Recent Developments in Inverse Problems - Abstract
Tepe, Jens
Terahertz (THz) tomography is a rather novel technique for nondestructive testing that is particularly suited for the testing of plastics and ceramics because THz radiation can easily pass through these materials. Previous publications show a large variety of conventional algorithms adapted from computerized tomography or ultrasound tomography which were directly applied to THz tomography. These conventional algorithms neglect the specific nature of THz radiation, which results in poor reconstructions. THz radiation has a significantly larger wavelength than x-rays ($30-3000 mu m$), thereby reducing the lateral resolution. Also, typical wave phenomena occur, i.e. refraction at interfaces, reflection losses and the beam profile (Gaussian beam). These aspects need to be considered in the mathematical modelling. THz frequencies are, however, significantly higher than ultrasound frequencies. This prevents an efficient solution with ultrasound tomography algorithms.
As a result of an interdisciplinary collaboration between Saarland University and SKZ German Plastics Center (Würzburg, Germany) a hybrid algorithm specially designed for THz tomography has been developed. The aim is the efficient reconstruction of the complex refractive index $tilden=n ikappa$ inside a compact set $Omega subseteq mathbbR^2$, indicating defects or inhomogenities in the material. The THz tomography system provides both the transmittance $tau$ and the delayed travel time resp. path difference $L$ of a THz signal. The algorithm uses a priori information about the interface and layer geometry of the sample. The algebraic reconstruction technique is adapted by including refraction (Snell's law) and reflection losses (Fresnel equations).
Our method is a modified ART for THz tomography, which reconstructs simultanously the complex refractive index from transmittance and travel time measurements and considers refraction and reflection losses. The algorithm takes the specific THz radiation properties into account and significantly improves the quality of the reconstructed images compared to conventional techniques. First promising results were obtained both with synthetic data as well as measurements acquired at SKZ German Plastics Center.
This is joint work with Thomas Schuster and Anne Wald.