Real-time inversion of two-dimensional Fresnel experimental database using orthogonality sampling method with single and multiple sources: the case of transverse electric polarized waves

TL;DR

The paper tackles real-time detection of small TE-polarized objects from 2D Fresnel data by developing an orthogonality sampling method (OSM) indicator tied to an asymptotic scattering expansion. It first establishes a single-source indicator whose structure reduces to a series of Bessel functions, revealing peaks at object locations but also artifacts that depend on frequency and emitter position. To overcome these limitations, the authors formulate a multisource indicator (MSM) with a corresponding Bessel-function–based expansion, which yields improved localization and enables more robust, potentially unique object identification. Numerical tests on synthetic data and a 2D Fresnel experimental dataset show that single-source OSM can indicate presence at certain frequencies, while MSM with multiple sources and frequency fusion markedly enhances boundary detection and shape recovery, especially at higher frequencies. The work provides practical guidance for real-time imaging in TE-polarized, Fresnel-based inverse problems and points to future 3D extensions and diverse measurement geometries.

Abstract

This paper concerns an application of the orthogonality sampling method (OSM) for a real-time identification of small objects from two-dimensional Fresnel experimental dataset in transverse electric polarization. First, we apply the OSM with a single source by designing an indicator function based on the asymptotic expansion formula for the scattered field in the presence of small objects. We demonstrate that the indicator function can be expressed by an infinite series of Bessel functions of integer order of the first kind, the range of the signal receiver, and the location of the emitter. Based on this, we then investigate the applicability and limitations of the designed OSM. Specifically, we find that the imaging performance is strongly dependent on the source and the applied frequency. We then apply the OSM with multiple sources to improve imaging performance. Based on the identified structure of the OSM with a single source, we design an indicator function with multiple sources and demonstrate that it can be expressed by an infinite series of the Bessel function of integer order of the first kind, and we explain that objects can be identified uniquely using the designed OSM. Numerical simulation results obtained with the Fresnel experimental dataset demonstrate the advantages and disadvantages of the OSM with a single source and confirm that the designed OSM with multiple sources improves imaging performance.

Figures (21)

• Figure 1: Receiver arrangements corresponding to the emitter location.
• Figure 2: Plots of $|\mathcal{D}_{\mathop{\mathrm{OSM}}\limits}^{(1)}(x)|$ for $-0.1\leq x\leq0.1$ at $f=2,6,10GHz$.
• Figure 3: Plots of $|\mathcal{D}_{\mathop{\mathrm{OSM}}\limits}^{(2)}(x)|$ for $-0.1\leq x\leq0.1$ at $f=2,6,10GHz$.
• Figure 4: Plots of $|\mathcal{D}_{\mathop{\mathrm{OSM}}\limits}(x)|$ for $-0.1\leq x\leq0.1$ at $f=2,6,10GHz$.
• Figure 5: Antenna arrangements with emitters $\mathcal{A}_1$, $\mathcal{A}_{10}$, and $\mathcal{A}_{25}$.

Theorems & Definitions (32)

• Lemma 2.1
• Remark 3.1: Test vectors
• Lemma 3.1
• proof
• Theorem 3.1
• proof
• Remark 3.2: Dependence on the emitter location
• Remark 3.3: Structure of the factor $\mathcal{E}_{\mathop{\mathrm{OSM}}\limits}(\mathbf{r},m)$
• Remark 3.4: Influence of the factor $\mathcal{E}_{\mathop{\mathrm{OSM}}\limits}(\mathbf{r},m)$
• Remark 3.5: Limitation of object detection