Abstract

A laboratory system has demonstrated the measurement of three degrees of vibrational freedom simultaneously through heterodyne speckle imaging. The random interference pattern generated by the illumination of a rough surface with coherent light can be exploited to extract information about the surface motion. The optical speckle pattern is heterodyne mixed with a coherent reference. The recorded optical data is then processed to extract three dimensions of surface motion. Axial velocity is measured by demodulating the received time-varying intensity of high amplitude pixels. Tilt, a gradient of surface displacement, is calculated by measuring speckle translation following extraction of the speckle pattern from the mixed signal. This paper discusses the laboratory sensor concept, signal processing, and experimental results compared with numeric simulations.

© 2016 Optical Society of America

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References

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  1. R. Jones and C. Wykes, Holographic and Speckle Interferometry, Vol. 6 (Cambridge University, 1989).
    [Crossref]
  2. P. Hariharan, Basics of Interferometry (Academic, 2010).
  3. P. Jacquot and J. M. Fournier, Interferometry in Speckle Light: Theory and Applications (Springer Science and Business Media, 2012).
  4. M. L. Prado, N. Bolognini, and M. Tebaldi, “Analysis of tilt by modulated speckles generated with a double aperture pupil mask,” Opt. Commun. 338, 473–478 (2015).
    [Crossref]
  5. B. Redding, A. Davis, C. Kirkendall, and A. Dandridge, “Measuring vibrational motion in the presence of speckle using off-axis holography,” Appl. Opt. 55(6), 1406–1411 (2016).
    [Crossref] [PubMed]
  6. T. W. Du Bosq and E. Repasi, “Detector integration time dependent atmospheric turbulence imaging simulation,” Proc. SPIE 9452, 94520B (2015).
    [Crossref]
  7. P. Reu, D. P. Rohe, and L. D. Jacobs, “Comparison of DIC and LDV for practical vibration and modal measurements,” Mech. Syst. Signal Pr. (in press).
  8. B. Weekes and D. Ewins, “Multi-frequency, 3D ODS measurement by continuous scan laser Doppler vibrometry,” Mech. Syst. Signal Pr. 58, 325–339 (2015).
    [Crossref]
  9. J. M. Reyes and P. Avitabile, “Use of 3D scanning laser vibrometer for full field strain measurements,” in Experimental Techniques, Rotating Machinery, and Acoustics, Vol. 8 (Springer International, 2015), pp. 197–209.
  10. H. Yan, H. Z. Duan, L. T Li, Y. R. Liang, J. Luo, and H. C. Yeh, “A dual-heterodyne laser interferometer for simultaneous measurement of linear and angular displacements,” Rev. Sci. Instrum. 86, 123102 (2015).
    [Crossref]
  11. A. Pouya and M. Alireza, “Laser Doppler interferometry (LDI) to obtain full stiffness tensor: a case study on a deformation zone in Sweden,” in ASEG Extended Abstracts, (2015), pp. 1–4.
  12. S. Pasquet, L. Bodet, Q. Vitale, F. Rejiba, R. Gurin, R. Mourgues, and V. Tournat, “Laser-Doppler acoustic probing of granular media with varying water levels,” Phys. Procedia 70, 799–802 (2015).
    [Crossref]
  13. J. G. Chen, R. W. Haupt, and O. Buyukozturk, “Operational and defect parameters concerning the acoustic-laser vibrometry method for FRP-reinforced concrete,” NDTE Int. 71, 43–53 (2015).
    [Crossref]
  14. J. Bencteux, “Holographic laser Doppler imaging of pulsatile blood flow,” J. Biomed. Opt. 20, 066006 (2015).
    [Crossref] [PubMed]
  15. F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging Sci. Techn. 59, 10402 (2015).
    [Crossref]
  16. X. Lai and H. Torp, “Interpolation methods for time-delay estimation using cross- correlation method for blood velocity measurement,” IEEE T. Ultrason. Ferr. 46(2), 277–290 (1999).
    [Crossref]
  17. J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).
  18. H. J. Tiziani, “Analysis of mechanical oscillations by speckling,” Appl. Opt. 11(12), 2911–2917 (1972).
    [Crossref] [PubMed]
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    [Crossref]
  20. L. F. Rojas-Ochoa, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A 21, (9)1799–1804 (2004).
    [Crossref]
  21. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).
  22. B. K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with dc offset compensation in quadrature doppler radar receiver systems,” IEEE T. Microw. Theory 55(5), 1073–1079 (2007).
    [Crossref]
  23. G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282(18), 3693–3700 (2009).
    [Crossref]
  24. J. C. Dainty, Laser Speckle and Related Phenomena, Topics in Applied Physics, Vol. 9 (Springer-Verlag, 1975).
    [Crossref]

2016 (1)

2015 (8)

T. W. Du Bosq and E. Repasi, “Detector integration time dependent atmospheric turbulence imaging simulation,” Proc. SPIE 9452, 94520B (2015).
[Crossref]

B. Weekes and D. Ewins, “Multi-frequency, 3D ODS measurement by continuous scan laser Doppler vibrometry,” Mech. Syst. Signal Pr. 58, 325–339 (2015).
[Crossref]

H. Yan, H. Z. Duan, L. T Li, Y. R. Liang, J. Luo, and H. C. Yeh, “A dual-heterodyne laser interferometer for simultaneous measurement of linear and angular displacements,” Rev. Sci. Instrum. 86, 123102 (2015).
[Crossref]

S. Pasquet, L. Bodet, Q. Vitale, F. Rejiba, R. Gurin, R. Mourgues, and V. Tournat, “Laser-Doppler acoustic probing of granular media with varying water levels,” Phys. Procedia 70, 799–802 (2015).
[Crossref]

J. G. Chen, R. W. Haupt, and O. Buyukozturk, “Operational and defect parameters concerning the acoustic-laser vibrometry method for FRP-reinforced concrete,” NDTE Int. 71, 43–53 (2015).
[Crossref]

J. Bencteux, “Holographic laser Doppler imaging of pulsatile blood flow,” J. Biomed. Opt. 20, 066006 (2015).
[Crossref] [PubMed]

F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging Sci. Techn. 59, 10402 (2015).
[Crossref]

M. L. Prado, N. Bolognini, and M. Tebaldi, “Analysis of tilt by modulated speckles generated with a double aperture pupil mask,” Opt. Commun. 338, 473–478 (2015).
[Crossref]

2009 (1)

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282(18), 3693–3700 (2009).
[Crossref]

2007 (1)

B. K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with dc offset compensation in quadrature doppler radar receiver systems,” IEEE T. Microw. Theory 55(5), 1073–1079 (2007).
[Crossref]

2004 (1)

1999 (1)

X. Lai and H. Torp, “Interpolation methods for time-delay estimation using cross- correlation method for blood velocity measurement,” IEEE T. Ultrason. Ferr. 46(2), 277–290 (1999).
[Crossref]

1987 (1)

1972 (1)

Alireza, M.

A. Pouya and M. Alireza, “Laser Doppler interferometry (LDI) to obtain full stiffness tensor: a case study on a deformation zone in Sweden,” in ASEG Extended Abstracts, (2015), pp. 1–4.

Arizaga, R.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282(18), 3693–3700 (2009).
[Crossref]

Avitabile, P.

J. M. Reyes and P. Avitabile, “Use of 3D scanning laser vibrometer for full field strain measurements,” in Experimental Techniques, Rotating Machinery, and Acoustics, Vol. 8 (Springer International, 2015), pp. 197–209.

Bencteux, J.

J. Bencteux, “Holographic laser Doppler imaging of pulsatile blood flow,” J. Biomed. Opt. 20, 066006 (2015).
[Crossref] [PubMed]

Bodet, L.

S. Pasquet, L. Bodet, Q. Vitale, F. Rejiba, R. Gurin, R. Mourgues, and V. Tournat, “Laser-Doppler acoustic probing of granular media with varying water levels,” Phys. Procedia 70, 799–802 (2015).
[Crossref]

Bolognini, N.

M. L. Prado, N. Bolognini, and M. Tebaldi, “Analysis of tilt by modulated speckles generated with a double aperture pupil mask,” Opt. Commun. 338, 473–478 (2015).
[Crossref]

Boric-Lubecke, O.

B. K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with dc offset compensation in quadrature doppler radar receiver systems,” IEEE T. Microw. Theory 55(5), 1073–1079 (2007).
[Crossref]

Buyukozturk, O.

J. G. Chen, R. W. Haupt, and O. Buyukozturk, “Operational and defect parameters concerning the acoustic-laser vibrometry method for FRP-reinforced concrete,” NDTE Int. 71, 43–53 (2015).
[Crossref]

Chen, J. G.

J. G. Chen, R. W. Haupt, and O. Buyukozturk, “Operational and defect parameters concerning the acoustic-laser vibrometry method for FRP-reinforced concrete,” NDTE Int. 71, 43–53 (2015).
[Crossref]

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena, Topics in Applied Physics, Vol. 9 (Springer-Verlag, 1975).
[Crossref]

Dandridge, A.

Davis, A.

Du Bosq, T. W.

T. W. Du Bosq and E. Repasi, “Detector integration time dependent atmospheric turbulence imaging simulation,” Proc. SPIE 9452, 94520B (2015).
[Crossref]

Duan, H. Z.

H. Yan, H. Z. Duan, L. T Li, Y. R. Liang, J. Luo, and H. C. Yeh, “A dual-heterodyne laser interferometer for simultaneous measurement of linear and angular displacements,” Rev. Sci. Instrum. 86, 123102 (2015).
[Crossref]

Elz, D.

F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging Sci. Techn. 59, 10402 (2015).
[Crossref]

Ewins, D.

B. Weekes and D. Ewins, “Multi-frequency, 3D ODS measurement by continuous scan laser Doppler vibrometry,” Mech. Syst. Signal Pr. 58, 325–339 (2015).
[Crossref]

Fournier, J. M.

P. Jacquot and J. M. Fournier, Interferometry in Speckle Light: Theory and Applications (Springer Science and Business Media, 2012).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).

Gurin, R.

S. Pasquet, L. Bodet, Q. Vitale, F. Rejiba, R. Gurin, R. Mourgues, and V. Tournat, “Laser-Doppler acoustic probing of granular media with varying water levels,” Phys. Procedia 70, 799–802 (2015).
[Crossref]

Hariharan, P.

P. Hariharan, Basics of Interferometry (Academic, 2010).

Haupt, R. W.

J. G. Chen, R. W. Haupt, and O. Buyukozturk, “Operational and defect parameters concerning the acoustic-laser vibrometry method for FRP-reinforced concrete,” NDTE Int. 71, 43–53 (2015).
[Crossref]

Jacobs, L. D.

P. Reu, D. P. Rohe, and L. D. Jacobs, “Comparison of DIC and LDV for practical vibration and modal measurements,” Mech. Syst. Signal Pr. (in press).

Jacquot, P.

P. Jacquot and J. M. Fournier, Interferometry in Speckle Light: Theory and Applications (Springer Science and Business Media, 2012).

Jones, R.

R. Jones and C. Wykes, Holographic and Speckle Interferometry, Vol. 6 (Cambridge University, 1989).
[Crossref]

Kirkendall, C.

Lacoste, D.

Lai, X.

X. Lai and H. Torp, “Interpolation methods for time-delay estimation using cross- correlation method for blood velocity measurement,” IEEE T. Ultrason. Ferr. 46(2), 277–290 (1999).
[Crossref]

Lenke, R.

Li, L. T

H. Yan, H. Z. Duan, L. T Li, Y. R. Liang, J. Luo, and H. C. Yeh, “A dual-heterodyne laser interferometer for simultaneous measurement of linear and angular displacements,” Rev. Sci. Instrum. 86, 123102 (2015).
[Crossref]

Liang, Y. R.

H. Yan, H. Z. Duan, L. T Li, Y. R. Liang, J. Luo, and H. C. Yeh, “A dual-heterodyne laser interferometer for simultaneous measurement of linear and angular displacements,” Rev. Sci. Instrum. 86, 123102 (2015).
[Crossref]

Lubecke, V. M.

B. K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with dc offset compensation in quadrature doppler radar receiver systems,” IEEE T. Microw. Theory 55(5), 1073–1079 (2007).
[Crossref]

Luo, J.

H. Yan, H. Z. Duan, L. T Li, Y. R. Liang, J. Luo, and H. C. Yeh, “A dual-heterodyne laser interferometer for simultaneous measurement of linear and angular displacements,” Rev. Sci. Instrum. 86, 123102 (2015).
[Crossref]

Mendez, E.

Mourgues, R.

S. Pasquet, L. Bodet, Q. Vitale, F. Rejiba, R. Gurin, R. Mourgues, and V. Tournat, “Laser-Doppler acoustic probing of granular media with varying water levels,” Phys. Procedia 70, 799–802 (2015).
[Crossref]

ODonnell, K.

Park, B. K.

B. K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with dc offset compensation in quadrature doppler radar receiver systems,” IEEE T. Microw. Theory 55(5), 1073–1079 (2007).
[Crossref]

Pasquet, S.

S. Pasquet, L. Bodet, Q. Vitale, F. Rejiba, R. Gurin, R. Mourgues, and V. Tournat, “Laser-Doppler acoustic probing of granular media with varying water levels,” Phys. Procedia 70, 799–802 (2015).
[Crossref]

Pouya, A.

A. Pouya and M. Alireza, “Laser Doppler interferometry (LDI) to obtain full stiffness tensor: a case study on a deformation zone in Sweden,” in ASEG Extended Abstracts, (2015), pp. 1–4.

Prado, M. L.

M. L. Prado, N. Bolognini, and M. Tebaldi, “Analysis of tilt by modulated speckles generated with a double aperture pupil mask,” Opt. Commun. 338, 473–478 (2015).
[Crossref]

Rabal, H.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282(18), 3693–3700 (2009).
[Crossref]

Redding, B.

Rejiba, F.

S. Pasquet, L. Bodet, Q. Vitale, F. Rejiba, R. Gurin, R. Mourgues, and V. Tournat, “Laser-Doppler acoustic probing of granular media with varying water levels,” Phys. Procedia 70, 799–802 (2015).
[Crossref]

Repasi, E.

T. W. Du Bosq and E. Repasi, “Detector integration time dependent atmospheric turbulence imaging simulation,” Proc. SPIE 9452, 94520B (2015).
[Crossref]

Reu, P.

P. Reu, D. P. Rohe, and L. D. Jacobs, “Comparison of DIC and LDV for practical vibration and modal measurements,” Mech. Syst. Signal Pr. (in press).

Reyes, J. M.

J. M. Reyes and P. Avitabile, “Use of 3D scanning laser vibrometer for full field strain measurements,” in Experimental Techniques, Rotating Machinery, and Acoustics, Vol. 8 (Springer International, 2015), pp. 197–209.

Rohe, D. P.

P. Reu, D. P. Rohe, and L. D. Jacobs, “Comparison of DIC and LDV for practical vibration and modal measurements,” Mech. Syst. Signal Pr. (in press).

Rojas-Ochoa, L. F.

Scheffold, F.

Schmidt, M.

F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging Sci. Techn. 59, 10402 (2015).
[Crossref]

Schurtenberger, P.

Sendra, G.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282(18), 3693–3700 (2009).
[Crossref]

Tebaldi, M.

M. L. Prado, N. Bolognini, and M. Tebaldi, “Analysis of tilt by modulated speckles generated with a double aperture pupil mask,” Opt. Commun. 338, 473–478 (2015).
[Crossref]

Tenner, F.

F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging Sci. Techn. 59, 10402 (2015).
[Crossref]

Tiziani, H. J.

Torp, H.

X. Lai and H. Torp, “Interpolation methods for time-delay estimation using cross- correlation method for blood velocity measurement,” IEEE T. Ultrason. Ferr. 46(2), 277–290 (1999).
[Crossref]

Tournat, V.

S. Pasquet, L. Bodet, Q. Vitale, F. Rejiba, R. Gurin, R. Mourgues, and V. Tournat, “Laser-Doppler acoustic probing of granular media with varying water levels,” Phys. Procedia 70, 799–802 (2015).
[Crossref]

Trivi, M.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282(18), 3693–3700 (2009).
[Crossref]

Vitale, Q.

S. Pasquet, L. Bodet, Q. Vitale, F. Rejiba, R. Gurin, R. Mourgues, and V. Tournat, “Laser-Doppler acoustic probing of granular media with varying water levels,” Phys. Procedia 70, 799–802 (2015).
[Crossref]

Weekes, B.

B. Weekes and D. Ewins, “Multi-frequency, 3D ODS measurement by continuous scan laser Doppler vibrometry,” Mech. Syst. Signal Pr. 58, 325–339 (2015).
[Crossref]

Wykes, C.

R. Jones and C. Wykes, Holographic and Speckle Interferometry, Vol. 6 (Cambridge University, 1989).
[Crossref]

Yan, H.

H. Yan, H. Z. Duan, L. T Li, Y. R. Liang, J. Luo, and H. C. Yeh, “A dual-heterodyne laser interferometer for simultaneous measurement of linear and angular displacements,” Rev. Sci. Instrum. 86, 123102 (2015).
[Crossref]

Yeh, H. C.

H. Yan, H. Z. Duan, L. T Li, Y. R. Liang, J. Luo, and H. C. Yeh, “A dual-heterodyne laser interferometer for simultaneous measurement of linear and angular displacements,” Rev. Sci. Instrum. 86, 123102 (2015).
[Crossref]

Zalevsky, Z.

F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging Sci. Techn. 59, 10402 (2015).
[Crossref]

Appl. Opt. (2)

IEEE T. Microw. Theory (1)

B. K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with dc offset compensation in quadrature doppler radar receiver systems,” IEEE T. Microw. Theory 55(5), 1073–1079 (2007).
[Crossref]

IEEE T. Ultrason. Ferr. (1)

X. Lai and H. Torp, “Interpolation methods for time-delay estimation using cross- correlation method for blood velocity measurement,” IEEE T. Ultrason. Ferr. 46(2), 277–290 (1999).
[Crossref]

J. Biomed. Opt. (1)

J. Bencteux, “Holographic laser Doppler imaging of pulsatile blood flow,” J. Biomed. Opt. 20, 066006 (2015).
[Crossref] [PubMed]

J. Imaging Sci. Techn. (1)

F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging Sci. Techn. 59, 10402 (2015).
[Crossref]

J. Opt. Soc. Am. A (2)

Mech. Syst. Signal Pr. (1)

B. Weekes and D. Ewins, “Multi-frequency, 3D ODS measurement by continuous scan laser Doppler vibrometry,” Mech. Syst. Signal Pr. 58, 325–339 (2015).
[Crossref]

NDTE Int. (1)

J. G. Chen, R. W. Haupt, and O. Buyukozturk, “Operational and defect parameters concerning the acoustic-laser vibrometry method for FRP-reinforced concrete,” NDTE Int. 71, 43–53 (2015).
[Crossref]

Opt. Commun. (2)

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282(18), 3693–3700 (2009).
[Crossref]

M. L. Prado, N. Bolognini, and M. Tebaldi, “Analysis of tilt by modulated speckles generated with a double aperture pupil mask,” Opt. Commun. 338, 473–478 (2015).
[Crossref]

Phys. Procedia (1)

S. Pasquet, L. Bodet, Q. Vitale, F. Rejiba, R. Gurin, R. Mourgues, and V. Tournat, “Laser-Doppler acoustic probing of granular media with varying water levels,” Phys. Procedia 70, 799–802 (2015).
[Crossref]

Proc. SPIE (1)

T. W. Du Bosq and E. Repasi, “Detector integration time dependent atmospheric turbulence imaging simulation,” Proc. SPIE 9452, 94520B (2015).
[Crossref]

Rev. Sci. Instrum. (1)

H. Yan, H. Z. Duan, L. T Li, Y. R. Liang, J. Luo, and H. C. Yeh, “A dual-heterodyne laser interferometer for simultaneous measurement of linear and angular displacements,” Rev. Sci. Instrum. 86, 123102 (2015).
[Crossref]

Other (9)

A. Pouya and M. Alireza, “Laser Doppler interferometry (LDI) to obtain full stiffness tensor: a case study on a deformation zone in Sweden,” in ASEG Extended Abstracts, (2015), pp. 1–4.

J. M. Reyes and P. Avitabile, “Use of 3D scanning laser vibrometer for full field strain measurements,” in Experimental Techniques, Rotating Machinery, and Acoustics, Vol. 8 (Springer International, 2015), pp. 197–209.

P. Reu, D. P. Rohe, and L. D. Jacobs, “Comparison of DIC and LDV for practical vibration and modal measurements,” Mech. Syst. Signal Pr. (in press).

R. Jones and C. Wykes, Holographic and Speckle Interferometry, Vol. 6 (Cambridge University, 1989).
[Crossref]

P. Hariharan, Basics of Interferometry (Academic, 2010).

P. Jacquot and J. M. Fournier, Interferometry in Speckle Light: Theory and Applications (Springer Science and Business Media, 2012).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).

J. C. Dainty, Laser Speckle and Related Phenomena, Topics in Applied Physics, Vol. 9 (Springer-Verlag, 1975).
[Crossref]

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).

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Figures (9)

Fig. 1
Fig. 1 Components of motion observed by heterodyne speckle imager. Velocity is measured in the axial direction z of the interrogation beam. Tilting motion is measured about the x and y axes.
Fig. 2
Fig. 2 Geometry diagram.
Fig. 3
Fig. 3 Schematic of heterodyne speckle imager with a dynamic diffuse-scatterer for the target. BS, beam splitter; AOM 1, 40MHz acousto-optic modulator ; AOM 2, 40.01MHz acousto-optic modulator; L1, 750mm bi-convex lens; L2, 500mm bi-convex lens; L3, 250mm plano-convex lens; BE/SF, 5X Keplerian beam expander and 50µm spatial filter; PF, polarizing filter; FPA, 64×64 pixel focal plane array, 30k frames/s.
Fig. 4
Fig. 4 Dynamic diffuse target velocity profile measured by a commercial Polytec LDV and the laboratory sensor. A single frequency, 159Hz, is shown.
Fig. 5
Fig. 5 Axial velocity amplitude at various positions on the diffuse target. Four simultaneous frequencies were present on the dynamic measurement surface.
Fig. 6
Fig. 6 Pixel shift velocity corresponding to tilt velocity, acquired simultaneously with axial velocity. Four simultaneous frequencies were present on the dynamic measurement surface.
Fig. 7
Fig. 7 Speckle patterns generated (a) experimentally and by (b) numeric model.
Fig. 8
Fig. 8 Pixel shift calculations peformed on modeled and experimental data.
Fig. 9
Fig. 9 Variance in pixel shift calculation due to increasing incident beam diameter, i.e., reducing speckle size.

Equations (30)

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

Δ P = d 1 + d 2 d 3 d 4
Δ P = ( ξ ξ o ) [ sin ( β ) ( 1 cos ( θ ) ) + ( 1 + cos ( β ) ) sin ( θ ) ] d 4 ( 1 + cos ( β ) )
Δ P ( ξ ξ o ) θ ( 1 + cos ( β ) ) d 4 ( 1 + cos ( β ) ) .
Δ P 2 ( ξ ξ o ) θ 2 d 4 .
U 1 ( x , y ) = e j k z j λ z e j k 2 z ( x 2 + y 2 ) u o ( ξ , η ) e j 2 π λ z ( x ξ + y η ) d ξ d η
κ = e j k z j λ z e j k 2 z ( x 2 + y 2 ) .
f x = x λ z , f y = y λ z
U 1 ( x , y ) = κ [ u o ( ξ , η ) ] ( f x , f y )
u o ( ξ , η ) u o ( ξ , η ) e j k Δ P = u o ( ξ , η ) e j 2 k ( θ ξ o + d 4 ) e j 2 k θ ξ .
U 2 ( x , y ) = κ e j 2 k ( θ ξ o + d 4 ) [ u o ( ξ , η ) e j 2 k θ ξ ] ( f x , f y ) .
U 2 ( x , y ) = κ e j 2 k ( θ ξ o + d 4 ) M ( f x 2 θ λ , f y ) = κ e j 2 k ( θ ξ o + d 4 ) M ( 1 λ z ( x 2 θ z ) , y λ z )
U 1 ( x 2 θ z , y ) = e j k z j λ z e j k 2 z ( x 2 θ z ) 2 e j k 2 z y 2 M ( 1 λ z ( x 2 θ z ) , y λ z ) = κ e j 2 k θ x e j 2 k z θ 2 M ( 1 λ z ( x 2 θ z ) , y λ z ) = κ M ( 1 λ z ( x 2 θ z ) , y λ z ) e j 2 k θ x e j 2 k z θ 2 = e j 2 k ( θ ξ o + d 4 ) U 2 ( x , y ) e j 2 k θ x e j 2 k z θ 2 .
U 2 ( x , y ) = e j 2 k ( θ ξ o + d 4 ) e j 2 k x θ e j 2 k z θ 2 U 1 ( x 2 θ z , y ) .
I 2 ( x , y ) = U 2 ( x , y ) U 2 * ( x , y ) = U 1 ( x 2 θ z , y ) U 1 * ( x 2 θ z , y ) = I 1 ( x 2 θ z , y )
U m ( x , y , t ) = κ e j 2 k ( θ ( t ) ξ o + ϕ ( t ) η o + d 4 ( t ) ) M ( x ( t ) , y ( t ) ) e j ω o t
x ( t ) = 1 λ z ( x 2 θ ( t ) z ) y ( t ) = 1 λ z ( y 2 ϕ ( t ) z ) .
M ( x ( t ) , y ( t ) ) = | M | ( x ( t ) , y ( t ) ) e j α M ( x ( t ) , y ( t ) ) U m ( x , y , t ) = κ | M | e j ( ω o t + α M ) e j 2 k ( θ ( t ) ξ o + ϕ ( t ) η o + d 4 ( t ) ) .
U r ( x , y , t ) = κ Re j ( ω o + ω L O ) t .
U t ( x , y , t ) = U r ( x , y , t ) + U m ( x , y , t ) .
I ( x , y , t ) = U t U t * = U r U r * + U m U m * + U r U m * + U r * U m
I ( x , y , t ) = 1 λ 2 z 2 [ R 2 + | M | 2 + 2 R | M | cos ( ω L O t + 2 k ( θ ( t ) ξ o + ϕ ( t ) η o + d 4 ( t ) ) α M ) ] .
ψ ( t ) = 4 π λ ( θ ( t ) ξ o + ϕ ( t ) η o + d 4 ( t ) ) α M .
I h ( x , y , t ) = P [ I ( x , y , t ) ]
2 R | M ( x , y , t ) | ( I h ( x , y , t ) 2 + H ( I h ( x , y , t ) ) 2 )
Δ θ = s 2 z .
Q d e m o d ( t ) = P [ 2 I h ( t ) sin ( ω L O t ) ] I d e m o d ( t ) = P [ 2 I h ( t ) cos ( ω L O t ) ]
ψ u n w r a p [ tan 1 ( Q d e m o d ( t ) I d e m o d ( t ) ) ] .
ν = λ 4 π ( ψ t + α M t ) .
A s = ( λ z ) 2 A o
u o ( ξ , η ) A o ( ξ , η ) e ζ ( ξ , η )

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