The contactless measurement of the temperature is interesting for many applications, e.g., bioreactors. One way to do this is to utilize the fact that the speed of sound is temperature dependent. An average temperature along a propagation path of ultrasonic waves can be determined from their propagation time if the length of the propagation path is known.
This thesis deals with the ultrasound-based measurement of the temperature along several paths in a single plane and the reconstruction of the temperature distribution in this plane. This reconstruction is an ill-posed inverse problem. Therefore, different methods for solving such problems are considered and tested for the reconstruction of temperature distributions. A compromise must be found between the desired accuracy of the reconstruction and the number of ultrasonic transducers used and thus the number of available measurement paths. The directional emission characteristic of ultrasonic transducers further limits the number of possible measurement paths. Hence, possibilities of influencing the sound field of these transducers are examined to make more measurement paths usable with the same number of transducers.
In addition to the reconstruction of the entire temperature distribution, the mere detection of hotspots is also considered. Figure 1 shows the result of reconstructing a temperature distribution with two hotspots of different temperatures from simulated measurement data. The reconstruction is carried out with Tikhonov regularization. It can be seen that both the position and the temperature of the hotspots can be reconstructed well.