Abstract

Because of the effect of defocusing and incomplete overlap between the laser beam and the receiver field of view, elastic lidar systems are unable to fully capture the close-range backscatter signal. Here we propose a method to empirically estimate and correct such effects, allowing to retrieve the lidar signal in the region of incomplete overlap. The technique is straightforward to implement. It produces an optimized numerical correction by the use of a simple geometrical model of the optical apparatus and the analysis of two lidar acquisitions taken at different elevation angles. Examples of synthetic and experimental data are shown to demonstrate the validity of the technique.

© 2011 Optical Society of America

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  1. S. H. Melfi, J. D. Spinhirne, S.-H. Chou, and S. P. Palm, “Lidar observations of vertically organized convection in the planetary boundary layer over the ocean,” J. Climate Appl. Meteor. 24, 806–821 (1985).
    [CrossRef]
  2. D. Cooper and W. Eichinger, “Structure of the atmosphere in an urban planetary boundary layer from lidar and radiosonde observations,” J. Geophys. Res. 99, 22937–22948 (1994).
    [CrossRef]
  3. V. Matthias and J. Bosenberg, “Aerosol climatology for the planetary boundary layer derived from regular lidar measurements,” Atmos. Res. 63, 221–245 (2002).
    [CrossRef]
  4. Y. Sasano, H. Shimizu, N. Takeuchi, and M. Okuda, “Geometrical form factor in the laser radar equation: an experimental determination,” Appl. Opt. 18, 3908–3910 (1979)
    [CrossRef] [PubMed]
  5. K. Tomine, C. Hirayama, K. Michimoto, and N. Takeuchi, “Experimental determination of the crossover function in the laser radar equation for days with a light mist,” Appl. Opt. 28, 2194–2195 (1989).
    [CrossRef] [PubMed]
  6. S. W. Dho, Y. J. Park, and H. J. Kong, “Experimental determination of a geometric form factor in a lidar equation for an inhomogeneous atmosphere,” Appl. Opt. 36, 6009–6010(1997).
    [CrossRef] [PubMed]
  7. T. A. Berkoff, E. J. Welton, V. S. Scott, and J. D. Spinhirne, “Investigation of overlap correction technique for the micro-pulse lidar NETwork (MPLNET),” in Proceedings of IEEE Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2003), Vol. 7, pp. 4395–4397.
    [CrossRef]
  8. U. Wandinger and A. Ansmann, “Experimental determination of the lidar overlap profile with Raman lidar,” Appl. Opt. 41, 511–514 (2002).
    [CrossRef] [PubMed]
  9. D. W. Roberts and G. G. Gimmestad, “Optimizing lidar dynamic range by engineering the crossover region,” Proc. SPIE 4723, 120–129 (2002).
    [CrossRef]
  10. T. Halldorsson and J. Langerholc, “Geometrical form factors for the lidar function,” Appl. Opt. 17, 240–244 (1978).
    [CrossRef] [PubMed]
  11. K. Stelmaszczyk, M. DellAglio, S. Chudzyski, T. Stacewicz, and L. Woste, “Analytical function for lidar geometrical compression form-factor calculations,” Appl. Opt. 44, 1323–1331 (2005).
    [CrossRef] [PubMed]
  12. G. M. Ancellet, M. J. Kavaya, R. T. Menzies, and A. M. Brothers, “Lidar telescope overlap function and effects of misalignment for unstable resonator transmitter and coherent receiver,” Appl. Opt. 25, 2886–2890 (1986).
    [CrossRef] [PubMed]
  13. R. Velotta, B. Bartoli, R. Capobianco, L. Fiorani, and N. Spinelli, “Analysis of the receiver response in lidar measurements,” Appl. Opt. 37, 6999–7007 (1998).
    [CrossRef]
  14. U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C. (1976).
  15. C. Cattrall, J. Reagan, K. Thome, and O. Dubovik, “Variability of aerosol and spectral lidar and backscatter and extinction ratios of key aerosol types derived from selected Aerosol Robotic Network locations,” J. Geophys. Res. 110, D10S11(2005).
    [CrossRef]
  16. P. B. Russell, T. J. Swissler, and M. P. McCormick, “Methodology for error analysis and simulation of lidar aerosol measurements,” Appl. Opt. 18, 3783–3797 (1979).
    [CrossRef] [PubMed]

2005 (2)

C. Cattrall, J. Reagan, K. Thome, and O. Dubovik, “Variability of aerosol and spectral lidar and backscatter and extinction ratios of key aerosol types derived from selected Aerosol Robotic Network locations,” J. Geophys. Res. 110, D10S11(2005).
[CrossRef]

K. Stelmaszczyk, M. DellAglio, S. Chudzyski, T. Stacewicz, and L. Woste, “Analytical function for lidar geometrical compression form-factor calculations,” Appl. Opt. 44, 1323–1331 (2005).
[CrossRef] [PubMed]

2002 (3)

U. Wandinger and A. Ansmann, “Experimental determination of the lidar overlap profile with Raman lidar,” Appl. Opt. 41, 511–514 (2002).
[CrossRef] [PubMed]

V. Matthias and J. Bosenberg, “Aerosol climatology for the planetary boundary layer derived from regular lidar measurements,” Atmos. Res. 63, 221–245 (2002).
[CrossRef]

D. W. Roberts and G. G. Gimmestad, “Optimizing lidar dynamic range by engineering the crossover region,” Proc. SPIE 4723, 120–129 (2002).
[CrossRef]

1998 (1)

1997 (1)

1994 (1)

D. Cooper and W. Eichinger, “Structure of the atmosphere in an urban planetary boundary layer from lidar and radiosonde observations,” J. Geophys. Res. 99, 22937–22948 (1994).
[CrossRef]

1989 (1)

1986 (1)

1985 (1)

S. H. Melfi, J. D. Spinhirne, S.-H. Chou, and S. P. Palm, “Lidar observations of vertically organized convection in the planetary boundary layer over the ocean,” J. Climate Appl. Meteor. 24, 806–821 (1985).
[CrossRef]

1979 (2)

1978 (1)

Ancellet, G. M.

Ansmann, A.

Bartoli, B.

Berkoff, T. A.

T. A. Berkoff, E. J. Welton, V. S. Scott, and J. D. Spinhirne, “Investigation of overlap correction technique for the micro-pulse lidar NETwork (MPLNET),” in Proceedings of IEEE Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2003), Vol. 7, pp. 4395–4397.
[CrossRef]

Bosenberg, J.

V. Matthias and J. Bosenberg, “Aerosol climatology for the planetary boundary layer derived from regular lidar measurements,” Atmos. Res. 63, 221–245 (2002).
[CrossRef]

Brothers, A. M.

Capobianco, R.

Cattrall, C.

C. Cattrall, J. Reagan, K. Thome, and O. Dubovik, “Variability of aerosol and spectral lidar and backscatter and extinction ratios of key aerosol types derived from selected Aerosol Robotic Network locations,” J. Geophys. Res. 110, D10S11(2005).
[CrossRef]

Chou, S.-H.

S. H. Melfi, J. D. Spinhirne, S.-H. Chou, and S. P. Palm, “Lidar observations of vertically organized convection in the planetary boundary layer over the ocean,” J. Climate Appl. Meteor. 24, 806–821 (1985).
[CrossRef]

Chudzyski, S.

Cooper, D.

D. Cooper and W. Eichinger, “Structure of the atmosphere in an urban planetary boundary layer from lidar and radiosonde observations,” J. Geophys. Res. 99, 22937–22948 (1994).
[CrossRef]

DellAglio, M.

Dho, S. W.

Dubovik, O.

C. Cattrall, J. Reagan, K. Thome, and O. Dubovik, “Variability of aerosol and spectral lidar and backscatter and extinction ratios of key aerosol types derived from selected Aerosol Robotic Network locations,” J. Geophys. Res. 110, D10S11(2005).
[CrossRef]

Eichinger, W.

D. Cooper and W. Eichinger, “Structure of the atmosphere in an urban planetary boundary layer from lidar and radiosonde observations,” J. Geophys. Res. 99, 22937–22948 (1994).
[CrossRef]

Fiorani, L.

Gimmestad, G. G.

D. W. Roberts and G. G. Gimmestad, “Optimizing lidar dynamic range by engineering the crossover region,” Proc. SPIE 4723, 120–129 (2002).
[CrossRef]

Halldorsson, T.

Hirayama, C.

Kavaya, M. J.

Kong, H. J.

Langerholc, J.

Matthias, V.

V. Matthias and J. Bosenberg, “Aerosol climatology for the planetary boundary layer derived from regular lidar measurements,” Atmos. Res. 63, 221–245 (2002).
[CrossRef]

McCormick, M. P.

Melfi, S. H.

S. H. Melfi, J. D. Spinhirne, S.-H. Chou, and S. P. Palm, “Lidar observations of vertically organized convection in the planetary boundary layer over the ocean,” J. Climate Appl. Meteor. 24, 806–821 (1985).
[CrossRef]

Menzies, R. T.

Michimoto, K.

Okuda, M.

Palm, S. P.

S. H. Melfi, J. D. Spinhirne, S.-H. Chou, and S. P. Palm, “Lidar observations of vertically organized convection in the planetary boundary layer over the ocean,” J. Climate Appl. Meteor. 24, 806–821 (1985).
[CrossRef]

Park, Y. J.

Reagan, J.

C. Cattrall, J. Reagan, K. Thome, and O. Dubovik, “Variability of aerosol and spectral lidar and backscatter and extinction ratios of key aerosol types derived from selected Aerosol Robotic Network locations,” J. Geophys. Res. 110, D10S11(2005).
[CrossRef]

Roberts, D. W.

D. W. Roberts and G. G. Gimmestad, “Optimizing lidar dynamic range by engineering the crossover region,” Proc. SPIE 4723, 120–129 (2002).
[CrossRef]

Russell, P. B.

Sasano, Y.

Scott, V. S.

T. A. Berkoff, E. J. Welton, V. S. Scott, and J. D. Spinhirne, “Investigation of overlap correction technique for the micro-pulse lidar NETwork (MPLNET),” in Proceedings of IEEE Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2003), Vol. 7, pp. 4395–4397.
[CrossRef]

Shimizu, H.

Spinelli, N.

Spinhirne, J. D.

S. H. Melfi, J. D. Spinhirne, S.-H. Chou, and S. P. Palm, “Lidar observations of vertically organized convection in the planetary boundary layer over the ocean,” J. Climate Appl. Meteor. 24, 806–821 (1985).
[CrossRef]

T. A. Berkoff, E. J. Welton, V. S. Scott, and J. D. Spinhirne, “Investigation of overlap correction technique for the micro-pulse lidar NETwork (MPLNET),” in Proceedings of IEEE Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2003), Vol. 7, pp. 4395–4397.
[CrossRef]

Stacewicz, T.

Stelmaszczyk, K.

Swissler, T. J.

Takeuchi, N.

Thome, K.

C. Cattrall, J. Reagan, K. Thome, and O. Dubovik, “Variability of aerosol and spectral lidar and backscatter and extinction ratios of key aerosol types derived from selected Aerosol Robotic Network locations,” J. Geophys. Res. 110, D10S11(2005).
[CrossRef]

Tomine, K.

Velotta, R.

Wandinger, U.

Welton, E. J.

T. A. Berkoff, E. J. Welton, V. S. Scott, and J. D. Spinhirne, “Investigation of overlap correction technique for the micro-pulse lidar NETwork (MPLNET),” in Proceedings of IEEE Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2003), Vol. 7, pp. 4395–4397.
[CrossRef]

Woste, L.

Appl. Opt. (9)

T. Halldorsson and J. Langerholc, “Geometrical form factors for the lidar function,” Appl. Opt. 17, 240–244 (1978).
[CrossRef] [PubMed]

P. B. Russell, T. J. Swissler, and M. P. McCormick, “Methodology for error analysis and simulation of lidar aerosol measurements,” Appl. Opt. 18, 3783–3797 (1979).
[CrossRef] [PubMed]

Y. Sasano, H. Shimizu, N. Takeuchi, and M. Okuda, “Geometrical form factor in the laser radar equation: an experimental determination,” Appl. Opt. 18, 3908–3910 (1979)
[CrossRef] [PubMed]

G. M. Ancellet, M. J. Kavaya, R. T. Menzies, and A. M. Brothers, “Lidar telescope overlap function and effects of misalignment for unstable resonator transmitter and coherent receiver,” Appl. Opt. 25, 2886–2890 (1986).
[CrossRef] [PubMed]

S. W. Dho, Y. J. Park, and H. J. Kong, “Experimental determination of a geometric form factor in a lidar equation for an inhomogeneous atmosphere,” Appl. Opt. 36, 6009–6010(1997).
[CrossRef] [PubMed]

R. Velotta, B. Bartoli, R. Capobianco, L. Fiorani, and N. Spinelli, “Analysis of the receiver response in lidar measurements,” Appl. Opt. 37, 6999–7007 (1998).
[CrossRef]

U. Wandinger and A. Ansmann, “Experimental determination of the lidar overlap profile with Raman lidar,” Appl. Opt. 41, 511–514 (2002).
[CrossRef] [PubMed]

K. Stelmaszczyk, M. DellAglio, S. Chudzyski, T. Stacewicz, and L. Woste, “Analytical function for lidar geometrical compression form-factor calculations,” Appl. Opt. 44, 1323–1331 (2005).
[CrossRef] [PubMed]

K. Tomine, C. Hirayama, K. Michimoto, and N. Takeuchi, “Experimental determination of the crossover function in the laser radar equation for days with a light mist,” Appl. Opt. 28, 2194–2195 (1989).
[CrossRef] [PubMed]

Atmos. Res. (1)

V. Matthias and J. Bosenberg, “Aerosol climatology for the planetary boundary layer derived from regular lidar measurements,” Atmos. Res. 63, 221–245 (2002).
[CrossRef]

J. Climate Appl. Meteor. (1)

S. H. Melfi, J. D. Spinhirne, S.-H. Chou, and S. P. Palm, “Lidar observations of vertically organized convection in the planetary boundary layer over the ocean,” J. Climate Appl. Meteor. 24, 806–821 (1985).
[CrossRef]

J. Geophys. Res. (2)

D. Cooper and W. Eichinger, “Structure of the atmosphere in an urban planetary boundary layer from lidar and radiosonde observations,” J. Geophys. Res. 99, 22937–22948 (1994).
[CrossRef]

C. Cattrall, J. Reagan, K. Thome, and O. Dubovik, “Variability of aerosol and spectral lidar and backscatter and extinction ratios of key aerosol types derived from selected Aerosol Robotic Network locations,” J. Geophys. Res. 110, D10S11(2005).
[CrossRef]

Proc. SPIE (1)

D. W. Roberts and G. G. Gimmestad, “Optimizing lidar dynamic range by engineering the crossover region,” Proc. SPIE 4723, 120–129 (2002).
[CrossRef]

Other (2)

U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C. (1976).

T. A. Berkoff, E. J. Welton, V. S. Scott, and J. D. Spinhirne, “Investigation of overlap correction technique for the micro-pulse lidar NETwork (MPLNET),” in Proceedings of IEEE Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2003), Vol. 7, pp. 4395–4397.
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Conventional lidar design approach. Taken from Roberts and Gimmestad [9].

Fig. 2
Fig. 2

Three schematic views of a lidar system are proposed. In all, the views are the lens, the pinhole, the lens plane, and the optical axis represented. On the right side of the lens the regions of different defocusing are presented and on the left side, using the same colors, their images. The region focused totally outside the pinhole is filled with diagonal lines. The region focused partially within the pinhole is filled with horizontal lines. The region focused inside the pinhole is filled with vertical lines. In the different views points and their images are considered. From each point we projected the pinhole extremes and the center onto the lens plane to show the intersection with the lens: in A there is full intersection, in B there is partial intersection, and in C there is no intersection.

Fig. 3
Fig. 3

Description of the defocusing effect within the FOV using the lidar parameters collected in Table 1. The solid lines represent the laser beam borders (light gray) and the FOV borders (dark gray). The nonwhite area is the geometrical FOV, the gray from 0 (white) to 1 (black) shows the region where the effect of defocusing is present, so that points in that area are only partially imaged through the pinhole. In this example, defocusing effects affects the laser returns from near the ground up to 1.34 km .

Fig. 4
Fig. 4

Simulation of molecular backscatter coefficient profiles measures by a lidar at two different elevation angles (solid gray line, 90 ° elevation angle, solid black line 40 ° elevation angle), using the nominal overlap function depicted in Fig. 5. A random noise is applied to each profile according to the model of noise plotted in Fig. 10 and discussed in Appendix B. The noise level has been chosen to produce a relative error of 5% at 1500 m of range. The profiles corrected according to our method have also been plotted as dashed gray lines. The solid thicker gay line represents the atmospheric backscatter coefficient, from standard atmosphere model.

Fig. 5
Fig. 5

Comparison of the theoretical function (dashed gray) used to generate profiles in Fig. 4. The result of our algorithm (black dots) of Section 3A and the overlap function estimated fitting with Eq. (10) (solid black).

Fig. 6
Fig. 6

Distributions of the results obtained using our technique on 1500 couple of synthetic profiles generated with elevations 40 ° and 90 ° applying noise as in Fig. 4, using a relative error of 15% at 1500 m . A Angles α and β; B angle α and pinhole displacement d x ; C sagittal angle β and pinhole displacement d x ; D distribution of the 1500 overlap curves. Solid gray line represents the average overlap function while the dashed gray line represents its relative error.

Fig. 7
Fig. 7

Calibration of the three acquired range corrected signals over molecular backscatter coefficient profiles for 532 nm . The calibration was performed using an iterative scheme to correct for extinction assuming a lidar ratio value of 40 sr.

Fig. 8
Fig. 8

Different overlap functions Γ: the black solid line results from the lidar optical model, with the system parameters as in Table 1, i.e., the nominal overlap function. The gray dotted and dashed lines are two different experimental determinations of Γ obtained by our iterative technique. The light gray solid line is the average of the two experimental ones.

Fig. 9
Fig. 9

Comparison between the different overlap functions: the black solid line is the nominal overlap, as in Fig. 8; the black dashed line is the reference overlap correction curve obtained from the Raman calibration; the dotted gray line is Γ t , the result of the fitting procedure of the free parameters of our lidar optical model, constrained by the average of two experimental Γ, depicted as a light gray solid line in Fig. 8.

Fig. 10
Fig. 10

The solid black line is the relative systematic error, computed as the absolute value of the differences between our proposed corrections and the Raman calibrated signal, divided by the latter. The solid gray line is the relative random error of the lidar signal. The dashed black line is the relative uncertainty attributable to the experimentally retrieved correction function Γ, computed by propagating the relative random error of the lidar signals in the iterative procedure as described in the text. The dashed gray line represents the number of iterations needed, step by step, to obtain the results presented.

Tables (1)

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Table 1 Lidar System Specifications

Equations (26)

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S 0 min = 2 d d t d r θ r 2 α + θ t ,
S 0 max = 2 d + d t d r θ r 2 α θ t .
1 S + 1 S i = 1 f ,
M = f S f .
y c ( S , d ) = f S i f d i = d ,
R ( S ) = s i S i f r h = S f r h ,
γ ( S , d ) = A [ d r 2 , R ( S ) , | y c ( S , d ) | ] π d r 2 4 ,
d E ( r , S ) = { 1 / ( π * R d ( S ) 2 ) , if     r R d ( S ) 0 , if     r > R d ( S ) ,
E ( S ) = 0 2 π 0 d E ( r , S ) d r d θ = 1.
Γ ( S ) = 0 2 π 0 R d ( S ) γ ( S , d ( r , θ , S ) ) d E ( r , S ) d r d θ .
R d ( S ) d t + θ t S 2
d c ( S ) [ ( d 0 2 + α S ) 2 + S 2 β 2 ] 1 / 2 ,
d ( r , θ , S ) 2 = d c ( S ) 2 2 r d c ( S ) cos ( θ ) + r 2 .
y c [ S , d ( r , θ , S ) ] = d ( r , θ , S ) ( f + d x ) | f S d x / f + d x | ,
R ( S ) = S r h | f S d x / f + d x | .
n = int [ ln ( S 0 min S 0 ) ln ( sin ω 1 sin ω 2 ) 1 ] .
s 0 = d r f r h .
S 1 max = 2 d + d r + d t θ r θ t 2 α .
θ r < 2 α + θ t 2 d r f ( d + d t / 2 ) r h .
X 2 ( r ) X 1 ( r sin ω ) ,
Γ 1 ( r ) = X 1 ( r sin ω ) X 2 ( r ) .
X 1 1 ( r ) = X 1 ( r ) Γ 1 ( r ) = X 1 ( r ) X 1 ( r sin ω ) X 2 ( r ) ,
Γ 2 ( r ) = X 1 1 ( r sin ω ) X 2 ( r ) = X 1 ( r sin ω ) Γ 1 ( r sin ω ) X 2 ( r ) = X 1 ( r sin ω ) X 1 ( r sin 2 ω ) X 2 ( r ) X 2 ( r sin ω ) .
Γ n ( r ) = i = 0 n X 1 ( r sin i 1 ω ) X 2 ( r sin i ω ) .
Γ n ( r ) = X 1 ( r sin n 1 ω ) X 2 ( r ) i = 1 n X 1 ( r sin i ω ) X 2 ( r sin i ω ) .
ϵ Γ n ( r ) = i = 0 n [ ϵ X 1 ( r sin i 1 ω ) + ϵ X 2 ( r sin i ω ) ] .

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