Robust Permittivity Reconstruction With the Transmission and Reflection Method at mm-Wave Frequencies

Abstract

The permittivity reconstruction with the transmission and reflection method usually requires time-gating to mitigate distorted measurement data. State-of-the-art approaches reduce the available bandwidth as they introduce ringing. Available frequency extension approaches to avoid a bandwidth reduction are not based on a physically meaningful estimate. In this work, we propose a method that takes advantage of the information already given by the measurement to calculate a reasonable frequency extension. The inverse problem of the actual permittivity reconstruction is most commonly approached by the Baker-Jarvis algorithm from the National Institute of Standards and Technology (NIST) which considers the magnitude of one single complex number. It is calculated from the difference between measurement and model of the scattering matrix. In this article, we demonstrate the superiority of matching all four scattering parameters individually instead. This results in particular in a wider range of initial start parameters with proper convergence to the desired solution and more reliable reconstruction results for optimizations with unknown sample thickness. The benefits of the novel reconstruction techniques are demonstrated and evaluated in detail on simulation and measurement data in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V$</tex-math> </inline-formula> band.