Abstract

Imaging the full acoustic field around an object by use of an optical phase contrast method is used to accelerate the data acquisition in photoacoustic tomography. Images obtained with a CCD-camera at a certain time show a projection of the instantaneous pressure field in a given direction. In this work a reconstruction method is presented to obtain the two-dimensional initial pressure distribution by back propagating the observed wave pattern in Radon space. Numerical simulations are used to prove the accuracy of the reconstruction algorithm and to demonstrate a method for correcting limited data artifacts. Finally, the overall performance is shown with experimentally obtained data.

© 2010 OSA

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    [CrossRef] [PubMed]
  3. E. Z. Zhang, J. G. Laufer, R. B. Pedley, and P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
    [CrossRef] [PubMed]
  4. P. C. Beard, A. M. Hurrell, and T. N. Mills, “Characterization of a polymer film optical fiber hydrophone for use in the range 1 to 20 MHz: a comparison with PVDF needle and membrane hydrophones,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47(1), 256–264 (2000).
    [CrossRef]
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2009

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser Optoacoustic Imaging System for Detection of Breast Cancer,” J. Biomed. Opt. 14(2), 024007 (2009).
[CrossRef] [PubMed]

E. Z. Zhang, J. G. Laufer, R. B. Pedley, and P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
[CrossRef] [PubMed]

X. Pan, E. Y. Sidky, and M. Vannier, “Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?” Inverse Probl. 25(12), 123009 (2009).
[CrossRef]

G. Paltauf, R. Nuster, and P. Burgholzer, “Weight factors for limited angle photoacoustic tomography,” Phys. Med. Biol. 54(11), 3303–3314 (2009).
[CrossRef] [PubMed]

2007

M. Haltmeier, O. Scherzer, P. Burgholzer, R. Nuster, and G. Paltauf, “Thermoacoustic tomography & the circular Radon transform: Exact inversion formula,” Math. Models Meth. Appl. Sci. 17(4), 635–655 (2007).
[CrossRef]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Experimental evaluation of reconstruction algorithms for limited view photoacoustic tomography with line detectors,” Inverse Probl. 23(6), S81–S94 (2007).
[CrossRef]

I. Núñez and J. A. Ferrari, “Bright versus dark schlieren imaging: quantitative analysis of quasi-sinusoidal phase objects,” Appl. Opt. 46(5), 725–729 (2007).
[CrossRef] [PubMed]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Photoacoustic tomography using a Mach-Zehnder interferometer as an acoustic line detector,” Appl. Opt. 46(16), 3352–3358 (2007).
[CrossRef] [PubMed]

2006

M. H. Xu and L. V. Wang, “Photoacoustic Imaging in Biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006).
[CrossRef]

C. I. Zanelli and S. M. Howard, “Schlieren metrology for high frequency medical ultrasound,” Ultrasonics 44(Suppl 1), e105–e107 (2006).
[CrossRef] [PubMed]

Th. Neumann and H. Ermert, “Schlieren visualization of ultrasonic wave fields with high spatial resolution,” Ultrasonics 44(Suppl 1), e1561–e1566 (2006).
[CrossRef] [PubMed]

E. K. Reichel and B. G. Zagar, “Phase contrast method for measuring ultrasonic fields,” IEEE Trans. Instrum. Meas. 55(4), 1356–1361 (2006).
[CrossRef]

2005

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

2004

J. J. Niederhauser, M. Jaeger, and M. Frenz, “Real-Time Three-Dimensional Optoacoustic Imaging Using an Acoustic Lens System,” Appl. Phys. Lett. 85(5), 846–848 (2004).
[CrossRef]

N. Kudo, H. Ouchi, K. Yamamoto, and H. Sekimizu, “A simple Schlieren system for visualizing a sound field of pulsed ultrasound,” J. Phys.: Conf. Ser. 1, 146–149 (2004).
[CrossRef]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20(5), 1663–1673 (2004).
[CrossRef]

2002

J. J. Niederhauser, D. Frauchiger, H. P. Weber, and M. Frenz, “Real-Time Optoacoustic Imaging Using a Schlieren Transducer,” Appl. Phys. Lett. 81(4), 571–573 (2002).
[CrossRef]

2000

P. C. Beard, A. M. Hurrell, and T. N. Mills, “Characterization of a polymer film optical fiber hydrophone for use in the range 1 to 20 MHz: a comparison with PVDF needle and membrane hydrophones,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47(1), 256–264 (2000).
[CrossRef]

1996

B. Schneider and K. K. Shung, “Quantitative Analysis of Pulsed Ultrasonic Beam Patterns Using a Schlieren System,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43(6), 1181–1186 (1996).
[CrossRef]

P. C. Beard and T. N. Mills, “Extrinsic optical-fiber ultrasound sensor using a thin polymer film as a low-finesse Fabry-Perot interferometer,” Appl. Opt. 35(4), 663–675 (1996).
[CrossRef] [PubMed]

Beard, P. C.

E. Z. Zhang, J. G. Laufer, R. B. Pedley, and P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
[CrossRef] [PubMed]

P. C. Beard, A. M. Hurrell, and T. N. Mills, “Characterization of a polymer film optical fiber hydrophone for use in the range 1 to 20 MHz: a comparison with PVDF needle and membrane hydrophones,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47(1), 256–264 (2000).
[CrossRef]

P. C. Beard and T. N. Mills, “Extrinsic optical-fiber ultrasound sensor using a thin polymer film as a low-finesse Fabry-Perot interferometer,” Appl. Opt. 35(4), 663–675 (1996).
[CrossRef] [PubMed]

Burgholzer, P.

G. Paltauf, R. Nuster, and P. Burgholzer, “Weight factors for limited angle photoacoustic tomography,” Phys. Med. Biol. 54(11), 3303–3314 (2009).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, P. Burgholzer, R. Nuster, and G. Paltauf, “Thermoacoustic tomography & the circular Radon transform: Exact inversion formula,” Math. Models Meth. Appl. Sci. 17(4), 635–655 (2007).
[CrossRef]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Experimental evaluation of reconstruction algorithms for limited view photoacoustic tomography with line detectors,” Inverse Probl. 23(6), S81–S94 (2007).
[CrossRef]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Photoacoustic tomography using a Mach-Zehnder interferometer as an acoustic line detector,” Appl. Opt. 46(16), 3352–3358 (2007).
[CrossRef] [PubMed]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20(5), 1663–1673 (2004).
[CrossRef]

Conjusteau, A.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser Optoacoustic Imaging System for Detection of Breast Cancer,” J. Biomed. Opt. 14(2), 024007 (2009).
[CrossRef] [PubMed]

Ermert, H.

Th. Neumann and H. Ermert, “Schlieren visualization of ultrasonic wave fields with high spatial resolution,” Ultrasonics 44(Suppl 1), e1561–e1566 (2006).
[CrossRef] [PubMed]

Ermilov, S. A.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser Optoacoustic Imaging System for Detection of Breast Cancer,” J. Biomed. Opt. 14(2), 024007 (2009).
[CrossRef] [PubMed]

Ferrari, J. A.

Frauchiger, D.

J. J. Niederhauser, D. Frauchiger, H. P. Weber, and M. Frenz, “Real-Time Optoacoustic Imaging Using a Schlieren Transducer,” Appl. Phys. Lett. 81(4), 571–573 (2002).
[CrossRef]

Frenz, M.

J. J. Niederhauser, M. Jaeger, and M. Frenz, “Real-Time Three-Dimensional Optoacoustic Imaging Using an Acoustic Lens System,” Appl. Phys. Lett. 85(5), 846–848 (2004).
[CrossRef]

J. J. Niederhauser, D. Frauchiger, H. P. Weber, and M. Frenz, “Real-Time Optoacoustic Imaging Using a Schlieren Transducer,” Appl. Phys. Lett. 81(4), 571–573 (2002).
[CrossRef]

Haltmeier, M.

M. Haltmeier, O. Scherzer, P. Burgholzer, R. Nuster, and G. Paltauf, “Thermoacoustic tomography & the circular Radon transform: Exact inversion formula,” Math. Models Meth. Appl. Sci. 17(4), 635–655 (2007).
[CrossRef]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Experimental evaluation of reconstruction algorithms for limited view photoacoustic tomography with line detectors,” Inverse Probl. 23(6), S81–S94 (2007).
[CrossRef]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Photoacoustic tomography using a Mach-Zehnder interferometer as an acoustic line detector,” Appl. Opt. 46(16), 3352–3358 (2007).
[CrossRef] [PubMed]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20(5), 1663–1673 (2004).
[CrossRef]

Hofer, C.

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

Howard, S. M.

C. I. Zanelli and S. M. Howard, “Schlieren metrology for high frequency medical ultrasound,” Ultrasonics 44(Suppl 1), e105–e107 (2006).
[CrossRef] [PubMed]

Hurrell, A. M.

P. C. Beard, A. M. Hurrell, and T. N. Mills, “Characterization of a polymer film optical fiber hydrophone for use in the range 1 to 20 MHz: a comparison with PVDF needle and membrane hydrophones,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47(1), 256–264 (2000).
[CrossRef]

Jaeger, M.

J. J. Niederhauser, M. Jaeger, and M. Frenz, “Real-Time Three-Dimensional Optoacoustic Imaging Using an Acoustic Lens System,” Appl. Phys. Lett. 85(5), 846–848 (2004).
[CrossRef]

Khamapirad, T.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser Optoacoustic Imaging System for Detection of Breast Cancer,” J. Biomed. Opt. 14(2), 024007 (2009).
[CrossRef] [PubMed]

Kudo, N.

N. Kudo, H. Ouchi, K. Yamamoto, and H. Sekimizu, “A simple Schlieren system for visualizing a sound field of pulsed ultrasound,” J. Phys.: Conf. Ser. 1, 146–149 (2004).
[CrossRef]

Lacewell, R.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser Optoacoustic Imaging System for Detection of Breast Cancer,” J. Biomed. Opt. 14(2), 024007 (2009).
[CrossRef] [PubMed]

Laufer, J. G.

E. Z. Zhang, J. G. Laufer, R. B. Pedley, and P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
[CrossRef] [PubMed]

Leonard, M. H.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser Optoacoustic Imaging System for Detection of Breast Cancer,” J. Biomed. Opt. 14(2), 024007 (2009).
[CrossRef] [PubMed]

Mehta, K.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser Optoacoustic Imaging System for Detection of Breast Cancer,” J. Biomed. Opt. 14(2), 024007 (2009).
[CrossRef] [PubMed]

Miller, T.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser Optoacoustic Imaging System for Detection of Breast Cancer,” J. Biomed. Opt. 14(2), 024007 (2009).
[CrossRef] [PubMed]

Mills, T. N.

P. C. Beard, A. M. Hurrell, and T. N. Mills, “Characterization of a polymer film optical fiber hydrophone for use in the range 1 to 20 MHz: a comparison with PVDF needle and membrane hydrophones,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47(1), 256–264 (2000).
[CrossRef]

P. C. Beard and T. N. Mills, “Extrinsic optical-fiber ultrasound sensor using a thin polymer film as a low-finesse Fabry-Perot interferometer,” Appl. Opt. 35(4), 663–675 (1996).
[CrossRef] [PubMed]

Neumann, Th.

Th. Neumann and H. Ermert, “Schlieren visualization of ultrasonic wave fields with high spatial resolution,” Ultrasonics 44(Suppl 1), e1561–e1566 (2006).
[CrossRef] [PubMed]

Niederhauser, J. J.

J. J. Niederhauser, M. Jaeger, and M. Frenz, “Real-Time Three-Dimensional Optoacoustic Imaging Using an Acoustic Lens System,” Appl. Phys. Lett. 85(5), 846–848 (2004).
[CrossRef]

J. J. Niederhauser, D. Frauchiger, H. P. Weber, and M. Frenz, “Real-Time Optoacoustic Imaging Using a Schlieren Transducer,” Appl. Phys. Lett. 81(4), 571–573 (2002).
[CrossRef]

Núñez, I.

Nuster, R.

G. Paltauf, R. Nuster, and P. Burgholzer, “Weight factors for limited angle photoacoustic tomography,” Phys. Med. Biol. 54(11), 3303–3314 (2009).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, P. Burgholzer, R. Nuster, and G. Paltauf, “Thermoacoustic tomography & the circular Radon transform: Exact inversion formula,” Math. Models Meth. Appl. Sci. 17(4), 635–655 (2007).
[CrossRef]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Experimental evaluation of reconstruction algorithms for limited view photoacoustic tomography with line detectors,” Inverse Probl. 23(6), S81–S94 (2007).
[CrossRef]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Photoacoustic tomography using a Mach-Zehnder interferometer as an acoustic line detector,” Appl. Opt. 46(16), 3352–3358 (2007).
[CrossRef] [PubMed]

Oraevsky, A. A.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser Optoacoustic Imaging System for Detection of Breast Cancer,” J. Biomed. Opt. 14(2), 024007 (2009).
[CrossRef] [PubMed]

Ouchi, H.

N. Kudo, H. Ouchi, K. Yamamoto, and H. Sekimizu, “A simple Schlieren system for visualizing a sound field of pulsed ultrasound,” J. Phys.: Conf. Ser. 1, 146–149 (2004).
[CrossRef]

Paltauf, G.

G. Paltauf, R. Nuster, and P. Burgholzer, “Weight factors for limited angle photoacoustic tomography,” Phys. Med. Biol. 54(11), 3303–3314 (2009).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, P. Burgholzer, R. Nuster, and G. Paltauf, “Thermoacoustic tomography & the circular Radon transform: Exact inversion formula,” Math. Models Meth. Appl. Sci. 17(4), 635–655 (2007).
[CrossRef]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Experimental evaluation of reconstruction algorithms for limited view photoacoustic tomography with line detectors,” Inverse Probl. 23(6), S81–S94 (2007).
[CrossRef]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Photoacoustic tomography using a Mach-Zehnder interferometer as an acoustic line detector,” Appl. Opt. 46(16), 3352–3358 (2007).
[CrossRef] [PubMed]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20(5), 1663–1673 (2004).
[CrossRef]

Pan, X.

X. Pan, E. Y. Sidky, and M. Vannier, “Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?” Inverse Probl. 25(12), 123009 (2009).
[CrossRef]

Pedley, R. B.

E. Z. Zhang, J. G. Laufer, R. B. Pedley, and P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
[CrossRef] [PubMed]

Reichel, E. K.

E. K. Reichel and B. G. Zagar, “Phase contrast method for measuring ultrasonic fields,” IEEE Trans. Instrum. Meas. 55(4), 1356–1361 (2006).
[CrossRef]

Scherzer, O.

M. Haltmeier, O. Scherzer, P. Burgholzer, R. Nuster, and G. Paltauf, “Thermoacoustic tomography & the circular Radon transform: Exact inversion formula,” Math. Models Meth. Appl. Sci. 17(4), 635–655 (2007).
[CrossRef]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20(5), 1663–1673 (2004).
[CrossRef]

Schneider, B.

B. Schneider and K. K. Shung, “Quantitative Analysis of Pulsed Ultrasonic Beam Patterns Using a Schlieren System,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43(6), 1181–1186 (1996).
[CrossRef]

Sekimizu, H.

N. Kudo, H. Ouchi, K. Yamamoto, and H. Sekimizu, “A simple Schlieren system for visualizing a sound field of pulsed ultrasound,” J. Phys.: Conf. Ser. 1, 146–149 (2004).
[CrossRef]

Shung, K. K.

B. Schneider and K. K. Shung, “Quantitative Analysis of Pulsed Ultrasonic Beam Patterns Using a Schlieren System,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43(6), 1181–1186 (1996).
[CrossRef]

Sidky, E. Y.

X. Pan, E. Y. Sidky, and M. Vannier, “Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?” Inverse Probl. 25(12), 123009 (2009).
[CrossRef]

Vannier, M.

X. Pan, E. Y. Sidky, and M. Vannier, “Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?” Inverse Probl. 25(12), 123009 (2009).
[CrossRef]

Wang, L. V.

M. H. Xu and L. V. Wang, “Photoacoustic Imaging in Biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006).
[CrossRef]

Weber, H. P.

J. J. Niederhauser, D. Frauchiger, H. P. Weber, and M. Frenz, “Real-Time Optoacoustic Imaging Using a Schlieren Transducer,” Appl. Phys. Lett. 81(4), 571–573 (2002).
[CrossRef]

Xu, M. H.

M. H. Xu and L. V. Wang, “Photoacoustic Imaging in Biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006).
[CrossRef]

Yamamoto, K.

N. Kudo, H. Ouchi, K. Yamamoto, and H. Sekimizu, “A simple Schlieren system for visualizing a sound field of pulsed ultrasound,” J. Phys.: Conf. Ser. 1, 146–149 (2004).
[CrossRef]

Zagar, B. G.

E. K. Reichel and B. G. Zagar, “Phase contrast method for measuring ultrasonic fields,” IEEE Trans. Instrum. Meas. 55(4), 1356–1361 (2006).
[CrossRef]

Zanelli, C. I.

C. I. Zanelli and S. M. Howard, “Schlieren metrology for high frequency medical ultrasound,” Ultrasonics 44(Suppl 1), e105–e107 (2006).
[CrossRef] [PubMed]

Zhang, E. Z.

E. Z. Zhang, J. G. Laufer, R. B. Pedley, and P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
[CrossRef] [PubMed]

Appl. Opt.

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[CrossRef]

J. J. Niederhauser, D. Frauchiger, H. P. Weber, and M. Frenz, “Real-Time Optoacoustic Imaging Using a Schlieren Transducer,” Appl. Phys. Lett. 81(4), 571–573 (2002).
[CrossRef]

IEEE Trans. Instrum. Meas.

E. K. Reichel and B. G. Zagar, “Phase contrast method for measuring ultrasonic fields,” IEEE Trans. Instrum. Meas. 55(4), 1356–1361 (2006).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

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[CrossRef]

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X. Pan, E. Y. Sidky, and M. Vannier, “Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?” Inverse Probl. 25(12), 123009 (2009).
[CrossRef]

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[CrossRef]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Experimental evaluation of reconstruction algorithms for limited view photoacoustic tomography with line detectors,” Inverse Probl. 23(6), S81–S94 (2007).
[CrossRef]

J. Biomed. Opt.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser Optoacoustic Imaging System for Detection of Breast Cancer,” J. Biomed. Opt. 14(2), 024007 (2009).
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N. Kudo, H. Ouchi, K. Yamamoto, and H. Sekimizu, “A simple Schlieren system for visualizing a sound field of pulsed ultrasound,” J. Phys.: Conf. Ser. 1, 146–149 (2004).
[CrossRef]

Math. Models Meth. Appl. Sci.

M. Haltmeier, O. Scherzer, P. Burgholzer, R. Nuster, and G. Paltauf, “Thermoacoustic tomography & the circular Radon transform: Exact inversion formula,” Math. Models Meth. Appl. Sci. 17(4), 635–655 (2007).
[CrossRef]

Phys. Med. Biol.

E. Z. Zhang, J. G. Laufer, R. B. Pedley, and P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Graphical representation of the reconstruction procedure. FFD measures linear projections of p ( x , T ) onto planes E σ (left). The Radon transform of the projection image reduces the 2D wave propagation to sets of two counter-propagating plane waves (right).

Fig. 2
Fig. 2

Numerical examples proving the performance of the reconstruction method. (a) Mathematical phantom representing the projection of the initial pressure distribution. (b) Computed acoustic wave pattern at time T = 8 µs. (c)-(d) Radon transform of the acoustic wave pattern and the reconstruction procedure in Radon space. (e) Reconstruction of the initial 2d source. (f) Horizontal and vertical profiles through the center of images (a) and (e) .

Fig. 3
Fig. 3

(a) Computed acoustic wave pattern with added 20% noise. (b) Result of reconstruction from noisy data.

Fig. 4
Fig. 4

Numerical examples for limited data reconstruction. (a) The effect of missing data on the Radon transformed image. (c) and (d) Reconstruction from limited data with and without proposed correction method. (b) Comparison of horizontal and vertical profiles. Red line: without correction, blue line: with correction, black dotted line: original source distribution.

Fig. 5
Fig. 5

Experimental setup to capture a snap shot of the acoustic wave pattern at time T. M: mirror, BS: beam splitter, PH: pin hole.

Fig. 6
Fig. 6

(a) Captured acoustic wave pattern. (b) Reconstructed projection of the initial pressure distribution. The inset shows the plastisol phantom.

Equations (12)

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2 t 2 p ( x , t ) = c 2 Δ p ( x , t ) ,         ( x , t ) R 3 × ( 0 , ) ,                   p ( x , 0 ) = p 0 ( x ) ,                   x R 3 ,               t p ( x , 0 ) = 0 ,                           x R 3 .              
(X σ h )( q ): = h ( x ( q ,   s ) ) d s
P σ ( q ,   T ): = (X σ p )( q , T ) = p ( x ( q ,   s ),T ) d s .
( X σ Δ q , s p ) ( q , t ) = Δ q ( X σ p ) ( q , t ) ,
0 = X σ ( 2 t 2 Δ q , s ) p ( q , t ) = 2 t 2 ( X σ p ) ( q , t ) Δ q ( X σ p ) ( q , t ) .
P σ ( q , t ): = (X σ p )( q , t ) = p ( x ( q ,   s ),t ) d s
2 t 2 P σ ( q , t ) = c 2 Δ P σ ( q , t ) ,         ( q , t ) R 2 × ( 0 , ) ,                   P σ ( q , 0 ) = P σ , 0 ( q ): = (X σ p 0 )( q ) ,                   q R 2 ,               t P σ ( q , 0 ) = 0 ,                         q R 2           .    
( R P σ ) ( d , φ , t ) : = P σ ( d ( cos φ , sin φ ) + u ( sin φ , cos φ ) , t ) d u
2 t 2 ( R P σ ) ( d , φ , t ) = c 2 2 d 2 ( R P σ ) ( d , φ , t ) ,             ( R P σ ) ( d , φ , 0 ) = ( R P σ , 0 ) ( d , φ ) ,     t         ( R P σ ) ( d , φ , 0 ) = 0.        
    ( R P σ ) ( d , φ , t ) = 1 2 [     ( R P σ , 0 ) ( d c t , φ ) + ( R P σ , 0 ) ( d + c t , φ ) ] .
    ( R P σ ) ( d + c T , φ , T ) + ( R P σ ) ( d c T , φ , T ) =     ( R P σ , 0 ) ( d , φ ) + ( R P σ ) ( d , φ ,2 T ) .
( R P σ , 0 ) ( d , φ ) = { ( R P σ ) ( d + c T , φ , T ) + ( R P σ ) ( d c T , φ , T ), if  d [ r , r ] 0, if  d [ r , r ]

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