Abstract

The lidar crossover function f(R) in the lidar equation accounts for the incomplete overlap of the laser-pulse volume and the receiver field of view at short ranges and so is pertinent to near-surface returns from aerosols and precipitation. Using a Gaussian-intensity transverse profile for the laser pulse we present a comparatively simple formulation for f(R) and provide some numerical results for realistic lidar geometries, including the effects of optical axes misalignment. It is shown that for lidar systems constrained to narrow beam-widths (~1 mrad) for polarization or other observations, accurate alignment is of great importance to lidar operations.

© 1982 Optical Society of America

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References

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  1. L. J. Battan, Radar Observation of the Atmosphere (U. Chicago Press, Chicago, 1973).
  2. H. W. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]
  3. P. Belland, J. P. Crenn, Appl. Opt. 21, 522 (1982).
    [CrossRef] [PubMed]
  4. G. C. Mooradian, M. Geller, L. B. Stots, D. H. Stephens, R. A. Krautwald, Appl. Opt. 18, 429 (1979).
    [CrossRef] [PubMed]
  5. J. S. Ryan, A. I. Carswell, J. Opt. Soc. Am. 68, 900 (1978).
    [CrossRef]
  6. J. Riegl, M. Bernhard, Appl. Opt. 13, 931 (1974).
    [CrossRef] [PubMed]
  7. J. Harms, Appl. Opt. 18, 1559 (1979).
    [CrossRef] [PubMed]
  8. T. Halldórsson, J. Langerholc, Appl. Opt. 17, 240 (1978).
    [CrossRef] [PubMed]
  9. K. Sassen, J. Appl. Meteor. 15, 292 (1976).
    [CrossRef]
  10. K. N. Liou, R. M. Schotland, J. Atmos. Sci. 28, 772 (1971).
    [CrossRef]
  11. Q. Cai, K. N. Liou, J. Atmos. Sci. 38, 1452 (1981).
    [CrossRef]

1982

1981

Q. Cai, K. N. Liou, J. Atmos. Sci. 38, 1452 (1981).
[CrossRef]

1979

1978

1976

K. Sassen, J. Appl. Meteor. 15, 292 (1976).
[CrossRef]

1974

1971

K. N. Liou, R. M. Schotland, J. Atmos. Sci. 28, 772 (1971).
[CrossRef]

1966

Battan, L. J.

L. J. Battan, Radar Observation of the Atmosphere (U. Chicago Press, Chicago, 1973).

Belland, P.

Bernhard, M.

Cai, Q.

Q. Cai, K. N. Liou, J. Atmos. Sci. 38, 1452 (1981).
[CrossRef]

Carswell, A. I.

Crenn, J. P.

Geller, M.

Halldórsson, T.

Harms, J.

Kogelnik, H. W.

Krautwald, R. A.

Langerholc, J.

Li, T.

Liou, K. N.

Q. Cai, K. N. Liou, J. Atmos. Sci. 38, 1452 (1981).
[CrossRef]

K. N. Liou, R. M. Schotland, J. Atmos. Sci. 28, 772 (1971).
[CrossRef]

Mooradian, G. C.

Riegl, J.

Ryan, J. S.

Sassen, K.

K. Sassen, J. Appl. Meteor. 15, 292 (1976).
[CrossRef]

Schotland, R. M.

K. N. Liou, R. M. Schotland, J. Atmos. Sci. 28, 772 (1971).
[CrossRef]

Stephens, D. H.

Stots, L. B.

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Figures (5)

Fig. 1
Fig. 1

Schematic depiction of the lidar crossover effect as the edge of the Gaussian pulse (cross-hatched region) just enters the receiver field of view. The edges of the laser pulse, wt and θt, are shown corresponding to three standard deviations of the Gaussian profile.

Fig. 2
Fig. 2

Crossover functions f(R) for a Gaussian beam for lidars using matched full-angle transmitter (2θt) and receiver (2θr) beamwidths of 1, 3, and 5 mrad.

Fig. 3
Fig. 3

Crossover functions f(R) for Gaussian (solid lines) and uniform (dashed lines) laser pulses for a transmitter-divergence angle of 1.0 mrad and receiver fields of view of 1 and 3 mrad.

Fig. 4
Fig. 4

Crossover function f(R) for Gaussian (solid line) and uniform (dashed line) laser pulses for a transmitter-divergence angle of 10 mrad and a receiver field of view of 1 mrad.

Fig. 5
Fig. 5

Effects on the crossover function f(R) for a Gaussian-beam lidar using matched 1.0-mrad beamwidths as optical-axis alignment errors of ±0.1 and ±0.5 mrad are simulated.

Equations (4)

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2 A 2 4 + A 2 exp - 2 B 2 4 + A 2 .
x = ( A 2 2 + B 2 ) 1 / 3 - [ 1 - 2 ( 2 + B 2 ) 2 9 ( 2 + B 2 ) 2 ] [ 2 ( 2 + 2 B 2 ) 9 ( 2 + B 2 ) 2 ] 1 / 2 ,
f ( R ) = r t 2 ( ϕ t - sin ϕ t ) + r r 2 ( ϕ r - sin ϕ r ) 2 π r t 2 ,
ϕ t = 2 cos - 1 ( r t 2 - r r 2 + s 2 2 r t s ) , ϕ r = 2 cos - 1 ( r r 2 - r t 2 + s 2 2 r r s ) .

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