Reconstruction of Temperature Fields from Ultrasonic Travel Time Measurements

In this contribution we present a technique for measuring temperature fields using ultrasound. Since it requires no sensors within the measurement volume, this is of interest for many applications, such as bioreactors. Due to the temperature dependence of the speed of sound, the average temperature along the path between a transmitter and a receiver can be determined from the travel time of the ultrasound. If this is done for several paths in one plane, the temperature field can be reconstructed from the measured data by solving an ill-posed inverse problem. To do this, we utilize Tikhonov regularization and methods from compressed sensing, which can be used if the temperature field can be transformed into a sparse representation. We show reconstruction results of both methods and compare them.