Thermoacoustic tomography with integrating area and line detectors

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Thermoacoustic Tomography with Integrating Area and Line Detectors Peter Burgholzer, Christian Hofer, G¨ unther Paltauf, Markus Haltmeier, and Otmar Scherzer, Associate Member, IEEE Abstract—Thermoacoustic (optoacoustic, photoacoustic) tomography is based on the generation of acoustic waves by illumination of a sample with a short electromagnetic pulse. The absorption density inside the sample is reconstructed from the acoustic pressure measured outside the illuminated sample. So far measurement data have been collected with small detectors as approximations of point detectors. Here, a novel measurement setup applying integrating detectors (e.g., lines or planes made of piezoelectric films) is presented. That way, the pressure is integrated along one or two dimensions, enabling the use of numerically efficient algorithms, such as algorithms for the inverse radon transformation, for thermoacoustic tomography. To reconstruct a three-dimensional sample, either an area detector has to be moved tangential around a sphere that encloses the sample or an array of line detectors is rotated around a single axis. The line detectors can be focused on cross sections perpendicular to the rotation axis using a synthetic aperture (SAFT) or by scanning with a cylindrical lens detector. Measurements were made with piezoelectric polyvinylidene fluoride film detectors and evaluated by comparison with numerical simulations. The resolution achieved in the resulting tomography images is demonstrated on the example of the reconstructed cross section of a grape.

I. Introduction hermoacoustic tomography, also known as optoacoustic or photoacoustic tomography, is an emerging technology for the imaging of semitransparent, turbid media with applications mainly in the diagnostics of biological tissue [1]–[3]. Its advantages over conventional imaging techniques based on x-rays, ultrasound, or magnetic resonance are the application of nonionizing radiation, an enhanced contrast for many important tissue structures, and the relatively low cost (mainly compared to magnetic resonance imaging). It combines the advantages of pure optical imaging with those of ultrasound imaging. Whereas in optical imaging the contrast is usually high with a poor image resolution due to the diffuse nature of light propagation, in ultrasonic imaging the contrast between structures with similar acoustic properties (e.g., different soft tissue constituents) is relatively low with a high spatial resolution.

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Manuscript received November 4, 2004; accepted February 8, 2005. The work of M.H. and O.S. has been supported by the Austrian Science Fund (FWF), Proj. Nr. Y123-INF. P. Burgholzer and C. Hofer are with Upper Austrian Research, Hafenstraße 47-51, A-4020 Linz, Austria (e-mail: [email protected]). G. Paltauf is with Karl-Franzens-Universit¨ at Graz, Department of Physics, Universit¨ atsplatz 5, A-8010 Graz, Austria. M. Haltmeier and O. Scherzer are with the Department of Computer Science, Universit¨ at Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria.

Due to the conversion of absorbed electromagnetic radiation into sound waves, thermoacoustics is able to generate images that at the same time show high optical contrast and ultrasonic resolution. Thermoacoustic methods have been proposed for a variety of medical diagnostic applications. Recently the imaging of small animals that are models for basic medical research has become an important application [3], [4]. In humans, thermoacoustic methods have been investigated for the examination of skin vasculature [5]–[8], mammography [9]–[12], and the monitoring of heat-induced changes in tissue optical properties [13]. Thermoacoustic imaging is not only able to reveal the optical structure of an object, but it also is capable of providing information about its chemical composition as a result of the dependence of the acoustic signal amplitude on the absorption coefficient [4], [14], [15]. For image reconstruction, the inverse problem of thermoelastic sound generation has to be solved. Pulsed-laser heating causes a three-dimensional distribution of absorbed energy that becomes the source of a sound wave. The resulting acoustic signals measured outside the object allow for the reconstruction of the original energy density distribution. In the literature, analytic formulas to calculate the density function from the signals have been derived for various detector array geometries, such as planes, spheres, cylinders, and circles [16]–[20]. These algorithms assume that the data are collected with small acoustic detectors at the sample surface. To be able to generate images with constant, high spatial resolution throughout the three-dimensional image space, the conventional approach would require the use of ultrasound detectors that are much smaller than the imaged object. Our new approach is to apply specially shaped detectors that are larger than the imaged object to acquire acoustic signals. This approach is based on the fact that such a detector receives a signal that is not an approximate projection over a spherical surface (as is the case with detectors smaller than the object) but rather an exact projection over an area (or line) that is determined by the shape of the detector itself. For instance, it is shown in Section II from the properties of thermoacoustically excited waves that a large planar receiver measures a wave as it would be generated in an object in which the initial distribution of absorbed energy (the volumetric energy density) is averaged over planes parallel to the receiver surface. A signal acquired in this way corresponds to the projection of the energy density along those planes, and the time axis multiplied with the speed of sound gives the distance of the

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projection plane to the detector plane. A set of signals acquired by rotating the plane detector around the object, either around a single axis or around the surface of a sphere, exactly corresponds to the radon transform of the distribution of absorbed energy density. Well-established methods of computerized tomography, therefore, can be used to reconstruct the density distribution from the measured signals [21]. The resolution of small structures reconstructed from data measured with a point transducer is physically limited by the detector size [22]. There is no such limit for the proposed tomography method as the reconstruction algorithm assumes detector dimensions larger than the sample dimensions. Spatial resolution is limited only by the bandwidth of the detector, allowing for high resolution images. In Section II the novel imaging technique for twodimensional integrating detectors is presented, a measurement setup is described, and imaging results for a twodimensional sample are given. In Section III the imaging technique for one-dimensional detectors is described, and the focusing properties for cylindrical lens detectors are measured and simulated. With one of these cylindrical detectors, the cross section of a grape is reconstructed. Section IV concludes the work and gives an outlook on future work. II. Two-Dimensional Integrating Detectors—Large Area Detectors In typical pulsed thermoacoustic measurements, the electromagnetic pulse duration is shorter than the acoustic transit time d/c of an acoustic wave propagating with the speed of sound c through a sample with a characteristic size d. Therefore, the laser pulse can be described by a temporal Dirac function, and the initial pressure distribution p0 is proportional to the volumetric density W of the locally absorbed electromagnetic energy. The wave equation for the pressure p as a function of space
x and time t is [19]:
2  ∂ 2 − c ∆ p(
x, t) = 0, (1) ∂t2 x, 0) = 0, where with p(
x, 0) = p0 (
x) = ΓW (
x) and ∂p ∂t (
Γ = β c2 /Cp is the Grueneisen parameter with the thermal expansion coefficient β and the specific heat capacity Cp . A large area detector is a two-dimensional object that integrates the pressure, e.g., over x2 and x3 . In Cartesian coordinates, we can use the decomposition of the Laplacian ∆ = ∆1 + ∆2 with: ∂2 , ∂x21 ∂2 ∂2 ∆2 = + 2, 2 ∂x2 ∂x3

∆1 =

(2)

and the Green’s formula to show that, for a planar detector, the wave equation is reduced to one dimension:
2  ∂ 2 − c ∆ (3) 1 p = 0, ∂t2

 p (x1 , x2 , x3 , t) d x2 d x3 . where p (x1 , t) = The Fourier transform of (3) with respect to time is the Helmholtz equation, and the solution of (3) is given by [19]:  1 p (x1 , t) = (4) P (k) cos(ωt)ejkx1 dk 2π with ω = c · |k|. The initial conditions for the pressure in (4) determine the Fourier transformed pressure P (k). Inserting these initial conditions in (4) gives the solution of (3) in the time domain. D’Alemberts’s formula is the unique solution for a planar detector area: p (x1 , t) =

1 1 p (x1 + ct) + p0 (x1 − ct) 2 0 2

(5)

where p0 (x1 ) = p (x1 , 0). Similar solutions can be found for spherical detector areas. At the time t a planar detector area at x1 = 0 measures the integral of p0 over the plane x1 = ct (the sample should be on the side of the detector with x1 > 0). As discussed in an earlier paper [21], a pressure signal measured with the planar detector, therefore, is a projection over x2 –x3 -planes, and a set of such projections in different directions is a three-dimensional radon transform of an object. For a full reconstruction of a three-dimensional object, the planar detector has to be moved tangentially around a sphere that encloses the object. If the detector plane is rotated around a single axis, only the structure of the object in a plane perpendicular to this axis can be imaged. This reduced scan is suitable for objects that are translationally invariant along the direction of the rotation axis. Using the inversion formula of the radon transform, p0 can be reconstructed. In the presented work, a filtered backprojection algorithm [23] was applied for the image reconstruction from experimental data. An experimental setup for the collection of imaging data to recover an object that is translationally invariant along the rotation axis (two-dimensional object) is shown in Fig. 1. The object was mounted on a frame in a water tank and was illuminated homogenously by a 20 ps short Nd:YAG laser pulse. The thermoacoustic pressure signal was recorded with a 25-µm thick film of piezoelectric PVDF, which generated an electric signal proportional to the total pressure acting on it. The piezoelectric film was glued on the flat surface of an acrylic glass block, and its electric signal was picked up from aluminum coatings on either side of the film, amplified with a high-speed current amplifier with a 3-dB bandwidth of 12 MHz and recorded with a digital storage oscilloscope. For this bandwidth, the theoretical spatial resolution in water (sound velocity 1500 m/s) is 125 µm. This could be verified with a sample made of a grid of black lines printed onto a transparent film. The width of the printed lines and the spaces between them were equal. The film was mounted perpendicularly to the detector plane with the individual lines oriented parallel to the detector plane.

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acquire three-dimensional imaging data. It has to be emphasized that this scanning procedure would not require more data to be stored than with a point-like detector as, in both cases, the data sets have to be three-dimensional: two dimensions are needed for the position on the sphere and a third dimension is needed for the time. A more convenient way to collect three-dimensional imaging data is presented in Section III. III. One-Dimensional Integrating Detectors—Line and Cylindrical Detectors

Fig. 1. Experimental setup for the thermoacoustic imaging of twodimensional objects. The sample is rotated in 5◦ steps while it is illuminated by a short laser pulse. The thermoacoustic pressure is detected with a flat piezoelectric polymer film detector.

For a lattice parameter of 200 µm, the individual lines can be separated easily; and for a lattice parameter of 100 µm, the line signals overlap (Fig. 2). In the following experiment, an object consisting of three cylindrical absorbers with diameters of 2, 3, and 4 mm was mounted on a frame and rotated. The object fit into a cylinder with a diameter of D = 10 mm. Therefore, the detecting √ film had to include a disc with a diameter of at least 10 8 (≈28) mm to ensure that all the signals in the time D/c were integrated by the detector. In order to be able to create space between the rotated object and the detector, a 50 × 40 mm film was used. Every 5◦ the sample was illuminated by a short laser pulse, much shorter than the acoustic transit time for the smallest structure in the object. The smallest structure resolvable with the bandwidth of 12 MHz has a size of 125 µm and an acoustic transit time of 83 ns. For the inversion of the two-dimensional radon transform, the filtered backprojection algorithm with linear interpolation was applied; and for frequency domain filtering, the Ram-Lak filter was multiplied by a Hann window [23]. Fig. 3 shows the numerical reconstruction of the three cylinders. A large area detector only has temporal but no lateral spatial resolution. This experiment demonstrates that acoustic signals collected with this detector can be used to reconstruct an image of objects smaller than the detector. This is in contrast to approaches using small detectors rotating around the sample in which a resolution better than the detector size can be achieved only for areas near the rotation axis [3], [24]. Although the presented experimental setup for imaging of two-dimensional objects only is of limited use, scanning the detector plane around the surface of a sphere that encloses the object would allow one to

In an experimental setup, it is easier to rotate the detector around a single axis than to scan it tangentially over the surface of a sphere. To be able to reconstruct a three-dimensional object, information about its structure in the direction of the rotation axis is needed; this can be accomplished by using either an array of line detectors, which can be focused with a synthetic aperture (SAFT), or by scanning in the direction of the rotation axis with a single, cylindrical lens detector. In both cases, the general principle that the detector dimension exceeds the size of the object is maintained. A suitable line detector array consists of lines that are perpendicular to the axis around which the object is rotated and have constant distance from that axis. In other words, the planar detector described above is resolved in lines perpendicular to the rotation axis. We assume that the object is rotated around an axis parallel to the x2 axis and that the lines of the detector are located in the x3 = 0 plane perpendicular to this axis in the x1 direction (same coordinate system as in Fig. 4). For planar detectors, (5) shows a simple, direct relationship between the measured pressure signal p (x1 , t) and the radon transform p0 , expressed as plane projections of the initial pressure distribution p0 . In the case of a line detector array, this relationship is more complicated as the projections p (x1 , x3 , t) =  p (x1 , x2 , x3 , t) d x1 for t = 0 need to be reconstructed from the measurements p (x2 , x3 = 0, t). A suitable algorithm is the two-dimensional Fourier-transform image reconstruction described by K¨ ostli and Beard [25]. These projections, when measured from all directions around a single rotation axis, form a radon transform in terms of line projections, from which the full three-dimensional structure of the object can be obtained by applying the inverse radon transform. A thermoacoustic tomograph based on line detector arrays is in development and will be presented in a future work. To directly image single planes with x2 = const., it is possible to use a cylindrical lens detector with its axis parallel to the x1 -axis instead of the line detector array (see Fig. 4). Such a cylindrical detector focuses primarily on a plane with x2 = const. which contains the cylinder axis. The amount of focusing is determined by the ratio of the detector height in the x2 -direction and the cylinder radius. Therefore, for each plane x2 = const., the measured pressure signal p (x2 , x3 = 0, t) shows a direct relation to

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Fig. 2. Planar detector measurements of acoustic waves emitted from absorbing lines oriented parallel to the detector surface, arranged in a grid. The spatial resolution corresponds to the bandwidth of the detector. For a bandwidth of 12 MHz and for a line-grid with a lattice parameter of 200 µm, the individual lines can be separated easily (left graph), for a lattice parameter of 100 µm the line signals overlap (right graph).

Fig. 3. Numerical reconstruction applying the two-dimensional inverse radon transformation to the data measured with the experimental setup shown in Fig. 1.

p (x2 , x3 , t = 0) corresponding to (5). The initial pressure distribution p0 can be reconstructed by a two-dimensional inverse radon transform. The detector gets the maximum signal when the acoustic source lies in the focal plane; however, signals also can be detected for out-of-plane sources. Therefore, the response generated by a point source on two cylindrical lens detectors made of acrylic glass and a 28 µm thick piezo film was measured and calculated. The detectors were fabricated by gluing a 44 × 12 mm piece of PVDF film on a concave cylindrical surface with a radius of either 18 mm (detector FD1) or 7 mm (detector FD2). The radius was chosen in such a way that the total height

Fig. 4. Measurement data from a cylindrical lens detector, focused on a cross section perpendicular to the rotation axis, can be used for two-dimensional reconstruction of a three-dimensional object.

of the curved detector divided by the radius was 2/3 for FD1 and 3/2 for FD2. A black dot at the end of a 0.6-mm core diameter glass fiber served as a thermoacoustic point source. The fiber was illuminated by a 20 ps short Nd:YAG laser pulse, and the point source was scanned over a plane perpendicular to the axis of the cylinder detector using a two-dimensional translation stage with a step size of 0.25 mm (see Fig. 5). At each position the total detected signal energy, defined as the time integral of the squared pressure, was measured. The results for both detectors are shown in Fig. 6. For comparison, Fig. 7 shows results of a simulation using a solution of the two-dimensional wave equation for a Gaussian source with the finite difference method.

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Fig. 7. Simulation with the finite-difference method for a Gaussian source. Top, detector FD1 with a cylinder radius of 18 mm. Bottom, detector FD2 with a cylinder radius of 7 mm.

Fig. 5. Experimental setup for measuring the response of a cylindrical lens detector for a point source. The relative position of point source and detector can be changed with an x-y stage mounted in a vertical position.

Both, experiment and simulation, suggest that detector FD1 with a cylinder radius of 18 mm and a length of 44 mm is suitable for a three-dimensional thermoacoustic tomograph for objects with a detector distance between 8 mm and 16 mm in the focal plane. The rotation axis should have a distance of 12 mm to the detector. Fig. 8 shows an image of the cross section of a grape taken with this tomograph. The rotating grape was illuminated at angular steps of 5◦ by a laser pulse with 20 ps pulse duration as described in Section II. From the measured signal, a cross section perpendicular to the rotation axis was reconstructed by means of the two-dimensional inverse radon transform. Inside the grape the 0.6-mm diameter pin that fixed the grape and a grain could be detected clearly. Similar to the planar detector, the image resolution in the displayed x1 –x3 -plane is given only by the temporal resolution of the detector, independent of the location in the plane. However, the resolution in the x2 direction is limited by the size of the cylindrical detector, causing cross-talk between closely neighboring imaging planes. Optimizing the focusing properties of the cylindrical lens detector can minimize this cross-talk. An additional approach, the use of deconvolution methods, which are known from microscopic section imaging [26], will be addressed in future studies.

IV. Conclusions Fig. 6. Total detected signal energy, definded as the time integral of the square of the measured pressure, for a point source as function of the relative position to the detector. Top, detector FD1 with a cylinder radius of 18 mm. Bottom, detector FD2 with a cylinder radius of 7 mm.

Measurements with one- or two-dimensional integrating detectors enable the use of numerically efficient and stable algorithms for thermoacoustic tomography. We have demonstrated the working principle with piezoelectric polymer film detectors, achieving a resolution of 125 µm at a measurement bandwidth of 12 MHz. An advantage of

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Fig. 8. Cross-section image of a grape. The small circle inside is the cross section of the 0.6-mm diameter pin that fixed the grape. The other object inside the grape is a grain, which clearly could be detected. The darker region between the two objects is a shadow due to the high light absorption of the steel pin as well as the grape grain.

the proposed thermoacoustic imaging system is that the spatial resolution is limited only by the frequency bandwidth of the detector and the laser-pulse duration. A spatial resolution of several micrometers should be possible with picosecond laser pulses and high bandwidth piezoelectric or optical detectors. Sensors based on optical waveguides and interferometry present promising candidates for optical line detectors, and future work will focus on the development and characterization of such high-frequency, optical line detectors and improved cylindrical detectors with the aim to develop three-dimensional thermoacoustic tomography with high spatial resolution.

Acknowledgment The authors wish to thank Prof. S. Bauer (University of Linz) for his helpful advice.

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[5] R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, and F. F. M. De Mul, “In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor,” IEEE J. Select. Topics Quantum Electron., vol. 9, pp. 343–346, Mar.–Apr. 30, 2003. [6] G. Paltauf, “Dual-wavelength optoacoustic imaging,” Novel Optical Instrumentation for Biomedical Applications, Proc. SPIE, vol. 5143, pp. 41–49, 2003. [7] G. Paltauf, K. P. K¨ ostli, D. Frauchiger, and M. Frenz, “Spectral optoacoustic imaging using a scanning transducer,” Hybrid Novel Imaging New Opt. Instrum. Biomed. Applications, vol. 4434, pp. 81–88, 2001. [8] J. A. Viator, G. Au, G. Paltauf, S. L. Jacques, S. A. Prahl, H. Ren, Z. Chen, and J. S. Nelson, “Clinical testing of a photoacoustic probe for port wine stain depth determination,” Lasers Surg. Med., vol. 30, pp. 141–148, 2002. [9] R. A. Kruger, K. M. Stantz, and W. L. Kiser, “Thermoacoustic CT of the breast,” Proc. SPIE, vol. 4682, pp. 521–525, 2002. [10] R. A. Kruger, K. D. Miller, H. E. Reynolds, W. L. Kiser, D. R. Reinecke, and G. A. Kruger, “Breast cancer in vivo: Contrast enhancement with thermoacoustic Ct at 434 Mhz—Feasibility study,” Radiology, vol. 216, pp. 279–283, July 2000. [11] V. A. Andreev, A. A. Karabutov, S. V. Solomatin, E. V. Savateeva, V. Aleynikov, Y. V. Zhulina, R. D. Fleming, and A. A. Oraevsky, “Opto-acoustic tomography of breast cancer with arcarray-transducer,” Biomed. Optoacoust., vol. 3916, pp. 36–47, 2000. [12] A. Kharine, S. Manohar, R. Seeton, R. G. M. Kolkman, R. A. Bolt, W. Steenbergen, and F. F. M. De Mul, “Poly(vinyl alcohol) gels for use as tissue phantoms in photoacoustic mammography,” Phys. Med. Biol., vol. 48, pp. 357–370, Feb. 7, 2003. [13] U. Oberheide, I. Bruder, H. Welling, W. Ertmer, and H. Lubatschowski, “Optoacoustic imaging for optimization of laser cyclophotocoagulation,” J. Biomed. Opt., vol. 8, pp. 281–287, Apr. 2003. [14] G. Paltauf and M. Steininger, “Spectral optoacoustic imaging using a wavelength-multiplexing technique,” Photons plus ultrasound: Imaging and sensing, Proc. SPIE, vol. 5320, pp. 128–137, 2004. [15] R. Esenaliev, I. V. Larina, K. V. Larin, D. J. Deyo, M. Motamedi, and D. S. Prough, “Optoacoustic technique for noninvasive monitoring of blood oxygenation: A feasibility study,” Appl. Opt., vol. 41, pp. 4722–4731, 2002. [16] Y. Xu, D. Z. Feng, and L. H. V. Wang, “Exact frequency-domain reconstruction for thermoacoustic tomography—I: Planar geometry,” IEEE Trans. Med. Imag., vol. 21, pp. 823–828, 2002. [17] M. H. Xu and L. H. V. Wang, “Time-domain reconstruction for thermoacoustic tomography in a spherical geometry,” IEEE Trans. Med. Imag., vol. 21, pp. 814–822, 2002. [18] Y. Xu, M. H. Xu, and L. H. V. Wang, “Exact frequency-domain reconstruction for thermoacoustic tomography—II: Cylindrical geometry,” IEEE Trans. Med. Imag., vol. 21, pp. 829–833, 2002. [19] K. P. Kostli, D. Frauchiger, J. J. Niederhauser, G. Paltauf, H. P. Weber, and M. Frenz, “Optoacoustic imaging using a threedimensional reconstruction algorithm,” IEEE J. Select. Topics Quantum Electron., vol. 7, pp. 918–923, 2001. [20] D. Finch, S. K. Patch, and Rakesh, “Determining a function from its mean values over a family of spheres,” SIAM J. Math. Anal., vol. 35, pp. 1213–1240, 2003. [21] M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Problems, vol. 20, pp. 1663–1673, 2004. [22] P. Liu, “Image reconstruction from photoacoustic pressure signals,” Proc. Conf. Laser—Tissue Interaction VII, Proc. SPIE, vol. 2681, pp. 285–296, 1996. [23] F. Natterer, “The mathematics of computerized tomography,” in Classics in Applied Mathematics. Philadelphia: Society for Industrial and Applied Mathematics (SIAM), 2001, pp. 102–111. [24] M. H. Xu and L. H. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E, vol. 67, pp. 56605-1–56605-15, 2003. [25] K. P. K¨ ostli and P. C. Beard, “Two-dimensional photoacoustic imaging by use of Fourier-transform image reconstruction and a detector with an anisotropic response,” Appl. Opt., vol. 42, pp. 1899–1908, 2003.

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Peter Burgholzer received his Ph.D. in technical science from the Johannes-KeplerUniversity of Linz, Austria, in 1993 with a thesis on X-ray texture measurements and anisotropy of aluminum and was head of the instrumentation group in the research department of the Austria Metall AG (AMAG). Postdoctoral studies in Ispra in Italy, at the Institute of Advanced Materials of the Joint Research Center (JRC) of the European Commission were devoted to fracture mechanics of high temperature materials for nuclear fusion. Since 1998 he has been lecturer at the University of Applied Sciences Upper Austria, teaching SMP (sensors, instrumentation and testing) and non-destructive testing. Since 2000 he has been head of the Sensor department of the Upper Austrian Research. His main working area is non-destructive testing with optical methods. His research interests include laser ultrasound and thermoacoustic imaging.

Christian Hofer was born in Wels, Austria, on September 17, 1974. He received the M.S. degree in mechatronics from the Johannes Kepler University, Linz, Austria, in 2001. Since 2002 he has been working for the Sensor department of the Upper Austrian Research GmbH. His research interests include thermoacoustics and laser ultrasound.

G¨ unther Paltauf received his Ph.D. in experimental physics from the Karl-FranzensUniversit¨ at Graz in 1993 with a thesis on laser-induced ablation mechanisms. Postdoctoral studies in Graz, at the Institute of Applied Physics at the University of Bern, Switzerland, and at the Oregon Medical Laser Center in Portland, OR, were devoted to photomechanical laser-material interactions and to methods to characterize materials, mostly biological tissue, by use of laser-thermoacoustics. In 2001 he returned to

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the University of Graz, where he is now an associate professor with the department of physics. His current research interests include pulsed laser-material interactions and thermoacoustic spectroscopy and imaging.

Markus Haltmeier received his M.S. degree in Mathematics from the University of Innsbruck, Austria, in 2002. Currently he is working towards the Ph.D. degree in Mathematics at University of Innsbruck. His research interests include applied mathematics and inverse problems.

Otmar Scherzer (A’98) received his Ph.D. in Mathematics from the University of Linz, Austria, in 1990. He was at the Industrial Mathematics Institute at the University of Linz until 1999. From 1999–2000 he visited the University of Munich, Munich, Germany, and from 2000–2001 he was Professor at the University of Bayreuth, Bayreuth, Germany. Since 2001 he is Professor at the Department of Computer Science at the University of Innsbruck, Innsbruck, Austria. From 1995 to 1996 he had an Erwin Schr¨ odinger Scholarship of the Austrian Science Foundation (FWF) for visiting Texas A&M University and the University of Delaware. Otmar Scherzer received the Award of the Austrian Mathematical Society (1998) and the START-prize of the FWF in 1999. He is in the editorial board of Numerical Functional Analysis and Optimization and Inverse Problems. His research interest include image processing and inverse problems.