Abstract

We present a method to determine the speed of sound in tissue using a double-ring photoacoustic sensor working in reflection mode. This method uses the cross-correlation between the laser-induced ultrasound waves detected by two concentric ring shaped sensors, while a priori information about the depth-position of the photoacoustic source is not required. We demonstrate the concept by estimating the speed of sound in water as a function of temperature. Comparison of the estimated speed with values reported in literature shows an average systematic error of 0.1% and a standard deviation of 0.1%. Furthermore, we demonstrate that the method can be applied to layered media. The method has application in the correction of photoacoustic and ultrasound images afflicted by local speed variations in tissue. Additionally, the concept shows promise in monitoring temperature changes which are reflected in speed of sound changes in tissue.

© 2007 Optical Society of America

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References

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  1. H.F. Zhang, K. Maslov, G. Stoica, L.V. Wang, "Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging," Nat. Biotechnol. 24, 848-851 (2006).
    [CrossRef] [PubMed]
  2. R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, "Thermoacoustic computed tomography using a conventional linear transducer array," Med. Phys. 30,856-860 (2003).
    [CrossRef] [PubMed]
  3. R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, F. F. M. de Mul, "In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor," IEEE J Sel Top Quantum Electron 9, 343-346 (2003).
    [CrossRef]
  4. R. G. M. Kolkman, N. Bosschaart, B. Kok, T. G. van Leeuwen, W. Steenbergen, "Photoacoustic imaging of valves in superficial veins," Lasers Surg. Med. 38, 740-744 (2006)
    [CrossRef] [PubMed]
  5. J. J. Niederhauser, M. Jaeger, R. Lemor R, P. Weber, and M. Frenz, "Combined ultrasound and optoacoustic system for real-time high-contrast vascular imaging in vivo," IEEE Trans. Med. Imaging 24, 436-440 (2005).
    [CrossRef] [PubMed]
  6. R. I. Siphanto, K. K. Thumma, R. G. M. Kolkman, T. G. van Leeuwen, F. F. M. de Mul, J. W. van Neck, L. N. A. van Adrichem, W. Steenbergen, "Serial noninvasive photoacoustic imaging of neovascularization in tumor angiogenesis," Opt. Express 13, 89-95 (2005).
    [CrossRef] [PubMed]
  7. J. C. Bamber, "Acoustical characteristics of biological media," in Encyclopedia of Acoustics, M. J. Crocker Ed., (J. Wiley & Sons, New York, 1997), pp. 1703-1726.
  8. R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, T. G. van Leeuwen, "Photoacoustic imaging with a double-ring sensor featuring a narrow aperture," J. Biomed. Optics 9, 1327-1335 (2004)
    [CrossRef]
  9. R. G. M. Kolkman, J.H.G.M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen, T. G. van Leeuwen, "Photoacoustic determination of blood vessel diameter," Phys. Med. Biol. 49, 4745-4756 (2004)
    [CrossRef] [PubMed]
  10. C. G. A. Hoelen, F. F. M. de Mul, "A new theoretical approach to photoacoustic signal generation," J Acoust. Soc. Am. 106, 695-706 (1999).
    [CrossRef]
  11. J. Lubbers, and R. Graaff, "A simple and accurate formula for the sound velocity in water," Ultrasound Med. Biol. 24, 1065 (1998).
    [CrossRef] [PubMed]
  12. J. Ophir, and T. Lin, "A calibration-free method for measurement of sound speed in biological tissue samples," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 35, 573 (1988).
    [CrossRef] [PubMed]
  13. M. E. Anderson, and G. E. Trahey, "The direct estimation of sound speed using pulse-echo ultrasound," J. Acoust. Soc. Am. 104, 3099 (1998).
    [CrossRef] [PubMed]
  14. Z. Yuan, Q. Zhang, H. Jiang, "Simultaneous reconstruction of acoutic and optical properties of heterogeneous media by quantitative photoacoustic tomography," Opt. Express 14, 6749-6754 (2006).
    [CrossRef] [PubMed]

2006

R. G. M. Kolkman, N. Bosschaart, B. Kok, T. G. van Leeuwen, W. Steenbergen, "Photoacoustic imaging of valves in superficial veins," Lasers Surg. Med. 38, 740-744 (2006)
[CrossRef] [PubMed]

H.F. Zhang, K. Maslov, G. Stoica, L.V. Wang, "Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging," Nat. Biotechnol. 24, 848-851 (2006).
[CrossRef] [PubMed]

Z. Yuan, Q. Zhang, H. Jiang, "Simultaneous reconstruction of acoutic and optical properties of heterogeneous media by quantitative photoacoustic tomography," Opt. Express 14, 6749-6754 (2006).
[CrossRef] [PubMed]

2005

J. J. Niederhauser, M. Jaeger, R. Lemor R, P. Weber, and M. Frenz, "Combined ultrasound and optoacoustic system for real-time high-contrast vascular imaging in vivo," IEEE Trans. Med. Imaging 24, 436-440 (2005).
[CrossRef] [PubMed]

R. I. Siphanto, K. K. Thumma, R. G. M. Kolkman, T. G. van Leeuwen, F. F. M. de Mul, J. W. van Neck, L. N. A. van Adrichem, W. Steenbergen, "Serial noninvasive photoacoustic imaging of neovascularization in tumor angiogenesis," Opt. Express 13, 89-95 (2005).
[CrossRef] [PubMed]

2004

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, T. G. van Leeuwen, "Photoacoustic imaging with a double-ring sensor featuring a narrow aperture," J. Biomed. Optics 9, 1327-1335 (2004)
[CrossRef]

R. G. M. Kolkman, J.H.G.M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen, T. G. van Leeuwen, "Photoacoustic determination of blood vessel diameter," Phys. Med. Biol. 49, 4745-4756 (2004)
[CrossRef] [PubMed]

2003

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, "Thermoacoustic computed tomography using a conventional linear transducer array," Med. Phys. 30,856-860 (2003).
[CrossRef] [PubMed]

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, F. F. M. de Mul, "In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor," IEEE J Sel Top Quantum Electron 9, 343-346 (2003).
[CrossRef]

1999

C. G. A. Hoelen, F. F. M. de Mul, "A new theoretical approach to photoacoustic signal generation," J Acoust. Soc. Am. 106, 695-706 (1999).
[CrossRef]

1998

J. Lubbers, and R. Graaff, "A simple and accurate formula for the sound velocity in water," Ultrasound Med. Biol. 24, 1065 (1998).
[CrossRef] [PubMed]

M. E. Anderson, and G. E. Trahey, "The direct estimation of sound speed using pulse-echo ultrasound," J. Acoust. Soc. Am. 104, 3099 (1998).
[CrossRef] [PubMed]

1988

J. Ophir, and T. Lin, "A calibration-free method for measurement of sound speed in biological tissue samples," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 35, 573 (1988).
[CrossRef] [PubMed]

Anderson, M. E.

M. E. Anderson, and G. E. Trahey, "The direct estimation of sound speed using pulse-echo ultrasound," J. Acoust. Soc. Am. 104, 3099 (1998).
[CrossRef] [PubMed]

Bosschaart, N.

R. G. M. Kolkman, N. Bosschaart, B. Kok, T. G. van Leeuwen, W. Steenbergen, "Photoacoustic imaging of valves in superficial veins," Lasers Surg. Med. 38, 740-744 (2006)
[CrossRef] [PubMed]

de Mul, F .F. M.

de Mul, F. F. M.

R. G. M. Kolkman, J.H.G.M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen, T. G. van Leeuwen, "Photoacoustic determination of blood vessel diameter," Phys. Med. Biol. 49, 4745-4756 (2004)
[CrossRef] [PubMed]

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, F. F. M. de Mul, "In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor," IEEE J Sel Top Quantum Electron 9, 343-346 (2003).
[CrossRef]

C. G. A. Hoelen, F. F. M. de Mul, "A new theoretical approach to photoacoustic signal generation," J Acoust. Soc. Am. 106, 695-706 (1999).
[CrossRef]

Graaff, R.

J. Lubbers, and R. Graaff, "A simple and accurate formula for the sound velocity in water," Ultrasound Med. Biol. 24, 1065 (1998).
[CrossRef] [PubMed]

Hoelen, C.G.A.

C. G. A. Hoelen, F. F. M. de Mul, "A new theoretical approach to photoacoustic signal generation," J Acoust. Soc. Am. 106, 695-706 (1999).
[CrossRef]

Hondebrink, E.

R. G. M. Kolkman, J.H.G.M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen, T. G. van Leeuwen, "Photoacoustic determination of blood vessel diameter," Phys. Med. Biol. 49, 4745-4756 (2004)
[CrossRef] [PubMed]

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, T. G. van Leeuwen, "Photoacoustic imaging with a double-ring sensor featuring a narrow aperture," J. Biomed. Optics 9, 1327-1335 (2004)
[CrossRef]

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, F. F. M. de Mul, "In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor," IEEE J Sel Top Quantum Electron 9, 343-346 (2003).
[CrossRef]

Hopman, J. C. W.

R. G. M. Kolkman, J.H.G.M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen, T. G. van Leeuwen, "Photoacoustic determination of blood vessel diameter," Phys. Med. Biol. 49, 4745-4756 (2004)
[CrossRef] [PubMed]

Jaeger, M.

J. J. Niederhauser, M. Jaeger, R. Lemor R, P. Weber, and M. Frenz, "Combined ultrasound and optoacoustic system for real-time high-contrast vascular imaging in vivo," IEEE Trans. Med. Imaging 24, 436-440 (2005).
[CrossRef] [PubMed]

Jiang, H.

Kiser, W.L.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, "Thermoacoustic computed tomography using a conventional linear transducer array," Med. Phys. 30,856-860 (2003).
[CrossRef] [PubMed]

Klaessens, J. H. G. M.

R. G. M. Kolkman, J.H.G.M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen, T. G. van Leeuwen, "Photoacoustic determination of blood vessel diameter," Phys. Med. Biol. 49, 4745-4756 (2004)
[CrossRef] [PubMed]

Kok, B.

R. G. M. Kolkman, N. Bosschaart, B. Kok, T. G. van Leeuwen, W. Steenbergen, "Photoacoustic imaging of valves in superficial veins," Lasers Surg. Med. 38, 740-744 (2006)
[CrossRef] [PubMed]

Kolkman, R. G. M.

R. G. M. Kolkman, N. Bosschaart, B. Kok, T. G. van Leeuwen, W. Steenbergen, "Photoacoustic imaging of valves in superficial veins," Lasers Surg. Med. 38, 740-744 (2006)
[CrossRef] [PubMed]

R. I. Siphanto, K. K. Thumma, R. G. M. Kolkman, T. G. van Leeuwen, F. F. M. de Mul, J. W. van Neck, L. N. A. van Adrichem, W. Steenbergen, "Serial noninvasive photoacoustic imaging of neovascularization in tumor angiogenesis," Opt. Express 13, 89-95 (2005).
[CrossRef] [PubMed]

R. G. M. Kolkman, J.H.G.M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen, T. G. van Leeuwen, "Photoacoustic determination of blood vessel diameter," Phys. Med. Biol. 49, 4745-4756 (2004)
[CrossRef] [PubMed]

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, F. F. M. de Mul, "In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor," IEEE J Sel Top Quantum Electron 9, 343-346 (2003).
[CrossRef]

Kolkman, R.G.M.

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, T. G. van Leeuwen, "Photoacoustic imaging with a double-ring sensor featuring a narrow aperture," J. Biomed. Optics 9, 1327-1335 (2004)
[CrossRef]

Kruger, G. A.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, "Thermoacoustic computed tomography using a conventional linear transducer array," Med. Phys. 30,856-860 (2003).
[CrossRef] [PubMed]

Kruger, R. A.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, "Thermoacoustic computed tomography using a conventional linear transducer array," Med. Phys. 30,856-860 (2003).
[CrossRef] [PubMed]

Lin, T.

J. Ophir, and T. Lin, "A calibration-free method for measurement of sound speed in biological tissue samples," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 35, 573 (1988).
[CrossRef] [PubMed]

Lubbers, J.

J. Lubbers, and R. Graaff, "A simple and accurate formula for the sound velocity in water," Ultrasound Med. Biol. 24, 1065 (1998).
[CrossRef] [PubMed]

Maslov, K.

H.F. Zhang, K. Maslov, G. Stoica, L.V. Wang, "Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging," Nat. Biotechnol. 24, 848-851 (2006).
[CrossRef] [PubMed]

Niederhauser, J. J.

J. J. Niederhauser, M. Jaeger, R. Lemor R, P. Weber, and M. Frenz, "Combined ultrasound and optoacoustic system for real-time high-contrast vascular imaging in vivo," IEEE Trans. Med. Imaging 24, 436-440 (2005).
[CrossRef] [PubMed]

Ophir, J.

J. Ophir, and T. Lin, "A calibration-free method for measurement of sound speed in biological tissue samples," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 35, 573 (1988).
[CrossRef] [PubMed]

Reinecke, D. R.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, "Thermoacoustic computed tomography using a conventional linear transducer array," Med. Phys. 30,856-860 (2003).
[CrossRef] [PubMed]

Siphanto, R. I.

Steenbergen, W.

R. G. M. Kolkman, N. Bosschaart, B. Kok, T. G. van Leeuwen, W. Steenbergen, "Photoacoustic imaging of valves in superficial veins," Lasers Surg. Med. 38, 740-744 (2006)
[CrossRef] [PubMed]

R. I. Siphanto, K. K. Thumma, R. G. M. Kolkman, T. G. van Leeuwen, F. F. M. de Mul, J. W. van Neck, L. N. A. van Adrichem, W. Steenbergen, "Serial noninvasive photoacoustic imaging of neovascularization in tumor angiogenesis," Opt. Express 13, 89-95 (2005).
[CrossRef] [PubMed]

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, T. G. van Leeuwen, "Photoacoustic imaging with a double-ring sensor featuring a narrow aperture," J. Biomed. Optics 9, 1327-1335 (2004)
[CrossRef]

R. G. M. Kolkman, J.H.G.M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen, T. G. van Leeuwen, "Photoacoustic determination of blood vessel diameter," Phys. Med. Biol. 49, 4745-4756 (2004)
[CrossRef] [PubMed]

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, F. F. M. de Mul, "In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor," IEEE J Sel Top Quantum Electron 9, 343-346 (2003).
[CrossRef]

Stoica, G.

H.F. Zhang, K. Maslov, G. Stoica, L.V. Wang, "Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging," Nat. Biotechnol. 24, 848-851 (2006).
[CrossRef] [PubMed]

Thijssen, J. M.

R. G. M. Kolkman, J.H.G.M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen, T. G. van Leeuwen, "Photoacoustic determination of blood vessel diameter," Phys. Med. Biol. 49, 4745-4756 (2004)
[CrossRef] [PubMed]

Thumma, K. K.

Trahey, G. E.

M. E. Anderson, and G. E. Trahey, "The direct estimation of sound speed using pulse-echo ultrasound," J. Acoust. Soc. Am. 104, 3099 (1998).
[CrossRef] [PubMed]

van Adrichem, L. N. A.

van Leeuwen, T. G.

R. G. M. Kolkman, N. Bosschaart, B. Kok, T. G. van Leeuwen, W. Steenbergen, "Photoacoustic imaging of valves in superficial veins," Lasers Surg. Med. 38, 740-744 (2006)
[CrossRef] [PubMed]

R. I. Siphanto, K. K. Thumma, R. G. M. Kolkman, T. G. van Leeuwen, F. F. M. de Mul, J. W. van Neck, L. N. A. van Adrichem, W. Steenbergen, "Serial noninvasive photoacoustic imaging of neovascularization in tumor angiogenesis," Opt. Express 13, 89-95 (2005).
[CrossRef] [PubMed]

R. G. M. Kolkman, J.H.G.M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen, T. G. van Leeuwen, "Photoacoustic determination of blood vessel diameter," Phys. Med. Biol. 49, 4745-4756 (2004)
[CrossRef] [PubMed]

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, T. G. van Leeuwen, "Photoacoustic imaging with a double-ring sensor featuring a narrow aperture," J. Biomed. Optics 9, 1327-1335 (2004)
[CrossRef]

van Neck, J. W.

Wang, L.V.

H.F. Zhang, K. Maslov, G. Stoica, L.V. Wang, "Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging," Nat. Biotechnol. 24, 848-851 (2006).
[CrossRef] [PubMed]

Yuan, Z.

Zhang, H.F.

H.F. Zhang, K. Maslov, G. Stoica, L.V. Wang, "Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging," Nat. Biotechnol. 24, 848-851 (2006).
[CrossRef] [PubMed]

Zhang, Q.

IEEE J Sel Top Quantum Electron

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, F. F. M. de Mul, "In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor," IEEE J Sel Top Quantum Electron 9, 343-346 (2003).
[CrossRef]

IEEE Trans. Med. Imaging

J. J. Niederhauser, M. Jaeger, R. Lemor R, P. Weber, and M. Frenz, "Combined ultrasound and optoacoustic system for real-time high-contrast vascular imaging in vivo," IEEE Trans. Med. Imaging 24, 436-440 (2005).
[CrossRef] [PubMed]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

J. Ophir, and T. Lin, "A calibration-free method for measurement of sound speed in biological tissue samples," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 35, 573 (1988).
[CrossRef] [PubMed]

J Acoust. Soc. Am.

C. G. A. Hoelen, F. F. M. de Mul, "A new theoretical approach to photoacoustic signal generation," J Acoust. Soc. Am. 106, 695-706 (1999).
[CrossRef]

J. Acoust. Soc. Am.

M. E. Anderson, and G. E. Trahey, "The direct estimation of sound speed using pulse-echo ultrasound," J. Acoust. Soc. Am. 104, 3099 (1998).
[CrossRef] [PubMed]

J. Biomed. Optics

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, T. G. van Leeuwen, "Photoacoustic imaging with a double-ring sensor featuring a narrow aperture," J. Biomed. Optics 9, 1327-1335 (2004)
[CrossRef]

Lasers Surg. Med.

R. G. M. Kolkman, N. Bosschaart, B. Kok, T. G. van Leeuwen, W. Steenbergen, "Photoacoustic imaging of valves in superficial veins," Lasers Surg. Med. 38, 740-744 (2006)
[CrossRef] [PubMed]

Med. Phys.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, "Thermoacoustic computed tomography using a conventional linear transducer array," Med. Phys. 30,856-860 (2003).
[CrossRef] [PubMed]

Nat. Biotechnol.

H.F. Zhang, K. Maslov, G. Stoica, L.V. Wang, "Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging," Nat. Biotechnol. 24, 848-851 (2006).
[CrossRef] [PubMed]

Opt. Express

Phys. Med. Biol.

R. G. M. Kolkman, J.H.G.M. Klaessens, E. Hondebrink, J. C. W. Hopman, F. F. M. de Mul, W. Steenbergen, J. M. Thijssen, T. G. van Leeuwen, "Photoacoustic determination of blood vessel diameter," Phys. Med. Biol. 49, 4745-4756 (2004)
[CrossRef] [PubMed]

Ultrasound Med. Biol.

J. Lubbers, and R. Graaff, "A simple and accurate formula for the sound velocity in water," Ultrasound Med. Biol. 24, 1065 (1998).
[CrossRef] [PubMed]

Other

J. C. Bamber, "Acoustical characteristics of biological media," in Encyclopedia of Acoustics, M. J. Crocker Ed., (J. Wiley & Sons, New York, 1997), pp. 1703-1726.

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Figures (8)

Fig. 1.
Fig. 1.

Time-delays δt in and δt out when using a double-ring PA sensor to detect acoustic waves from a source located at depth z0 .

Fig. 2.
Fig. 2.

Calculated C 0(c) curves for various depth locations z 0 of PA source, assuming c 0=1540 m/s and τpp= 40 ns.

Fig. 3.
Fig. 3.

Schematic overview of layered tissue, consisting of three layers with thickness di , and speed of sound ci .

Fig. 4.
Fig. 4.

Schematic overview of the layered phantom, consisting of two layers: a layer of water with thickness dwater , and speed of sound cwater , and a sheet of rubber or Perspex with thickness dsheet , and speed of sound csheet .

Fig. 5.
Fig. 5.

C 0(c) curve of the speed of sound in water at 26.4 °C. The actual speed of sound is determined by fitting equation 5 to the C 0(c) curve as depicted by the dashed line.

Fig. 6.
Fig. 6.

Speed of sound, as determined with our correlation method, as a function of temperature. The model of Lubbers & Graaff [11] (using their coefficients C2) is plotted for comparison (dashed line).

Fig. 7.
Fig. 7.

C 0(c) curves of the water-rubber layered system (a) and the water-perspex layered system (b). The speed of sound of c water and the effective speed of sound c eff are determined by fitting equation 5 to the C 0(c) curve as depicted by the dashed lines.

Fig. 8.
Fig. 8.

Photoacoustic images of a 200 μm diameter black hair immersed in water. Images are reconstructed as a function of speed of sound A - 1492 m/s (equal to the actual speed of sound), B - 1515 m/s, and C - 1540 m/s.

Tables (1)

Tables Icon

Table 1. Speed of sound and thickness of a layer of Perspex and Silicone rubber as estimated with the PA cross-correlation method compared with values obtained from pulse-echo ultrasound measurements and thickness measured with a caliper.

Equations (6)

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

P ( r , t ) = P max ( r ) e t τ 1 2 τ pp exp [ 1 2 ( t τ 1 2 τ pp ) 2 ] ,
z i = ( ct i ' ) 2 R i 2 = ( c c 0 ) 2 ( z 0 2 + R i 2 ) R i 2 ,
C 0 ( c ) π 2 τ pp [ 2 ( τ in ( c ) τ out ( c ) 1 2 τ pp ) 2 ] exp [ 1 4 ( τ in ( c ) τ out ( c ) 1 2 τ pp ) 2 ] ,
τ i ( c ) = c 2 c 0 2 ( z 0 2 + R i 2 ) R i 2 c .
C 0 ( c ) π 2 τ pp [ 2 ( c c 0 c 0 2 ) 2 ( A c c 0 c 0 B ) 2 ] exp [ 1 4 ( c c 0 c 0 2 ) 2 ( A c c 0 c 0 B ) 2 ]
1 c 0 = 1 z 0 i = 1 N d i c i .

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