Mathematical and experimental validation of the bifocusing method tailored for bistatic measurement

TL;DR

This paper develops and validates a bifocusing imaging method for identifying small dielectric inhomogeneities in a bistatic setup, analyzing resolution limits related to the bistatic angle through mathematical and experimental means.

Contribution

It provides a mathematical analysis of the bifocusing method's resolution limits in bistatic measurements and validates these findings with numerical simulations.

Findings

Resolution degrades as the bistatic angle approaches 180°.

Target identification is impossible at a 180° bistatic angle.

High-resolution imaging is achievable when the bistatic angle is near 0°.

Abstract

In this paper, we design a bifocusing-based imaging strategy for the rapid identification of small penetrable dielectric inhomogeneities within a two-dimensional bistatic measurement setup. To address the applicability and limitation, we carefully explore the mathematical structure of the indicator function by establishing a relationship involving the infinite series of Bessel functions, the material characteristics, and the bistatic angle. Through this theoretical result, we rigorously verify that the imaging resolution degrades as the bistatic angle approaches $\SI{180}{\degree}$, and specifically, that target identification becomes impossible when the bistatic angle is $\SI{180}{\degree}$. Conversely, relatively high-resolution results are obtained when the bistatic angle is close to $\SI{0}{\degree}$. The theoretical findings are validated through numerical simulations using the Fresnel experimental dataset, which confirm the applicability and limitations of the proposed method for both dielectric and metallic objects.