Abstract

Interferometric imaging is a well-established method to image phase objects by mixing the image wavefront with a reference one on a CCD camera. It has also been applied to fast transient phenomena, mostly through the analysis of single interferograms. It is shown that, for repetitive phenomena, multiphase acquisition brings significant advantages. A 1MHz focused sound field emitted by a hemispherical piezotransducer in water is imaged as an example. Quantitative image analysis provides high resolution sound field profiles. Pressure at focus determined by this method agrees with measurements from a fiber-optic probe hydrophone. This confirms that multiphase interferometric imaging can indeed provide quantitative measurements.

© 2010 Optical Society of America

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References

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  1. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1988), Vol. 26, pp. 349–393.
    [CrossRef]
  2. J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1990), Vol. 28, pp. 271–359.
    [CrossRef]
  3. V. I. Vlad and D. Malacara, “Direct spatial reconstruction of optical phase from phase-modulated images,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1994), Vol. 33, pp. 261–317.
    [CrossRef]
  4. G. W. Willard, “Focusing ultrasonic radiators,” J. Acoust. Soc. Am. 21, 360–375 (1949).
    [CrossRef]
  5. C. F. Ying, “Photoelastic visualization and theoretical analysis of scatterings of ultrasound pulses in solids,” in Physical Acoustics, R.N.Thurston, ed. (Academic, 1990), Vol. 19, pp. 291–343.
  6. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  7. T. Ezure, K. Mizutani, and H. Masuyama, “Optical measurement of sound fields estimated from multiple interference images using Mach–Zehnder interferometer,” Electron. Commun. Jpn. Part 2 87, 20–27 (2004).
    [CrossRef]
  8. O. J. Løkberg, “Sound in flight: measurement of sound fields by use of TV holography,” Appl. Opt. 33, 2574–2584 (1994).
    [CrossRef] [PubMed]
  9. R. C. Gutierrez, K. V. Schcheglov, and T. Tang, “Interferometric system for precision imaging of vibrating structures,” U.S. patent 6,219,145, B1 (17 April 2001), http://www.freepatentsonline.com/6219145.pdf.
  10. J. A. Conway, J. V. Osborn, and J. D. Fowler, “Stroboscopic imaging interferometer for MEMS performance measurement,” in Aerospace Report TR-2007,8555, http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA470710.
  11. J. S. Harris, R. L. Fusek, and J. S. Marcheski, “Stroboscopic interferometer,” Appl. Opt. 18, 2368–2371 (1979).
    [CrossRef] [PubMed]
  12. O. Y. Kwon, D. M. Shough, and R. A. Williams, “Stroboscopic phase-shifting interferometry,” Opt. Lett. 12, 855–857(1987).
    [CrossRef] [PubMed]
  13. E. Abraham, K. Minoshima, and H. Matsumoto, “Femtosecond laser-induced breakdown in water: time-resolved shadow imaging and two-color interferometric imaging,” Opt. Commun. 176, 441–452 (2000).
    [CrossRef]
  14. K. T. Gahagan, D. S. Moore, D. J. Funk, J. H. Reho, and R. L. Rabie, “Ultrafast interferometric microscopy for laser-driven shock-wave characterization,” J. Appl. Phys. 92, 3679–2682(2002).
    [CrossRef]
  15. V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, and D. von der Linde, “Femtosecond time-resolved interferometric microscopy,” Appl. Phys. A 78, 483–489 (2004).
    [CrossRef]
  16. D. J. Funk, D. S. Moore, S. D. McGrane, J. H. Reho, and R. L. Rabie, “Ultrafast spatial interferometry: a tool for characterizing material phase and hydrodynamic motion in laser-excited metals,” Appl. Phys. A 81, 295–302 (2005).
    [CrossRef]
  17. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 309–310.
  18. The apparatus is, in fact, designed for working with low temperature samples protected by four windows on each side.
  19. R. A. Fine and F. J. Millero, “Compressibility of water as a function of temperature and pressure,” J. Chem. Phys. 59, 5529–5536 (1973).
    [CrossRef]
  20. C. J. Morgan, “Least-squares estimation in phase-measurement inteferometry,” Opt. Lett. 7, 368–370 (1982).
    [CrossRef] [PubMed]
  21. J. J. Chyou, S. J. Chen, and Y. K. Chen, “Two-dimensionnal phase unwrapping with a multichannel least-mean-square algorithm,” Appl. Opt. 43, 5655–5661 (2004).
    [CrossRef] [PubMed]
  22. M. Deutsch and I. Beniaminy, “Inversion of Abel’s integral equation for experimental data,” J. Appl. Phys. 54, 137–143(1983).
    [CrossRef]
  23. J. Staudenraus and W. Eisenmenger, “Fiber-optic probe hydrophone for ultrasonic and shock-wave measurements in water,” Ultrasonics 31, 267–273 (1993).
    [CrossRef]
  24. J. E. Parsons, C. A. Cain, and J. B. Fowlkes, “Cost-effective assembly of a basic fiber-optic hydrophone for measurements of high-amplitude therapeutic ultrasound fields,” J. Acoust. Soc. Am. 119, 1432–1440 (2006).
    [CrossRef] [PubMed]
  25. J. Schwider, R. Burow, K. E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432(1983).
    [CrossRef] [PubMed]
  26. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
    [CrossRef] [PubMed]
  27. K. Davitt, A. Arvengas, and F. Caupin, “Water at the cavitation limit: density of the metastable liquid and size of the critical bubble,” Europhys. Lett. 90, 16002(2010).
    [CrossRef]
  28. “Release on the refractive index of ordinary water substance as a function of wavelength, temperature and pressure,” http://www.iapws.org/relguide/rindex.pdf.
  29. K. Davitt, E. Rolley, F. Caupin, A. Arvengas, and S. Balibar, “Equation of state of water under negative pressure,” J. Chem. Phys. (to be published).
  30. The fact that the lasers used in both methods have different wavelengths (532nm and 808nm) introduces a negligible correction.

2010 (1)

K. Davitt, A. Arvengas, and F. Caupin, “Water at the cavitation limit: density of the metastable liquid and size of the critical bubble,” Europhys. Lett. 90, 16002(2010).
[CrossRef]

2006 (1)

J. E. Parsons, C. A. Cain, and J. B. Fowlkes, “Cost-effective assembly of a basic fiber-optic hydrophone for measurements of high-amplitude therapeutic ultrasound fields,” J. Acoust. Soc. Am. 119, 1432–1440 (2006).
[CrossRef] [PubMed]

2005 (1)

D. J. Funk, D. S. Moore, S. D. McGrane, J. H. Reho, and R. L. Rabie, “Ultrafast spatial interferometry: a tool for characterizing material phase and hydrodynamic motion in laser-excited metals,” Appl. Phys. A 81, 295–302 (2005).
[CrossRef]

2004 (3)

J. J. Chyou, S. J. Chen, and Y. K. Chen, “Two-dimensionnal phase unwrapping with a multichannel least-mean-square algorithm,” Appl. Opt. 43, 5655–5661 (2004).
[CrossRef] [PubMed]

T. Ezure, K. Mizutani, and H. Masuyama, “Optical measurement of sound fields estimated from multiple interference images using Mach–Zehnder interferometer,” Electron. Commun. Jpn. Part 2 87, 20–27 (2004).
[CrossRef]

V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, and D. von der Linde, “Femtosecond time-resolved interferometric microscopy,” Appl. Phys. A 78, 483–489 (2004).
[CrossRef]

2002 (1)

K. T. Gahagan, D. S. Moore, D. J. Funk, J. H. Reho, and R. L. Rabie, “Ultrafast interferometric microscopy for laser-driven shock-wave characterization,” J. Appl. Phys. 92, 3679–2682(2002).
[CrossRef]

2000 (1)

E. Abraham, K. Minoshima, and H. Matsumoto, “Femtosecond laser-induced breakdown in water: time-resolved shadow imaging and two-color interferometric imaging,” Opt. Commun. 176, 441–452 (2000).
[CrossRef]

1994 (1)

1993 (1)

J. Staudenraus and W. Eisenmenger, “Fiber-optic probe hydrophone for ultrasonic and shock-wave measurements in water,” Ultrasonics 31, 267–273 (1993).
[CrossRef]

1987 (2)

1983 (2)

1982 (2)

1979 (1)

1973 (1)

R. A. Fine and F. J. Millero, “Compressibility of water as a function of temperature and pressure,” J. Chem. Phys. 59, 5529–5536 (1973).
[CrossRef]

1949 (1)

G. W. Willard, “Focusing ultrasonic radiators,” J. Acoust. Soc. Am. 21, 360–375 (1949).
[CrossRef]

Abraham, E.

E. Abraham, K. Minoshima, and H. Matsumoto, “Femtosecond laser-induced breakdown in water: time-resolved shadow imaging and two-color interferometric imaging,” Opt. Commun. 176, 441–452 (2000).
[CrossRef]

Arvengas, A.

K. Davitt, A. Arvengas, and F. Caupin, “Water at the cavitation limit: density of the metastable liquid and size of the critical bubble,” Europhys. Lett. 90, 16002(2010).
[CrossRef]

K. Davitt, E. Rolley, F. Caupin, A. Arvengas, and S. Balibar, “Equation of state of water under negative pressure,” J. Chem. Phys. (to be published).

Balibar, S.

K. Davitt, E. Rolley, F. Caupin, A. Arvengas, and S. Balibar, “Equation of state of water under negative pressure,” J. Chem. Phys. (to be published).

Beniaminy, I.

M. Deutsch and I. Beniaminy, “Inversion of Abel’s integral equation for experimental data,” J. Appl. Phys. 54, 137–143(1983).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 309–310.

Burow, R.

Cain, C. A.

J. E. Parsons, C. A. Cain, and J. B. Fowlkes, “Cost-effective assembly of a basic fiber-optic hydrophone for measurements of high-amplitude therapeutic ultrasound fields,” J. Acoust. Soc. Am. 119, 1432–1440 (2006).
[CrossRef] [PubMed]

Caupin, F.

K. Davitt, A. Arvengas, and F. Caupin, “Water at the cavitation limit: density of the metastable liquid and size of the critical bubble,” Europhys. Lett. 90, 16002(2010).
[CrossRef]

K. Davitt, E. Rolley, F. Caupin, A. Arvengas, and S. Balibar, “Equation of state of water under negative pressure,” J. Chem. Phys. (to be published).

Chen, S. J.

Chen, Y. K.

Chyou, J. J.

Conway, J. A.

J. A. Conway, J. V. Osborn, and J. D. Fowler, “Stroboscopic imaging interferometer for MEMS performance measurement,” in Aerospace Report TR-2007,8555, http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA470710.

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1988), Vol. 26, pp. 349–393.
[CrossRef]

Davitt, K.

K. Davitt, A. Arvengas, and F. Caupin, “Water at the cavitation limit: density of the metastable liquid and size of the critical bubble,” Europhys. Lett. 90, 16002(2010).
[CrossRef]

K. Davitt, E. Rolley, F. Caupin, A. Arvengas, and S. Balibar, “Equation of state of water under negative pressure,” J. Chem. Phys. (to be published).

Deutsch, M.

M. Deutsch and I. Beniaminy, “Inversion of Abel’s integral equation for experimental data,” J. Appl. Phys. 54, 137–143(1983).
[CrossRef]

Eiju, T.

Eisenmenger, W.

J. Staudenraus and W. Eisenmenger, “Fiber-optic probe hydrophone for ultrasonic and shock-wave measurements in water,” Ultrasonics 31, 267–273 (1993).
[CrossRef]

Elssner, K. E.

Ezure, T.

T. Ezure, K. Mizutani, and H. Masuyama, “Optical measurement of sound fields estimated from multiple interference images using Mach–Zehnder interferometer,” Electron. Commun. Jpn. Part 2 87, 20–27 (2004).
[CrossRef]

Fine, R. A.

R. A. Fine and F. J. Millero, “Compressibility of water as a function of temperature and pressure,” J. Chem. Phys. 59, 5529–5536 (1973).
[CrossRef]

Fowler, J. D.

J. A. Conway, J. V. Osborn, and J. D. Fowler, “Stroboscopic imaging interferometer for MEMS performance measurement,” in Aerospace Report TR-2007,8555, http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA470710.

Fowlkes, J. B.

J. E. Parsons, C. A. Cain, and J. B. Fowlkes, “Cost-effective assembly of a basic fiber-optic hydrophone for measurements of high-amplitude therapeutic ultrasound fields,” J. Acoust. Soc. Am. 119, 1432–1440 (2006).
[CrossRef] [PubMed]

Funk, D. J.

D. J. Funk, D. S. Moore, S. D. McGrane, J. H. Reho, and R. L. Rabie, “Ultrafast spatial interferometry: a tool for characterizing material phase and hydrodynamic motion in laser-excited metals,” Appl. Phys. A 81, 295–302 (2005).
[CrossRef]

K. T. Gahagan, D. S. Moore, D. J. Funk, J. H. Reho, and R. L. Rabie, “Ultrafast interferometric microscopy for laser-driven shock-wave characterization,” J. Appl. Phys. 92, 3679–2682(2002).
[CrossRef]

Fusek, R. L.

Gahagan, K. T.

K. T. Gahagan, D. S. Moore, D. J. Funk, J. H. Reho, and R. L. Rabie, “Ultrafast interferometric microscopy for laser-driven shock-wave characterization,” J. Appl. Phys. 92, 3679–2682(2002).
[CrossRef]

Grzanna, J.

Gutierrez, R. C.

R. C. Gutierrez, K. V. Schcheglov, and T. Tang, “Interferometric system for precision imaging of vibrating structures,” U.S. patent 6,219,145, B1 (17 April 2001), http://www.freepatentsonline.com/6219145.pdf.

Hariharan, P.

Harris, J. S.

Ina, H.

Kobayashi, S.

Kwon, O. Y.

Løkberg, O. J.

Malacara, D.

V. I. Vlad and D. Malacara, “Direct spatial reconstruction of optical phase from phase-modulated images,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1994), Vol. 33, pp. 261–317.
[CrossRef]

Marcheski, J. S.

Masuyama, H.

T. Ezure, K. Mizutani, and H. Masuyama, “Optical measurement of sound fields estimated from multiple interference images using Mach–Zehnder interferometer,” Electron. Commun. Jpn. Part 2 87, 20–27 (2004).
[CrossRef]

Matsumoto, H.

E. Abraham, K. Minoshima, and H. Matsumoto, “Femtosecond laser-induced breakdown in water: time-resolved shadow imaging and two-color interferometric imaging,” Opt. Commun. 176, 441–452 (2000).
[CrossRef]

McGrane, S. D.

D. J. Funk, D. S. Moore, S. D. McGrane, J. H. Reho, and R. L. Rabie, “Ultrafast spatial interferometry: a tool for characterizing material phase and hydrodynamic motion in laser-excited metals,” Appl. Phys. A 81, 295–302 (2005).
[CrossRef]

Merkel, K.

Millero, F. J.

R. A. Fine and F. J. Millero, “Compressibility of water as a function of temperature and pressure,” J. Chem. Phys. 59, 5529–5536 (1973).
[CrossRef]

Minoshima, K.

E. Abraham, K. Minoshima, and H. Matsumoto, “Femtosecond laser-induced breakdown in water: time-resolved shadow imaging and two-color interferometric imaging,” Opt. Commun. 176, 441–452 (2000).
[CrossRef]

Mizutani, K.

T. Ezure, K. Mizutani, and H. Masuyama, “Optical measurement of sound fields estimated from multiple interference images using Mach–Zehnder interferometer,” Electron. Commun. Jpn. Part 2 87, 20–27 (2004).
[CrossRef]

Moore, D. S.

D. J. Funk, D. S. Moore, S. D. McGrane, J. H. Reho, and R. L. Rabie, “Ultrafast spatial interferometry: a tool for characterizing material phase and hydrodynamic motion in laser-excited metals,” Appl. Phys. A 81, 295–302 (2005).
[CrossRef]

K. T. Gahagan, D. S. Moore, D. J. Funk, J. H. Reho, and R. L. Rabie, “Ultrafast interferometric microscopy for laser-driven shock-wave characterization,” J. Appl. Phys. 92, 3679–2682(2002).
[CrossRef]

Morgan, C. J.

Oreb, B. F.

Osborn, J. V.

J. A. Conway, J. V. Osborn, and J. D. Fowler, “Stroboscopic imaging interferometer for MEMS performance measurement,” in Aerospace Report TR-2007,8555, http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA470710.

Parsons, J. E.

J. E. Parsons, C. A. Cain, and J. B. Fowlkes, “Cost-effective assembly of a basic fiber-optic hydrophone for measurements of high-amplitude therapeutic ultrasound fields,” J. Acoust. Soc. Am. 119, 1432–1440 (2006).
[CrossRef] [PubMed]

Rabie, R. L.

D. J. Funk, D. S. Moore, S. D. McGrane, J. H. Reho, and R. L. Rabie, “Ultrafast spatial interferometry: a tool for characterizing material phase and hydrodynamic motion in laser-excited metals,” Appl. Phys. A 81, 295–302 (2005).
[CrossRef]

K. T. Gahagan, D. S. Moore, D. J. Funk, J. H. Reho, and R. L. Rabie, “Ultrafast interferometric microscopy for laser-driven shock-wave characterization,” J. Appl. Phys. 92, 3679–2682(2002).
[CrossRef]

Reho, J. H.

D. J. Funk, D. S. Moore, S. D. McGrane, J. H. Reho, and R. L. Rabie, “Ultrafast spatial interferometry: a tool for characterizing material phase and hydrodynamic motion in laser-excited metals,” Appl. Phys. A 81, 295–302 (2005).
[CrossRef]

K. T. Gahagan, D. S. Moore, D. J. Funk, J. H. Reho, and R. L. Rabie, “Ultrafast interferometric microscopy for laser-driven shock-wave characterization,” J. Appl. Phys. 92, 3679–2682(2002).
[CrossRef]

Rolley, E.

K. Davitt, E. Rolley, F. Caupin, A. Arvengas, and S. Balibar, “Equation of state of water under negative pressure,” J. Chem. Phys. (to be published).

Schcheglov, K. V.

R. C. Gutierrez, K. V. Schcheglov, and T. Tang, “Interferometric system for precision imaging of vibrating structures,” U.S. patent 6,219,145, B1 (17 April 2001), http://www.freepatentsonline.com/6219145.pdf.

Schwider, J.

Shough, D. M.

Sokolowski-Tinten, K.

V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, and D. von der Linde, “Femtosecond time-resolved interferometric microscopy,” Appl. Phys. A 78, 483–489 (2004).
[CrossRef]

Spolaczyk, R.

Staudenraus, J.

J. Staudenraus and W. Eisenmenger, “Fiber-optic probe hydrophone for ultrasonic and shock-wave measurements in water,” Ultrasonics 31, 267–273 (1993).
[CrossRef]

Takeda, M.

Tang, T.

R. C. Gutierrez, K. V. Schcheglov, and T. Tang, “Interferometric system for precision imaging of vibrating structures,” U.S. patent 6,219,145, B1 (17 April 2001), http://www.freepatentsonline.com/6219145.pdf.

Temnov, V. V.

V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, and D. von der Linde, “Femtosecond time-resolved interferometric microscopy,” Appl. Phys. A 78, 483–489 (2004).
[CrossRef]

Vlad, V. I.

V. I. Vlad and D. Malacara, “Direct spatial reconstruction of optical phase from phase-modulated images,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1994), Vol. 33, pp. 261–317.
[CrossRef]

von der Linde, D.

V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, and D. von der Linde, “Femtosecond time-resolved interferometric microscopy,” Appl. Phys. A 78, 483–489 (2004).
[CrossRef]

Willard, G. W.

G. W. Willard, “Focusing ultrasonic radiators,” J. Acoust. Soc. Am. 21, 360–375 (1949).
[CrossRef]

Williams, R. A.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 309–310.

Ying, C. F.

C. F. Ying, “Photoelastic visualization and theoretical analysis of scatterings of ultrasound pulses in solids,” in Physical Acoustics, R.N.Thurston, ed. (Academic, 1990), Vol. 19, pp. 291–343.

Zhou, P.

V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, and D. von der Linde, “Femtosecond time-resolved interferometric microscopy,” Appl. Phys. A 78, 483–489 (2004).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. A (2)

V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, and D. von der Linde, “Femtosecond time-resolved interferometric microscopy,” Appl. Phys. A 78, 483–489 (2004).
[CrossRef]

D. J. Funk, D. S. Moore, S. D. McGrane, J. H. Reho, and R. L. Rabie, “Ultrafast spatial interferometry: a tool for characterizing material phase and hydrodynamic motion in laser-excited metals,” Appl. Phys. A 81, 295–302 (2005).
[CrossRef]

Electron. Commun. Jpn. Part 2 (1)

T. Ezure, K. Mizutani, and H. Masuyama, “Optical measurement of sound fields estimated from multiple interference images using Mach–Zehnder interferometer,” Electron. Commun. Jpn. Part 2 87, 20–27 (2004).
[CrossRef]

Europhys. Lett. (1)

K. Davitt, A. Arvengas, and F. Caupin, “Water at the cavitation limit: density of the metastable liquid and size of the critical bubble,” Europhys. Lett. 90, 16002(2010).
[CrossRef]

J. Acoust. Soc. Am. (2)

J. E. Parsons, C. A. Cain, and J. B. Fowlkes, “Cost-effective assembly of a basic fiber-optic hydrophone for measurements of high-amplitude therapeutic ultrasound fields,” J. Acoust. Soc. Am. 119, 1432–1440 (2006).
[CrossRef] [PubMed]

G. W. Willard, “Focusing ultrasonic radiators,” J. Acoust. Soc. Am. 21, 360–375 (1949).
[CrossRef]

J. Appl. Phys. (2)

K. T. Gahagan, D. S. Moore, D. J. Funk, J. H. Reho, and R. L. Rabie, “Ultrafast interferometric microscopy for laser-driven shock-wave characterization,” J. Appl. Phys. 92, 3679–2682(2002).
[CrossRef]

M. Deutsch and I. Beniaminy, “Inversion of Abel’s integral equation for experimental data,” J. Appl. Phys. 54, 137–143(1983).
[CrossRef]

J. Chem. Phys. (1)

R. A. Fine and F. J. Millero, “Compressibility of water as a function of temperature and pressure,” J. Chem. Phys. 59, 5529–5536 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

E. Abraham, K. Minoshima, and H. Matsumoto, “Femtosecond laser-induced breakdown in water: time-resolved shadow imaging and two-color interferometric imaging,” Opt. Commun. 176, 441–452 (2000).
[CrossRef]

Opt. Lett. (2)

Ultrasonics (1)

J. Staudenraus and W. Eisenmenger, “Fiber-optic probe hydrophone for ultrasonic and shock-wave measurements in water,” Ultrasonics 31, 267–273 (1993).
[CrossRef]

Other (11)

“Release on the refractive index of ordinary water substance as a function of wavelength, temperature and pressure,” http://www.iapws.org/relguide/rindex.pdf.

K. Davitt, E. Rolley, F. Caupin, A. Arvengas, and S. Balibar, “Equation of state of water under negative pressure,” J. Chem. Phys. (to be published).

The fact that the lasers used in both methods have different wavelengths (532nm and 808nm) introduces a negligible correction.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 309–310.

The apparatus is, in fact, designed for working with low temperature samples protected by four windows on each side.

R. C. Gutierrez, K. V. Schcheglov, and T. Tang, “Interferometric system for precision imaging of vibrating structures,” U.S. patent 6,219,145, B1 (17 April 2001), http://www.freepatentsonline.com/6219145.pdf.

J. A. Conway, J. V. Osborn, and J. D. Fowler, “Stroboscopic imaging interferometer for MEMS performance measurement,” in Aerospace Report TR-2007,8555, http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA470710.

C. F. Ying, “Photoelastic visualization and theoretical analysis of scatterings of ultrasound pulses in solids,” in Physical Acoustics, R.N.Thurston, ed. (Academic, 1990), Vol. 19, pp. 291–343.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1988), Vol. 26, pp. 349–393.
[CrossRef]

J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1990), Vol. 28, pp. 271–359.
[CrossRef]

V. I. Vlad and D. Malacara, “Direct spatial reconstruction of optical phase from phase-modulated images,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1994), Vol. 33, pp. 261–317.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup: b, attenuated laser beam; tr1, trigger pulse sent by the laser 170 μs before the laser pulse; AFG, function generator; tr2, trigger pulse for the CCD camera; PT, piezo transducer driven by the amplifier RF; S 1 , scanning plates for the interferometer; S 2 , compensating plates. The inset shows how the optical path for the beam b 1 is changed by moving the separator of S 1 plates by h.

Fig. 2
Fig. 2

Measured phase ϕ ( x , z ) results from the integration of the optical phase shift over the beam path in the cell. Dashed circle with diameter D, limit of the sound field.

Fig. 3
Fig. 3

(a) Image of the interference field above the piezo hemisphere. Dashed–dotted white line shows its axis and the dashed line outlines the profile of its meridian section. (b) Phase field determined from 25 similar images with stepped optical phase. Nontransparent regions of the field of view appear as random numbers.

Fig. 4
Fig. 4

(a) Pressure map computed from the phase map Fig. 3b by Abel inversion from pixel 1 to 414. Area from x = 414 to x = 500 are filled by symmetry. (b) Time variations of the computed pressure at the focus while the sound pulse goes through (solid curve). The transducer excitation voltage is also plotted (dashed curve), starting at t = 0 .

Fig. 5
Fig. 5

Comparison of refractive index modulations obtained from the fiber-optic probe hydrophone (gray solid curve) and from inverse Abel transform of the phase map (dark dashed curve).

Equations (9)

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ψ = ψ 0 + 2 π h a ( 1 + s h a ) ,
I ( t , p ) = I 0 ( t ) [ 1 + C ( t ) cos ( ϕ ( t ) ψ ( p ) ) ] ,
ϕ ( x , z ) = 2 π λ l / 2 l / 2 d y δ n ( x 2 + y 2 , z ) .
ϕ ( x , z ) = 2 π λ d y δ n ( x 2 + y 2 , z ) ,
ϕ m < δ x λ s D λ o .
δ P ( x , z ) = ( n ( x , z , y ) n 0 ) / ( n / P ) ,
δ ϕ = δ I / I 0 C N p .
R = [ n f ( n w + δ n w ) n f + ( n w + δ n w ) ] 2 ,
δ n f = δ n w n f / P n w / P .

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