Abstract

A description is given of the design, operation, and test over a 2-km path (roundtrip) of a continuous wave, coherent laser array receiver that uses two independent aperture–receivers whose intermediate frequencies are electro-optically co-phased in real time and then added as a proposed way to overcome effective aperture limitations imposed by atmospheric turbulence and to mitigate signal fading associated with atmospheric turbulence and speckle effects. The experiment resulted in a mean carrier-to-noise ratio increase of 1.8, which is within 1% of the theoretical predictions, when the two signals were phase locked, versus no increase without phase locking. Further, the carrier fading strength, or normalized carrier-to-noise ratio variance, was reduced by a factor of 0.53, which is within 2% of the theoretical prediction. The bandwidth of the electro-optic phase-locked loop was measured to be of the order of 600 Hz, which is adequate to compensate for atmospheric refractive turbulence fluctuations.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. R. Kahn, “Ratio squarer,” Proc. IRE 42, 1704–••• (1954).
  2. D. G. Brennan, “Linear diversity combining techniques,” Proc. IRE 47, 1075–1102 (1959).
    [CrossRef]
  3. J. D. Parsons, “Diversity techniques in communications receivers,” in Advanced Signal Processing, D. A. Creasey, ed. (Peregrinus, London, 1985), Chap. 6.
    [CrossRef]
  4. I. Goldstein, P. A. Miles, A. Chabot, “Heterodyne measurements of light propagation through atmospheric turbulence,” Proc. IEEE 53, 1172–1180 (1965).
    [CrossRef]
  5. D. L. Fried, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–67 (1967).
    [CrossRef]
  6. D. Fink, S. N. Vodopia, “Coherent detection SNR of an array of detectors,” Appl. Opt. 15, 453–454 (1976).
    [CrossRef] [PubMed]
  7. J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 20, 3292–3313 (1981).
    [CrossRef] [PubMed]
  8. H. T. Yura, W. G. McKinley, “Aperture averaging of scintillation for space-to-ground optical communication applications,” Appl. Opt. 22, 1608–1609 (1983).
    [CrossRef] [PubMed]
  9. W. B. Veldkamp, E. J. Van Allen, “Binary holographic LO beam multiplexer for IR imaging detector arrays,” Appl. Opt. 22, 1497–1507 (1983).
    [CrossRef] [PubMed]
  10. W. B. Veldkamp, “Holographic local-oscillator beam multiplexing for array heterodyne detection,” Appl. Opt. 22, 891–900 (1983).
    [CrossRef] [PubMed]
  11. W. B. Veldkamp, C. J. Kastner, “Beam profile shaping for laser radars that use detector arrays,” Appl. Opt. 21, 345–356 (1982).
    [CrossRef] [PubMed]
  12. J. H. Shapiro, “Heterodyne mixing efficiency for detector arrays,” Appl. Opt. 26, 3600–3606 (1987).
    [CrossRef] [PubMed]
  13. B. E. Edwards, “Design aspects of an infrared laser radar,” Laser Appl. 1, 47–50 (1982).
  14. K. P. Chan, D. K. Killinger, “Enhanced detection of atmospheric-turbulence-distorted 1-μm coherent lidar returns using a two-dimensional heterodyne array,” Opt. Lett. 17, 1237–1239 (1992).
    [CrossRef] [PubMed]
  15. N. Sugimoto, K. P. Chan, D. K. Killinger, “Optimal heterodyne detector array size for 1-μm coherent lidar propagation through atmospheric turbulence,” Appl. Opt. 30, 2609–2616 (1991).
    [CrossRef] [PubMed]
  16. K. P. Chan, D. K. Killinger, “Coherent summation of spatially distorted laser Doppler signals by using a two-dimensional heterodyne detector array,” Opt. Lett. 17, 1237–1239 (1992).
    [CrossRef] [PubMed]
  17. C. G. Bachman, Laser Radar Systems and Techniques (Artech, Wayland, Mass., 1979), Chap. 2.
  18. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 2.
  19. This equation results by following an analysis similar to Parsons’ analysis for the mean CNR.3 In this case up to the fourth moment of the field amplitude is required to calculate the second moment of the CNR, which is then used to derive the normalized CNR variance.
  20. J. Y. Wang, A. P. Pruitt, “Effects of speckle on the range precision of a scanning lidar,” Appl. Opt. 31, 801–808 (1992).
    [CrossRef] [PubMed]
  21. J. F. Holmes, J. S. Peacock, D. C. Draper, “Optical remote sensing of surface roughness through optical turbulence,” Appl. Opt. 33, 7770–7776 (1994).
    [CrossRef] [PubMed]
  22. R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991), Chap. 2.
  23. V. S. Gudimetla, J. F. Holmes, “Probability density function of the intensity for a laser-generated speckle field after propagation through the turbulent atmosphere,” J. Opt. Soc. Am. 72, 1213–1218 (1982).
    [CrossRef]
  24. N. E. Zirkind, J. H. Shapiro, “Adaptive optics for large aperture coherent laser radars,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE999, 117–135 (1989).
  25. J. E. Pearson, “Compensation of propagation distortions using coherent optical adaptive techniques (COAT),” in Optical Design Problems in Laser Systems, W. R. Sooy, ed., Proc. SPIE69, 21–22 (1975).
  26. S. A. Kokorowski, T. R. O’Meara, R. C. Lind, T. Calderone, “Automatic speckle cancellation techniques for multidither adaptive optics,” Appl. Opt. 19, 371–381 (1980).
    [CrossRef] [PubMed]

1994 (1)

1992 (3)

1991 (1)

N. Sugimoto, K. P. Chan, D. K. Killinger, “Optimal heterodyne detector array size for 1-μm coherent lidar propagation through atmospheric turbulence,” Appl. Opt. 30, 2609–2616 (1991).
[CrossRef] [PubMed]

1987 (1)

1983 (3)

1982 (3)

1981 (1)

1980 (1)

1976 (1)

1967 (1)

D. L. Fried, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–67 (1967).
[CrossRef]

1965 (1)

I. Goldstein, P. A. Miles, A. Chabot, “Heterodyne measurements of light propagation through atmospheric turbulence,” Proc. IEEE 53, 1172–1180 (1965).
[CrossRef]

1959 (1)

D. G. Brennan, “Linear diversity combining techniques,” Proc. IRE 47, 1075–1102 (1959).
[CrossRef]

1954 (1)

L. R. Kahn, “Ratio squarer,” Proc. IRE 42, 1704–••• (1954).

Bachman, C. G.

C. G. Bachman, Laser Radar Systems and Techniques (Artech, Wayland, Mass., 1979), Chap. 2.

Brennan, D. G.

D. G. Brennan, “Linear diversity combining techniques,” Proc. IRE 47, 1075–1102 (1959).
[CrossRef]

Calderone, T.

Capron, B. A.

Chabot, A.

I. Goldstein, P. A. Miles, A. Chabot, “Heterodyne measurements of light propagation through atmospheric turbulence,” Proc. IEEE 53, 1172–1180 (1965).
[CrossRef]

Chan, K. P.

K. P. Chan, D. K. Killinger, “Enhanced detection of atmospheric-turbulence-distorted 1-μm coherent lidar returns using a two-dimensional heterodyne array,” Opt. Lett. 17, 1237–1239 (1992).
[CrossRef] [PubMed]

K. P. Chan, D. K. Killinger, “Coherent summation of spatially distorted laser Doppler signals by using a two-dimensional heterodyne detector array,” Opt. Lett. 17, 1237–1239 (1992).
[CrossRef] [PubMed]

N. Sugimoto, K. P. Chan, D. K. Killinger, “Optimal heterodyne detector array size for 1-μm coherent lidar propagation through atmospheric turbulence,” Appl. Opt. 30, 2609–2616 (1991).
[CrossRef] [PubMed]

Draper, D. C.

Edwards, B. E.

B. E. Edwards, “Design aspects of an infrared laser radar,” Laser Appl. 1, 47–50 (1982).

Fink, D.

Fried, D. L.

D. L. Fried, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–67 (1967).
[CrossRef]

Goldstein, I.

I. Goldstein, P. A. Miles, A. Chabot, “Heterodyne measurements of light propagation through atmospheric turbulence,” Proc. IEEE 53, 1172–1180 (1965).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 2.

Gudimetla, V. S.

Harney, R. C.

Holmes, J. F.

Kahn, L. R.

L. R. Kahn, “Ratio squarer,” Proc. IRE 42, 1704–••• (1954).

Kastner, C. J.

Killinger, D. K.

K. P. Chan, D. K. Killinger, “Enhanced detection of atmospheric-turbulence-distorted 1-μm coherent lidar returns using a two-dimensional heterodyne array,” Opt. Lett. 17, 1237–1239 (1992).
[CrossRef] [PubMed]

K. P. Chan, D. K. Killinger, “Coherent summation of spatially distorted laser Doppler signals by using a two-dimensional heterodyne detector array,” Opt. Lett. 17, 1237–1239 (1992).
[CrossRef] [PubMed]

N. Sugimoto, K. P. Chan, D. K. Killinger, “Optimal heterodyne detector array size for 1-μm coherent lidar propagation through atmospheric turbulence,” Appl. Opt. 30, 2609–2616 (1991).
[CrossRef] [PubMed]

Kokorowski, S. A.

Lind, R. C.

McKinley, W. G.

Miles, P. A.

I. Goldstein, P. A. Miles, A. Chabot, “Heterodyne measurements of light propagation through atmospheric turbulence,” Proc. IEEE 53, 1172–1180 (1965).
[CrossRef]

O’Meara, T. R.

Parsons, J. D.

J. D. Parsons, “Diversity techniques in communications receivers,” in Advanced Signal Processing, D. A. Creasey, ed. (Peregrinus, London, 1985), Chap. 6.
[CrossRef]

Peacock, J. S.

Pearson, J. E.

J. E. Pearson, “Compensation of propagation distortions using coherent optical adaptive techniques (COAT),” in Optical Design Problems in Laser Systems, W. R. Sooy, ed., Proc. SPIE69, 21–22 (1975).

Pruitt, A. P.

Shapiro, J. H.

Sugimoto, N.

N. Sugimoto, K. P. Chan, D. K. Killinger, “Optimal heterodyne detector array size for 1-μm coherent lidar propagation through atmospheric turbulence,” Appl. Opt. 30, 2609–2616 (1991).
[CrossRef] [PubMed]

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991), Chap. 2.

Van Allen, E. J.

Veldkamp, W. B.

Vodopia, S. N.

Wang, J. Y.

Yura, H. T.

Zirkind, N. E.

N. E. Zirkind, J. H. Shapiro, “Adaptive optics for large aperture coherent laser radars,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE999, 117–135 (1989).

Appl. Opt. (1)

N. Sugimoto, K. P. Chan, D. K. Killinger, “Optimal heterodyne detector array size for 1-μm coherent lidar propagation through atmospheric turbulence,” Appl. Opt. 30, 2609–2616 (1991).
[CrossRef] [PubMed]

Appl. Opt. (10)

D. Fink, S. N. Vodopia, “Coherent detection SNR of an array of detectors,” Appl. Opt. 15, 453–454 (1976).
[CrossRef] [PubMed]

J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 20, 3292–3313 (1981).
[CrossRef] [PubMed]

H. T. Yura, W. G. McKinley, “Aperture averaging of scintillation for space-to-ground optical communication applications,” Appl. Opt. 22, 1608–1609 (1983).
[CrossRef] [PubMed]

W. B. Veldkamp, E. J. Van Allen, “Binary holographic LO beam multiplexer for IR imaging detector arrays,” Appl. Opt. 22, 1497–1507 (1983).
[CrossRef] [PubMed]

W. B. Veldkamp, “Holographic local-oscillator beam multiplexing for array heterodyne detection,” Appl. Opt. 22, 891–900 (1983).
[CrossRef] [PubMed]

W. B. Veldkamp, C. J. Kastner, “Beam profile shaping for laser radars that use detector arrays,” Appl. Opt. 21, 345–356 (1982).
[CrossRef] [PubMed]

J. H. Shapiro, “Heterodyne mixing efficiency for detector arrays,” Appl. Opt. 26, 3600–3606 (1987).
[CrossRef] [PubMed]

J. Y. Wang, A. P. Pruitt, “Effects of speckle on the range precision of a scanning lidar,” Appl. Opt. 31, 801–808 (1992).
[CrossRef] [PubMed]

J. F. Holmes, J. S. Peacock, D. C. Draper, “Optical remote sensing of surface roughness through optical turbulence,” Appl. Opt. 33, 7770–7776 (1994).
[CrossRef] [PubMed]

S. A. Kokorowski, T. R. O’Meara, R. C. Lind, T. Calderone, “Automatic speckle cancellation techniques for multidither adaptive optics,” Appl. Opt. 19, 371–381 (1980).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Laser Appl. (1)

B. E. Edwards, “Design aspects of an infrared laser radar,” Laser Appl. 1, 47–50 (1982).

Opt. Lett. (1)

K. P. Chan, D. K. Killinger, “Coherent summation of spatially distorted laser Doppler signals by using a two-dimensional heterodyne detector array,” Opt. Lett. 17, 1237–1239 (1992).
[CrossRef] [PubMed]

Opt. Lett. (1)

Proc. IRE (1)

L. R. Kahn, “Ratio squarer,” Proc. IRE 42, 1704–••• (1954).

Proc. IEEE (2)

I. Goldstein, P. A. Miles, A. Chabot, “Heterodyne measurements of light propagation through atmospheric turbulence,” Proc. IEEE 53, 1172–1180 (1965).
[CrossRef]

D. L. Fried, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–67 (1967).
[CrossRef]

Proc. IRE (1)

D. G. Brennan, “Linear diversity combining techniques,” Proc. IRE 47, 1075–1102 (1959).
[CrossRef]

Other (7)

J. D. Parsons, “Diversity techniques in communications receivers,” in Advanced Signal Processing, D. A. Creasey, ed. (Peregrinus, London, 1985), Chap. 6.
[CrossRef]

C. G. Bachman, Laser Radar Systems and Techniques (Artech, Wayland, Mass., 1979), Chap. 2.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 2.

This equation results by following an analysis similar to Parsons’ analysis for the mean CNR.3 In this case up to the fourth moment of the field amplitude is required to calculate the second moment of the CNR, which is then used to derive the normalized CNR variance.

N. E. Zirkind, J. H. Shapiro, “Adaptive optics for large aperture coherent laser radars,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE999, 117–135 (1989).

J. E. Pearson, “Compensation of propagation distortions using coherent optical adaptive techniques (COAT),” in Optical Design Problems in Laser Systems, W. R. Sooy, ed., Proc. SPIE69, 21–22 (1975).

R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991), Chap. 2.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Space-diversity receiver architectures: (a) selection, (b) EG, (c) MR.

Fig. 2
Fig. 2

Mean CNR for the MR, EG, and selection coherent array receivers.

Fig. 3
Fig. 3

Normalized CNR variance for the MR, EG, and selection coherent array receivers.

Fig. 4
Fig. 4

Portions of the simulated signals: (a) one of eight simulated array element RF signals plus narrow-band noise with a specified mean CNR = 0 dB, (b) incoherent sum of eight signals, (c) coherent sum of eight signals.

Fig. 5
Fig. 5

Dual-aperture offset-homodyne transceiver.

Fig. 6
Fig. 6

Closed loop (solid curve) and open loop (dotted curve) of the sinusoidally modulated optical carrier: (a) power spectra, (b) amplitude spectra.

Fig. 7
Fig. 7

Signal spectra for the 2-km (round-trip) field experiment, with coherent addition (top trace), incoherent addition (middle trace), and typical single channel spectra (lower trace): (a) power spectra, (b) amplitude spectra.

Fig. 8
Fig. 8

Portions of simultaneously collected subsampled RF signals: (a) monostatic, (b) bistatic, (c) EG coherent sum.

Tables (2)

Tables Icon

Table 1 Summary of Calculated Moments of the CNR for a Simulated Eight-Aperture Coherent Array

Tables Icon

Table 2 Dual-Aperture Coherent Array CNR Statisticsa

Equations (17)

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

x ( t ) = a ( t ) cos [ ω c t + ϕ ( t ) ] + n ( t ) ,
δ ( t ) = 1 / 2 a 2 ( t ) E [ n 2 ( t ) ] = η γ ( t ) P ( t ) h ν B ,
a ( t ) = [ 2 η γ ( t ) P ( t ) ] 1 / 2 ,
E [ n 2 ( t ) ] = h ν B .
δ ¯ = E [ δ ( t ) ] = η E [ γ ( t ) P ( t ) ] h ν B .
Δ sum ( t ) = η { i = 1 M G i ( t ) [ γ i ( t ) P s i ( t ) ] 1 / 2 } h ν B i = 1 M G i 2 ( t ) .
G i ( t ) = k a i ( t ) = k [ 2 η γ i ( t ) P s i ( t ) ] 1 / 2 ,
Δ MR ( t ) = η h ν B i = 1 M γ i ( t ) P s i ( t ) = i = 1 M δ i ( t ) .
E [ Δ EG ( t ) ] = [ 1 + ( M - 1 ) π / 4 ] δ ¯ .
σ ^ Δ EG 2 = 2 [ - ( 2 π 2 - 8 π ) M 2 + ( 5 π 2 - 20 π + 16 ) M - ( 3 π 2 - 12 π + 8 ) ] M ( π M + 4 - π ) 2 ,
E [ Δ S n ( t ) ] = n ! M δ ¯ n k = 0 M - 1 [ M - 1 k ] ( - 1 ) k ( k + 1 ) n + 1 ,
σ ^ Δ S 2 = 2 M k = 0 M - 1 ( M - 1 k ) ( - 1 ) k ( k + 1 ) 3 [ k = 0 M - 1 ( M - 1 k ) ( - 1 ) k ( k + 1 ) 2 ] 2 - 1.
E [ Δ S ( t ) ] [ 0.815 + 0.94 ln ( M ) ] δ ¯             for 1 M 50 ,
σ ^ Δ S 2 0.8 M - 0.62             for             1 M 50.
δ ¯ = E [ x 2 ( t ) ] E [ n 2 ( t ) ] - 1 ,
E [ δ 2 ( t ) ] = 2 E [ n 2 ( t ) ] { E [ x 4 ( t ) ] 3 E [ n 2 ( t ) ] - 2 E [ x 2 ( t ) ] + E [ n 2 ( t ) ] } ,
σ ^ δ 2 = E [ δ 2 ( t ) ] / δ ¯ 2 - 1.

Metrics