Abstract

This study introduces optical feedback interferometry as a simple and effective technique for the two-dimensional visualisation of acoustic fields. We present imaging results for several pressure distributions including those for progressive waves, standing waves, as well as the diffraction and interference patterns of the acoustic waves. The proposed solution has the distinct advantage of extreme optical simplicity and robustness thus opening the way to a low cost acoustic field imaging system based on mass produced laser diodes.

© 2014 Optical Society of America

Full Article  |  PDF Article
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  1. T. Fjield, X. Fan, and K. Hynynen, “A parametric study of the concentric-ring transducer design for MRI guided ultrasound surgery,” J. Acoust. Soc. Am. 100, 1220–1230 (1996).
    [Crossref] [PubMed]
  2. O. Manneberg, J. Svennebring, H. M. Hertz, and M. Wiklund, “Wedge transducer design for two-dimensional ultrasonic manipulation in a microfluidic chip,” J. Micromech. Microeng. 18, 095025 (2008).
    [Crossref]
  3. C. E. Ebbing and T. H. Hodgson, “Diagnostic tests for locating noise sources: Classical techniques and signal processing techniques,” Noise Control Eng. 3, 30–46 (1974).
    [Crossref]
  4. K. Prestwich, “The energetics of acoustic signaling in anurans and insects,” Amer. Zool. 34, 625–643 (1994).
  5. R. Wimberger-Friedl, “The assessment of orientation, stress and density distributions in injection-molded amorphous polymers by optical techniques,” Prog. Polym. Sci. 20, 369–401 (1995).
    [Crossref]
  6. R. Malkin and D. Robert, “High sensitivity non-contact method for dynamic quantification of elastic waves and strains in transparent media,” Measurement 55, 51–57 (2014).
    [Crossref]
  7. D. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. Zellers, G. Frye, and H. Wohltjen, Acoustic Wave Sensors: Theory, Design, & Physico-Chemical Applications (Academic, 1996).
  8. A. J. Ricco, R. M. Crooks, and G. C. Osbourn, “Surface acoustic wave chemical sensor arrays: new chemically sensitive interfaces combined with novel cluster analysis to detect volatile organic compounds and mixtures,” Acc. Chem. Res. 31, 289–296 (1998).
    [Crossref]
  9. E. G. Williams, J. Maynard, and E. Skudrzyk, “Sound source reconstructions using a microphone array,” J. Acoust. Soc. Am. 68, 340–344 (1980).
    [Crossref]
  10. P. A. Chinnery, V. F. Humphrey, and C. Beckett, “The schlieren image of two-dimensional ultrasonic fields and cavity resonances,” J. Acoust. Soc. Am. 101, 250–256 (1997).
    [Crossref]
  11. X. Jia, G. Quentin, and M. Lassoued, “Optical heterodyne detection of pulsed ultrasonic pressures,” IEEE Trans. Sonics Ultrason. 40, 67–69 (1993).
    [Crossref]
  12. T. A. Pitts and J. F. Greenleaf, “Three-dimensional optical measurement of instantaneous pressure,” J. Acoust. Soc. Am. 108, 2873–2883 (2000).
    [Crossref]
  13. N.-E. Molin, Optical Methods for Acoustics and Vibration Measurements, in Springer Handbook of Acoustics, T. D. Rossing, ed. (Springer, 2007).
  14. L. Zipser, H. Franke, E. Olsson, N.-E. Molin, and M. Sjödahl, “Reconstructing two-dimensional acoustic object fields by use of digital phase conjugation of scanning laser vibrometry recordings,” Appl. Opt. 42, 5831–5838 (2003).
    [Crossref] [PubMed]
  15. R. Malkin, T. Todd, and D. Robert, “A simple method for quantitative imaging of 2D acoustic fields using refracto-vibrometry,” J. Sound Vib. 333, 4473–4482 (2014).
    [Crossref]
  16. A. Torras-Rosell, S. Barrera-Figueroa, and F. Jacobsen, “Sound field reconstruction using acousto-optic tomography,” J. Acoust. Soc. Am. 131, 3786–3793 (2012).
    [Crossref] [PubMed]
  17. G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A, Pure Appl. Opt. 4, S283–S294 (2002).
    [Crossref]
  18. R. Kliese, T. Taimre, A. Bakar, Y. L. Lim, K. Bertling, M. Nikolić, J. Perchoux, T. Bosch, and A. D. Rakić, “Solving self-mixing equations for arbitrary feedback levels: a concise algorithm,” Appl. Opt. 53, 3723–3736 (2014).
    [Crossref] [PubMed]
  19. K. Otsuka, K. Abe, J.-Y. Ko, and T.-S. Lim, “Real-time nanometer-vibration measurement with a self-mixing microchip solid-state laser,” Opt. Lett. 27, 1339–1341 (2002).
    [Crossref]
  20. M. Kössl and I. J. Russell, “Basilar membrane resonance in the cochlea of the mustached bat,” Proc. Natl. Acad. Sci. USA 92, 276–279 (1995).
    [Crossref] [PubMed]
  21. E. Sadıkoğlu, E. Bilgiç, and B. Karaböce, “A laser pistonphone based on self-mixing interferometry for the absolute calibration of measurement microphones,” Appl. Acoustics 65, 833–840 (2004).
    [Crossref]
  22. M. Fathi and S. Donati, “Simultaneous measurement of thickness and refractive index by a single-channel self-mixing interferometer,” IET Optoelectron. 6, 7–12 (2012).
    [Crossref]
  23. L. Xu, S. Zhang, Y. Tan, and L. Sun, “Simultaneous measurement of refractive-index and thickness for optical materials by laser feedback interferometry,” Rev. Sci. Instrum. 85, 083111 (2014).
    [Crossref] [PubMed]
  24. A. A. A. Bakar, Y. L. Lim, S. J. Wilson, M. Fuentes, K. Bertling, T. Taimre, T. Bosch, and A. D. Rakić, “On the feasibility of self-mixing interferometer sensing for detection of the surface electrocardiographic signal using a customized electro-optic phase modulator,” Physiol. Meas. 34, 281–289 (2013).
    [Crossref] [PubMed]
  25. F. E. Jones, “Simplified equation for calculating the refractivity of air,” Appl. Opt. 19, 4129–4130 (1980).
    [Crossref] [PubMed]
  26. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566–1573 (1996).
    [Crossref] [PubMed]
  27. T. Young, “The Bakerian lecture: Experiments and calculations relative to physical optics,” Phil. Trans. R. Soc. Lond. 94, 1–16 (1804).
    [Crossref]
  28. L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, Fundamentals of Acoustics (John Wiley & Sons, 2000)

2014 (4)

R. Malkin and D. Robert, “High sensitivity non-contact method for dynamic quantification of elastic waves and strains in transparent media,” Measurement 55, 51–57 (2014).
[Crossref]

R. Malkin, T. Todd, and D. Robert, “A simple method for quantitative imaging of 2D acoustic fields using refracto-vibrometry,” J. Sound Vib. 333, 4473–4482 (2014).
[Crossref]

L. Xu, S. Zhang, Y. Tan, and L. Sun, “Simultaneous measurement of refractive-index and thickness for optical materials by laser feedback interferometry,” Rev. Sci. Instrum. 85, 083111 (2014).
[Crossref] [PubMed]

R. Kliese, T. Taimre, A. Bakar, Y. L. Lim, K. Bertling, M. Nikolić, J. Perchoux, T. Bosch, and A. D. Rakić, “Solving self-mixing equations for arbitrary feedback levels: a concise algorithm,” Appl. Opt. 53, 3723–3736 (2014).
[Crossref] [PubMed]

2013 (1)

A. A. A. Bakar, Y. L. Lim, S. J. Wilson, M. Fuentes, K. Bertling, T. Taimre, T. Bosch, and A. D. Rakić, “On the feasibility of self-mixing interferometer sensing for detection of the surface electrocardiographic signal using a customized electro-optic phase modulator,” Physiol. Meas. 34, 281–289 (2013).
[Crossref] [PubMed]

2012 (2)

A. Torras-Rosell, S. Barrera-Figueroa, and F. Jacobsen, “Sound field reconstruction using acousto-optic tomography,” J. Acoust. Soc. Am. 131, 3786–3793 (2012).
[Crossref] [PubMed]

M. Fathi and S. Donati, “Simultaneous measurement of thickness and refractive index by a single-channel self-mixing interferometer,” IET Optoelectron. 6, 7–12 (2012).
[Crossref]

2008 (1)

O. Manneberg, J. Svennebring, H. M. Hertz, and M. Wiklund, “Wedge transducer design for two-dimensional ultrasonic manipulation in a microfluidic chip,” J. Micromech. Microeng. 18, 095025 (2008).
[Crossref]

2004 (1)

E. Sadıkoğlu, E. Bilgiç, and B. Karaböce, “A laser pistonphone based on self-mixing interferometry for the absolute calibration of measurement microphones,” Appl. Acoustics 65, 833–840 (2004).
[Crossref]

2003 (1)

2002 (2)

K. Otsuka, K. Abe, J.-Y. Ko, and T.-S. Lim, “Real-time nanometer-vibration measurement with a self-mixing microchip solid-state laser,” Opt. Lett. 27, 1339–1341 (2002).
[Crossref]

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A, Pure Appl. Opt. 4, S283–S294 (2002).
[Crossref]

2000 (1)

T. A. Pitts and J. F. Greenleaf, “Three-dimensional optical measurement of instantaneous pressure,” J. Acoust. Soc. Am. 108, 2873–2883 (2000).
[Crossref]

1998 (1)

A. J. Ricco, R. M. Crooks, and G. C. Osbourn, “Surface acoustic wave chemical sensor arrays: new chemically sensitive interfaces combined with novel cluster analysis to detect volatile organic compounds and mixtures,” Acc. Chem. Res. 31, 289–296 (1998).
[Crossref]

1997 (1)

P. A. Chinnery, V. F. Humphrey, and C. Beckett, “The schlieren image of two-dimensional ultrasonic fields and cavity resonances,” J. Acoust. Soc. Am. 101, 250–256 (1997).
[Crossref]

1996 (2)

T. Fjield, X. Fan, and K. Hynynen, “A parametric study of the concentric-ring transducer design for MRI guided ultrasound surgery,” J. Acoust. Soc. Am. 100, 1220–1230 (1996).
[Crossref] [PubMed]

P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566–1573 (1996).
[Crossref] [PubMed]

1995 (2)

R. Wimberger-Friedl, “The assessment of orientation, stress and density distributions in injection-molded amorphous polymers by optical techniques,” Prog. Polym. Sci. 20, 369–401 (1995).
[Crossref]

M. Kössl and I. J. Russell, “Basilar membrane resonance in the cochlea of the mustached bat,” Proc. Natl. Acad. Sci. USA 92, 276–279 (1995).
[Crossref] [PubMed]

1994 (1)

K. Prestwich, “The energetics of acoustic signaling in anurans and insects,” Amer. Zool. 34, 625–643 (1994).

1993 (1)

X. Jia, G. Quentin, and M. Lassoued, “Optical heterodyne detection of pulsed ultrasonic pressures,” IEEE Trans. Sonics Ultrason. 40, 67–69 (1993).
[Crossref]

1980 (2)

E. G. Williams, J. Maynard, and E. Skudrzyk, “Sound source reconstructions using a microphone array,” J. Acoust. Soc. Am. 68, 340–344 (1980).
[Crossref]

F. E. Jones, “Simplified equation for calculating the refractivity of air,” Appl. Opt. 19, 4129–4130 (1980).
[Crossref] [PubMed]

1974 (1)

C. E. Ebbing and T. H. Hodgson, “Diagnostic tests for locating noise sources: Classical techniques and signal processing techniques,” Noise Control Eng. 3, 30–46 (1974).
[Crossref]

1804 (1)

T. Young, “The Bakerian lecture: Experiments and calculations relative to physical optics,” Phil. Trans. R. Soc. Lond. 94, 1–16 (1804).
[Crossref]

Abe, K.

Bakar, A.

Bakar, A. A. A.

A. A. A. Bakar, Y. L. Lim, S. J. Wilson, M. Fuentes, K. Bertling, T. Taimre, T. Bosch, and A. D. Rakić, “On the feasibility of self-mixing interferometer sensing for detection of the surface electrocardiographic signal using a customized electro-optic phase modulator,” Physiol. Meas. 34, 281–289 (2013).
[Crossref] [PubMed]

Ballantine, D.

D. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. Zellers, G. Frye, and H. Wohltjen, Acoustic Wave Sensors: Theory, Design, & Physico-Chemical Applications (Academic, 1996).

Barrera-Figueroa, S.

A. Torras-Rosell, S. Barrera-Figueroa, and F. Jacobsen, “Sound field reconstruction using acousto-optic tomography,” J. Acoust. Soc. Am. 131, 3786–3793 (2012).
[Crossref] [PubMed]

Beckett, C.

P. A. Chinnery, V. F. Humphrey, and C. Beckett, “The schlieren image of two-dimensional ultrasonic fields and cavity resonances,” J. Acoust. Soc. Am. 101, 250–256 (1997).
[Crossref]

Bertling, K.

R. Kliese, T. Taimre, A. Bakar, Y. L. Lim, K. Bertling, M. Nikolić, J. Perchoux, T. Bosch, and A. D. Rakić, “Solving self-mixing equations for arbitrary feedback levels: a concise algorithm,” Appl. Opt. 53, 3723–3736 (2014).
[Crossref] [PubMed]

A. A. A. Bakar, Y. L. Lim, S. J. Wilson, M. Fuentes, K. Bertling, T. Taimre, T. Bosch, and A. D. Rakić, “On the feasibility of self-mixing interferometer sensing for detection of the surface electrocardiographic signal using a customized electro-optic phase modulator,” Physiol. Meas. 34, 281–289 (2013).
[Crossref] [PubMed]

Bilgiç, E.

E. Sadıkoğlu, E. Bilgiç, and B. Karaböce, “A laser pistonphone based on self-mixing interferometry for the absolute calibration of measurement microphones,” Appl. Acoustics 65, 833–840 (2004).
[Crossref]

Bosch, T.

R. Kliese, T. Taimre, A. Bakar, Y. L. Lim, K. Bertling, M. Nikolić, J. Perchoux, T. Bosch, and A. D. Rakić, “Solving self-mixing equations for arbitrary feedback levels: a concise algorithm,” Appl. Opt. 53, 3723–3736 (2014).
[Crossref] [PubMed]

A. A. A. Bakar, Y. L. Lim, S. J. Wilson, M. Fuentes, K. Bertling, T. Taimre, T. Bosch, and A. D. Rakić, “On the feasibility of self-mixing interferometer sensing for detection of the surface electrocardiographic signal using a customized electro-optic phase modulator,” Physiol. Meas. 34, 281–289 (2013).
[Crossref] [PubMed]

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A, Pure Appl. Opt. 4, S283–S294 (2002).
[Crossref]

Chinnery, P. A.

P. A. Chinnery, V. F. Humphrey, and C. Beckett, “The schlieren image of two-dimensional ultrasonic fields and cavity resonances,” J. Acoust. Soc. Am. 101, 250–256 (1997).
[Crossref]

Ciddor, P. E.

Coppens, A. B.

L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, Fundamentals of Acoustics (John Wiley & Sons, 2000)

Crooks, R. M.

A. J. Ricco, R. M. Crooks, and G. C. Osbourn, “Surface acoustic wave chemical sensor arrays: new chemically sensitive interfaces combined with novel cluster analysis to detect volatile organic compounds and mixtures,” Acc. Chem. Res. 31, 289–296 (1998).
[Crossref]

Donati, S.

M. Fathi and S. Donati, “Simultaneous measurement of thickness and refractive index by a single-channel self-mixing interferometer,” IET Optoelectron. 6, 7–12 (2012).
[Crossref]

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A, Pure Appl. Opt. 4, S283–S294 (2002).
[Crossref]

Ebbing, C. E.

C. E. Ebbing and T. H. Hodgson, “Diagnostic tests for locating noise sources: Classical techniques and signal processing techniques,” Noise Control Eng. 3, 30–46 (1974).
[Crossref]

Fan, X.

T. Fjield, X. Fan, and K. Hynynen, “A parametric study of the concentric-ring transducer design for MRI guided ultrasound surgery,” J. Acoust. Soc. Am. 100, 1220–1230 (1996).
[Crossref] [PubMed]

Fathi, M.

M. Fathi and S. Donati, “Simultaneous measurement of thickness and refractive index by a single-channel self-mixing interferometer,” IET Optoelectron. 6, 7–12 (2012).
[Crossref]

Fjield, T.

T. Fjield, X. Fan, and K. Hynynen, “A parametric study of the concentric-ring transducer design for MRI guided ultrasound surgery,” J. Acoust. Soc. Am. 100, 1220–1230 (1996).
[Crossref] [PubMed]

Franke, H.

Frey, A. R.

L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, Fundamentals of Acoustics (John Wiley & Sons, 2000)

Frye, G.

D. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. Zellers, G. Frye, and H. Wohltjen, Acoustic Wave Sensors: Theory, Design, & Physico-Chemical Applications (Academic, 1996).

Fuentes, M.

A. A. A. Bakar, Y. L. Lim, S. J. Wilson, M. Fuentes, K. Bertling, T. Taimre, T. Bosch, and A. D. Rakić, “On the feasibility of self-mixing interferometer sensing for detection of the surface electrocardiographic signal using a customized electro-optic phase modulator,” Physiol. Meas. 34, 281–289 (2013).
[Crossref] [PubMed]

Giuliani, G.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A, Pure Appl. Opt. 4, S283–S294 (2002).
[Crossref]

Greenleaf, J. F.

T. A. Pitts and J. F. Greenleaf, “Three-dimensional optical measurement of instantaneous pressure,” J. Acoust. Soc. Am. 108, 2873–2883 (2000).
[Crossref]

Hertz, H. M.

O. Manneberg, J. Svennebring, H. M. Hertz, and M. Wiklund, “Wedge transducer design for two-dimensional ultrasonic manipulation in a microfluidic chip,” J. Micromech. Microeng. 18, 095025 (2008).
[Crossref]

Hodgson, T. H.

C. E. Ebbing and T. H. Hodgson, “Diagnostic tests for locating noise sources: Classical techniques and signal processing techniques,” Noise Control Eng. 3, 30–46 (1974).
[Crossref]

Humphrey, V. F.

P. A. Chinnery, V. F. Humphrey, and C. Beckett, “The schlieren image of two-dimensional ultrasonic fields and cavity resonances,” J. Acoust. Soc. Am. 101, 250–256 (1997).
[Crossref]

Hynynen, K.

T. Fjield, X. Fan, and K. Hynynen, “A parametric study of the concentric-ring transducer design for MRI guided ultrasound surgery,” J. Acoust. Soc. Am. 100, 1220–1230 (1996).
[Crossref] [PubMed]

Jacobsen, F.

A. Torras-Rosell, S. Barrera-Figueroa, and F. Jacobsen, “Sound field reconstruction using acousto-optic tomography,” J. Acoust. Soc. Am. 131, 3786–3793 (2012).
[Crossref] [PubMed]

Jia, X.

X. Jia, G. Quentin, and M. Lassoued, “Optical heterodyne detection of pulsed ultrasonic pressures,” IEEE Trans. Sonics Ultrason. 40, 67–69 (1993).
[Crossref]

Jones, F. E.

Karaböce, B.

E. Sadıkoğlu, E. Bilgiç, and B. Karaböce, “A laser pistonphone based on self-mixing interferometry for the absolute calibration of measurement microphones,” Appl. Acoustics 65, 833–840 (2004).
[Crossref]

Kinsler, L. E.

L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, Fundamentals of Acoustics (John Wiley & Sons, 2000)

Kliese, R.

Ko, J.-Y.

Kössl, M.

M. Kössl and I. J. Russell, “Basilar membrane resonance in the cochlea of the mustached bat,” Proc. Natl. Acad. Sci. USA 92, 276–279 (1995).
[Crossref] [PubMed]

Lassoued, M.

X. Jia, G. Quentin, and M. Lassoued, “Optical heterodyne detection of pulsed ultrasonic pressures,” IEEE Trans. Sonics Ultrason. 40, 67–69 (1993).
[Crossref]

Lim, T.-S.

Lim, Y. L.

R. Kliese, T. Taimre, A. Bakar, Y. L. Lim, K. Bertling, M. Nikolić, J. Perchoux, T. Bosch, and A. D. Rakić, “Solving self-mixing equations for arbitrary feedback levels: a concise algorithm,” Appl. Opt. 53, 3723–3736 (2014).
[Crossref] [PubMed]

A. A. A. Bakar, Y. L. Lim, S. J. Wilson, M. Fuentes, K. Bertling, T. Taimre, T. Bosch, and A. D. Rakić, “On the feasibility of self-mixing interferometer sensing for detection of the surface electrocardiographic signal using a customized electro-optic phase modulator,” Physiol. Meas. 34, 281–289 (2013).
[Crossref] [PubMed]

Malkin, R.

R. Malkin, T. Todd, and D. Robert, “A simple method for quantitative imaging of 2D acoustic fields using refracto-vibrometry,” J. Sound Vib. 333, 4473–4482 (2014).
[Crossref]

R. Malkin and D. Robert, “High sensitivity non-contact method for dynamic quantification of elastic waves and strains in transparent media,” Measurement 55, 51–57 (2014).
[Crossref]

Manneberg, O.

O. Manneberg, J. Svennebring, H. M. Hertz, and M. Wiklund, “Wedge transducer design for two-dimensional ultrasonic manipulation in a microfluidic chip,” J. Micromech. Microeng. 18, 095025 (2008).
[Crossref]

Martin, S. J.

D. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. Zellers, G. Frye, and H. Wohltjen, Acoustic Wave Sensors: Theory, Design, & Physico-Chemical Applications (Academic, 1996).

Maynard, J.

E. G. Williams, J. Maynard, and E. Skudrzyk, “Sound source reconstructions using a microphone array,” J. Acoust. Soc. Am. 68, 340–344 (1980).
[Crossref]

Molin, N.-E.

Nikolic, M.

Norgia, M.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A, Pure Appl. Opt. 4, S283–S294 (2002).
[Crossref]

Olsson, E.

Osbourn, G. C.

A. J. Ricco, R. M. Crooks, and G. C. Osbourn, “Surface acoustic wave chemical sensor arrays: new chemically sensitive interfaces combined with novel cluster analysis to detect volatile organic compounds and mixtures,” Acc. Chem. Res. 31, 289–296 (1998).
[Crossref]

Otsuka, K.

Perchoux, J.

Pitts, T. A.

T. A. Pitts and J. F. Greenleaf, “Three-dimensional optical measurement of instantaneous pressure,” J. Acoust. Soc. Am. 108, 2873–2883 (2000).
[Crossref]

Prestwich, K.

K. Prestwich, “The energetics of acoustic signaling in anurans and insects,” Amer. Zool. 34, 625–643 (1994).

Quentin, G.

X. Jia, G. Quentin, and M. Lassoued, “Optical heterodyne detection of pulsed ultrasonic pressures,” IEEE Trans. Sonics Ultrason. 40, 67–69 (1993).
[Crossref]

Rakic, A. D.

R. Kliese, T. Taimre, A. Bakar, Y. L. Lim, K. Bertling, M. Nikolić, J. Perchoux, T. Bosch, and A. D. Rakić, “Solving self-mixing equations for arbitrary feedback levels: a concise algorithm,” Appl. Opt. 53, 3723–3736 (2014).
[Crossref] [PubMed]

A. A. A. Bakar, Y. L. Lim, S. J. Wilson, M. Fuentes, K. Bertling, T. Taimre, T. Bosch, and A. D. Rakić, “On the feasibility of self-mixing interferometer sensing for detection of the surface electrocardiographic signal using a customized electro-optic phase modulator,” Physiol. Meas. 34, 281–289 (2013).
[Crossref] [PubMed]

Ricco, A. J.

A. J. Ricco, R. M. Crooks, and G. C. Osbourn, “Surface acoustic wave chemical sensor arrays: new chemically sensitive interfaces combined with novel cluster analysis to detect volatile organic compounds and mixtures,” Acc. Chem. Res. 31, 289–296 (1998).
[Crossref]

D. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. Zellers, G. Frye, and H. Wohltjen, Acoustic Wave Sensors: Theory, Design, & Physico-Chemical Applications (Academic, 1996).

Robert, D.

R. Malkin and D. Robert, “High sensitivity non-contact method for dynamic quantification of elastic waves and strains in transparent media,” Measurement 55, 51–57 (2014).
[Crossref]

R. Malkin, T. Todd, and D. Robert, “A simple method for quantitative imaging of 2D acoustic fields using refracto-vibrometry,” J. Sound Vib. 333, 4473–4482 (2014).
[Crossref]

Russell, I. J.

M. Kössl and I. J. Russell, “Basilar membrane resonance in the cochlea of the mustached bat,” Proc. Natl. Acad. Sci. USA 92, 276–279 (1995).
[Crossref] [PubMed]

Sadikoglu, E.

E. Sadıkoğlu, E. Bilgiç, and B. Karaböce, “A laser pistonphone based on self-mixing interferometry for the absolute calibration of measurement microphones,” Appl. Acoustics 65, 833–840 (2004).
[Crossref]

Sanders, J. V.

L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, Fundamentals of Acoustics (John Wiley & Sons, 2000)

Sjödahl, M.

Skudrzyk, E.

E. G. Williams, J. Maynard, and E. Skudrzyk, “Sound source reconstructions using a microphone array,” J. Acoust. Soc. Am. 68, 340–344 (1980).
[Crossref]

Sun, L.

L. Xu, S. Zhang, Y. Tan, and L. Sun, “Simultaneous measurement of refractive-index and thickness for optical materials by laser feedback interferometry,” Rev. Sci. Instrum. 85, 083111 (2014).
[Crossref] [PubMed]

Svennebring, J.

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L. Xu, S. Zhang, Y. Tan, and L. Sun, “Simultaneous measurement of refractive-index and thickness for optical materials by laser feedback interferometry,” Rev. Sci. Instrum. 85, 083111 (2014).
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Wiklund, M.

O. Manneberg, J. Svennebring, H. M. Hertz, and M. Wiklund, “Wedge transducer design for two-dimensional ultrasonic manipulation in a microfluidic chip,” J. Micromech. Microeng. 18, 095025 (2008).
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A. A. A. Bakar, Y. L. Lim, S. J. Wilson, M. Fuentes, K. Bertling, T. Taimre, T. Bosch, and A. D. Rakić, “On the feasibility of self-mixing interferometer sensing for detection of the surface electrocardiographic signal using a customized electro-optic phase modulator,” Physiol. Meas. 34, 281–289 (2013).
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D. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. Zellers, G. Frye, and H. Wohltjen, Acoustic Wave Sensors: Theory, Design, & Physico-Chemical Applications (Academic, 1996).

Xu, L.

L. Xu, S. Zhang, Y. Tan, and L. Sun, “Simultaneous measurement of refractive-index and thickness for optical materials by laser feedback interferometry,” Rev. Sci. Instrum. 85, 083111 (2014).
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Zhang, S.

L. Xu, S. Zhang, Y. Tan, and L. Sun, “Simultaneous measurement of refractive-index and thickness for optical materials by laser feedback interferometry,” Rev. Sci. Instrum. 85, 083111 (2014).
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O. Manneberg, J. Svennebring, H. M. Hertz, and M. Wiklund, “Wedge transducer design for two-dimensional ultrasonic manipulation in a microfluidic chip,” J. Micromech. Microeng. 18, 095025 (2008).
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R. Malkin, T. Todd, and D. Robert, “A simple method for quantitative imaging of 2D acoustic fields using refracto-vibrometry,” J. Sound Vib. 333, 4473–4482 (2014).
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T. Young, “The Bakerian lecture: Experiments and calculations relative to physical optics,” Phil. Trans. R. Soc. Lond. 94, 1–16 (1804).
[Crossref]

Physiol. Meas. (1)

A. A. A. Bakar, Y. L. Lim, S. J. Wilson, M. Fuentes, K. Bertling, T. Taimre, T. Bosch, and A. D. Rakić, “On the feasibility of self-mixing interferometer sensing for detection of the surface electrocardiographic signal using a customized electro-optic phase modulator,” Physiol. Meas. 34, 281–289 (2013).
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L. Xu, S. Zhang, Y. Tan, and L. Sun, “Simultaneous measurement of refractive-index and thickness for optical materials by laser feedback interferometry,” Rev. Sci. Instrum. 85, 083111 (2014).
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D. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. Zellers, G. Frye, and H. Wohltjen, Acoustic Wave Sensors: Theory, Design, & Physico-Chemical Applications (Academic, 1996).

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Supplementary Material (3)

» Media 1: MP4 (616 KB)     
» Media 2: MP4 (933 KB)     
» Media 3: MP4 (1203 KB)     

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the setup used for acoustic field measurements.

Fig. 2
Fig. 2

Typical signals from a single pixel. (a) Stimulus from signal generator. (b) Signal wave just next to the ultrasonic transmitter (x = 0 mm, y = 0 mm). (c) Signal wave at furthest point away from transmitter in the scan area in line with the axis of sound propagation (x = 40 mm, y = 0 mm). (d) Signal wave from area with minimal sound propagation (x = 0 mm, y = 20 mm). For further information about these three regions, see Fig. 3.

Fig. 3
Fig. 3

Propagation of the acoustic field with the ultrasonic transmitter propagating the field into free space (see also Media 1); Left: Measured, Right: Simulation. (a) Image at t = 0 s. (b) Amplitude of acoustic field. (c) Phase of acoustic field.

Fig. 4
Fig. 4

Propagation of the acoustic field through two slits (see also Media 2); Left: Measured, Right: Simulation. (a) Image at t = 0 s. (b) Amplitude of acoustic field. (c) Phase of acoustic field.

Fig. 5
Fig. 5

Measured signal with a reflector (aluminium block in lower right corner, indicated in red) partially blocking the sound field (see also Media 3); (a) Image at t = 0 s. (b) Amplitude of acoustic field. (c) Phase of acoustic field.

Fig. 6
Fig. 6

Comparison between the acoustic fields from flat and curved retroreflector screens. (a) Flat retroreflector screen (external cavity constant). (b) Curved retroreflector screen (external cavity changing along the x axis).

Equations (7)

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P F = P 0 [ 1 + m cos ( ω F τ ) ] ,
δ τ = 0 L 2 δ n ( z ) c d z .
p ( x , y , z , r , t ) = A ( r ) e j ( ω t k r ) ,
r = [ ( x x i ) 2 + ( y y i ) 2 + ( z z i ) 2 ] 1 / 2 ,
P ( x , y , z , r , t ) S A ( r ) e j ( ω t k r ) d S ,
P ( x , y , z , t ) i = 1 n p ( x , y , z , r i , t ) .
P ˜ ( x , y , t ) z P ( x , y , z , t ) .

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