Imposing Zernike representation for imaging two-dimensional targets

Abstract

To overcome the ill-posedness of the inverse scattering problem, we introduce an appropriate way of representing the unknown permittivity profile which benefits from two a priori pieces of information which are commonly encountered. First, the unknown permittivity map has a limited spatial support which can be contained within a circular investigation area. Second, from physical reasoning based on the scattering operator, there is only a limited number of independent parameters that can be retrieved from the measured fields. Both pieces of a priori information can be adequately introduced by representing the unknown permittivity profile in terms of a Zernike polynomial expansion, correctly truncated according to the number of independent parameters. To investigate the effectiveness of such a Zernike representation, the reconstructions obtained from experimentally acquired data in the circular microwave scanner developed at the Institut Fresnel are analyzed.

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.…”

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

“…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]. …”