Abstract

A fiber-based 1.5μm heterodyne lidar that is easily switched between pulse-pair and cw modes is described. In laboratory experiments using well-controlled vibrating targets, and in computer simulations, the performance of the two modes is compared given the same average laser power. The accuracy of Doppler frequency (target velocity) estimates, and the signal-to-noise ratio in spectrally resolved plots of vibrational features, are evaluated. When the target-induced frequency modulation is wideband, pulse-pair often has clearly higher carrier-to-noise. But its advantage in signal-to-noise is smaller because combining the more numerous cw measurements improves the estimates of vibration frequencies and amplitudes. They are combined here through autocorrelation-based demodulation, one of several methods that can outperform phase-differencing.

© 2007 Optical Society of America

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  1. C. J. Karlsson, F. Å. A. Olsson, D. Letalick, and M. Harris, "All-fiber multifunction continuous-wave coherent laser radar at 1.55 μm for range, speed, vibration, and wind measurements," Appl. Opt. 39, 3716-3726 (2000).
    [CrossRef]
  2. A. L. Kachelmyer and K. I. Schultz, "Laser vibration sensing," Lincoln Lab. J. 8, 3-28 (1995).
  3. C. A. 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]
  4. K. D. Ridley and E. Jakeman, "Signal-to-noise analysis of FM demodulation in the presence of multiplicative and additive noise," Signal Process. 80, 1895-1907 (2000).
    [CrossRef]
  5. S. M. Hannon, J. A. L. 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]
  6. R. Foord, R. Jones, J. M. Vaughan, and D. V. Willetts, "Precise comparison of experimental and theoretical SNRs in CO2 laser heterodyne systems," Appl. Opt. 22, 3787-3795 (1983). We conventionally say "ratio" instead of "quotient," not distinguishing between C:N and C/N.
    [CrossRef] [PubMed]
  7. P. F. Panter, Modulation, Noise, and Spectral Analysis (McGraw-Hill, 1965), Chap. 14.
  8. C. A. Hill, M. Harris, K. D. Ridley, J.-P. Cariou, and V. Jolivet, "Un lidar vibromètre à 1.5 μm en modes impulsionnel et cw," presented at OPTRO 2005, Paris, France, May 2005.
  9. R. J. A. Tough, D. Blacknell, and S. Quegan, "A statistical description of polarimetric and interferometric synthetic aperture radar data," Proc. R. Soc. London Ser. A 449, 567-589 (1995).
    [CrossRef]
  10. K. Miller and M. Rochwarger, "A covariance approach to spectral moment estimation," IEEE Trans. Inf. Theory 18, 588-596 (1972).
    [CrossRef]
  11. G. W. Lank, I. S. Reed, and G. E. Pollon, "A semicoherent detection and Doppler estimation statistic," IEEE Trans. Aerosp. Electron. Syst. 9, 151-165 (1973).
    [CrossRef]
  12. M. Ghogho, A. Swami, and T. S. Durrani, "Frequency estimation in the presence of Doppler spread: performance analysis," IEEE Trans. Signal Process. 49, 777-789 (2001).
    [CrossRef]
  13. B. J. Rye and R. M. Hardesty, "Discrete spectral peak estimation in incoherent backscatter heterodyne lidar, I: Spectral accumulation and the Cramer-Rao lower bound," IEEE Trans. Geosci. Remote Sens. 31, 16-27 (1993).
    [CrossRef]
  14. B. J. Rye and R. M. Hardesty, "Discrete spectral peak estimation in incoherent backscatter heterodyne lidar, II: Correlogram accumulation," IEEE Trans. Geosci. Remote Sens. 31, 28-35 (1993).
    [CrossRef]
  15. D. C. Rife and R. R. Boorstyn, "Single tone parameter estimation from discrete-time observations," IEEE Trans. Inf. Theory 20, 591-598 (1974).
    [CrossRef]
  16. D. G. Youmans, "Spectral estimation of Doppler spread vibrating targets using coherent ladar," Proc. SPIE 5412, 229-240 (2004).
    [CrossRef]

2004 (1)

D. G. Youmans, "Spectral estimation of Doppler spread vibrating targets using coherent ladar," Proc. SPIE 5412, 229-240 (2004).
[CrossRef]

2003 (1)

2001 (1)

M. Ghogho, A. Swami, and T. S. Durrani, "Frequency estimation in the presence of Doppler spread: performance analysis," IEEE Trans. Signal Process. 49, 777-789 (2001).
[CrossRef]

2000 (2)

K. D. Ridley and E. Jakeman, "Signal-to-noise analysis of FM demodulation in the presence of multiplicative and additive noise," Signal Process. 80, 1895-1907 (2000).
[CrossRef]

C. J. Karlsson, F. Å. A. Olsson, D. Letalick, and M. Harris, "All-fiber multifunction continuous-wave coherent laser radar at 1.55 μm for range, speed, vibration, and wind measurements," Appl. Opt. 39, 3716-3726 (2000).
[CrossRef]

1998 (1)

S. M. Hannon, J. A. L. 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]

1995 (2)

A. L. Kachelmyer and K. I. Schultz, "Laser vibration sensing," Lincoln Lab. J. 8, 3-28 (1995).

R. J. A. Tough, D. Blacknell, and S. Quegan, "A statistical description of polarimetric and interferometric synthetic aperture radar data," Proc. R. Soc. London Ser. A 449, 567-589 (1995).
[CrossRef]

1993 (2)

B. J. Rye and R. M. Hardesty, "Discrete spectral peak estimation in incoherent backscatter heterodyne lidar, I: Spectral accumulation and the Cramer-Rao lower bound," IEEE Trans. Geosci. Remote Sens. 31, 16-27 (1993).
[CrossRef]

B. J. Rye and R. M. Hardesty, "Discrete spectral peak estimation in incoherent backscatter heterodyne lidar, II: Correlogram accumulation," IEEE Trans. Geosci. Remote Sens. 31, 28-35 (1993).
[CrossRef]

1983 (1)

1974 (1)

D. C. Rife and R. R. Boorstyn, "Single tone parameter estimation from discrete-time observations," IEEE Trans. Inf. Theory 20, 591-598 (1974).
[CrossRef]

1973 (1)

G. W. Lank, I. S. Reed, and G. E. Pollon, "A semicoherent detection and Doppler estimation statistic," IEEE Trans. Aerosp. Electron. Syst. 9, 151-165 (1973).
[CrossRef]

1972 (1)

K. Miller and M. Rochwarger, "A covariance approach to spectral moment estimation," IEEE Trans. Inf. Theory 18, 588-596 (1972).
[CrossRef]

Blacknell, D.

R. J. A. Tough, D. Blacknell, and S. Quegan, "A statistical description of polarimetric and interferometric synthetic aperture radar data," Proc. R. Soc. London Ser. A 449, 567-589 (1995).
[CrossRef]

Boorstyn, R. R.

D. C. Rife and R. R. Boorstyn, "Single tone parameter estimation from discrete-time observations," IEEE Trans. Inf. Theory 20, 591-598 (1974).
[CrossRef]

Bruns, D.

S. M. Hannon, J. A. L. 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]

Cariou, J.-P.

C. A. Hill, M. Harris, K. D. Ridley, J.-P. Cariou, and V. Jolivet, "Un lidar vibromètre à 1.5 μm en modes impulsionnel et cw," presented at OPTRO 2005, Paris, France, May 2005.

Durrani, T. S.

M. Ghogho, A. Swami, and T. S. Durrani, "Frequency estimation in the presence of Doppler spread: performance analysis," IEEE Trans. Signal Process. 49, 777-789 (2001).
[CrossRef]

Foord, R.

Gatt, P.

S. M. Hannon, J. A. L. 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]

Ghogho, M.

M. Ghogho, A. Swami, and T. S. Durrani, "Frequency estimation in the presence of Doppler spread: performance analysis," IEEE Trans. Signal Process. 49, 777-789 (2001).
[CrossRef]

Hannon, S. M.

S. M. Hannon, J. A. L. 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]

Hardesty, R. M.

B. J. Rye and R. M. Hardesty, "Discrete spectral peak estimation in incoherent backscatter heterodyne lidar, II: Correlogram accumulation," IEEE Trans. Geosci. Remote Sens. 31, 28-35 (1993).
[CrossRef]

B. J. Rye and R. M. Hardesty, "Discrete spectral peak estimation in incoherent backscatter heterodyne lidar, I: Spectral accumulation and the Cramer-Rao lower bound," IEEE Trans. Geosci. Remote Sens. 31, 16-27 (1993).
[CrossRef]

Harris, M.

Henderson, S. W.

S. M. Hannon, J. A. L. 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]

Hill, C. A.

C. A. 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]

C. A. Hill, M. Harris, K. D. Ridley, J.-P. Cariou, and V. Jolivet, "Un lidar vibromètre à 1.5 μm en modes impulsionnel et cw," presented at OPTRO 2005, Paris, France, May 2005.

Jakeman, E.

C. A. 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]

K. D. Ridley and E. Jakeman, "Signal-to-noise analysis of FM demodulation in the presence of multiplicative and additive noise," Signal Process. 80, 1895-1907 (2000).
[CrossRef]

Jolivet, V.

C. A. Hill, M. Harris, K. D. Ridley, J.-P. Cariou, and V. Jolivet, "Un lidar vibromètre à 1.5 μm en modes impulsionnel et cw," presented at OPTRO 2005, Paris, France, May 2005.

Jones, R.

Kachelmyer, A. L.

A. L. Kachelmyer and K. I. Schultz, "Laser vibration sensing," Lincoln Lab. J. 8, 3-28 (1995).

Karlsson, C. J.

Lank, G. W.

G. W. Lank, I. S. Reed, and G. E. Pollon, "A semicoherent detection and Doppler estimation statistic," IEEE Trans. Aerosp. Electron. Syst. 9, 151-165 (1973).
[CrossRef]

Letalick, D.

Lutzmann, P.

Miller, K.

K. Miller and M. Rochwarger, "A covariance approach to spectral moment estimation," IEEE Trans. Inf. Theory 18, 588-596 (1972).
[CrossRef]

Olsson, F. Å. A.

Panter, P. F.

P. F. Panter, Modulation, Noise, and Spectral Analysis (McGraw-Hill, 1965), Chap. 14.

Pollon, G. E.

G. W. Lank, I. S. Reed, and G. E. Pollon, "A semicoherent detection and Doppler estimation statistic," IEEE Trans. Aerosp. Electron. Syst. 9, 151-165 (1973).
[CrossRef]

Quegan, S.

R. J. A. Tough, D. Blacknell, and S. Quegan, "A statistical description of polarimetric and interferometric synthetic aperture radar data," Proc. R. Soc. London Ser. A 449, 567-589 (1995).
[CrossRef]

Reed, I. S.

G. W. Lank, I. S. Reed, and G. E. Pollon, "A semicoherent detection and Doppler estimation statistic," IEEE Trans. Aerosp. Electron. Syst. 9, 151-165 (1973).
[CrossRef]

Ridley, K. D.

C. A. 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]

K. D. Ridley and E. Jakeman, "Signal-to-noise analysis of FM demodulation in the presence of multiplicative and additive noise," Signal Process. 80, 1895-1907 (2000).
[CrossRef]

C. A. Hill, M. Harris, K. D. Ridley, J.-P. Cariou, and V. Jolivet, "Un lidar vibromètre à 1.5 μm en modes impulsionnel et cw," presented at OPTRO 2005, Paris, France, May 2005.

Rife, D. C.

D. C. Rife and R. R. Boorstyn, "Single tone parameter estimation from discrete-time observations," IEEE Trans. Inf. Theory 20, 591-598 (1974).
[CrossRef]

Rochwarger, M.

K. Miller and M. Rochwarger, "A covariance approach to spectral moment estimation," IEEE Trans. Inf. Theory 18, 588-596 (1972).
[CrossRef]

Rye, B. J.

B. J. Rye and R. M. Hardesty, "Discrete spectral peak estimation in incoherent backscatter heterodyne lidar, I: Spectral accumulation and the Cramer-Rao lower bound," IEEE Trans. Geosci. Remote Sens. 31, 16-27 (1993).
[CrossRef]

B. J. Rye and R. M. Hardesty, "Discrete spectral peak estimation in incoherent backscatter heterodyne lidar, II: Correlogram accumulation," IEEE Trans. Geosci. Remote Sens. 31, 28-35 (1993).
[CrossRef]

Schultz, K. I.

A. L. Kachelmyer and K. I. Schultz, "Laser vibration sensing," Lincoln Lab. J. 8, 3-28 (1995).

Stoneman, R.

S. M. Hannon, J. A. L. 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. Swami, and T. S. Durrani, "Frequency estimation in the presence of Doppler spread: performance analysis," IEEE Trans. Signal Process. 49, 777-789 (2001).
[CrossRef]

Thomson, J. A. L.

S. M. Hannon, J. A. L. 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]

Tough, R. J. A.

R. J. A. Tough, D. Blacknell, and S. Quegan, "A statistical description of polarimetric and interferometric synthetic aperture radar data," Proc. R. Soc. London Ser. A 449, 567-589 (1995).
[CrossRef]

Vaughan, J. M.

Willetts, D. V.

Youmans, D. G.

D. G. Youmans, "Spectral estimation of Doppler spread vibrating targets using coherent ladar," Proc. SPIE 5412, 229-240 (2004).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Aerosp. Electron. Syst. (1)

G. W. Lank, I. S. Reed, and G. E. Pollon, "A semicoherent detection and Doppler estimation statistic," IEEE Trans. Aerosp. Electron. Syst. 9, 151-165 (1973).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

B. J. Rye and R. M. Hardesty, "Discrete spectral peak estimation in incoherent backscatter heterodyne lidar, I: Spectral accumulation and the Cramer-Rao lower bound," IEEE Trans. Geosci. Remote Sens. 31, 16-27 (1993).
[CrossRef]

B. J. Rye and R. M. Hardesty, "Discrete spectral peak estimation in incoherent backscatter heterodyne lidar, II: Correlogram accumulation," IEEE Trans. Geosci. Remote Sens. 31, 28-35 (1993).
[CrossRef]

IEEE Trans. Inf. Theory (2)

D. C. Rife and R. R. Boorstyn, "Single tone parameter estimation from discrete-time observations," IEEE Trans. Inf. Theory 20, 591-598 (1974).
[CrossRef]

K. Miller and M. Rochwarger, "A covariance approach to spectral moment estimation," IEEE Trans. Inf. Theory 18, 588-596 (1972).
[CrossRef]

IEEE Trans. Signal Process. (1)

M. Ghogho, A. Swami, and T. S. Durrani, "Frequency estimation in the presence of Doppler spread: performance analysis," IEEE Trans. Signal Process. 49, 777-789 (2001).
[CrossRef]

Lincoln Lab. J. (1)

A. L. Kachelmyer and K. I. Schultz, "Laser vibration sensing," Lincoln Lab. J. 8, 3-28 (1995).

Proc. R. Soc. London Ser. A (1)

R. J. A. Tough, D. Blacknell, and S. Quegan, "A statistical description of polarimetric and interferometric synthetic aperture radar data," Proc. R. Soc. London Ser. A 449, 567-589 (1995).
[CrossRef]

Proc. SPIE (2)

D. G. Youmans, "Spectral estimation of Doppler spread vibrating targets using coherent ladar," Proc. SPIE 5412, 229-240 (2004).
[CrossRef]

S. M. Hannon, J. A. L. 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]

Signal Process. (1)

K. D. Ridley and E. Jakeman, "Signal-to-noise analysis of FM demodulation in the presence of multiplicative and additive noise," Signal Process. 80, 1895-1907 (2000).
[CrossRef]

Other (2)

P. F. Panter, Modulation, Noise, and Spectral Analysis (McGraw-Hill, 1965), Chap. 14.

C. A. Hill, M. Harris, K. D. Ridley, J.-P. Cariou, and V. Jolivet, "Un lidar vibromètre à 1.5 μm en modes impulsionnel et cw," presented at OPTRO 2005, Paris, France, May 2005.

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Figures (12)

Fig. 1
Fig. 1

Pulse-pair format.

Fig. 2
Fig. 2

Schematic of laboratory dual-mode 1.5 μm lidar. OI = optical isolator; FPC = fiber polarization controller; AOM = acousto-optic modulator; R = receive channel; BPLO = backpropagated local oscillator (optical); GGS = ground-glass screen; LO = local oscillator (electrical 80 MHz signal driving both the AOM and the mixer); A∕D = analog-to-digital converter; PC = personal computer.

Fig. 3
Fig. 3

Filtered in-phase time series for one pulse-pair waveform. The output from the I port of the I∕Q mixer is low-pass-filtered in hardware, digitized with 8 bit resolution at 10 6 samples∕s, then low-pass-filtered in software. 600 filtered samples covering 600 μs are shown. The pulse duration is t p 20 μ s , and the pulse separation is T s 500 μ s . The pulse-pair repetition rate, 1∕T, can be varied to match the expected signal waveform characteristics.

Fig. 4
Fig. 4

Experimental pulsed versus cw comparison for narrowband FM ( f m = 185 Hz , β < 1 ) and speckle bandwidth B speck 75 Hz . Pulse-pair parameters are T 1 / 600   s , t p = 20 μ s , and T s = 500 μ s . The cw CNR is roughly 10.5 dB in 2   kHz bandwidth, and the pulsed CNR is roughly 13 dB in 50   kHz ; the average received powers are nearly equal. The two curves are spectral estimates derived from 7 s stretches of the estimated frequency d ϕ / d t . The signal at 185 Hz is clear in both modes. Its strength is nearly the same for both, but the average noise level is slightly higher for pulsed mode.

Fig. 5
Fig. 5

Experimental pulsed versus cw comparison for wideband FM ( f m = 30 H z , β 120 ) and B s p e c k 370 H z . Pulse-pair parameters are T 1 / 200   s , t p = 20 μs , and T s = 100 μs . The cw CNR is roughly 4 dB in 10 kHz bandwidth, and the pulsed CNR is roughly 10.5 dB in 50 kHz ; the average received powers are nearly equal.

Fig. 6
Fig. 6

Cochannel interference: pulsed versus cw spectral estimates when two targets with nearly equal modulation frequencies ( 80 Hz ) are simultaneously illuminated. The cw data allow the artificial quantity d ϕ / d t to be found unambiguously; all the spectral peaks are at multiples of 80 Hz . The pulsed mode shows aliasing and spurious spectral peaks. The pulsed estimate has been vertically shifted by 10 4 for clarity. T 1 / 1000   s , t p 20 μs and T s = 100 μs . The CNRs for the two individual targets are roughly equal. Equal average powers for cw and pulsed modes are not assured here.

Fig. 7
Fig. 7

PDF of phase differences for CNR p = 10 , ψ = 2.5 rad , slow speckle limit.

Fig. 8
Fig. 8

Bias as a function of ψ for CNR p of 1, 4, and 16.

Fig. 9
Fig. 9

Root-mean-square deviation of phase shift measurement, as a function of ψ, for CNR p of 1, 4, and 32.

Fig. 10
Fig. 10

Histograms of frequency estimates from simulations of phase differencing followed by averaging over 100 samples, compared with Eq. (5) (solid curves).

Fig. 11
Fig. 11

Histograms of frequency estimates from simulations using the autocorrelation technique averaging over 100 samples, compared with Eq. (5) (solid curves).

Fig. 12
Fig. 12

Comparison of MATLAB simulated pulsed and cw results for the parameters of Fig. 5. The autocorrelation demodulation uses a block length of 100 samples and a delay of 3 samples. The plot is extended to 100 Hz to show the weak feature at 3 f m = 90 Hz ; this harmonic distortion is attributable to phase ambiguities, and rapidly worsens for delays longer than 3 samples. The peaks at f m = 30 Hz are normalized to 0 dB for clarity.

Equations (10)

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CNR c w = P η λ h c B c w ,
CNR p = P T η λ 2 h c B p t p ,
CNR p CNR c w = T 2 t p B cw B p .
E ( t ) = H ( t ) A ( t ) exp [ i β   cos ( 2 π f m t ) ] + N ( t ) .
P ( Δ ϕ ) = 1 k 0 2 2 π ( 1 α 2 ) 3 / 2 [ α sin 1 α + π α 2 + 1 α 2 ] .
Δ ϕ = k 0   sin   ψ 1 k 0 2 cos 2 ψ cos 1 ( k 0   cos   ψ ) .
δ = ( Δ ϕ ψ 1 ) 2 ,
Δ ϕ 2 = π 2 3 π sin 1 ( k 0   cos   ψ ) + [ sin 1 ( k 0   cos   ψ ) ] 2 1 2 L i 2 ( k 0 2 ) ,
f ^ a c = 1 2 π T s   arg ( S j S j + 1 * ) .
CNR = x 2 + y 2 x N 2 + y N 2 1 ,

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