Abstract

Although pulsed coherent laser radar vibrometry has been introduced as an improvement over its continuous wave (CW) counterpart, it remains very sensitive to decorrelation noises, such as speckle, and other disturbances of its measurement. Taking advantage of more polyvalent polypulse waveforms, we address the issue with advanced signal processing. We have conducted what we believe is the first extensive comparison of processing techniques considering CW, pulse-pair, and polypulse emissions. In this framework, we introduce a computationally efficient maximum likelihood estimator and test signal tracking on pseudo-time-frequency representations (TFRs), which, respectively, help deal with speckle noise and fading of the signal in harsh noise conditions. Our comparison on simulated signals is validated on a 1.55μm all-fiber vibrometer experiment with an apparatus simulating vibration and strong speckle noise. Results show the advantage of the estimators that take into account actual noise statistics, and call for a wider use of TFRs to track the vibration-modulated signal.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

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  1. P. Gueguen, V. Jolivet, C. Michel, and A.-S. Schveitzer, “Comparison of velocimeter and coherent lidar measurements for building frequency assessment,” Bull. Earthquake Eng. 8, 327–338 (2010).
    [CrossRef]
  2. W. Kranz, “Target classification by laser vibration sensing,” Proc. SPIE 1181, 301–306 (1989).
    [CrossRef]
  3. S. M. Hannon, J. A. Thomson, S. W. Henderson, P. Gatt, R. Stoneman, and D. Bruns, “Agile multiple pulse coherent lidar for range and micro-Doppler measurement,” Proc. SPIE 3380, 259–269 (1998).
    [CrossRef]
  4. P. Gatt, S. W. Henderson, and B. Krause, “Poly-pulse coherent lidar waveforms for coherent lidar measurements,” presented at the Coherent Optical Technologies and Applications Conference, Whistler, Canada, 25 June 2006.
  5. S. W. Henderson, J. A. Thomson, S. M. Hannon, and P. Gatt, “Comparison of pulsed waveform and CW lidar for remote vibration measurement,” presented at the 10th Coherent Laser Radar Conference, Mount Hood, Oregon, 28 June 1999.
  6. C. Hill, M. Harris, and K. D. Ridley, “Fiber-based 1.5 μm lidar vibrometer in pulsed and continuous modes,” Appl. Opt. 46, 4376–4385 (2007).
    [CrossRef] [PubMed]
  7. P. Gatt, S. W. Henderson, and S. M. Hannon, “Noise mechanisms impacting micro-Doppler lidar signals: theory and experiment” Tech. Rep. (Coherent Technologies, Incorporated, 2000).
  8. C. Hill, M. Harris, K. D. Ridley, E. Jakeman, and P. Lutzmann, “Lidar frequency modulation vibrometry in the presence of speckle,” Appl. Opt. 42, 1091–1100 (2003).
    [CrossRef] [PubMed]
  9. A. Ishimaru, “The beam wave case and remote sensing,” in Topics in Applied Physics 25: Laser Beam Propagation in the Atmosphere, J.W.Strohbehn, ed. (Springer, 1978), pp. 129–170.
  10. A. L. Kachelmyer and K. I. Schultz, “Spectrogram processing of laser vibration data,” Proc. SPIE 1936, 78–88 (1993).
    [CrossRef]
  11. D. G. Youmans, “Joint time-frequency transform processing for linear and sinusoidal FM coherent ladars,” Proc. SPIE 5087, 46–57 (2003).
    [CrossRef]
  12. W. F. Buell, B. A. Shadwick, and R. W. Farley, “Bayesian spectrum analysis for laser vibrometry processing,” Tech. Rep. (Institute for Advanced Physics, 2000).
  13. B. J. Rye and R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar,” IEEE Trans. Geosci. Remote Sensing 31, 16–35 (1993).
    [CrossRef]
  14. D. G. Youmans, “Target spectral estimation using direct detection and coherent detection ladar,” Proc. SPIE 5791, 97–108(2005).
    [CrossRef]
  15. B. C. Lovell and R. C. Williamson, “The statistical performance of some instantaneous frequency estimators,” IEEE Trans. Signal Process. 40, 1708–1723 (1992).
    [CrossRef]
  16. M. Ghogho, A. K. Nandi, and A. Swami, “Cramér-Rao bounds and maximum likelihood estimation for random amplitude phase-modulated signals,” IEEE Trans. Signal Process. 49, 2905–2916 (2001).
    [CrossRef]
  17. J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency FM-noise-induced lineshape: a theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
    [CrossRef]
  18. C. Spiegelberg, J. Geng, Y. Hu, Y. Kaneda, S. Jiang, and N. Peyghambarian, “Low-noise narrow-linewidth fiber laser at 1550 nm,” J. Lightwave Technol. 22, 57–62 (2004).
    [CrossRef]
  19. O. Michel, A. Hero, and P. Flandrin, “Graphes de représentation minimaux, entropies et divergences: applications,” Traitement du Signal 17, 287–297 (2000).
  20. T. Thayaparan, L. Stankovic, I. Djurovic, S. Penamati, and K. Venkataramaniah, “Intelligent target recognition using micro-Doppler radar signatures,” Proc. SPIE 7308, 17–28(2009).
    [CrossRef]
  21. D. N. Schimpf and C. Ruchert, “Compensation of pulse-distortion in saturated laser amplifiers,” Opt. Express 16, 17637–17646 (2008).
    [CrossRef] [PubMed]

2010 (1)

P. Gueguen, V. Jolivet, C. Michel, and A.-S. Schveitzer, “Comparison of velocimeter and coherent lidar measurements for building frequency assessment,” Bull. Earthquake Eng. 8, 327–338 (2010).
[CrossRef]

2009 (1)

T. Thayaparan, L. Stankovic, I. Djurovic, S. Penamati, and K. Venkataramaniah, “Intelligent target recognition using micro-Doppler radar signatures,” Proc. SPIE 7308, 17–28(2009).
[CrossRef]

2008 (1)

2007 (1)

2005 (2)

D. G. Youmans, “Target spectral estimation using direct detection and coherent detection ladar,” Proc. SPIE 5791, 97–108(2005).
[CrossRef]

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency FM-noise-induced lineshape: a theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[CrossRef]

2004 (1)

2003 (2)

D. G. Youmans, “Joint time-frequency transform processing for linear and sinusoidal FM coherent ladars,” Proc. SPIE 5087, 46–57 (2003).
[CrossRef]

C. Hill, M. Harris, K. D. Ridley, E. Jakeman, and P. Lutzmann, “Lidar frequency modulation vibrometry in the presence of speckle,” Appl. Opt. 42, 1091–1100 (2003).
[CrossRef] [PubMed]

2001 (1)

M. Ghogho, A. K. Nandi, and A. Swami, “Cramér-Rao bounds and maximum likelihood estimation for random amplitude phase-modulated signals,” IEEE Trans. Signal Process. 49, 2905–2916 (2001).
[CrossRef]

2000 (1)

O. Michel, A. Hero, and P. Flandrin, “Graphes de représentation minimaux, entropies et divergences: applications,” Traitement du Signal 17, 287–297 (2000).

1998 (1)

S. M. Hannon, J. A. Thomson, S. W. Henderson, P. Gatt, R. Stoneman, and D. Bruns, “Agile multiple pulse coherent lidar for range and micro-Doppler measurement,” Proc. SPIE 3380, 259–269 (1998).
[CrossRef]

1993 (2)

A. L. Kachelmyer and K. I. Schultz, “Spectrogram processing of laser vibration data,” Proc. SPIE 1936, 78–88 (1993).
[CrossRef]

B. J. Rye and R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar,” IEEE Trans. Geosci. Remote Sensing 31, 16–35 (1993).
[CrossRef]

1992 (1)

B. C. Lovell and R. C. Williamson, “The statistical performance of some instantaneous frequency estimators,” IEEE Trans. Signal Process. 40, 1708–1723 (1992).
[CrossRef]

1989 (1)

W. Kranz, “Target classification by laser vibration sensing,” Proc. SPIE 1181, 301–306 (1989).
[CrossRef]

Alabedra, R.

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency FM-noise-induced lineshape: a theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[CrossRef]

Bellon, M.

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency FM-noise-induced lineshape: a theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[CrossRef]

Bruns, D.

S. M. Hannon, J. A. Thomson, S. W. Henderson, P. Gatt, R. Stoneman, and D. Bruns, “Agile multiple pulse coherent lidar for range and micro-Doppler measurement,” Proc. SPIE 3380, 259–269 (1998).
[CrossRef]

Buell, W. F.

W. F. Buell, B. A. Shadwick, and R. W. Farley, “Bayesian spectrum analysis for laser vibrometry processing,” Tech. Rep. (Institute for Advanced Physics, 2000).

Djurovic, I.

T. Thayaparan, L. Stankovic, I. Djurovic, S. Penamati, and K. Venkataramaniah, “Intelligent target recognition using micro-Doppler radar signatures,” Proc. SPIE 7308, 17–28(2009).
[CrossRef]

Farley, R. W.

W. F. Buell, B. A. Shadwick, and R. W. Farley, “Bayesian spectrum analysis for laser vibrometry processing,” Tech. Rep. (Institute for Advanced Physics, 2000).

Flandrin, P.

O. Michel, A. Hero, and P. Flandrin, “Graphes de représentation minimaux, entropies et divergences: applications,” Traitement du Signal 17, 287–297 (2000).

Gatt, P.

S. M. Hannon, J. A. Thomson, S. W. Henderson, P. Gatt, R. Stoneman, and D. Bruns, “Agile multiple pulse coherent lidar for range and micro-Doppler measurement,” Proc. SPIE 3380, 259–269 (1998).
[CrossRef]

P. Gatt, S. W. Henderson, and B. Krause, “Poly-pulse coherent lidar waveforms for coherent lidar measurements,” presented at the Coherent Optical Technologies and Applications Conference, Whistler, Canada, 25 June 2006.

S. W. Henderson, J. A. Thomson, S. M. Hannon, and P. Gatt, “Comparison of pulsed waveform and CW lidar for remote vibration measurement,” presented at the 10th Coherent Laser Radar Conference, Mount Hood, Oregon, 28 June 1999.

P. Gatt, S. W. Henderson, and S. M. Hannon, “Noise mechanisms impacting micro-Doppler lidar signals: theory and experiment” Tech. Rep. (Coherent Technologies, Incorporated, 2000).

Geng, J.

Ghogho, M.

M. Ghogho, A. K. Nandi, and A. Swami, “Cramér-Rao bounds and maximum likelihood estimation for random amplitude phase-modulated signals,” IEEE Trans. Signal Process. 49, 2905–2916 (2001).
[CrossRef]

Gosalbes, J.-M.

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency FM-noise-induced lineshape: a theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[CrossRef]

Gueguen, P.

P. Gueguen, V. Jolivet, C. Michel, and A.-S. Schveitzer, “Comparison of velocimeter and coherent lidar measurements for building frequency assessment,” Bull. Earthquake Eng. 8, 327–338 (2010).
[CrossRef]

Hannon, S. M.

S. M. Hannon, J. A. Thomson, S. W. Henderson, P. Gatt, R. Stoneman, and D. Bruns, “Agile multiple pulse coherent lidar for range and micro-Doppler measurement,” Proc. SPIE 3380, 259–269 (1998).
[CrossRef]

P. Gatt, S. W. Henderson, and S. M. Hannon, “Noise mechanisms impacting micro-Doppler lidar signals: theory and experiment” Tech. Rep. (Coherent Technologies, Incorporated, 2000).

S. W. Henderson, J. A. Thomson, S. M. Hannon, and P. Gatt, “Comparison of pulsed waveform and CW lidar for remote vibration measurement,” presented at the 10th Coherent Laser Radar Conference, Mount Hood, Oregon, 28 June 1999.

Hardesty, R. M.

B. J. Rye and R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar,” IEEE Trans. Geosci. Remote Sensing 31, 16–35 (1993).
[CrossRef]

Harris, M.

Henderson, S. W.

S. M. Hannon, J. A. Thomson, S. W. Henderson, P. Gatt, R. Stoneman, and D. Bruns, “Agile multiple pulse coherent lidar for range and micro-Doppler measurement,” Proc. SPIE 3380, 259–269 (1998).
[CrossRef]

P. Gatt, S. W. Henderson, and B. Krause, “Poly-pulse coherent lidar waveforms for coherent lidar measurements,” presented at the Coherent Optical Technologies and Applications Conference, Whistler, Canada, 25 June 2006.

S. W. Henderson, J. A. Thomson, S. M. Hannon, and P. Gatt, “Comparison of pulsed waveform and CW lidar for remote vibration measurement,” presented at the 10th Coherent Laser Radar Conference, Mount Hood, Oregon, 28 June 1999.

P. Gatt, S. W. Henderson, and S. M. Hannon, “Noise mechanisms impacting micro-Doppler lidar signals: theory and experiment” Tech. Rep. (Coherent Technologies, Incorporated, 2000).

Hero, A.

O. Michel, A. Hero, and P. Flandrin, “Graphes de représentation minimaux, entropies et divergences: applications,” Traitement du Signal 17, 287–297 (2000).

Hill, C.

Hu, Y.

Ishimaru, A.

A. Ishimaru, “The beam wave case and remote sensing,” in Topics in Applied Physics 25: Laser Beam Propagation in the Atmosphere, J.W.Strohbehn, ed. (Springer, 1978), pp. 129–170.

Jakeman, E.

Jiang, S.

Jolivet, V.

P. Gueguen, V. Jolivet, C. Michel, and A.-S. Schveitzer, “Comparison of velocimeter and coherent lidar measurements for building frequency assessment,” Bull. Earthquake Eng. 8, 327–338 (2010).
[CrossRef]

Kachelmyer, A. L.

A. L. Kachelmyer and K. I. Schultz, “Spectrogram processing of laser vibration data,” Proc. SPIE 1936, 78–88 (1993).
[CrossRef]

Kaneda, Y.

Kranz, W.

W. Kranz, “Target classification by laser vibration sensing,” Proc. SPIE 1181, 301–306 (1989).
[CrossRef]

Krause, B.

P. Gatt, S. W. Henderson, and B. Krause, “Poly-pulse coherent lidar waveforms for coherent lidar measurements,” presented at the Coherent Optical Technologies and Applications Conference, Whistler, Canada, 25 June 2006.

Lovell, B. C.

B. C. Lovell and R. C. Williamson, “The statistical performance of some instantaneous frequency estimators,” IEEE Trans. Signal Process. 40, 1708–1723 (1992).
[CrossRef]

Lutzmann, P.

Michel, C.

P. Gueguen, V. Jolivet, C. Michel, and A.-S. Schveitzer, “Comparison of velocimeter and coherent lidar measurements for building frequency assessment,” Bull. Earthquake Eng. 8, 327–338 (2010).
[CrossRef]

Michel, O.

O. Michel, A. Hero, and P. Flandrin, “Graphes de représentation minimaux, entropies et divergences: applications,” Traitement du Signal 17, 287–297 (2000).

Myara, M.

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency FM-noise-induced lineshape: a theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[CrossRef]

Nandi, A. K.

M. Ghogho, A. K. Nandi, and A. Swami, “Cramér-Rao bounds and maximum likelihood estimation for random amplitude phase-modulated signals,” IEEE Trans. Signal Process. 49, 2905–2916 (2001).
[CrossRef]

Orsal, B.

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency FM-noise-induced lineshape: a theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[CrossRef]

Penamati, S.

T. Thayaparan, L. Stankovic, I. Djurovic, S. Penamati, and K. Venkataramaniah, “Intelligent target recognition using micro-Doppler radar signatures,” Proc. SPIE 7308, 17–28(2009).
[CrossRef]

Perez, J.-P.

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency FM-noise-induced lineshape: a theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[CrossRef]

Peyghambarian, N.

Ridley, K. D.

Ruchert, C.

Rye, B. J.

B. J. Rye and R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar,” IEEE Trans. Geosci. Remote Sensing 31, 16–35 (1993).
[CrossRef]

Schimpf, D. N.

Schultz, K. I.

A. L. Kachelmyer and K. I. Schultz, “Spectrogram processing of laser vibration data,” Proc. SPIE 1936, 78–88 (1993).
[CrossRef]

Schveitzer, A.-S.

P. Gueguen, V. Jolivet, C. Michel, and A.-S. Schveitzer, “Comparison of velocimeter and coherent lidar measurements for building frequency assessment,” Bull. Earthquake Eng. 8, 327–338 (2010).
[CrossRef]

Shadwick, B. A.

W. F. Buell, B. A. Shadwick, and R. W. Farley, “Bayesian spectrum analysis for laser vibrometry processing,” Tech. Rep. (Institute for Advanced Physics, 2000).

Signoret, P.

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency FM-noise-induced lineshape: a theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[CrossRef]

Spiegelberg, C.

Stankovic, L.

T. Thayaparan, L. Stankovic, I. Djurovic, S. Penamati, and K. Venkataramaniah, “Intelligent target recognition using micro-Doppler radar signatures,” Proc. SPIE 7308, 17–28(2009).
[CrossRef]

Stoneman, R.

S. M. Hannon, J. A. Thomson, S. W. Henderson, P. Gatt, R. Stoneman, and D. Bruns, “Agile multiple pulse coherent lidar for range and micro-Doppler measurement,” Proc. SPIE 3380, 259–269 (1998).
[CrossRef]

Swami, A.

M. Ghogho, A. K. Nandi, and A. Swami, “Cramér-Rao bounds and maximum likelihood estimation for random amplitude phase-modulated signals,” IEEE Trans. Signal Process. 49, 2905–2916 (2001).
[CrossRef]

Thayaparan, T.

T. Thayaparan, L. Stankovic, I. Djurovic, S. Penamati, and K. Venkataramaniah, “Intelligent target recognition using micro-Doppler radar signatures,” Proc. SPIE 7308, 17–28(2009).
[CrossRef]

Thomson, J. A.

S. M. Hannon, J. A. Thomson, S. W. Henderson, P. Gatt, R. Stoneman, and D. Bruns, “Agile multiple pulse coherent lidar for range and micro-Doppler measurement,” Proc. SPIE 3380, 259–269 (1998).
[CrossRef]

S. W. Henderson, J. A. Thomson, S. M. Hannon, and P. Gatt, “Comparison of pulsed waveform and CW lidar for remote vibration measurement,” presented at the 10th Coherent Laser Radar Conference, Mount Hood, Oregon, 28 June 1999.

Tourrenc, J.-P.

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency FM-noise-induced lineshape: a theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[CrossRef]

Venkataramaniah, K.

T. Thayaparan, L. Stankovic, I. Djurovic, S. Penamati, and K. Venkataramaniah, “Intelligent target recognition using micro-Doppler radar signatures,” Proc. SPIE 7308, 17–28(2009).
[CrossRef]

Williamson, R. C.

B. C. Lovell and R. C. Williamson, “The statistical performance of some instantaneous frequency estimators,” IEEE Trans. Signal Process. 40, 1708–1723 (1992).
[CrossRef]

Youmans, D. G.

D. G. Youmans, “Target spectral estimation using direct detection and coherent detection ladar,” Proc. SPIE 5791, 97–108(2005).
[CrossRef]

D. G. Youmans, “Joint time-frequency transform processing for linear and sinusoidal FM coherent ladars,” Proc. SPIE 5087, 46–57 (2003).
[CrossRef]

Appl. Opt. (2)

Bull. Earthquake Eng. (1)

P. Gueguen, V. Jolivet, C. Michel, and A.-S. Schveitzer, “Comparison of velocimeter and coherent lidar measurements for building frequency assessment,” Bull. Earthquake Eng. 8, 327–338 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency FM-noise-induced lineshape: a theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing (1)

B. J. Rye and R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar,” IEEE Trans. Geosci. Remote Sensing 31, 16–35 (1993).
[CrossRef]

IEEE Trans. Signal Process. (2)

B. C. Lovell and R. C. Williamson, “The statistical performance of some instantaneous frequency estimators,” IEEE Trans. Signal Process. 40, 1708–1723 (1992).
[CrossRef]

M. Ghogho, A. K. Nandi, and A. Swami, “Cramér-Rao bounds and maximum likelihood estimation for random amplitude phase-modulated signals,” IEEE Trans. Signal Process. 49, 2905–2916 (2001).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (1)

Proc. SPIE (6)

T. Thayaparan, L. Stankovic, I. Djurovic, S. Penamati, and K. Venkataramaniah, “Intelligent target recognition using micro-Doppler radar signatures,” Proc. SPIE 7308, 17–28(2009).
[CrossRef]

D. G. Youmans, “Target spectral estimation using direct detection and coherent detection ladar,” Proc. SPIE 5791, 97–108(2005).
[CrossRef]

A. L. Kachelmyer and K. I. Schultz, “Spectrogram processing of laser vibration data,” Proc. SPIE 1936, 78–88 (1993).
[CrossRef]

D. G. Youmans, “Joint time-frequency transform processing for linear and sinusoidal FM coherent ladars,” Proc. SPIE 5087, 46–57 (2003).
[CrossRef]

W. Kranz, “Target classification by laser vibration sensing,” Proc. SPIE 1181, 301–306 (1989).
[CrossRef]

S. M. Hannon, J. A. Thomson, S. W. Henderson, P. Gatt, R. Stoneman, and D. Bruns, “Agile multiple pulse coherent lidar for range and micro-Doppler measurement,” Proc. SPIE 3380, 259–269 (1998).
[CrossRef]

Traitement du Signal (1)

O. Michel, A. Hero, and P. Flandrin, “Graphes de représentation minimaux, entropies et divergences: applications,” Traitement du Signal 17, 287–297 (2000).

Other (5)

W. F. Buell, B. A. Shadwick, and R. W. Farley, “Bayesian spectrum analysis for laser vibrometry processing,” Tech. Rep. (Institute for Advanced Physics, 2000).

P. Gatt, S. W. Henderson, and B. Krause, “Poly-pulse coherent lidar waveforms for coherent lidar measurements,” presented at the Coherent Optical Technologies and Applications Conference, Whistler, Canada, 25 June 2006.

S. W. Henderson, J. A. Thomson, S. M. Hannon, and P. Gatt, “Comparison of pulsed waveform and CW lidar for remote vibration measurement,” presented at the 10th Coherent Laser Radar Conference, Mount Hood, Oregon, 28 June 1999.

A. Ishimaru, “The beam wave case and remote sensing,” in Topics in Applied Physics 25: Laser Beam Propagation in the Atmosphere, J.W.Strohbehn, ed. (Springer, 1978), pp. 129–170.

P. Gatt, S. W. Henderson, and S. M. Hannon, “Noise mechanisms impacting micro-Doppler lidar signals: theory and experiment” Tech. Rep. (Coherent Technologies, Incorporated, 2000).

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Figures (9)

Fig. 1
Fig. 1

Diagram of a heterodyne coherent lidar vibrometer with a MOPA configuration, convenient for emitting arbitrary waveforms using the same AOM as for the frequency shift.

Fig. 2
Fig. 2

Parameters of polypulse waveforms in amplitude modulation μ ( t ) : t p , pulse duration; T S , pulse separation; T m , polypulse duration; PRF, waveform repetition frequency; N p , pulse number per waveform; and μ max , maximal amplitude of μ ( t ) .

Fig. 3
Fig. 3

Comparison of velocity errors of PP, PPP, and ML estimators and theoretical CRB for the velocity error, as a function of average CNR, for the pulse pair ( 2 p ) and six-pulse ( 6 p ). Two thousand simulated waveforms with T S = 50 μs and t p = 2 μs at B speckle = 5 kHz . Only the ML estimator reaches the CRB.

Fig. 4
Fig. 4

TFRs obtained for simulated signals (six-pulse waveforms, PRF = 500 Hz , T S = 50 μs , and t p = 2 μs ) with matched filtering, AFT, and ML at low CNR ( 20 dB in 1 MHz ) and B speckle = 5 kHz . On the right side, temporal smoothing of the TFRs brings out the vibration trace.

Fig. 5
Fig. 5

Average vibration spectra simulated at a high CNR ( 30 dB in 1 MHz ) processed by the estimators giving the best SNR for CW, pulse pairs ( 2 p ), and six-pulse waveforms ( 6 p ). The noise floor is much lower with the ML estimator than with the PPP estimator.

Fig. 6
Fig. 6

Average SNRs obtained in simulation at B speckle = 5 kHz and high CNR [(top) 30 dB ] or low CNR [(bottom) 25 dB ] for CW, pulse pairs ( 2 p ), and six-pulse waveforms ( 6 p ). The suffix “-s” denotes smoothing is applied on the pseudo-TFR obtained using the preceding estimator.

Fig. 7
Fig. 7

Average SNRs at low CNR ( 20 dB ) plotted as a function of the ratio between analysis bandwidth B a and vibration bandwidth B vib , for CW, pulse pairs ( 2 p ), and six-pulse waveforms ( 6 p ).

Fig. 8
Fig. 8

Diagram of experimental apparatus allowing CW and polypulse operations. A rotating scatterer is used to create speckle noise with bandwidth B speckle = 5 kHz : EDFA, erbium-doped fiber amplifier; ATT, attenuator; Det, detector; HF, high frequency; ADC, analog-to-digital converter).

Fig. 9
Fig. 9

Experimental SNR plotted as a function of CNR (top) and experimental spectra at high CNR (bottom), averaged over 20 to 40 measurements, for CW, pulse pairs ( 2 p ), and six-pulse waveforms ( 6 p ).

Tables (2)

Tables Icon

Table 1 Implemented Instantaneous Frequency Estimators

Tables Icon

Table 2 Computation Times for Implemented Estimators

Equations (15)

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

i S ( t ) = μ ( t ) i het ( t ) + i b ( t ) = μ ( t ) i 0 m ( t ) exp ( j φ vib ( t ) ) + i b ( t ) ,
f ^ inst ( t = k / PRF ) = arg max f ( ( s ) T Q s 1 ( s ) ) ,
s ( p ) = i s k , p exp ( j 2 π f . p T S ) for     p = 1 , , N p , Q s = CNR peak Q m + I N p ,
Q m ( p , q ) = Q speckle ( p , q ) = Γ speckle ( ( p q ) T S ) = e B speckle 2 T S 2 ( p q ) 2 for     p , q = 1 , , N p .
Q ^ s = k ^ = 1 K s k . s k T with s k ( p ) = i s k , p exp ( j 2 π f ^ k . p T S ) for     p = 1 , , N p ,
σ v λ 2 [ Tr ( ( Q f Q 1 ) 2 ) ] 1 / 2 ,
Q ( u , v ) = μ max 2 i 0 2 Γ m ( ( u v ) Δ t ) e j 2 π f ( u v ) Δ t + σ b 2 δ ( u v ) ,
σ v λ 4 π 2 σ t CNR wf + 1 CNR wf ,
f ^ inst ( t ) = 1 2 π Δ t arg ( n = 1 N m i s ( t + n . Δ t ) i s * ( t + ( n 1 ) . Δ t ) )
f ^ inst ( t ) = B a 2 π arg ( B a | STFT ( t , f ) | 2 . exp ( j 2 π f B a ) d f )
f ^ inst ( t ) = arg max f ( S ref ( f ) | STFT ( t , f ) | 2 )
f ^ inst ( t = k / PRF ) = 1 2 π T S arg ( i s k , 2 i s k , 1 * )
f ^ inst ( t = k / PRF ) = 1 2 π T S arg ( p = 2 N p i s k , p i s k , p 1 * )
f ^ inst ( t = k / PRF ) = arg max f ( | arg ( Γ i s , k ( τ ) ) . h ( τ ) . exp ( j 2 π f τ ) d τ | )
f ^ inst ( t = k / PRF ) = arg max f ( | Polypulse   # k i s ( t ) . μ ( t ) . exp ( j 2 π f t ) d t | )

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