Abstract

Heterodyne efficiency of a coherent lidar system reflects the matching of phase and amplitude between a local oscillator (LO) beam and received signal beam and is, therefore, an indicator of system performance. One aspect of a lidar system that affects heterodyne efficiency is aberrations present in optical components. A method for including aberrations in the determination of heterodyne efficiency is presented. The effect of aberrations on heterodyne efficiency is demonstrated by including Seidel aberrations in the mixing of two perfectly matched gaussian beams. Results for this case are presented as animations that illustrate the behavior of the mixing as a function of time. Extension of this method to propagation through lidar optical systems is discussed.

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References

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  1. A. E. Siegman, The antenna properties of optical heterodyne receivers, Proc. IEEE 51, 1350-1358 (1966).
    [CrossRef]
  2. S. C. Cohen, Heterodyne detection: phase front alignment, beam spot size, and detector uniformity, Appl. Opt. 14, 1953-1959 (1975).
    [CrossRef] [PubMed]
  3. H. T. Yura, Optical heterodyne signal power obtained from finite sized sources of radiation, Appl. Opt. 13, 150-157 (1974).
    [CrossRef] [PubMed]
  4. B. J. Rye, Antenna parameters for incoherent backscatter heterodyne lidar, Appl. Opt. 18, 1390-1398 (1979).
    [CrossRef] [PubMed]
  5. B. J. Rye, Primary aberration contribution to incoherent backscatter heterodyne lidar returns, Appl. Opt. 21, 839-844 (1982).
    [CrossRef] [PubMed]
  6. R. G. Frehlich and M. J. Kavaya, Coherent laser radar performance for general atmospheric refractive turbulence, Appl. Opt. 30, 5325-5352 (1991).
    [CrossRef] [PubMed]
  7. R. G. Frehlich, Heterodyne efficiency for a coherent laser radar with diffuse or aerosol targets, J. Mod. Opt. 41,2115-2129 (1994).
    [CrossRef]
  8. Y. Zhao, M. J. Post, and R. M. Hardesty, Receiving efficiency of pulsed coherent lidars. 1: Theory, Appl. Opt. 29, 4111-4119 (1990).
    [CrossRef] [PubMed]
  9. Y. Zhao, M. J. Post, and R. M. Hardesty, Receiving efficiency of pulsed coherent lidars. 2: Applications , Appl. Opt. 29, 4120-4132 (1990).
    [CrossRef] [PubMed]
  10. J. W. Goodman, Introduction to Fourier optics, 2nd ed. (McGraw-Hill, New York, 1996).
  11. W. Welford, Aberrations of optical systems, (Adam Hilger, Bristol, 1989).
  12. M. Born and E. Wolf, Principles of Optics, 6th ed., (Pergamon,1987).
  13. C. A. DiMarzio and C.E. Harris, CAT detection system instrumentation , ER81-4147, Raytheon Company, Final report, Contract NAS8-32555 (1981).

Other

A. E. Siegman, The antenna properties of optical heterodyne receivers, Proc. IEEE 51, 1350-1358 (1966).
[CrossRef]

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

H. T. Yura, Optical heterodyne signal power obtained from finite sized sources of radiation, Appl. Opt. 13, 150-157 (1974).
[CrossRef] [PubMed]

B. J. Rye, Antenna parameters for incoherent backscatter heterodyne lidar, Appl. Opt. 18, 1390-1398 (1979).
[CrossRef] [PubMed]

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

R. G. Frehlich and M. J. Kavaya, Coherent laser radar performance for general atmospheric refractive turbulence, Appl. Opt. 30, 5325-5352 (1991).
[CrossRef] [PubMed]

R. G. Frehlich, Heterodyne efficiency for a coherent laser radar with diffuse or aerosol targets, J. Mod. Opt. 41,2115-2129 (1994).
[CrossRef]

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

Y. Zhao, M. J. Post, and R. M. Hardesty, Receiving efficiency of pulsed coherent lidars. 2: Applications , Appl. Opt. 29, 4120-4132 (1990).
[CrossRef] [PubMed]

J. W. Goodman, Introduction to Fourier optics, 2nd ed. (McGraw-Hill, New York, 1996).

W. Welford, Aberrations of optical systems, (Adam Hilger, Bristol, 1989).

M. Born and E. Wolf, Principles of Optics, 6th ed., (Pergamon,1987).

C. A. DiMarzio and C.E. Harris, CAT detection system instrumentation , ER81-4147, Raytheon Company, Final report, Contract NAS8-32555 (1981).

Supplementary Material (4)

» Media 1: MOV (1696 KB)     
» Media 2: MOV (1646 KB)     
» Media 3: MOV (1679 KB)     
» Media 4: MOV (1639 KB)     

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Figures (6)

Fig. 1a
Fig. 1a

Heterodyne mixing of two ideal gaussian beams in the presence of tilt, W011, (top left) and no aberration (top right) as a function of time. The detector integrated intensity as a function of time is also shown (bottom). [Media 1]

Fig. 1b
Fig. 1b

Heterodyne mixing of two ideal gaussian beams in the presence of spherical aberration, W040, (top left) and no aberration (top right) as a function of time. The detector integrated intensity as a function of time is also shown (bottom). [Media 2]

Fig. 1c
Fig. 1c

Heterodyne mixing of two ideal gaussian beams in the presence of coma aberration, W031, (top left) and no aberration (top right) as a function of time. The detector integrated intensity as a function of time is also shown (bottom). [Media 3]

Fig. 1d
Fig. 1d

Heterodyne mixing of two ideal gaussian beams in the presence of coma aberration, W022, (top left) and no aberration (top right) as a function of time. The detector integrated intensity as a function of time is also shown (bottom). [Media 4]

Fig. 2
Fig. 2

Reduction of heterodyne efficiency as a function of aberration in one of the beams. One way transmission assumed.

Fig. 3
Fig. 3

a) Phase distribution of a beam without aberrations after propagating through 16x telescope; b) Phase distribution of a beam with 0.1 wave rms aberration after propagating through 16x telescope

Equations (7)

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η H = D u S ( z , P ) u LO * ( P ) d P D u S * ( z , P ) u LO ( P ) d P P S P LO
SNR = P S hνB η H
u = u 0 exp [ ikW ( r , θ ) ]
W ( w ) = λ 1 . n , m W 1 , m , n η 1 ρ m cos n θ
K ( S , P ) = Lens h L t L d P L Optical Components . . . . h OC t OC d P OC Telescope Secondary Mirror h TS t TS d P TS Telescope Primary Mirror h TP t TP d P TP Window h W t W U ( S , P W ) d P W
h a = h a ( r 1 , r 2 ) = i λz exp [ ik 2 z ( r 1 r 2 ) 2 ]
t = t 0 exp [ ik W ( w ) ]

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