Abstract

We report on the calculation of the effective telescope area in lidar applications by a ray-tracing approach. This method allows one to consider the true experimental working conditions and hence to obtain accurate values of the effective telescope area as a function of the height. This in turn allows the retrieval of the signal from the ranges where the overlap function is not constant (e.g., lower ranges), thus increasing the useful range interval. Moreover, we show that the spherical mirrors are more appropriate than the parabolic ones for most of the lidar measurements, although a particular alignment procedure, such as the one we describe, must be used.

© 1998 Optical Society of America

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References

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  1. T. Halldórsson, J. Langerholc, “Geometrical form factors for the lidar function,” Appl. Opt. 17, 240–244 (1978).
    [CrossRef] [PubMed]
  2. J. Harms, W. Lahmann, C. Weitkamp, “Geometrical compression of lidar return signal,” Appl. Opt. 17, 1131–1135 (1978).
    [CrossRef] [PubMed]
  3. J. Harms, “Lidar return signal for coaxial and noncoaxial systems with central obstruction,” Appl. Opt. 18, 1559–1566 (1979).
    [CrossRef] [PubMed]
  4. K. Sassen, G. C. Dodd, “Lidar crossover function and misalignment effects,” Appl. Opt. 21, 3162–3165 (1982).
    [CrossRef] [PubMed]
  5. R. M. Measure, Laser Remote Sensing (Wiley, New York, 1984).
  6. L. Fiorani, “Une première mesure lidar combinée d’ozone et de vent, à partir d’une instrumentation et d’une méthodologie coup par coup,” Ph.D. dissertation (Ecole Polytechnique Fèdèrale de Lausanne, Lausanne, Switzerland, 1996).
  7. Y. Sasano, H. Shimizu, N. Takeuchi, M. Okuda, “Geometrical form factor in the laser radar equation: an experimental determination,” Appl. Opt. 18, 3908–3910 (1979).
    [CrossRef] [PubMed]
  8. G. M. Ancellet, M. J. Kavaya, R. T. Menzies, 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]
  9. R. T. Collis, P. B. Russel, “Lidar measurement of particles and gases by elastic backscattering and differential absorption,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, Berlin, 1976), pp. 71–151.
    [CrossRef]
  10. H. Rutten, M. van Venrooij, Telescope Optics (Willman-Bell, Richmond, Va., 1989).
  11. L. Fiorani, M. Armenante, R. Capobianco, N. Spinelli, X. Wang, “Self-aligning lidar for the continuous monitoring of the atmosphere,” Appl. Opt. 37, 4758–4764 (1998).
    [CrossRef]
  12. E. Durieux, L. Fiorani, B. Calpini, M. Flamm, L. Jaquet, H. Van den Bergh, “Tropospheric ozone measurements over the Great Athens Area during the MEDCAPHOT-TRACE campaign with a new shot-per-shot DIAL instrument. Experimental system and results,” Atmos. Environ. 32, 2141–2150 (1998).
    [CrossRef]

1998 (2)

E. Durieux, L. Fiorani, B. Calpini, M. Flamm, L. Jaquet, H. Van den Bergh, “Tropospheric ozone measurements over the Great Athens Area during the MEDCAPHOT-TRACE campaign with a new shot-per-shot DIAL instrument. Experimental system and results,” Atmos. Environ. 32, 2141–2150 (1998).
[CrossRef]

L. Fiorani, M. Armenante, R. Capobianco, N. Spinelli, X. Wang, “Self-aligning lidar for the continuous monitoring of the atmosphere,” Appl. Opt. 37, 4758–4764 (1998).
[CrossRef]

1986 (1)

1982 (1)

1979 (2)

1978 (2)

Ancellet, G. M.

Armenante, M.

Brothers, A. M.

Calpini, B.

E. Durieux, L. Fiorani, B. Calpini, M. Flamm, L. Jaquet, H. Van den Bergh, “Tropospheric ozone measurements over the Great Athens Area during the MEDCAPHOT-TRACE campaign with a new shot-per-shot DIAL instrument. Experimental system and results,” Atmos. Environ. 32, 2141–2150 (1998).
[CrossRef]

Capobianco, R.

Collis, R. T.

R. T. Collis, P. B. Russel, “Lidar measurement of particles and gases by elastic backscattering and differential absorption,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, Berlin, 1976), pp. 71–151.
[CrossRef]

Dodd, G. C.

Durieux, E.

E. Durieux, L. Fiorani, B. Calpini, M. Flamm, L. Jaquet, H. Van den Bergh, “Tropospheric ozone measurements over the Great Athens Area during the MEDCAPHOT-TRACE campaign with a new shot-per-shot DIAL instrument. Experimental system and results,” Atmos. Environ. 32, 2141–2150 (1998).
[CrossRef]

Fiorani, L.

E. Durieux, L. Fiorani, B. Calpini, M. Flamm, L. Jaquet, H. Van den Bergh, “Tropospheric ozone measurements over the Great Athens Area during the MEDCAPHOT-TRACE campaign with a new shot-per-shot DIAL instrument. Experimental system and results,” Atmos. Environ. 32, 2141–2150 (1998).
[CrossRef]

L. Fiorani, M. Armenante, R. Capobianco, N. Spinelli, X. Wang, “Self-aligning lidar for the continuous monitoring of the atmosphere,” Appl. Opt. 37, 4758–4764 (1998).
[CrossRef]

L. Fiorani, “Une première mesure lidar combinée d’ozone et de vent, à partir d’une instrumentation et d’une méthodologie coup par coup,” Ph.D. dissertation (Ecole Polytechnique Fèdèrale de Lausanne, Lausanne, Switzerland, 1996).

Flamm, M.

E. Durieux, L. Fiorani, B. Calpini, M. Flamm, L. Jaquet, H. Van den Bergh, “Tropospheric ozone measurements over the Great Athens Area during the MEDCAPHOT-TRACE campaign with a new shot-per-shot DIAL instrument. Experimental system and results,” Atmos. Environ. 32, 2141–2150 (1998).
[CrossRef]

Halldórsson, T.

Harms, J.

Jaquet, L.

E. Durieux, L. Fiorani, B. Calpini, M. Flamm, L. Jaquet, H. Van den Bergh, “Tropospheric ozone measurements over the Great Athens Area during the MEDCAPHOT-TRACE campaign with a new shot-per-shot DIAL instrument. Experimental system and results,” Atmos. Environ. 32, 2141–2150 (1998).
[CrossRef]

Kavaya, M. J.

Lahmann, W.

Langerholc, J.

Measure, R. M.

R. M. Measure, Laser Remote Sensing (Wiley, New York, 1984).

Menzies, R. T.

Okuda, M.

Russel, P. B.

R. T. Collis, P. B. Russel, “Lidar measurement of particles and gases by elastic backscattering and differential absorption,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, Berlin, 1976), pp. 71–151.
[CrossRef]

Rutten, H.

H. Rutten, M. van Venrooij, Telescope Optics (Willman-Bell, Richmond, Va., 1989).

Sasano, Y.

Sassen, K.

Shimizu, H.

Spinelli, N.

Takeuchi, N.

Van den Bergh, H.

E. Durieux, L. Fiorani, B. Calpini, M. Flamm, L. Jaquet, H. Van den Bergh, “Tropospheric ozone measurements over the Great Athens Area during the MEDCAPHOT-TRACE campaign with a new shot-per-shot DIAL instrument. Experimental system and results,” Atmos. Environ. 32, 2141–2150 (1998).
[CrossRef]

van Venrooij, M.

H. Rutten, M. van Venrooij, Telescope Optics (Willman-Bell, Richmond, Va., 1989).

Wang, X.

Weitkamp, C.

Appl. Opt. (7)

Atmos. Environ. (1)

E. Durieux, L. Fiorani, B. Calpini, M. Flamm, L. Jaquet, H. Van den Bergh, “Tropospheric ozone measurements over the Great Athens Area during the MEDCAPHOT-TRACE campaign with a new shot-per-shot DIAL instrument. Experimental system and results,” Atmos. Environ. 32, 2141–2150 (1998).
[CrossRef]

Other (4)

R. M. Measure, Laser Remote Sensing (Wiley, New York, 1984).

L. Fiorani, “Une première mesure lidar combinée d’ozone et de vent, à partir d’une instrumentation et d’une méthodologie coup par coup,” Ph.D. dissertation (Ecole Polytechnique Fèdèrale de Lausanne, Lausanne, Switzerland, 1996).

R. T. Collis, P. B. Russel, “Lidar measurement of particles and gases by elastic backscattering and differential absorption,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, Berlin, 1976), pp. 71–151.
[CrossRef]

H. Rutten, M. van Venrooij, Telescope Optics (Willman-Bell, Richmond, Va., 1989).

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Figures (7)

Fig. 1
Fig. 1

Image generated in the focal plane by a 8 × 8 lattice at different heights: (a) 300 m, (b) 5000 m, (c) 50,000 m. The primary mirror of the telescope (f T = 5 m) is parabolic.

Fig. 2
Fig. 2

Image of a 4 × 4 lattice set at 50,000 m. The telescope (f T = 5 m) is spherical. The image is detected at different distances z D from the focal plane (z = 0): (a) z D = 0 cm, (b) z D = 1.5 cm, (c) z D = 3 cm, (d) z D = 4.5 cm.

Fig. 3
Fig. 3

Effective telescope area for a biaxial lidar calculated by means of a ray-tracing program. The parameters of the system are reported in Table 2. Dotted curve, Gaussian beam; solid curve, uniform beam.

Fig. 4
Fig. 4

Ratio r between the spherical and the parabolic telescope effective area: (a) coaxial configuration and (b) biaxial configuration. The characteristics of the systems are listed in Table 2. For the parabolic telescope z D = 0, whereas for the spherical telescope z D = 2.5 cm. The apertures of 1 mrad (solid curve), 0.5 mrad (dashed curve), and 0.1 mrad (dotted curve) were simulated with a diaphragm of radii 4.6, 2.3, and 0.46 mm, respectively.

Fig. 5
Fig. 5

(a) Laser spot. Image on the focal plane of the laser spot (a) placed at different ranges: (b) 60 m, (c) 60 m but without considering the mounting used to send the laser to the atmosphere, (d) 50,000 m.

Fig. 6
Fig. 6

Experimental (solid curve) and calculated (dotted curve) lidar profile for a coaxial configuration. The lower curve is the telescope effective area. (a) γincl = 0. ± 0.2 mrad, (b) γincl = 0. ± 0.2 mrad but without considering the mounting used to send the laser to the atmosphere, (c) γincl = 4.1 ± 0.2 mrad.

Fig. 7
Fig. 7

Volume backscattering coefficient versus the range as obtained from the signal reported in Fig. 6.

Tables (2)

Tables Icon

Table 1 Characteristics of the Telescope Used in the Simulation to Obtain the Images

Tables Icon

Table 2 Characteristics of the Lidar System Analyzed in Ref. 1

Equations (6)

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P r z = P 0 η   c τ 2   β z A t z z - 2   exp - 2   0 z   α r d r ,
A t = A 0 = π r p 2 - r s 2 ,
A t z = E det E th   A 0 = ξ z A 0 ,
G x ,   y ,   z = A w 0 2 + δ l 2 z 2 exp - x - d 2 + y 2 w 0 2 + δ l 2 z 2 ,
D = 2 z δ l + w 0 M ,
D 2 f T δ l

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