Abstract

Two earlier computations of the optimal truncation of Gaussian beams for a simple, focused, coherent lidar that used an incoherent backscatter target with identical circular transmitter and receiver apertures differ because they refer to different receiver geometries. The definitions of heterodyne and system-antenna efficiencies are reviewed in light of the discrepancy and are used to compare the optical performance of systems with apertures illuminated by beam profiles that are not Gaussian. The heterodyne efficiency is less than 0.5 for all cases considered here.

© 1992 Optical Society of America

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References

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  1. A. Thompson, M. F. Dorian, “Heterodyne detection of monochromatic light scattered from a cloud of moving particles,” Rep. GDC-ERR-AN 1090 (General Dynamics Convair Division, San Diego, Calif., 1967).
  2. C. M. Sonnenschein, S. A. Horrigan, “Signal-to-noise relations for coaxial systems that heterodyne backscatter from the atmosphere,” Appl. Opt. 10, 1600–1604 (1971).
    [Crossref] [PubMed]
  3. B. J. Rye, “Primary aberration contribution to incoherent backscatter heterodyne lidar returns,” Appl. Opt. 21, 839–844 (1982).
    [Crossref] [PubMed]
  4. J. Y. Wang, “Optimum truncation of a lidar transmitted beam,” Appl. Opt. 27, 4470–4474 (1988).
    [Crossref] [PubMed]
  5. R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, G. D. Craig, R. W. George, E. H. Gleason, P. J. Marerro, E. J. Reinbold, J. E. Shirey, “Development of a laser Doppler system for the detection, tracking, and measurement of aircraft wake vortices,” Rep. FAA-RD-74-213 (Federal Aviation Administration, Washington, D.C., 1975).
  6. J. T. Priestley, NOAA Wave Propagation Laboratory, Boulder, Colo. 80303 (personal communication, 1980).
  7. D. M. Tratt, R. T. Menzies, “Unstable resonator antenna properties in coherent lidar applications: a comparative study,” Appl. Opt. 27, 3645–3649 (1988).
    [Crossref] [PubMed]
  8. Y. Zhao, M. J. Post, R. M. Hardesty, “Receiving efficiency of pulsed coherent lidars. 1: Theory,” Appl. Opt. 29, 4111–4119 (1990).
    [Crossref] [PubMed]
  9. B. J. Rye, R. G. Frehlich, “The truncated Gaussian lidar antenna problem revisited,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 165–168.
  10. B. J. Rye, “Refractive turbulence contribution to incoherent backscatter heterodyne lidar returns,” J. Opt. Soc. Am. 71, 687–691 (1981).
    [Crossref]
  11. A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Appl. Opt. 5, 1588–1594 (1966); Proc. IEEE 54, 1350–1356 (1966).
    [Crossref] [PubMed]
  12. R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric turbulence,” Appl. Opt. 30, 5325–5334 (1991).
    [Crossref] [PubMed]
  13. J. J. Degnan, B. J. Klein, “Optical antenna gain. 2: Receiving antennas,” Appl. Opt. 13, 2397–2401 (1974).
    [Crossref] [PubMed]
  14. D. Fink, “Coherent detection signal-to-noise,” Appl. Opt. 14, 689–670 (1975).
    [Crossref] [PubMed]
  15. S. C. Cohen, “Heterodyne detection: phase front alignment, beam spot size, and detector uniformity,” Appl. Opt. 14, 1953–1959 (1975).
    [Crossref] [PubMed]
  16. T. Takenaka, K. Tanaka, O. Fukumitsu, “Signal-to-noise ratio in optical heterodyne detection for Gaussian fields,” Appl. Opt. 17, 3466–3471 (1978).
    [Crossref] [PubMed]
  17. R. G. Frehlich, “Conditions for optimal performance of mono-static coherent laser radar,” Opt. Lett. 15, 643–645 (1990).
    [Crossref] [PubMed]
  18. M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1962), p. 263.
  19. J. E. Sipe, “Prescription for beam design: optimizing power transport to a target,” Opt. Lett. 14, 975–977 (1989).
    [Crossref] [PubMed]
  20. J. F. Kusters, B. J. Rye, A. C. Walker, “Spatial weighting in laboratory incoherent light scattering experiments,” Appl. Opt. 28, 657–664 (1989).
    [Crossref] [PubMed]
  21. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1958).

1991 (1)

1990 (2)

1989 (2)

1988 (2)

1982 (1)

1981 (1)

1978 (1)

1975 (2)

1974 (1)

1971 (1)

1966 (1)

Bilbro, J. W.

R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, G. D. Craig, R. W. George, E. H. Gleason, P. J. Marerro, E. J. Reinbold, J. E. Shirey, “Development of a laser Doppler system for the detection, tracking, and measurement of aircraft wake vortices,” Rep. FAA-RD-74-213 (Federal Aviation Administration, Washington, D.C., 1975).

Cohen, S. C.

Craig, G. D.

R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, G. D. Craig, R. W. George, E. H. Gleason, P. J. Marerro, E. J. Reinbold, J. E. Shirey, “Development of a laser Doppler system for the detection, tracking, and measurement of aircraft wake vortices,” Rep. FAA-RD-74-213 (Federal Aviation Administration, Washington, D.C., 1975).

Degnan, J. J.

Dorian, M. F.

A. Thompson, M. F. Dorian, “Heterodyne detection of monochromatic light scattered from a cloud of moving particles,” Rep. GDC-ERR-AN 1090 (General Dynamics Convair Division, San Diego, Calif., 1967).

Fink, D.

Frehlich, R. G.

R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric turbulence,” Appl. Opt. 30, 5325–5334 (1991).
[Crossref] [PubMed]

R. G. Frehlich, “Conditions for optimal performance of mono-static coherent laser radar,” Opt. Lett. 15, 643–645 (1990).
[Crossref] [PubMed]

B. J. Rye, R. G. Frehlich, “The truncated Gaussian lidar antenna problem revisited,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 165–168.

Fukumitsu, O.

George, R. W.

R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, G. D. Craig, R. W. George, E. H. Gleason, P. J. Marerro, E. J. Reinbold, J. E. Shirey, “Development of a laser Doppler system for the detection, tracking, and measurement of aircraft wake vortices,” Rep. FAA-RD-74-213 (Federal Aviation Administration, Washington, D.C., 1975).

Gleason, E. H.

R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, G. D. Craig, R. W. George, E. H. Gleason, P. J. Marerro, E. J. Reinbold, J. E. Shirey, “Development of a laser Doppler system for the detection, tracking, and measurement of aircraft wake vortices,” Rep. FAA-RD-74-213 (Federal Aviation Administration, Washington, D.C., 1975).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1958).

Hardesty, R. M.

Horrigan, S. A.

Huffaker, R. M.

R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, G. D. Craig, R. W. George, E. H. Gleason, P. J. Marerro, E. J. Reinbold, J. E. Shirey, “Development of a laser Doppler system for the detection, tracking, and measurement of aircraft wake vortices,” Rep. FAA-RD-74-213 (Federal Aviation Administration, Washington, D.C., 1975).

Jeffreys, H. B.

R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, G. D. Craig, R. W. George, E. H. Gleason, P. J. Marerro, E. J. Reinbold, J. E. Shirey, “Development of a laser Doppler system for the detection, tracking, and measurement of aircraft wake vortices,” Rep. FAA-RD-74-213 (Federal Aviation Administration, Washington, D.C., 1975).

Kavaya, M. J.

Klein, B. J.

Kusters, J. F.

Marerro, P. J.

R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, G. D. Craig, R. W. George, E. H. Gleason, P. J. Marerro, E. J. Reinbold, J. E. Shirey, “Development of a laser Doppler system for the detection, tracking, and measurement of aircraft wake vortices,” Rep. FAA-RD-74-213 (Federal Aviation Administration, Washington, D.C., 1975).

Menzies, R. T.

Post, M. J.

Priestley, J. T.

J. T. Priestley, NOAA Wave Propagation Laboratory, Boulder, Colo. 80303 (personal communication, 1980).

Reinbold, E. J.

R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, G. D. Craig, R. W. George, E. H. Gleason, P. J. Marerro, E. J. Reinbold, J. E. Shirey, “Development of a laser Doppler system for the detection, tracking, and measurement of aircraft wake vortices,” Rep. FAA-RD-74-213 (Federal Aviation Administration, Washington, D.C., 1975).

Rye, B. J.

Shirey, J. E.

R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, G. D. Craig, R. W. George, E. H. Gleason, P. J. Marerro, E. J. Reinbold, J. E. Shirey, “Development of a laser Doppler system for the detection, tracking, and measurement of aircraft wake vortices,” Rep. FAA-RD-74-213 (Federal Aviation Administration, Washington, D.C., 1975).

Siegman, A. E.

Sipe, J. E.

Skolnik, M. I.

M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1962), p. 263.

Sonnenschein, C. M.

Takenaka, T.

Tanaka, K.

Thompson, A.

A. Thompson, M. F. Dorian, “Heterodyne detection of monochromatic light scattered from a cloud of moving particles,” Rep. GDC-ERR-AN 1090 (General Dynamics Convair Division, San Diego, Calif., 1967).

Tratt, D. M.

Walker, A. C.

Wang, J. Y.

Weaver, E. A.

R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, G. D. Craig, R. W. George, E. H. Gleason, P. J. Marerro, E. J. Reinbold, J. E. Shirey, “Development of a laser Doppler system for the detection, tracking, and measurement of aircraft wake vortices,” Rep. FAA-RD-74-213 (Federal Aviation Administration, Washington, D.C., 1975).

Zhao, Y.

Appl. Opt. (12)

C. M. Sonnenschein, S. A. Horrigan, “Signal-to-noise relations for coaxial systems that heterodyne backscatter from the atmosphere,” Appl. Opt. 10, 1600–1604 (1971).
[Crossref] [PubMed]

B. J. Rye, “Primary aberration contribution to incoherent backscatter heterodyne lidar returns,” Appl. Opt. 21, 839–844 (1982).
[Crossref] [PubMed]

J. Y. Wang, “Optimum truncation of a lidar transmitted beam,” Appl. Opt. 27, 4470–4474 (1988).
[Crossref] [PubMed]

D. M. Tratt, R. T. Menzies, “Unstable resonator antenna properties in coherent lidar applications: a comparative study,” Appl. Opt. 27, 3645–3649 (1988).
[Crossref] [PubMed]

Y. Zhao, M. J. Post, R. M. Hardesty, “Receiving efficiency of pulsed coherent lidars. 1: Theory,” Appl. Opt. 29, 4111–4119 (1990).
[Crossref] [PubMed]

A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Appl. Opt. 5, 1588–1594 (1966); Proc. IEEE 54, 1350–1356 (1966).
[Crossref] [PubMed]

R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric turbulence,” Appl. Opt. 30, 5325–5334 (1991).
[Crossref] [PubMed]

J. J. Degnan, B. J. Klein, “Optical antenna gain. 2: Receiving antennas,” Appl. Opt. 13, 2397–2401 (1974).
[Crossref] [PubMed]

D. Fink, “Coherent detection signal-to-noise,” Appl. Opt. 14, 689–670 (1975).
[Crossref] [PubMed]

S. C. Cohen, “Heterodyne detection: phase front alignment, beam spot size, and detector uniformity,” Appl. Opt. 14, 1953–1959 (1975).
[Crossref] [PubMed]

T. Takenaka, K. Tanaka, O. Fukumitsu, “Signal-to-noise ratio in optical heterodyne detection for Gaussian fields,” Appl. Opt. 17, 3466–3471 (1978).
[Crossref] [PubMed]

J. F. Kusters, B. J. Rye, A. C. Walker, “Spatial weighting in laboratory incoherent light scattering experiments,” Appl. Opt. 28, 657–664 (1989).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Other (6)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1958).

M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1962), p. 263.

A. Thompson, M. F. Dorian, “Heterodyne detection of monochromatic light scattered from a cloud of moving particles,” Rep. GDC-ERR-AN 1090 (General Dynamics Convair Division, San Diego, Calif., 1967).

B. J. Rye, R. G. Frehlich, “The truncated Gaussian lidar antenna problem revisited,” in Coherent Laser Radar: Technology and Applications, Vol. 12 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 165–168.

R. M. Huffaker, H. B. Jeffreys, E. A. Weaver, J. W. Bilbro, G. D. Craig, R. W. George, E. H. Gleason, P. J. Marerro, E. J. Reinbold, J. E. Shirey, “Development of a laser Doppler system for the detection, tracking, and measurement of aircraft wake vortices,” Rep. FAA-RD-74-213 (Federal Aviation Administration, Washington, D.C., 1975).

J. T. Priestley, NOAA Wave Propagation Laboratory, Boulder, Colo. 80303 (personal communication, 1980).

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Figures (3)

Fig. 1
Fig. 1

Receiver geometries in schematic form. (a) Geometry I: the untruncated local oscillator is combined with the receiver signal. (b) Geometry II: the local oscillator beam is truncated in secondary optics designed to optimize the BPLO field by avoiding its truncation at the receiver aperture. (c) Alternate geometry II: the theoretically optimum geometry. The local oscillator is truncated directly by the receiver aperture, but the BPLO is again untruncated.

Fig. 2
Fig. 2

Autocorrelation functions of optical fields in the reference sphere of the aperture planes (see Appendix A or Ref. 3) for focused beams: a, μ M (b) for uniform illumination (also the optical transfer function for simple aperture); b, μ T (b) for Gaussian transmitter with γ T = 0.815 (see Table I); c, μ L (b) for Gaussian receiver with γ L = 1.186.

Fig. 3
Fig. 3

Integrand of the effective area functions given as follows: a, A T ′ or A R ′ [Eq. (A1)] with uniform illumination; the area under this curve is the aperture area, which is π because the aperture radius is normalized to unity; b, 〈A〉 [Eq. (7)] for uniform illumination; c, 〈A〉 for optimal unmatched Gaussian beam geometry, using autocorrelation functions shown in b and c of Fig. 2.

Tables (2)

Tables Icon

Table 1 Recomputed Parameters for Maximum System Efficiency and the Corresponding Heterodyne Efficiency in a Truncated Gaussian Beam Lidara

Tables Icon

Table II Heterodyne and System-Antenna Efficiencies for Different Transmitter and Receiver Beam Profilesa

Equations (13)

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

i 2 = 2 R i 2 T L P L P R ,
P R = A ρ π T T P T r 2 ,
A = ( λ r ) 2 - I T ( s ) I L ( s ) d 2 s T L P T T L P L .
i 2 = 2 R i 2 A ρ π T L P L T T P T r 2 .
S d = λ 2 ρ π P T - U 0 ( s ) 2 U L ( s ) 2 d 2 s ,
S d = A ρ π T L T T P T r 2 ,
A = - μ T ( b ) μ L * ( b ) d 2 b .
i 2 = 2 R i 2 ρ π T T P T T L P L r 2 - μ T ( b ) μ L * ( b ) d 2 b .
η a = T L T T A A T .
i R = R i A R ρ π T T P T r 2 ,             i L = R i P L ,
η h = i 2 2 i R i L = T L A A R .
A T = - μ T ( b ) d 2 b ,             A R = - μ L * ( b ) d 2 b ,
1 A = 1 A T + 1 A R .

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