Artificial Audio

Theses & Projects

Acoustic Tomography: Imaging Air Temperature with a Loudspeaker Array

The acoustics lab at LMS with its wave field synthesis loudspeaker array
The acoustics lab at LMS with its wave field synthesis loudspeaker array

The speed of sound in air depends on temperature: roughly 0.6 m/s per kelvin. A sound pulse travelling between a loudspeaker and a microphone therefore carries the integral of the temperature along its path. With many such paths, the temperature field can be reconstructed from the measured travel times, just as X-ray tomography reconstructs a body from line integrals of attenuation. This is acoustic travel-time tomography: a non-contact way to image air temperature, and later also airflow, in rooms, buildings, and outdoors [1].

Existing indoor systems use only a handful of transducers, so the inverse problem is badly conditioned and the reconstructions are coarse [2, 3]. Our lab has a large loudspeaker array (built for wave field synthesis) and microphone arrays, which together give hundreds of controllable propagation paths. The question of this thesis is how much such a dense, programmable array improves the reconstruction, and what limits it in practice.

Tasks

  • Set up the forward model: slowness on a 2D grid, straight-ray travel times, and the conversion between sound speed and temperature, including humidity and the effect of curved rays.
  • Simulate temperature fields (for example a heater plume) and study conditioning and resolution for sparse and dense array geometries.
  • Estimate travel times from measured room impulse responses with sub-sample accuracy, and quantify their uncertainty. Early reflections may add paths [3].
  • Reconstruct the field with classical methods (Tikhonov regularisation, SIRT) and, optionally, with a learned prior.
  • Run a lab experiment with a controlled heat source and validate against reference temperature sensors.

Prerequisites

Signal processing and linear algebra (least squares, regularisation), Python, and interest in practical measurements. Background in inverse problems or acoustics is helpful but not required.

References

  • [1] Othmani, C. et al. Acoustic tomographic reconstruction of temperature and flow fields with focus on atmosphere and enclosed spaces: A review. Appl. Therm. Eng. 223, 119953 (2023).
  • [2] Dokhanchi, N. S., Arnold, J., Vogel, A. & Voelker, C. Indoor air temperature measurements using ultrasonic travel-time tomography. Appl. Acoust. 218 (2024).
  • [3] Othmani, C., Merchel, S. & Altinsoy, M. E. Acoustic travel-time tomography technique to reconstruct the indoor temperature: How to improve the field reconstruction quality? (2024).
  • [4] Kak, A. C. & Slaney, M. Principles of Computerized Tomographic Imaging. SIAM (2001).

Contact

Prof. Sebastian J. Schlecht (sebastian.schlecht@fau.de).