Abstract

We report laboratory target vibration measurements that use an easily aligned and adjusted fiber-based 1.5-μm heterodyne lidar. The targets are simple spherically curved retroreflectors with well-controlled vibration frequencies and amplitudes. A rotating ground-glass screen creates Gaussian speckle. We wish to understand the modulated and fast-fading lidar returns seen from real targets. We frequency demodulated the recorded laboratory data by phase differencing to provide estimates of dϕ/dt, where ϕ is the phase of the received carrier-plus-noise phasor. Experimental results for signal strength and signal-to-noise ratio, for specific target modulation parameters, agree well with our recently developed dϕ/dt correlation-function theory.

© 2003 Optical Society of America

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References

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  2. C. J. Karlsson, F. Å. A. Olsson, D. Letalick, 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).
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    [CrossRef]
  5. K. D. Ridley, E. Jakeman, “Signal-to-noise analysis of FM demodulation in the presence of multiplicative and additive noise,” Signal Process. 80, 1895–1907 (2000).
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    [CrossRef]
  9. D. N. Barr, “Speckle effects on laser vibration sensor noise,” (U.S. Army Night Vision Laboratory, Ft. Belvoir, Va., 1985).
  10. H. Taub, D. L. Schilling, Principles of Communication Systems (McGraw-Hill, New York, 1971).
  11. M. S. Corrington, “Frequency modulation caused by common and adjacent channel interference,” RCA Rev. 7, 552–560 (1946).
  12. O. J. Dussarrat, D. F. Clark, T. J. Moir, “A new demodulation process to reduce cochannel interference for a laser vibrometer sensing system,” in Third International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE3411, 2–13 (1998).
    [CrossRef]
  13. S. O. Rice, “Noise in FM receivers,” in Proceedings of the Symposium on Time Series Analysis, M. Rosenblatt, ed. (Wiley, New York, 1963), pp. 395–414.
  14. J. F. Fontanella, D. E. Roberts, D. R. Shoup, “Wavelength selection for long range laser vibration sensing,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 107–124 (1998).
    [CrossRef]
  15. M. A. Jarzembski, V. Srivastava, “Spectral analysis of vibrational harmonic motion by use of a continuous-wave CO2 Doppler lidar,” J. Opt. Soc. Am. A 17, 1840–1845 (2000).
    [CrossRef]

2001

2000

1999

K. D. Ridley, E. Jakeman, “FM demodulation in the presence of multiplicative and additive noise,” Inverse Probl. 15, 989–1002 (1999).
[CrossRef]

1995

A. L. Kachelmyer, K. I. Schultz, “Laser vibration sensing,” Lincoln Lab. J. 8, 3–28 (1995).

1994

1946

M. S. Corrington, “Frequency modulation caused by common and adjacent channel interference,” RCA Rev. 7, 552–560 (1946).

Barr, D. N.

D. N. Barr, “Speckle effects on laser vibration sensor noise,” (U.S. Army Night Vision Laboratory, Ft. Belvoir, Va., 1985).

Clark, D. F.

O. J. Dussarrat, D. F. Clark, T. J. Moir, “A new demodulation process to reduce cochannel interference for a laser vibrometer sensing system,” in Third International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE3411, 2–13 (1998).
[CrossRef]

Constant, G.

Corrington, M. S.

M. S. Corrington, “Frequency modulation caused by common and adjacent channel interference,” RCA Rev. 7, 552–560 (1946).

Dussarrat, O. J.

O. J. Dussarrat, D. F. Clark, T. J. Moir, “A new demodulation process to reduce cochannel interference for a laser vibrometer sensing system,” in Third International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE3411, 2–13 (1998).
[CrossRef]

Eng, R. S.

R. S. Eng, C. Freed, C. L. Summers, “Dynamic speckle bandwidth and characterization of vibration frequency and amplitude using a CO2 laser vibrometer,” in Applied Laser Radar Technology, G. W. Kamerman, W. E. Keicher, eds., Proc. SPIE1936, 120–136 (1993).
[CrossRef]

Fontanella, J. F.

J. F. Fontanella, D. E. Roberts, D. R. Shoup, “Wavelength selection for long range laser vibration sensing,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 107–124 (1998).
[CrossRef]

Freed, C.

R. S. Eng, C. Freed, C. L. Summers, “Dynamic speckle bandwidth and characterization of vibration frequency and amplitude using a CO2 laser vibrometer,” in Applied Laser Radar Technology, G. W. Kamerman, W. E. Keicher, eds., Proc. SPIE1936, 120–136 (1993).
[CrossRef]

Harris, M.

Hill, C. A.

Jakeman, E.

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

K. D. Ridley, E. Jakeman, “FM demodulation in the presence of multiplicative and additive noise,” Inverse Probl. 15, 989–1002 (1999).
[CrossRef]

Jarzembski, M. A.

Kachelmyer, A. L.

A. L. Kachelmyer, K. I. Schultz, “Laser vibration sensing,” Lincoln Lab. J. 8, 3–28 (1995).

Karlsson, C. J.

Letalick, D.

Moir, T. J.

O. J. Dussarrat, D. F. Clark, T. J. Moir, “A new demodulation process to reduce cochannel interference for a laser vibrometer sensing system,” in Third International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE3411, 2–13 (1998).
[CrossRef]

Olsson, F. Å. A.

Panter, P. F.

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

Pearson, G. N.

Rice, S. O.

S. O. Rice, “Noise in FM receivers,” in Proceedings of the Symposium on Time Series Analysis, M. Rosenblatt, ed. (Wiley, New York, 1963), pp. 395–414.

Ridley, K. D.

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

K. D. Ridley, E. Jakeman, “FM demodulation in the presence of multiplicative and additive noise,” Inverse Probl. 15, 989–1002 (1999).
[CrossRef]

Roberts, D. E.

J. F. Fontanella, D. E. Roberts, D. R. Shoup, “Wavelength selection for long range laser vibration sensing,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 107–124 (1998).
[CrossRef]

Schilling, D. L.

H. Taub, D. L. Schilling, Principles of Communication Systems (McGraw-Hill, New York, 1971).

Schultz, K. I.

A. L. Kachelmyer, K. I. Schultz, “Laser vibration sensing,” Lincoln Lab. J. 8, 3–28 (1995).

Shoup, D. R.

J. F. Fontanella, D. E. Roberts, D. R. Shoup, “Wavelength selection for long range laser vibration sensing,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 107–124 (1998).
[CrossRef]

Srivastava, V.

Summers, C. L.

R. S. Eng, C. Freed, C. L. Summers, “Dynamic speckle bandwidth and characterization of vibration frequency and amplitude using a CO2 laser vibrometer,” in Applied Laser Radar Technology, G. W. Kamerman, W. E. Keicher, eds., Proc. SPIE1936, 120–136 (1993).
[CrossRef]

Taub, H.

H. Taub, D. L. Schilling, Principles of Communication Systems (McGraw-Hill, New York, 1971).

Vaughan, J. M.

Ward, C.

Appl. Opt.

Inverse Probl.

K. D. Ridley, E. Jakeman, “FM demodulation in the presence of multiplicative and additive noise,” Inverse Probl. 15, 989–1002 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Lincoln Lab. J.

A. L. Kachelmyer, K. I. Schultz, “Laser vibration sensing,” Lincoln Lab. J. 8, 3–28 (1995).

RCA Rev.

M. S. Corrington, “Frequency modulation caused by common and adjacent channel interference,” RCA Rev. 7, 552–560 (1946).

Signal Process.

K. D. Ridley, 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

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

R. S. Eng, C. Freed, C. L. Summers, “Dynamic speckle bandwidth and characterization of vibration frequency and amplitude using a CO2 laser vibrometer,” in Applied Laser Radar Technology, G. W. Kamerman, W. E. Keicher, eds., Proc. SPIE1936, 120–136 (1993).
[CrossRef]

D. N. Barr, “Speckle effects on laser vibration sensor noise,” (U.S. Army Night Vision Laboratory, Ft. Belvoir, Va., 1985).

H. Taub, D. L. Schilling, Principles of Communication Systems (McGraw-Hill, New York, 1971).

O. J. Dussarrat, D. F. Clark, T. J. Moir, “A new demodulation process to reduce cochannel interference for a laser vibrometer sensing system,” in Third International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE3411, 2–13 (1998).
[CrossRef]

S. O. Rice, “Noise in FM receivers,” in Proceedings of the Symposium on Time Series Analysis, M. Rosenblatt, ed. (Wiley, New York, 1963), pp. 395–414.

J. F. Fontanella, D. E. Roberts, D. R. Shoup, “Wavelength selection for long range laser vibration sensing,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 107–124 (1998).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic of our experiment with a 1.5-μm lidar. OI, optical isolator; FC, fiber coupler; GGS, ground-glass screen; BS, beam splitter; T1 and T2, two specular vibrating targets; BPLO, backpropagated local oscillator; R, receive aperture; FPC, fiber polarization controller; A/D, analog-to-digital.

Fig. 2
Fig. 2

Example of a demodulator output (dϕ/dt) spectral estimate, with a low-frequency noise level and a single modulation tone at 70 Hz. There is one specular target, and the ground-glass screen speckle decorrelation time6 is ∼2.5 ms. There appears to be at least one spurious signal (around 7 Hz), and this would be discounted when we estimate the noise level by averaging over several bins. The CNR and the noise levels are estimated after a software IF filter with an approximately rectangular profile and ∼2-kHz width.

Fig. 3
Fig. 3

Low-frequency noise level after frequency demodulation, expressed as (radians per second)2 per hertz bandwidth, or rad2 s-1, as a function of 〈CNR〉. As in Fig. 2 there is one specular target, and the ground-glass screen speckle decorrelation time6 is ∼2.5 ms. The solid curve is the prediction from Eq. (4).

Fig. 4
Fig. 4

Demodulator output (dϕ/dt) spectral estimates for a single specular target, in the presence of Gaussian speckle, for two values of 〈CNR〉. When 〈CNR〉 falls, the signal falls (signal suppression) and the noise increases.

Fig. 5
Fig. 5

Signal suppression factors for a tone signal observed after frequency demodulation with a single specular target vibrating at 70 Hz. The experimental arrangement is the same as for Fig. 2. Estimates of signal strength are made when experimental data are postprocessed for different 〈CNR〉 values with a 2-kHz IF bandwidth. Theory in the absence of speckle3 is [1 - exp(-CNR)]2. Theory in the presence of slow speckle5 is 2〈CNR〉2/[(1 + 〈CNR〉)(1 + 2〈CNR〉)]. Theory in the presence of fast speckle5,14 is (1 + 〈CNR〉-1)-2.

Fig. 6
Fig. 6

Demodulator output (dϕ/dt) spectral estimate for cochannel interference in the absence of dynamic speckle. There are two specular targets, separately vibrating at 79 and 130 Hz, each with a moderate β value around 3. The 130-Hz peak is clear, but the 79-Hz peak is lower than many of the cross terms. Compare with Fig. 7. (The vertical scale is the same as for Fig. 7, showing the relative spectral density in decibels. The curve thickness used for the plotting obscures the finest frequency detail.)

Fig. 7
Fig. 7

Demodulator output (dϕ/dt) spectral estimate for cochannel interference in the presence of dynamic speckle. Same as for Fig. 6 except that the ground-glass screen is rotating. Peaks at the two fundamental frequencies 79 and 130 Hz are now clear, although the average noise level is much higher.

Fig. 8
Fig. 8

Variation of the two signal strengths for cochannel interferers, as their relative carrier strength is varied by use of neutral-density filters between the beam splitter and the targets (see Fig. 1). The solid and dashed curves are from Eq. (9). The ground-glass screen is rotating, and the speckle modulations of the two carriers are largely independent.

Equations (9)

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SNR3/2β2Ec2/2ηfm.
SNR=BIF/2Δf2/fm2BresCNR
βmin2=4πAmin/λ2=2Bres/BIF/CNR=4ηBres/Ec2.
S0=3.27Bspeck1+1.1/CNR+γBIF1+1.1CNR,
S0=2 0ρ˙21-ρ2dt
Iϕ˙=X1Y˙1+X2Y˙2-Y1X˙1-Y2X˙2+X1Y˙2-Y1X˙2+X2Y˙1-Y2X˙1cosψ1-ψ2-X1X˙2+Y1Y˙2-X2X˙1-Y2Y˙1sinψ1-ψ2+12 Iψ˙1+ψ˙2+12I1-I2ψ˙1-ψ˙2.
Sω14ψ˙˜12+ψ˙˜221+I1-I2Ispeckle2+2ψ˙˜12-ψ˙˜22I1-I2Ispeckle+broadband noise.
1Iphase=1I1-I2, I1>I2=1I2-I1, I2>I1.
Sωψ˙˜121+η2+η2ψ˙˜221+η2.

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