Monostatic sampling methods in limited-aperture configuration

TL;DR

This paper develops and analyzes monostatic sampling methods for limited-aperture scattering problems in two dimensions, introducing a new asymptotic formula and a multi-frequency scheme to enhance imaging of inhomogeneities.

Contribution

It extends monostatic sampling methods to limited-aperture configurations and proposes a multi-frequency approach to improve imaging of small anomalies.

Findings

Asymptotic formula for the indicator function derived.

Imaging performance depends on measurement range and inhomogeneity properties.

Multi-frequency scheme enhances detection of small anomalies.

Abstract

We present monostatic sampling methods for limited-aperture scattering problems in two dimensions. The direct sampling method (DSM) is well known to provide a robust, stable, and fast numerical scheme for imaging inhomogeneities from multistatic measurements even with only one or two incident fields. However, in practical applications, monostatic measurements in limited-aperture configuration are frequently encountered. A monostatic sampling method (MSM) was studied in full-aperture configuration in recent literature. In this paper, we develop MSM in limited-aperture configuration and derive an asymptotic formula of the corresponding indicator function. Based on the asymptotic formula, we then analyze the imaging performance of the proposed method depending on the range of measurement directions and the geometric, material properties of inhomogeneities. Furthermore, we propose a modified numerical scheme with multi-frequency measurements that improve imaging performance, especially for small anomalies. Numerical simulations are presented to validate the analytical results.