Combining spatial support information and shape-based method for tomographic imaging inside a microwave cylindrical scanner

Abstract

International audienceA nonlinear inverse scattering problem is solved to retrieve the permittivity maps inside a microwave cylindrical scanner of circular cross-section. In this article, we show how we can improve this minimization scheme by taking advantage of several a priori pieces of information. In particular, a global representation based on a Zernike basis expansion is introduced in order to restrain the class of solutions to functions which have circular spatial support, as is the case with the encountered geometrical configuration. The level-set function formalism is also exploited as the targets are known to be homogeneous by parts. We will show how we can combine the spatial support information and the binary nature of the scatterer, with limited changes of the inversion algorithm. Both synthetic and experimental results will be presented in order to highlight the importance of combining all the pieces of available information

On the Calibration of a Multistatic Scattering Matrix Measured by a Fixed Circular Array of Antennas

“…This calibration has been tested in the specific configuration of a ring of antennas positioned inside a circular metallic enclosure. The validation of the entire quantitative imaging procedure is not presented in the current article, as it has been done already in other works [1,2]. Indeed, the effective and accurate reconstructed images that have been obtained from measured data which have been calibrated as described therein, are testifying of the quality of the calibration process.…”

“…This signal-to-noise ratio definitely needs to be improved. Nevertheless, interesting quantitative images have been obtained with this system for dielectric targets [1,2]. …”

“…Several algorithms have already been implemented to compute the field in this specific configuration, all of them being based on the method of moments with various types of Green functions [12,29,30]. Here, we prefer to use a finite element method (FEM) with conformal meshing adapted to the casing configuration [1,2,13]. It requires typically about 6 seconds of run time on a standard computer, for a firstorder triangular mesh with 45 000 nodes and for 64 emitting antennas.…”

“…This geometrical feature is fully exploited through a reorganization of the multistatic scattering matrix which highlights the inherent symmetries of the configuration. This calibration protocol has successfully been applied before to provide quantitative images of dielectric targets [1,2], but it was never described in detail.…”

“…In addition, the reorganization permits to detect antenna pairs which are not properly functioning and to estimate the signal-to-noise ratio. Experimental results obtained within a cylindrical cavity enclosed by a metallic casing are provided to assess the performance of the proposed calibration procedure.This calibration protocol, which is described here in detail, has already been applied to provide quantitative images of dielectric targets [1,2]. …”