Energetic vs Inference-Based Invisibility: Fisher-Information Analysis of Two-Layer Acoustic Near-Cloaks

TL;DR

This work addresses the mismatch between energy-based invisibility and an observer's ability to infer object parameters in acoustic scattering. It develops an exact 2D modal solution for a circular core surrounded by two concentric effective-fluid layers, designs the coating to cancel the dominant monopole and dipole at a target frequency, and analyzes joint size-material inference using the Fisher information matrix (FIM) and Cramér–Rao lower bounds (CRLBs) from noisy far-field data. Key contributions include a compact per-mode linear system $\mathbf{M}_m(\omega)\mathbf{u}_m=\mathbf{b}_m(\omega)$, a near-cloak design achieving substantial energy suppression (up to ~25 dB) while the information-based detectability reduces only modestly, and an analytic mechanism for the energetic-informational decoupling accompanied by design-space diagnostics. The results show that large reductions in total scattering can occur even when FIM-based parameter identifiability degrades only slightly, highlighting the need for multi-objective cloak design under physical bandwidth constraints. The work provides a task-aware framework for passive cloaks with practical implications for detection, classification, and robust design under bandwidth and material-passivity limits, with future extensions to elastodynamics outlined.

Abstract

Near-cloaks based on passive coatings can strongly suppress scattered-field energy in a narrow frequency band, yet an observer's ability to infer object parameters from noisy measurements need not decrease proportionally. We develop a fully theoretical two-dimensional (2D) framework for a coated acoustic cylinder in an air background. Using an exact cylindrical-harmonic solution of the Helmholtz equation, we compute the modal scattering coefficients a_m(omega) for a core of radius a surrounded by two concentric effective-fluid layers, and we design the coating to cancel the dominant low-order multipoles (monopole m=0 and dipole m=+/-1) at a target frequency, yielding a narrowband near-cloak. Beyond the conventional energetic metric (total scattering width), we quantify information-based detectability through the Fisher information matrix (FIM) and the associated Cramer-Rao lower bounds (CRLBs) for joint estimation of the size-material parameter vector x=[a, rho1, c1]^T from noisy far-field data. A representative air-background study exhibits an approximately 25 dB reduction in total scattering width near the design frequency, while tr(FIM) decreases by only a few dB, demonstrating that energy-based and inference-based notions of invisibility are distinct objectives. We further provide a low-order analytic argument clarifying the mechanism behind this energetic-informational decoupling and report design-space and local-robustness diagnostics that highlight persistent trade-offs between scattering suppression and parameter identifiability.

Figures (9)

• Figure 1: Geometry of the concentric two-layer near-cloak for a 2D cylinder in an air background. The core has radius $a$, and the coating layers extend to radii $b$ and $c$.
• Figure 2: Normalized scattering-width reduction relative to the bare cylinder, $10\log_{10}(\sigma_{\mathrm{bare}}/\sigma_{\mathrm{cloak}})$, versus frequency. The near-cloak is designed near $f_0\approx 500Hz$ and achieves a peak reduction of $\sim 25$ dB in this illustration.
• Figure 3: Magnitudes of multipole scattering coefficients $\left|a_m\right|$ at $f_0$ for bare and cloaked configurations. The coating suppresses the dominant monopole ($m=0$) and dipole ($m=1$) coefficients.
• Figure 4: Normalized information-based reduction relative to the bare cylinder, shown as $10\log_{10}(\mathrm{tr} I_{\mathrm{bare}}/\mathrm{tr} I_{\mathrm{cloak}})$ for joint estimation of $\bm{x}=[a,\rho_1,c_1]^T$ from noisy far-field data.
• Figure 5: Determinant-based Fisher-information reduction, $10\log_{10}(\det I_{\mathrm{bare}}/\det I_{\mathrm{cloak}})$, providing a D-optimality proxy that emphasizes worst-direction identifiability.