] [PubMed]
  9. S. R. Pal, A. I. Carswell, “Polarization properties of lidar scattering from clouds at 347 nm and 694 nm,” Appl. Opt. 17, 2321–2328 (1978).
    [CrossRef] [PubMed]
  10. K. Sassen, R. L. Petrilla, “Lidar depolarization from multiple scattering in marine stratus clouds,” Appl. Opt. 25, 1450–1459 (1986).
    [CrossRef] [PubMed]
  11. E. P. Shettle, “Models of aerosols, clouds and precipitation for atmospheric propagation studies,” in Atmospheric Propagation in the UV, Visible, IR and MM-Wave Region and Related System Aspects, AGARD Conf. Proc.454, 1–5 (1989), paper 15.
  12. T. Allen, Particle Size Measurement (Chapman & Hall, New York, 1981).
    [CrossRef]
  13. K. Sassen, H. Zhao, “Lidar multiple scattering in water droplet clouds: toward an improved treatment,” Opt. Rev. 2, 394–400 (1995).
    [CrossRef]
  14. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  15. J. R. Hodkinson, J. Greenleaves, “Computations of light-scattering and extinction by spheres according to diffraction and geometrical optics, and some comparisons with Mie theory,” J. Opt. Soc. Am. 53, 577–582 (1963).
    [CrossRef]
  16. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  17. S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, Amsterdam, 1977).
  18. M. Heuner, K. Leschonski, “Results obtained with a new instrument for the measurement of particle size distributions from diffraction patterns,” Part. Part. Syst. Charact. 2, 7–13 (1985).
    [CrossRef]
  19. D. H. Pollock, Countermeasure Systems, Vol. 7 of The Infrared & Electro-Optical Systems Handbook (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993).

1998

1997

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

1996

1995

1986

1985

M. Heuner, K. Leschonski, “Results obtained with a new instrument for the measurement of particle size distributions from diffraction patterns,” Part. Part. Syst. Charact. 2, 7–13 (1985).
[CrossRef]

1978

1977

1973

C. M. R. Platt, “Lidar and radiometer observations of cirrus clouds,” J. Atmos. Sci. 30, 1191–1204 (1973).
[CrossRef]

1963

Allen, R. J.

Allen, T.

T. Allen, Particle Size Measurement (Chapman & Hall, New York, 1981).
[CrossRef]

Bastille, C.

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

Benayahu, Y.

Ben-David, A.

Bissonnette, L. C.

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

Bissonnette, L. R.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Carswell, A. I.

Cohen, A.

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, “Calculation of doubly scattered lidar returns,” Ph.D. dissertation (University of Wisconsin, Madison, Wisc., 1972).

Fastig, S.

Greenleaves, J.

Heuner, M.

M. Heuner, K. Leschonski, “Results obtained with a new instrument for the measurement of particle size distributions from diffraction patterns,” Part. Part. Syst. Charact. 2, 7–13 (1985).
[CrossRef]

Hodkinson, J. R.

Hutt, D. L.

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Leschonski, K.

M. Heuner, K. Leschonski, “Results obtained with a new instrument for the measurement of particle size distributions from diffraction patterns,” Part. Part. Syst. Charact. 2, 7–13 (1985).
[CrossRef]

Pal, S. R.

Petrilla, R. L.

Platt, C. M. R.

R. J. Allen, C. M. R. Platt, “Lidar for multiple backscattering and depolarization observation,” Appl. Opt. 16, 3193–3199 (1977).
[CrossRef] [PubMed]

C. M. R. Platt, “Lidar and radiometer observations of cirrus clouds,” J. Atmos. Sci. 30, 1191–1204 (1973).
[CrossRef]

Pollock, D. H.

D. H. Pollock, Countermeasure Systems, Vol. 7 of The Infrared & Electro-Optical Systems Handbook (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993).

Roy, G.

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

Sassen, K.

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

K. Sassen, R. L. Petrilla, “Lidar depolarization from multiple scattering in marine stratus clouds,” Appl. Opt. 25, 1450–1459 (1986).
[CrossRef] [PubMed]

Shettle, E. P.

E. P. Shettle, “Models of aerosols, clouds and precipitation for atmospheric propagation studies,” in Atmospheric Propagation in the UV, Visible, IR and MM-Wave Region and Related System Aspects, AGARD Conf. Proc.454, 1–5 (1989), paper 15.

Twomey, S.

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

Vallée, G.

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

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Zhao, H.

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

Appl. Opt.

J. Atmos. Sci.

C. M. R. Platt, “Lidar and radiometer observations of cirrus clouds,” J. Atmos. Sci. 30, 1191–1204 (1973).
[CrossRef]

J. Opt. Soc. Am.

Opt. Eng.

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

Opt. Rev.

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

Part. Part. Syst. Charact.

M. Heuner, K. Leschonski, “Results obtained with a new instrument for the measurement of particle size distributions from diffraction patterns,” Part. Part. Syst. Charact. 2, 7–13 (1985).
[CrossRef]

Other

D. H. Pollock, Countermeasure Systems, Vol. 7 of The Infrared & Electro-Optical Systems Handbook (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

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

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

E. P. Shettle, “Models of aerosols, clouds and precipitation for atmospheric propagation studies,” in Atmospheric Propagation in the UV, Visible, IR and MM-Wave Region and Related System Aspects, AGARD Conf. Proc.454, 1–5 (1989), paper 15.

T. Allen, Particle Size Measurement (Chapman & Hall, New York, 1981).
[CrossRef]

E. W. Eloranta, “Calculation of doubly scattered lidar returns,” Ph.D. dissertation (University of Wisconsin, Madison, Wisc., 1972).

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 (19)

Fig. 1
Fig. 1

Phase function and depolarization of a C2-type cloud.

Fig. 2
Fig. 2

Phase function and depolarization of a fog-oil cloud.

Fig. 3
Fig. 3

Scattering processes that lead to secondary polarization.

Fig. 4
Fig. 4

Range-corrected s-polarization lidar return within FOV’s θ i and θ i+1 as a function of FOV θ i+1. The curves are for log-normal droplet-size distributions of several mean diameters and logarithmic standard deviations.

Fig. 5
Fig. 5

Range-corrected s-polarization lidar return within FOV θ i+1 as a function of FOV θ i+1.

Fig. 6
Fig. 6

Ideal lidar signals S i+1) - S i ) and signals with 20% white noise as function of FOV θ i+1 for a cloud made from log-normally distributed particles with median diameters of 10 and 0.8 µm. The distance to the lidar is 95 m, and the penetration depth is 6 m.

Fig. 7
Fig. 7

Effect of γ on the recovery of the initial density distribution: (a) x m = 10 µm, (b) x m = 0.8 µm. sig, Logarithmic standard deviation.

Fig. 8
Fig. 8

Influence of noise on choice of γ: (a) x m = 10 µm, (b) x m = 0.8 µm. sig, logarithmic standard deviation.

Fig. 9
Fig. 9

Volume density distributions of a generated water-droplet cloud measured with a Malvern Particle Sizer and of typical published values for fog-oil clouds.17

Fig. 10
Fig. 10

Aluminized glass plate with 32 etched irises. (a) The order of the irises was set to cover the maximum FOV difference within 1/4 of a turn. (b) The order of the rings is the same as for the irises.

Fig. 11
Fig. 11

Setup for the detection module used for sequential MFOV lidar measurements. FOV control is basically the ring or iris rotating dish assembly mounted on a precision translator.

Fig. 12
Fig. 12

Range-corrected lidar return p- and secondary s-polarization lidar return as functions of distance for 0.75- and 12-mrad total FOV’s for water droplet trial pvri0318.

Fig. 13
Fig. 13

Range-corrected lidar return p- and secondary s-polarization lidar return as functions of distance for 0.75- and 12-mrad total FOV’s for the fog-oil trial foh0301.

Fig. 14
Fig. 14

Range-corrected s-polarization lidar return within FOV’s θ i and θ i+1 as a function of FOV θ i+1 for a distance of 101 m (penetration depth of 6 m) and an optical depth (O.D.) of 0.4.

Fig. 15
Fig. 15

Range-corrected s-polarization lidar return within FOV θ i+1 as a function of FOV θ i+1 for a distance of 101 m (penetration depth of 6 m) and an optical depth of 0.4. The lidar return from a solid target located at a distance of 200 m is also plotted.

Fig. 16
Fig. 16

Range-corrected s-polarization lidar return within θ i+1 as a function of FOV θ i+1 for distances of 101 and 105 m (penetration depths of 6 and 10 m) and optical depths of 0.2, 0.4, and 0.8.

Fig. 17
Fig. 17

Comparison of particle-size density distributions obtained in two trials by application of matrix inversion to secondary-polarization MFOV measurements from water-droplet clouds with measurements made with the Malvern particle sizer. O.D., optical depth.

Fig. 18
Fig. 18

Comparison of the particle-size density distribution obtained by application of matrix inversion to the secondary-polarization MFOV measurements from fog-oil cloud with a published19 distribution.

Fig. 19
Fig. 19

Approximate relative lidar contributions of the three scattering orders as functions of apparent optical depth.

Tables (3)

Tables Icon

Table 1 Inner and Outer Ring Diameters Etched on the Rotating Glass Disk

Tables Icon

Table 2 Trial List Parameters

Tables Icon

Table 3 Comparison of the Measured Mean Valuesa

Equations (18)

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

tan β=zczc-ztan θ.
Szc, θj+1-θj=P0 exp-2αzc-zacτ2ρAzc2×xminxmax q0xzazcβjβj+1 x2Iz, x, β, n× sin βdβ]αzδz, x, β, ndzdx,
q0x=x-3q3xxminxmax x-3q3xdx,
Szc, Δθjzc2=i=1M C3q¯3x¯i×xixi+1zazcβjβj+1 x-1Iz, x, β, n×sin βdβαzδz, x, β, ndzdx.
S=Aq3,
Aij=C3xixi+1zazcβjβj+1 x-1Iz, β, x, nsin βdβ×αzδz, x, β, ndzdx,
δz, x, β, n=P2βcos2β-2P3βcosβ+P1β3P2βcos2β+2P3βcosβ+3P1β,
q=ATA+γH-1ATP,
q3x=1xσ2πexp-ln x-ln xm2/σ2,
IT=I0 exp-αz,
ID1=I01-exp-αz,
ΔITD1=-ITD11-exp-αzαΔz,
ITD1=I0 exp-αzexp1-exp-αz,
ID2=I01-exp-αzexp[1-exp-αz,
ITD2=I0 exp-αz-1expexp1-exp-αz,
ID3=I01-exp-αz-1expexp1-exp-αz,
ITD3=I0 exp- ID3αzdz,
ID4=I01-ITD3,

Metrics