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Photoacoustic Imaging (also known as thermoacoustic or optoacoustic imaging) is a novel imaging method which
combines the advantages of Diffuse Optical Imaging (high contrast) and Ultrasonic Imaging (high spatial resolution). A
short laser pulse excites the sample. The absorbed energy causes a thermoelastic expansion and thereby launches a
broadband ultrasonic wave (photoacoustic signal). This way one can measure the optical contrast of a sample with
ultrasonic resolution. For collecting photoacoustic signals our group introduced so called integrating detectors a few
years ago. Such integrating detectors integrate the pressure in one or two dimensions -a line or a plane detector,
respectively. Thereby the three dimensional imaging problem is reduced to a two or a one dimensional problem for the
projections and a two or three dimensional inverse radon transform as a second step to get the three dimensional initial
pressure distribution. The integrating detectors are mainly optical detectors and thus can provide a high bandwidth up to
several 100 MHz. Using these detectors the resolution is often limited by the acoustic attenuation in the sample itself,
because attenuation increases with higher frequencies.
Stoke's equation describes the attenuation of photoacoustic generated waves in liquids very well, which results in an
increase of the acoustic attenuation with the square of the frequency. For fat tissue an absorption coefficient which is
approximately linear proportional to frequency is reported. Presented measurements give an exponential power law
dependency with an exponent between 1.31 and 1.36 in fat tissue near the skin of a pig.
These equations describing frequency dependent acoustic attenuation have been solved in the past by decomposing the
pressure wave into plane waves damped in space, described by the complex part of the wave number equal to the
attenuation coefficient. One main result of this paper is that for Photoacoustic Tomography another description seems to
be very useful: like for a standing wave in a resonator the wave number is real but the frequency is complex. The
complex part of the frequency is the damping in time. Both descriptions are equivalent, but with the complex frequency
description acoustic attenuation can be included in all "k-space" methods well known in Photoacoustic Tomography just
by introducing a factor describing the exponential decay in time.
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