When an absorbing sample is illuminated by a pulsed electromagnetic wave, the absorbed power produces heat and results in mechanical expansion of the absorber (see figure 16). This thermoelastic expansion induces an acoustic pressure field
Here is the spherical mean operator
and is the normalized energy deposition function.
TCT is concerned with the inverse problem of recovering an unknown energy deposition function from temporal measurement data of the thermoacoustic pressure field taken on a surface outside the illuminated sample. Potential application of thermoacoustic imaging reach from non-destructive evaluation to medical applications [3,4,5]. In 1998 Kruger et. al.  developed a prototype of the world's first thermoacoustic breast scanner.
Existing reconstruction algorithms utilize the fact that a small receiver measures an acoustic signal that at a given time approximates the integral of the energy density function over the surface of a sphere with the detector in the center (see figure 17). To generate images with high spatial resolution throughout the three-dimensional object this would require the use of ultrasound detectors that are much smaller than the imaged object.
of the thermoacoustic pressure field over the planar detector surface . In practical experiments, the data required for imaging can be collected with relatively large piezo foils (see figure 19).
We have shown that is closely connected to the standard Radon transform of the energy deposition function . This fact can be utilized for efficient numerical algorithms for thermoacoustic imaging.
Since in our technique the finite size of the receivers is explicitly included the limitation of the spatial resolution is only determined by the frequency bandwidth of the detector. A spatial resolution less than one micrometer should be possible with high bandwidth receiver .
Experiments with large planar receivers have been performed by the Upper Austrian Research GmbH (http://www.uar.at) in cooperation with G. Paltauf (Uni Graz). Future joint work will be done to develop and characterize high frequency detectors with the aim to develop a thermoacoustic microscope.
valid for objects with cylindrical symmetry. Here is the Hilbert transform and is the unit vector orthogonal to the planar receiver.
The numerical reconstruction from the measurement data gathered with the set-up shown in figure 19 is plotted in figure 21.