Abstract

We report on remote and contactless photoacoustic imaging (PAI) for the inspection of solid materials using a two-wave mixing interferometer. In this Letter, a semitransparent sample was excited with picosecond laser pulses. The local absorption of the electromagnetic radiation led to generation of broadband ultrasonic waves inside the sample. Ultrasonic waves arriving at the sample surface were detected utilizing a two-wave mixing interferometer. After data acquisition, the initial pressure distribution was reconstructed using a Fourier space synthetic aperture technique algorithm. We show the potential of PAI for the inspection of semitransparent solid materials.

© 2010 Optical Society of America

Over the past few years, photoacoustic imaging (PAI) has become a major research area and already has shown promising results in various biomedical applications [1]. Nevertheless, to the best of our knowledge, so far PAI has not been used for the inspection of solid materials. In general, in PAI a volume of a semitransparent sample is illuminated with short pulses of electromagnetic radiation, e.g., short laser pulses. Depending on the spatially varying optical properties of the sample, the radiation is absorbed and scattered differently. Local absorption of the electromagnetic waves within the volume leads to local heating, thermal expansion, and, finally, to the emission of broadband ultrasonic waves. This is the well-known photoacoustic effect, which was first reported by Bell in 1880 [2]. Because of the short excitation pulses, thermal waves can be neglected. Reconstruction of the absorbed energy density inside the sample is performed after measuring the ultrasonic signals outside of the sample [3]. Thus, photoacoustic signals contain information on light absorption at ultrasonic resolution. Detection of the ultrasonic signals is usually performed with the aid of piezoelectric transducers; however, interferometric detection schemes have already been shown. Also, Paltauf et al., for example, reported on photoacoustic tomography using a free-beam Mach–Zehnder interferometer [4], and Grün et al. showed three-dimensional PAI utilizing fiber-based Fabry–Perot and Mach–Zehnder interferometers [5]. In both works, sensing of the ultrasonic waves was performed within a water tank. Payne et al. [6] and Carp and Venugopalan [7] performed interferometric measurements on air/water and air/Intralipid solution interfaces. All the works listed above used fluids as a coupling medium for imaging of biological samples or phantoms. Zhang et al. showed PAI on skin without the need of immersion by utilizing Fabry–Perot polymer film sensors [8]. These sensors, however, require physical contact with the sample. For applications in material inspection, e.g., for in-line process control, the requirement for a coupling medium or a coupled sensor is a serious limitation. In this Letter, we acquire photoacoustic signals at the surface of a solid material remotely without the need for a coupling medium or an attached sensor by using a two-wave mixing interferometer. Such interferometers were shown to be robust against environmental influences [9] and are therefore commonly used in industrial applications.

Figure 1 shows a schematic of the measurement setup. Ultrasonic waves are excited within a sample by pulses from a Q-switched Nd:YAG laser (Ekspla 2143B) at the fundamental wavelength of 1064nm. The pulses have a duration of 20ps and an energy of about 50mJ. For detection of the ultrasonic waves, an interferometer utilizing a frequency-doubled cw Nd:YAG laser (532nm, Cobolt Samba) with power of 1W is used. After expanding the beam to a diameter of 3.5mm, the laser power is attenuated by an optical density (OD) plate to 400mW. A half-wave plate (HW1) and a polarizing beam splitter (PBS1) are used to adjust the intensity ratio between the reference and signal beams. The reference beam, which is deflected by PBS1, is directed onto the photorefractive crystal (PRC) by mirror M1. The signal beam passes both polarizing beam splitters (PBS1 and PBS2) in transmission and is circularly polarized by a quarter-wave plate (QW). After expansion by a factor of 5 with a Keplerian telescope, formed by lenses L1 and L2, the beam is focused onto the sample surface by lens L3. Light back reflected from the sample surface is collected by lens L3 and reduced in diameter by the telescope. After another pass of the quarter-wave plate, the beam is deflected by polarizing beam splitter PBS2 and focused onto the photorefractive crystal by lens L4. The PRC is a Bi12SiO20 (BSO) crystal with a size of 5mm×5mm×5mm, cut along the [110] and [1¯10] crystallographic axes. A voltage of 4kV is applied in the [001] direction over evaporated gold contacts in order to operate the crystal in the drift regime. Interference of the signal and reference beams was measured with a fast photodiode (Hamamatsu S5973-02), which was amplified by a high-speed 60dB amplifier (Femto HSA-Y-1-60).

The inspected sample (Fig. 2) consisted of a white 3-mm-thick semitransparent polymer board. On the back of the board, we placed a layer of black silicon glue, which shows strong absorption in the near-IR region. The combination of these two materials is commonly used in automotive industries, e.g., to glue polymer oil pans to the car body. Three small holes were blanked into the silicon glue layer in order to simulate defects. To allow the ultrasonic waves to propagate in all directions, the back of the sample was filled with a transparent cast resin up to a thickness of 14mm. A tube made of polyethylene prevented leaking of the resin during casting. Optical transmission through the 3-mm-thick board was below 5% for the visual and near-IR regions. Inside the white polymer board, light is scattered diffusely, which impedes resolution of the small holes from the front side with purely optical means. However, the pulsed IR radiation, which was absorbed in the glue layer, led to the emission of ultrasonic waves, which could be detected at the sample surface with the two-wave mixing interferometer. A typical measurement is depicted as curve (I) in Fig. 3a. The data were averaged 32 times to enhance the signal-to-noise ratio. In contrast to biological samples, where only longitudinal ultrasonic waves occur, the trace also exhibits transversal waves. The wave arriving first (L1) is the longitudinal wave, with a speed of sound of 2010m/s. At t3μs, a transversal wave (T1) with a sonic velocity of 1000m/s is detected. The longitudinal wave is reflected at both the polymer/air and subsequently the polymer/glue interfaces, and it arrives at the surface a second time (L2). For 3D imaging, the sample was moved with a x, y translational stage (81×93 points with a step size of 0.25mm), covering a total scan area of 20mm×23mm.

To reconstruct the initial pressure distribution, in PAI a Fourier backward projection algorithm is commonly used [10], whereas in laser ultrasound reconstruction is often performed by applying a Fourier space synthetic aperture technique (F-SAFT) [11, 12]. Burgholzer et al. demonstrated that both algorithms show the same results if both the spatial and temporal discretization approach zero; however, for a finite discretization, the F-SAFT algorithm shows fewer artifacts than Fourier space backprojection [13]. In the latter approach, an interpolation step is needed before the inverse Fourier transform, as the wave vectors k for a constant frequency ω are located on a circle. Since, for the F-SAFT reconstruction, no interpolation is needed, such an algorithm was chosen for reconstruction. For both algorithms, the reconstructed physical quantity must obey the Helmholtz equation. This is fulfilled, e.g., for the pressure p or the velocity potential ϕ. The interferometric setup used only allows for a measurement of the displacement uz parallel to the detection laser beam [14], i.e., perpendicular to the object surface, a quantity which does not obey the Helmholtz equation. However, we can evaluate the pressure p by considering the emitted waves as plane ones. This is a good assumption, as the size of the plane emitter (i.e., the silicon glue) is much bigger than the surface-emitter distance. The pressure p is then proportional to the velocity v [15]:

p=ρ0·c·v.
Here ρ0 denotes the density of the sample, and c is the speed of sound in the medium. For plane waves, the velocity vector is perpendicular to the wavefront and thus perpendicular to the sample surface. Hence, calculation of the local pressure is possible over a time derivation of the surface displacement uz. In Fig. 3, curve (II), the derivative of the measured data is depicted. Before derivation, the data were filtered by a moving average filter and a wavelet filter. In the opposite case, where the size of the emitting inclusion is much smaller than the distance to the surface, e.g., a small emitting disc, the pressure is proportional to the time derivative of v [15]:
p=ρ0a22z·v˙.
Here a is the radius of the acoustic emitter, and z is the distance between the emitter and surface. In this case, the measured data have to be differentiated twice before reconstruction.

A F-SAFT reconstruction at a depth of 3.05mm after differentiation of the data is shown in Figs. 3b, 3c. This depth lies slightly below the polymer/glue interface, and therefore it is possible to assess the initial pressure in the glue layer. Figure 3b shows a reconstruction using the longitudinal speed of sound. For comparison, a photograph of the inspected region is depicted in Fig. 3d. The pictures show good agreement, and even details such as the small asymmetry of the big center hole are well reproduced. However, four additional small spots can be identified. Three spots appear in the right third of the image—one next to the small right hole and two beside the big hole in the center. A fourth spot appears at the left upper corner. All these spots are attributed to air bubbles between the polymer and the glue, which were created during the fabrication of the sample. These bubbles blocked, to a certain extent, the propagation of the excited waves to the surface. From the same data, another reconstruction was done using the transversal speed of sound, as depicted in Fig. 3c. Also, in this case, the features are well reproduced. The artifact in the lower part of the image is due to a surface acoustic wave that arrives at the same time as the transversal wave.

The presented experiments show the potential of PAI for detection or inspection of absorbing inclusions in a semitransparent host material. For more complex materials, which exhibit an inhomogeneous speed of sound, a time reversal algorithm [16, 17] can be used instead of a F-SAFT or Fourier reconstruction.

In summary, we reported on remote PAI of a polymer sample. Ultrasonic waves within the sample were excited by picosecond pulses from a Q-switched Nd:YAG laser. Remote measurement of the ultrasonic waves was performed utilizing a two-wave mixing interferometer with a BSO crystal. After differentiation of the data, the initial pressure distribution was reconstructed using a F-SAFT algorithm. In contrast to biomedical samples, where only longitudinal waves occur, in solid materials transversal waves also appear. Image reconstruction was accomplished with both wave types. This experiment shows the potential of PAI for the detection of absorbing inclusions in a semitransparent host material.

This work has been supported by the Christian Doppler Research Association, the Federal Ministry of Economy, Family and Youth, the industrial partner INPRO Innovationsgesellschaft für fortgeschrittene Produktionssysteme in der Fahrzeugindustrie mbH, the Austrian Science Fund under project number S10503-N20, the European Regional Development Fund in the framework of the European Union program Region 13, and the federal states of Upper Austria.

 figure: Fig. 1

Fig. 1 Schematic of the measurement setup: L1–L4, lenses; M1–M2, mirrors; BE, beam expander; HW1, half-wave plate; QW, quarter-wave plate; PBS1–PBS2, polarizing beam splitters; OD, optical density plate; PRC, photorefractive crystal.

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 figure: Fig. 2

Fig. 2 (a) Schematic of the sample and (b) photograph from the back side of the sample.

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 figure: Fig. 3

Fig. 3 (a) Curve (I): typical measurement taken with the PRC interferometer. Curve (II): time derivative of the measurement data after filtering. L1, T1, and L2 denote the longitudinal, transversal, and reflected longitudinal waves, respectively. (b) F-SAFT reconstruction using the longitudinal speed of sound. (c) F-SAFT reconstruction using the transversal speed of sound. The artifact at the bottom part of the image is due to a surface acoustic wave, which arrives at the same time as the transversal wave. (d) Photograph of the inspected region at the back of the sample (area 20mm×23mm).

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1. L. Wang, Nat. Photon. 3, 503 (2009). [CrossRef]  

2. A. G. Bell, Am. J. Sci. 20, 305 (1880).

3. N. Xu and L. V. Wang, Rev. Sci. Instrum. 77, 041101 (2006). [CrossRef]  

4. G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, Appl. Opt. 46, 3352 (2007). [CrossRef]   [PubMed]  

5. H. Grün, T. Berer, R. Nuster, G. Paltauf, and P. Burgholzer, J. Biomed. Opt. 15, 021306 (2010). [CrossRef]   [PubMed]  

6. B. P. Payne, V. Venugopalan, B. B. Mikic, and N. S. Nishioka, J. Biomed. Opt. 8, 273 (2003). [CrossRef]   [PubMed]  

7. S. A. Carp and V. Venugopalan, J. Biomed. Opt. 12, 064001 (2007). [CrossRef]  

8. E. Z. Zhang, J. G. Laufer, R. P. Pedley, and P. C. Beard, Phys. Med. Biol. 54, 1035 (2009). [CrossRef]   [PubMed]  

9. B. Pouet, R. Ing, S. Krishnaswamy, and D. Royer, Appl. Phys. Lett. 69, 3782 (1996). [CrossRef]  

10. K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, Phys. Med. Biol. 46, 1863 (2001). [CrossRef]   [PubMed]  

11. L. J. Busse, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 174 (1992). [CrossRef]   [PubMed]  

12. A. Blouin, D. Lévesque, C. Néron, D. Drolet, and J.-P. Monchalin, Opt. Express 2, 531 (1998). [CrossRef]   [PubMed]  

13. P. Burgholzer, T. Berer, H. Grün, H. Roitner, J. Bauer-Marschallinger, R. Nuster, and G. Paltauf, J. Phys. Conf. Ser. 214, 012009 (2010). [CrossRef]  

14. T. E. Blum, K. van Wijk, B. Pouet, and A. Wartelle, Rev. Sci. Instrum. 81, 073101 (2010). [CrossRef]   [PubMed]  

15. D. Royer and E. Dieulesaint, Elastic Waves in Solids I (Springer, 2000).

16. P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, Inverse Prob. 23, S65 (2007). [CrossRef]  

17. H. Grün, G. Paltauf, M. Haltmeier, and P. Burgholzer, Proc. SPIE 6631, 663107 (2007). [CrossRef]  

References

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  1. L. Wang, Nat. Photon. 3, 503 (2009).
    [Crossref]
  2. A. G. Bell, Am. J. Sci. 20, 305 (1880).
  3. N. Xu and L. V. Wang, Rev. Sci. Instrum. 77, 041101 (2006).
    [Crossref]
  4. G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, Appl. Opt. 46, 3352 (2007).
    [Crossref] [PubMed]
  5. H. Grün, T. Berer, R. Nuster, G. Paltauf, and P. Burgholzer, J. Biomed. Opt. 15, 021306 (2010).
    [Crossref] [PubMed]
  6. B. P. Payne, V. Venugopalan, B. B. Mikic, and N. S. Nishioka, J. Biomed. Opt. 8, 273 (2003).
    [Crossref] [PubMed]
  7. S. A. Carp and V. Venugopalan, J. Biomed. Opt. 12, 064001 (2007).
    [Crossref]
  8. E. Z. Zhang, J. G. Laufer, R. P. Pedley, and P. C. Beard, Phys. Med. Biol. 54, 1035 (2009).
    [Crossref] [PubMed]
  9. B. Pouet, R. Ing, S. Krishnaswamy, and D. Royer, Appl. Phys. Lett. 69, 3782 (1996).
    [Crossref]
  10. K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, Phys. Med. Biol. 46, 1863 (2001).
    [Crossref] [PubMed]
  11. L. J. Busse, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 174 (1992).
    [Crossref] [PubMed]
  12. A. Blouin, D. Lévesque, C. Néron, D. Drolet, and J.-P. Monchalin, Opt. Express 2, 531 (1998).
    [Crossref] [PubMed]
  13. P. Burgholzer, T. Berer, H. Grün, H. Roitner, J. Bauer-Marschallinger, R. Nuster, and G. Paltauf, J. Phys. Conf. Ser. 214, 012009 (2010).
    [Crossref]
  14. T. E. Blum, K. van Wijk, B. Pouet, and A. Wartelle, Rev. Sci. Instrum. 81, 073101 (2010).
    [Crossref] [PubMed]
  15. D. Royer and E. Dieulesaint, Elastic Waves in Solids I (Springer, 2000).
  16. P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, Inverse Prob. 23, S65 (2007).
    [Crossref]
  17. H. Grün, G. Paltauf, M. Haltmeier, and P. Burgholzer, Proc. SPIE 6631, 663107 (2007).
    [Crossref]

2010 (3)

H. Grün, T. Berer, R. Nuster, G. Paltauf, and P. Burgholzer, J. Biomed. Opt. 15, 021306 (2010).
[Crossref] [PubMed]

P. Burgholzer, T. Berer, H. Grün, H. Roitner, J. Bauer-Marschallinger, R. Nuster, and G. Paltauf, J. Phys. Conf. Ser. 214, 012009 (2010).
[Crossref]

T. E. Blum, K. van Wijk, B. Pouet, and A. Wartelle, Rev. Sci. Instrum. 81, 073101 (2010).
[Crossref] [PubMed]

2009 (2)

E. Z. Zhang, J. G. Laufer, R. P. Pedley, and P. C. Beard, Phys. Med. Biol. 54, 1035 (2009).
[Crossref] [PubMed]

L. Wang, Nat. Photon. 3, 503 (2009).
[Crossref]

2007 (4)

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, Appl. Opt. 46, 3352 (2007).
[Crossref] [PubMed]

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, Inverse Prob. 23, S65 (2007).
[Crossref]

H. Grün, G. Paltauf, M. Haltmeier, and P. Burgholzer, Proc. SPIE 6631, 663107 (2007).
[Crossref]

S. A. Carp and V. Venugopalan, J. Biomed. Opt. 12, 064001 (2007).
[Crossref]

2006 (1)

N. Xu and L. V. Wang, Rev. Sci. Instrum. 77, 041101 (2006).
[Crossref]

2003 (1)

B. P. Payne, V. Venugopalan, B. B. Mikic, and N. S. Nishioka, J. Biomed. Opt. 8, 273 (2003).
[Crossref] [PubMed]

2001 (1)

K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, Phys. Med. Biol. 46, 1863 (2001).
[Crossref] [PubMed]

1998 (1)

1996 (1)

B. Pouet, R. Ing, S. Krishnaswamy, and D. Royer, Appl. Phys. Lett. 69, 3782 (1996).
[Crossref]

1992 (1)

L. J. Busse, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 174 (1992).
[Crossref] [PubMed]

1880 (1)

A. G. Bell, Am. J. Sci. 20, 305 (1880).

Bauer-Marschallinger, J.

P. Burgholzer, T. Berer, H. Grün, H. Roitner, J. Bauer-Marschallinger, R. Nuster, and G. Paltauf, J. Phys. Conf. Ser. 214, 012009 (2010).
[Crossref]

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, Inverse Prob. 23, S65 (2007).
[Crossref]

Beard, P. C.

E. Z. Zhang, J. G. Laufer, R. P. Pedley, and P. C. Beard, Phys. Med. Biol. 54, 1035 (2009).
[Crossref] [PubMed]

Bebie, H.

K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, Phys. Med. Biol. 46, 1863 (2001).
[Crossref] [PubMed]

Bell, A. G.

A. G. Bell, Am. J. Sci. 20, 305 (1880).

Berer, T.

H. Grün, T. Berer, R. Nuster, G. Paltauf, and P. Burgholzer, J. Biomed. Opt. 15, 021306 (2010).
[Crossref] [PubMed]

P. Burgholzer, T. Berer, H. Grün, H. Roitner, J. Bauer-Marschallinger, R. Nuster, and G. Paltauf, J. Phys. Conf. Ser. 214, 012009 (2010).
[Crossref]

Blouin, A.

Blum, T. E.

T. E. Blum, K. van Wijk, B. Pouet, and A. Wartelle, Rev. Sci. Instrum. 81, 073101 (2010).
[Crossref] [PubMed]

Burgholzer, P.

P. Burgholzer, T. Berer, H. Grün, H. Roitner, J. Bauer-Marschallinger, R. Nuster, and G. Paltauf, J. Phys. Conf. Ser. 214, 012009 (2010).
[Crossref]

H. Grün, T. Berer, R. Nuster, G. Paltauf, and P. Burgholzer, J. Biomed. Opt. 15, 021306 (2010).
[Crossref] [PubMed]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, Appl. Opt. 46, 3352 (2007).
[Crossref] [PubMed]

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, Inverse Prob. 23, S65 (2007).
[Crossref]

H. Grün, G. Paltauf, M. Haltmeier, and P. Burgholzer, Proc. SPIE 6631, 663107 (2007).
[Crossref]

Busse, L. J.

L. J. Busse, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 174 (1992).
[Crossref] [PubMed]

Carp, S. A.

S. A. Carp and V. Venugopalan, J. Biomed. Opt. 12, 064001 (2007).
[Crossref]

Dieulesaint, E.

D. Royer and E. Dieulesaint, Elastic Waves in Solids I (Springer, 2000).

Drolet, D.

Frenz, M.

K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, Phys. Med. Biol. 46, 1863 (2001).
[Crossref] [PubMed]

Grün, H.

H. Grün, T. Berer, R. Nuster, G. Paltauf, and P. Burgholzer, J. Biomed. Opt. 15, 021306 (2010).
[Crossref] [PubMed]

P. Burgholzer, T. Berer, H. Grün, H. Roitner, J. Bauer-Marschallinger, R. Nuster, and G. Paltauf, J. Phys. Conf. Ser. 214, 012009 (2010).
[Crossref]

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, Inverse Prob. 23, S65 (2007).
[Crossref]

H. Grün, G. Paltauf, M. Haltmeier, and P. Burgholzer, Proc. SPIE 6631, 663107 (2007).
[Crossref]

Haltmeier, M.

H. Grün, G. Paltauf, M. Haltmeier, and P. Burgholzer, Proc. SPIE 6631, 663107 (2007).
[Crossref]

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, Inverse Prob. 23, S65 (2007).
[Crossref]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, Appl. Opt. 46, 3352 (2007).
[Crossref] [PubMed]

Ing, R.

B. Pouet, R. Ing, S. Krishnaswamy, and D. Royer, Appl. Phys. Lett. 69, 3782 (1996).
[Crossref]

Köstli, K. P.

K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, Phys. Med. Biol. 46, 1863 (2001).
[Crossref] [PubMed]

Krishnaswamy, S.

B. Pouet, R. Ing, S. Krishnaswamy, and D. Royer, Appl. Phys. Lett. 69, 3782 (1996).
[Crossref]

Laufer, J. G.

E. Z. Zhang, J. G. Laufer, R. P. Pedley, and P. C. Beard, Phys. Med. Biol. 54, 1035 (2009).
[Crossref] [PubMed]

Lévesque, D.

Mikic, B. B.

B. P. Payne, V. Venugopalan, B. B. Mikic, and N. S. Nishioka, J. Biomed. Opt. 8, 273 (2003).
[Crossref] [PubMed]

Monchalin, J.-P.

Néron, C.

Nishioka, N. S.

B. P. Payne, V. Venugopalan, B. B. Mikic, and N. S. Nishioka, J. Biomed. Opt. 8, 273 (2003).
[Crossref] [PubMed]

Nuster, R.

H. Grün, T. Berer, R. Nuster, G. Paltauf, and P. Burgholzer, J. Biomed. Opt. 15, 021306 (2010).
[Crossref] [PubMed]

P. Burgholzer, T. Berer, H. Grün, H. Roitner, J. Bauer-Marschallinger, R. Nuster, and G. Paltauf, J. Phys. Conf. Ser. 214, 012009 (2010).
[Crossref]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, Appl. Opt. 46, 3352 (2007).
[Crossref] [PubMed]

Paltauf, G.

H. Grün, T. Berer, R. Nuster, G. Paltauf, and P. Burgholzer, J. Biomed. Opt. 15, 021306 (2010).
[Crossref] [PubMed]

P. Burgholzer, T. Berer, H. Grün, H. Roitner, J. Bauer-Marschallinger, R. Nuster, and G. Paltauf, J. Phys. Conf. Ser. 214, 012009 (2010).
[Crossref]

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, Inverse Prob. 23, S65 (2007).
[Crossref]

H. Grün, G. Paltauf, M. Haltmeier, and P. Burgholzer, Proc. SPIE 6631, 663107 (2007).
[Crossref]

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, Appl. Opt. 46, 3352 (2007).
[Crossref] [PubMed]

Payne, B. P.

B. P. Payne, V. Venugopalan, B. B. Mikic, and N. S. Nishioka, J. Biomed. Opt. 8, 273 (2003).
[Crossref] [PubMed]

Pedley, R. P.

E. Z. Zhang, J. G. Laufer, R. P. Pedley, and P. C. Beard, Phys. Med. Biol. 54, 1035 (2009).
[Crossref] [PubMed]

Pouet, B.

T. E. Blum, K. van Wijk, B. Pouet, and A. Wartelle, Rev. Sci. Instrum. 81, 073101 (2010).
[Crossref] [PubMed]

B. Pouet, R. Ing, S. Krishnaswamy, and D. Royer, Appl. Phys. Lett. 69, 3782 (1996).
[Crossref]

Roitner, H.

P. Burgholzer, T. Berer, H. Grün, H. Roitner, J. Bauer-Marschallinger, R. Nuster, and G. Paltauf, J. Phys. Conf. Ser. 214, 012009 (2010).
[Crossref]

Royer, D.

B. Pouet, R. Ing, S. Krishnaswamy, and D. Royer, Appl. Phys. Lett. 69, 3782 (1996).
[Crossref]

D. Royer and E. Dieulesaint, Elastic Waves in Solids I (Springer, 2000).

van Wijk, K.

T. E. Blum, K. van Wijk, B. Pouet, and A. Wartelle, Rev. Sci. Instrum. 81, 073101 (2010).
[Crossref] [PubMed]

Venugopalan, V.

S. A. Carp and V. Venugopalan, J. Biomed. Opt. 12, 064001 (2007).
[Crossref]

B. P. Payne, V. Venugopalan, B. B. Mikic, and N. S. Nishioka, J. Biomed. Opt. 8, 273 (2003).
[Crossref] [PubMed]

Wang, L.

L. Wang, Nat. Photon. 3, 503 (2009).
[Crossref]

Wang, L. V.

N. Xu and L. V. Wang, Rev. Sci. Instrum. 77, 041101 (2006).
[Crossref]

Wartelle, A.

T. E. Blum, K. van Wijk, B. Pouet, and A. Wartelle, Rev. Sci. Instrum. 81, 073101 (2010).
[Crossref] [PubMed]

Weber, H. P.

K. P. Köstli, M. Frenz, H. Bebie, and H. P. Weber, Phys. Med. Biol. 46, 1863 (2001).
[Crossref] [PubMed]

Xu, N.

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Figures (3)

Fig. 1
Fig. 1 Schematic of the measurement setup: L1–L4, lenses; M1–M2, mirrors; BE, beam expander; HW1, half-wave plate; QW, quarter-wave plate; PBS1–PBS2, polarizing beam splitters; OD, optical density plate; PRC, photorefractive crystal.
Fig. 2
Fig. 2 (a) Schematic of the sample and (b) photograph from the back side of the sample.
Fig. 3
Fig. 3 (a) Curve (I): typical measurement taken with the PRC interferometer. Curve (II): time derivative of the measurement data after filtering. L1, T1, and L2 denote the longitudinal, transversal, and reflected longitudinal waves, respectively. (b) F-SAFT reconstruction using the longitudinal speed of sound. (c) F-SAFT reconstruction using the transversal speed of sound. The artifact at the bottom part of the image is due to a surface acoustic wave, which arrives at the same time as the transversal wave. (d) Photograph of the inspected region at the back of the sample (area 20 mm × 23 mm ).

Equations (2)

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p = ρ 0 · c · v .
p = ρ 0 a 2 2 z · v ˙ .

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