Abstract
In inverse scattering problems, the most accurate possible imaging results require plane waves impinging from all directions and scattered fields observed in all observation directions around the object. Since this full information is infrequently available in actual applications, this paper is concerned with the mathematical analysis and numerical simulations to estimate the achievable resolution in object reconstruction from the knowledge of the scattered far-field when limited data are available at a single frequency. The investigation focuses on evaluating the Number of Degrees of Freedom (NDF) and the Point Spread Function (PSF), which accounts for reconstructing a point-like unknown and depends on the NDF. The discussion concerns objects belonging to curve geometries, in this case, circumference and square scatterers. In addition, since the exact evaluation of the PSF can only be accomplished numerically, an approximated closed-form evaluation is introduced and compared with the exact one. The approximation accuracy of the PSF is verified by numerical results, at least within its main lobe region, which is the most critical as far as the resolution discussion is concerned. The main result of the analysis is the space variance of the PSF for the considered geometries, showing that the resolution is different over the investigation domain. Finally, two numerical applications of the PSF concept are shown, and their relevance in the presence of noisy data is outlined.
Highlights
The inverse scattering problem is concerned with reconstructing some geometric and/or physical properties of an unknown object from the scattered field data under the illumination of known incident plane waves and to recover the permittivity, the permeability, and the shape of the object
The novelty of the paper consists in the examination of the case of aspect-limited data, namely when the plane waves impinging from a limited angular range and the like the results of Section 3, the effect of the incidence and observation ranges on the resolution of two close point-like scattering objects can be predicted by comparing the reconstructions of [10] when the full data is available and a satisfactory reconstruction can be obtained even when the incidence and observation ranges do not span the round angle
The resolution analysis in linear inverse scattering problems allows to appreciate the performances of imaging algorithms as far as the capability of localizing point-like objects is concerned
Summary
The inverse scattering problem is concerned with reconstructing some geometric and/or physical properties of an unknown object from the scattered field data under the illumination of known incident plane waves and to recover the permittivity, the permeability, and the shape of the object. We address the evaluation of the achievable resolution in curve geometries when the number of directions of both the impinging plane waves and the observation angles is limited within an angular domain, giving rise to the so-called aspectlimited problem. It is very common in many practical instances whenever the angular domain around the scattering object is not fully available for sensing purposes as it occurs in many realistic applications such as seismic imaging, Ground-Penetrating Radar (GPR), and subsurface imaging. Equation (9) provides the analytical evaluation of (12) for the 2D geometry under consideration
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
