Abstract

We present a dual-probe homodyne quadrature laser interferometer for the measurements of displacement at two separate spatial locations. This is a coupled homodyne interferometer with inverted polarity of probe signals featuring a wide dynamic range and constant sensitivity. As an application of this dual-probe interferometer, we demonstrate how to locate the pulsed-laser interaction site on a plate without knowing the propagation velocities of the laser-induced mechanical waves.

© 2012 Optical Society of America

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References

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  1. A. D. W. McKie, J. W. Wagner, J. B. Spicer, and J. B. Deaton, “Dual-beam interferometer for the accurate determination of surface-wave velocity,” Appl. Opt. 30, 4034–4039(1991).
    [Crossref]
  2. J. Huang and J. D. Achenbach, “Dual-probe laser interferometer,” J. Acoust. Soc. Am. 90, 1269–1274 (1991).
    [Crossref]
  3. H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, “Direct and indirect dual-probe interferometers for accurate surface wave measurements,” Meas. Sci. Technol. 5, 1480–1490 (1994).
    [Crossref]
  4. M. G. Somekh, M. Liu, H. P. Ho, and C. W. See, “An accurate non-contacting laser based system for surface wave velocity measurement,” Meas. Sci. Technol. 6, 1329–1337 (1995).
    [Crossref]
  5. M. Szabadi, P. Hess, A. J. Kellock, H. Coufal, and J. E. E. Baglin, “Elastic and mechanical properties of ion-implanted silicon determined by surface-acoustic-wave spectrometry,” Phys. Rev. B 58, 8941–8948 (1998).
    [Crossref]
  6. P. V. Bazylev, “A laser receiver of ultrasound with two measuring channels,” Instrum. Exp. Tech. 46, 99–100 (2003).
    [Crossref]
  7. S. Hurlebaus and L. J. Jacobs, “Dual-probe laser interferometer for structural health monitoring (L),” J. Acoust. Soc. Am. 119, 1923–1925 (2006).
    [Crossref]
  8. T. Požar, P. Gregorčič, and J. Možina, “A precise and wide-dynamic-range displacement-measuring homodyne quadrature laser interferometer,” Appl. Phys. B 105, 575–582(2011).
    [Crossref]
  9. T. Požar and J. Možina, “Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer,” Meas. Sci. Technol. 22, 085301 (2011).
    [Crossref]
  10. L. Berthe, R. Fabbro, P. Peyre, L. Tollier, and E. Bartnicki, “Shock waves from a water-confined laser-generated plasma,” J. Appl. Phys. 82, 2826–2832 (1997).
    [Crossref]
  11. K. Ding and L. Ye, Laser Shock Peening Performance and Process Simulation (CRC, 2006).
  12. W. Goldsmith, Impact: the Theory and Physical Behavior of Colliding Solids (Dover, 2001).
  13. G. C. McLaskey and S. D. Glaser, “Micromechanics of asperity rupture during laboratory stick slip experiments,” Geophys. Res. Lett. 38, L12302 (2011).
    [Crossref]
  14. Y. H. Pao, “Theory of acoustic emission,” in Elastic Waves and Non-Destructive Testing of MaterialsY. H. Pao, ed. (ASME, 1978), pp. 107–128.
  15. J. D. Aussel and J. P. Monchalin, “Precision laser-ultrasonic velocity measurement and elastic constant determination,” Ultrasonics 27, 165–177 (1989).
    [Crossref]
  16. P. Gregorčič, T. Požar, and J. Možina, “Quadrature phase-shift error analysis using a homodyne laser interferometer,” Opt. Express 17, 16322–16331 (2009).
    [Crossref]
  17. T. Požar, P. Gregorčič, and J. Možina, “Optimization of displacement-measuring quadrature interferometers considering the real properties of optical components,” Appl. Opt. 50, 1210–1219 (2011).
    [Crossref]
  18. C. U. Grosse and M. Ohtsu, Acoustic Emission Testing(Springer, 2008).
  19. J. D. Aussel, A. Lebrun, and J. C. Baboux, “Generating acoustic waves by laser: theoretical and experimental study of the emission source,” Ultrasonics 26, 245–255 (1988).
    [Crossref]
  20. N. N. Hsu, “Dynamic Green’s functions of an infinite plate—a computer program,” NBSIR 85-3234 (National Bureau of Standards, 1985), 85–3234.
  21. R. J. Dewhurst, D. A. Hutchins, S. B. Palmer, and C. B. Scruby, “Quantitative measurements of laser-generated acoustic waveforms,” J. Appl. Phys. 53, 4064–4071 (1982).
    [Crossref]
  22. G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313, 33–39 (1998).
    [Crossref]
  23. C. M. Wu and C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
    [Crossref]

2011 (4)

T. Požar, P. Gregorčič, and J. Možina, “A precise and wide-dynamic-range displacement-measuring homodyne quadrature laser interferometer,” Appl. Phys. B 105, 575–582(2011).
[Crossref]

T. Požar and J. Možina, “Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer,” Meas. Sci. Technol. 22, 085301 (2011).
[Crossref]

G. C. McLaskey and S. D. Glaser, “Micromechanics of asperity rupture during laboratory stick slip experiments,” Geophys. Res. Lett. 38, L12302 (2011).
[Crossref]

T. Požar, P. Gregorčič, and J. Možina, “Optimization of displacement-measuring quadrature interferometers considering the real properties of optical components,” Appl. Opt. 50, 1210–1219 (2011).
[Crossref]

2009 (1)

2006 (1)

S. Hurlebaus and L. J. Jacobs, “Dual-probe laser interferometer for structural health monitoring (L),” J. Acoust. Soc. Am. 119, 1923–1925 (2006).
[Crossref]

2003 (1)

P. V. Bazylev, “A laser receiver of ultrasound with two measuring channels,” Instrum. Exp. Tech. 46, 99–100 (2003).
[Crossref]

1998 (2)

M. Szabadi, P. Hess, A. J. Kellock, H. Coufal, and J. E. E. Baglin, “Elastic and mechanical properties of ion-implanted silicon determined by surface-acoustic-wave spectrometry,” Phys. Rev. B 58, 8941–8948 (1998).
[Crossref]

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313, 33–39 (1998).
[Crossref]

1997 (1)

L. Berthe, R. Fabbro, P. Peyre, L. Tollier, and E. Bartnicki, “Shock waves from a water-confined laser-generated plasma,” J. Appl. Phys. 82, 2826–2832 (1997).
[Crossref]

1996 (1)

C. M. Wu and C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
[Crossref]

1995 (1)

M. G. Somekh, M. Liu, H. P. Ho, and C. W. See, “An accurate non-contacting laser based system for surface wave velocity measurement,” Meas. Sci. Technol. 6, 1329–1337 (1995).
[Crossref]

1994 (1)

H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, “Direct and indirect dual-probe interferometers for accurate surface wave measurements,” Meas. Sci. Technol. 5, 1480–1490 (1994).
[Crossref]

1991 (2)

1989 (1)

J. D. Aussel and J. P. Monchalin, “Precision laser-ultrasonic velocity measurement and elastic constant determination,” Ultrasonics 27, 165–177 (1989).
[Crossref]

1988 (1)

J. D. Aussel, A. Lebrun, and J. C. Baboux, “Generating acoustic waves by laser: theoretical and experimental study of the emission source,” Ultrasonics 26, 245–255 (1988).
[Crossref]

1982 (1)

R. J. Dewhurst, D. A. Hutchins, S. B. Palmer, and C. B. Scruby, “Quantitative measurements of laser-generated acoustic waveforms,” J. Appl. Phys. 53, 4064–4071 (1982).
[Crossref]

Achenbach, J. D.

J. Huang and J. D. Achenbach, “Dual-probe laser interferometer,” J. Acoust. Soc. Am. 90, 1269–1274 (1991).
[Crossref]

Aussel, J. D.

J. D. Aussel and J. P. Monchalin, “Precision laser-ultrasonic velocity measurement and elastic constant determination,” Ultrasonics 27, 165–177 (1989).
[Crossref]

J. D. Aussel, A. Lebrun, and J. C. Baboux, “Generating acoustic waves by laser: theoretical and experimental study of the emission source,” Ultrasonics 26, 245–255 (1988).
[Crossref]

Baboux, J. C.

J. D. Aussel, A. Lebrun, and J. C. Baboux, “Generating acoustic waves by laser: theoretical and experimental study of the emission source,” Ultrasonics 26, 245–255 (1988).
[Crossref]

Baglin, J. E. E.

M. Szabadi, P. Hess, A. J. Kellock, H. Coufal, and J. E. E. Baglin, “Elastic and mechanical properties of ion-implanted silicon determined by surface-acoustic-wave spectrometry,” Phys. Rev. B 58, 8941–8948 (1998).
[Crossref]

Bartnicki, E.

L. Berthe, R. Fabbro, P. Peyre, L. Tollier, and E. Bartnicki, “Shock waves from a water-confined laser-generated plasma,” J. Appl. Phys. 82, 2826–2832 (1997).
[Crossref]

Bazylev, P. V.

P. V. Bazylev, “A laser receiver of ultrasound with two measuring channels,” Instrum. Exp. Tech. 46, 99–100 (2003).
[Crossref]

Berthe, L.

L. Berthe, R. Fabbro, P. Peyre, L. Tollier, and E. Bartnicki, “Shock waves from a water-confined laser-generated plasma,” J. Appl. Phys. 82, 2826–2832 (1997).
[Crossref]

Coufal, H.

M. Szabadi, P. Hess, A. J. Kellock, H. Coufal, and J. E. E. Baglin, “Elastic and mechanical properties of ion-implanted silicon determined by surface-acoustic-wave spectrometry,” Phys. Rev. B 58, 8941–8948 (1998).
[Crossref]

Deaton, J. B.

Dewhurst, R. J.

R. J. Dewhurst, D. A. Hutchins, S. B. Palmer, and C. B. Scruby, “Quantitative measurements of laser-generated acoustic waveforms,” J. Appl. Phys. 53, 4064–4071 (1982).
[Crossref]

Ding, K.

K. Ding and L. Ye, Laser Shock Peening Performance and Process Simulation (CRC, 2006).

Fabbro, R.

L. Berthe, R. Fabbro, P. Peyre, L. Tollier, and E. Bartnicki, “Shock waves from a water-confined laser-generated plasma,” J. Appl. Phys. 82, 2826–2832 (1997).
[Crossref]

Glaser, S. D.

G. C. McLaskey and S. D. Glaser, “Micromechanics of asperity rupture during laboratory stick slip experiments,” Geophys. Res. Lett. 38, L12302 (2011).
[Crossref]

Goldsmith, W.

W. Goldsmith, Impact: the Theory and Physical Behavior of Colliding Solids (Dover, 2001).

Gregorcic, P.

Grosse, C. U.

C. U. Grosse and M. Ohtsu, Acoustic Emission Testing(Springer, 2008).

Hess, P.

M. Szabadi, P. Hess, A. J. Kellock, H. Coufal, and J. E. E. Baglin, “Elastic and mechanical properties of ion-implanted silicon determined by surface-acoustic-wave spectrometry,” Phys. Rev. B 58, 8941–8948 (1998).
[Crossref]

Ho, H. P.

M. G. Somekh, M. Liu, H. P. Ho, and C. W. See, “An accurate non-contacting laser based system for surface wave velocity measurement,” Meas. Sci. Technol. 6, 1329–1337 (1995).
[Crossref]

H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, “Direct and indirect dual-probe interferometers for accurate surface wave measurements,” Meas. Sci. Technol. 5, 1480–1490 (1994).
[Crossref]

Hsu, N. N.

N. N. Hsu, “Dynamic Green’s functions of an infinite plate—a computer program,” NBSIR 85-3234 (National Bureau of Standards, 1985), 85–3234.

Huang, J.

J. Huang and J. D. Achenbach, “Dual-probe laser interferometer,” J. Acoust. Soc. Am. 90, 1269–1274 (1991).
[Crossref]

Hurlebaus, S.

S. Hurlebaus and L. J. Jacobs, “Dual-probe laser interferometer for structural health monitoring (L),” J. Acoust. Soc. Am. 119, 1923–1925 (2006).
[Crossref]

Hutchins, D. A.

R. J. Dewhurst, D. A. Hutchins, S. B. Palmer, and C. B. Scruby, “Quantitative measurements of laser-generated acoustic waveforms,” J. Appl. Phys. 53, 4064–4071 (1982).
[Crossref]

Jacobs, L. J.

S. Hurlebaus and L. J. Jacobs, “Dual-probe laser interferometer for structural health monitoring (L),” J. Acoust. Soc. Am. 119, 1923–1925 (2006).
[Crossref]

Jellison, G. E.

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313, 33–39 (1998).
[Crossref]

Kellock, A. J.

M. Szabadi, P. Hess, A. J. Kellock, H. Coufal, and J. E. E. Baglin, “Elastic and mechanical properties of ion-implanted silicon determined by surface-acoustic-wave spectrometry,” Phys. Rev. B 58, 8941–8948 (1998).
[Crossref]

Lebrun, A.

J. D. Aussel, A. Lebrun, and J. C. Baboux, “Generating acoustic waves by laser: theoretical and experimental study of the emission source,” Ultrasonics 26, 245–255 (1988).
[Crossref]

Liu, M.

M. G. Somekh, M. Liu, H. P. Ho, and C. W. See, “An accurate non-contacting laser based system for surface wave velocity measurement,” Meas. Sci. Technol. 6, 1329–1337 (1995).
[Crossref]

H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, “Direct and indirect dual-probe interferometers for accurate surface wave measurements,” Meas. Sci. Technol. 5, 1480–1490 (1994).
[Crossref]

McKie, A. D. W.

McLaskey, G. C.

G. C. McLaskey and S. D. Glaser, “Micromechanics of asperity rupture during laboratory stick slip experiments,” Geophys. Res. Lett. 38, L12302 (2011).
[Crossref]

Monchalin, J. P.

J. D. Aussel and J. P. Monchalin, “Precision laser-ultrasonic velocity measurement and elastic constant determination,” Ultrasonics 27, 165–177 (1989).
[Crossref]

Možina, J.

T. Požar and J. Možina, “Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer,” Meas. Sci. Technol. 22, 085301 (2011).
[Crossref]

T. Požar, P. Gregorčič, and J. Možina, “A precise and wide-dynamic-range displacement-measuring homodyne quadrature laser interferometer,” Appl. Phys. B 105, 575–582(2011).
[Crossref]

T. Požar, P. Gregorčič, and J. Možina, “Optimization of displacement-measuring quadrature interferometers considering the real properties of optical components,” Appl. Opt. 50, 1210–1219 (2011).
[Crossref]

P. Gregorčič, T. Požar, and J. Možina, “Quadrature phase-shift error analysis using a homodyne laser interferometer,” Opt. Express 17, 16322–16331 (2009).
[Crossref]

Ohtsu, M.

C. U. Grosse and M. Ohtsu, Acoustic Emission Testing(Springer, 2008).

Palmer, S. B.

R. J. Dewhurst, D. A. Hutchins, S. B. Palmer, and C. B. Scruby, “Quantitative measurements of laser-generated acoustic waveforms,” J. Appl. Phys. 53, 4064–4071 (1982).
[Crossref]

Pao, Y. H.

Y. H. Pao, “Theory of acoustic emission,” in Elastic Waves and Non-Destructive Testing of MaterialsY. H. Pao, ed. (ASME, 1978), pp. 107–128.

Peyre, P.

L. Berthe, R. Fabbro, P. Peyre, L. Tollier, and E. Bartnicki, “Shock waves from a water-confined laser-generated plasma,” J. Appl. Phys. 82, 2826–2832 (1997).
[Crossref]

Požar, T.

T. Požar and J. Možina, “Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer,” Meas. Sci. Technol. 22, 085301 (2011).
[Crossref]

T. Požar, P. Gregorčič, and J. Možina, “A precise and wide-dynamic-range displacement-measuring homodyne quadrature laser interferometer,” Appl. Phys. B 105, 575–582(2011).
[Crossref]

T. Požar, P. Gregorčič, and J. Možina, “Optimization of displacement-measuring quadrature interferometers considering the real properties of optical components,” Appl. Opt. 50, 1210–1219 (2011).
[Crossref]

P. Gregorčič, T. Požar, and J. Možina, “Quadrature phase-shift error analysis using a homodyne laser interferometer,” Opt. Express 17, 16322–16331 (2009).
[Crossref]

Scruby, C. B.

R. J. Dewhurst, D. A. Hutchins, S. B. Palmer, and C. B. Scruby, “Quantitative measurements of laser-generated acoustic waveforms,” J. Appl. Phys. 53, 4064–4071 (1982).
[Crossref]

See, C. W.

M. G. Somekh, M. Liu, H. P. Ho, and C. W. See, “An accurate non-contacting laser based system for surface wave velocity measurement,” Meas. Sci. Technol. 6, 1329–1337 (1995).
[Crossref]

H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, “Direct and indirect dual-probe interferometers for accurate surface wave measurements,” Meas. Sci. Technol. 5, 1480–1490 (1994).
[Crossref]

Somekh, M. G.

M. G. Somekh, M. Liu, H. P. Ho, and C. W. See, “An accurate non-contacting laser based system for surface wave velocity measurement,” Meas. Sci. Technol. 6, 1329–1337 (1995).
[Crossref]

H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, “Direct and indirect dual-probe interferometers for accurate surface wave measurements,” Meas. Sci. Technol. 5, 1480–1490 (1994).
[Crossref]

Spicer, J. B.

Su, C. S.

C. M. Wu and C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
[Crossref]

Szabadi, M.

M. Szabadi, P. Hess, A. J. Kellock, H. Coufal, and J. E. E. Baglin, “Elastic and mechanical properties of ion-implanted silicon determined by surface-acoustic-wave spectrometry,” Phys. Rev. B 58, 8941–8948 (1998).
[Crossref]

Tollier, L.

L. Berthe, R. Fabbro, P. Peyre, L. Tollier, and E. Bartnicki, “Shock waves from a water-confined laser-generated plasma,” J. Appl. Phys. 82, 2826–2832 (1997).
[Crossref]

Wagner, J. W.

Wu, C. M.

C. M. Wu and C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
[Crossref]

Ye, L.

K. Ding and L. Ye, Laser Shock Peening Performance and Process Simulation (CRC, 2006).

Appl. Opt. (2)

Appl. Phys. B (1)

T. Požar, P. Gregorčič, and J. Možina, “A precise and wide-dynamic-range displacement-measuring homodyne quadrature laser interferometer,” Appl. Phys. B 105, 575–582(2011).
[Crossref]

Geophys. Res. Lett. (1)

G. C. McLaskey and S. D. Glaser, “Micromechanics of asperity rupture during laboratory stick slip experiments,” Geophys. Res. Lett. 38, L12302 (2011).
[Crossref]

Instrum. Exp. Tech. (1)

P. V. Bazylev, “A laser receiver of ultrasound with two measuring channels,” Instrum. Exp. Tech. 46, 99–100 (2003).
[Crossref]

J. Acoust. Soc. Am. (2)

S. Hurlebaus and L. J. Jacobs, “Dual-probe laser interferometer for structural health monitoring (L),” J. Acoust. Soc. Am. 119, 1923–1925 (2006).
[Crossref]

J. Huang and J. D. Achenbach, “Dual-probe laser interferometer,” J. Acoust. Soc. Am. 90, 1269–1274 (1991).
[Crossref]

J. Appl. Phys. (2)

L. Berthe, R. Fabbro, P. Peyre, L. Tollier, and E. Bartnicki, “Shock waves from a water-confined laser-generated plasma,” J. Appl. Phys. 82, 2826–2832 (1997).
[Crossref]

R. J. Dewhurst, D. A. Hutchins, S. B. Palmer, and C. B. Scruby, “Quantitative measurements of laser-generated acoustic waveforms,” J. Appl. Phys. 53, 4064–4071 (1982).
[Crossref]

Meas. Sci. Technol. (4)

C. M. Wu and C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
[Crossref]

H. P. Ho, M. G. Somekh, M. Liu, and C. W. See, “Direct and indirect dual-probe interferometers for accurate surface wave measurements,” Meas. Sci. Technol. 5, 1480–1490 (1994).
[Crossref]

M. G. Somekh, M. Liu, H. P. Ho, and C. W. See, “An accurate non-contacting laser based system for surface wave velocity measurement,” Meas. Sci. Technol. 6, 1329–1337 (1995).
[Crossref]

T. Požar and J. Možina, “Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer,” Meas. Sci. Technol. 22, 085301 (2011).
[Crossref]

Opt. Express (1)

Phys. Rev. B (1)

M. Szabadi, P. Hess, A. J. Kellock, H. Coufal, and J. E. E. Baglin, “Elastic and mechanical properties of ion-implanted silicon determined by surface-acoustic-wave spectrometry,” Phys. Rev. B 58, 8941–8948 (1998).
[Crossref]

Thin Solid Films (1)

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313, 33–39 (1998).
[Crossref]

Ultrasonics (2)

J. D. Aussel, A. Lebrun, and J. C. Baboux, “Generating acoustic waves by laser: theoretical and experimental study of the emission source,” Ultrasonics 26, 245–255 (1988).
[Crossref]

J. D. Aussel and J. P. Monchalin, “Precision laser-ultrasonic velocity measurement and elastic constant determination,” Ultrasonics 27, 165–177 (1989).
[Crossref]

Other (5)

C. U. Grosse and M. Ohtsu, Acoustic Emission Testing(Springer, 2008).

K. Ding and L. Ye, Laser Shock Peening Performance and Process Simulation (CRC, 2006).

W. Goldsmith, Impact: the Theory and Physical Behavior of Colliding Solids (Dover, 2001).

Y. H. Pao, “Theory of acoustic emission,” in Elastic Waves and Non-Destructive Testing of MaterialsY. H. Pao, ed. (ASME, 1978), pp. 107–128.

N. N. Hsu, “Dynamic Green’s functions of an infinite plate—a computer program,” NBSIR 85-3234 (National Bureau of Standards, 1985), 85–3234.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic diagram of a dual-probe homodyne quadrature laser interferometer (dashed rectangle) applied to locate the intense laser-pulse matter interaction site on a plate. Within the plate, relative positions of the wave fronts are shown at a given instant just before the fastest wave experiences the first reflection.

Fig. 2.
Fig. 2.

Normalized distance r/h from the probe location to the epicenter as a function of the measured ratio of time intervals η.

Fig. 3.
Fig. 3.

The ratio between the relative uncertainties δξ/ξ and δη/η as a function of η indicates that the triple-echo method gives the most accurate results in the interval 1.1<η<1.8 or in the annulus h<r<7h.

Fig. 4.
Fig. 4.

Simplified displacement as a function of normalized time from which the location of the source of ultrasound is inferred. The pure longitudinal arrivals at the location of probe 1 yield positive displacements, while those detected by probe 2 have an inverted polarity.

Fig. 5.
Fig. 5.

Top view of the plate. Four laser-pulse interaction sites (A, A, B, and C) are drawn on the front side of the plate. Only the two fixed probes are located on the opposite side of the plate. The useful area is the area where the laser-pulse interaction site can be determined based on the DPHQLI and the triple-echo method.

Fig. 6.
Fig. 6.

Displacement as a function of time measured with the DPHQLI from which the location of the source of the ultrasound is inferred. The pure longitudinal arrivals that are detected by probe 1 are labeled above the waveform. Those detected by probe 2 are labeled underneath.

Fig. 7.
Fig. 7.

Photography of both DPHQLI’s probe beams and the assisting pointer beam of the pulsed-laser at the plane which is equal to the front plane of the plate and has a normal which is parallel with the beams.

Tables (1)

Tables Icon

Table 1. List of the Main DPHQLI’s Constituents Shown in Fig. 1

Equations (6)

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

x(t)=x0+Axsin(4πλu(t)+p0),y(t)=y0+Aycos(4πλu(t)),
u(t)=u1(t)u2(t).
tnP=dnPcP=ncP[h2+(rn)2]1/2=nhcP[1+(ξn)2]1/2,
η(ξ)=t5Pt3Pt3PtP=(ξ2+25)1/2(ξ2+9)1/2(ξ2+9)1/2(ξ2+1)1/2.
ξ(η)=rh=[(η+4)(η+2)(2η1)(η1)(η+1)η(η2)]1/2,
r(1±δrr)=hξ(1±[δhh+δξξ])=hξ(1±[δhh+{dξdηηξ}δηη])=hξ(η)(1±[δhh+{dξ(x)dx|x=ηηξ(η)}(δtt5Pt3P+δtt3PtP)]),

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