dorsal/arxiv
View SchemaEnergetic vs Inference-Based Invisibility: Fisher-Information Analysis of Two-Layer Acoustic Near-Cloaks
| Authors | J. Sumaya-Martinez, J. Mulia-Rodriguez |
|---|---|
| Categories | |
| ArXiv ID | 2601.06091vv1 |
| URL | https://arxiv.org/abs/2601.06091 |
| License | http://creativecommons.org/licenses/by/4.0/ |
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.
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"abstract": "Near-cloaks based on passive coatings can strongly suppress scattered-field energy in a narrow frequency band, yet an observer\u0027s 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.",
"arxiv_id": "2601.06091",
"authors": [
"J. Sumaya-Martinez",
"J. Mulia-Rodriguez"
],
"categories": [
"physics.optics",
"cond-mat.soft",
"physics.flu-dyn"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Energetic vs Inference-Based Invisibility: Fisher-Information Analysis of Two-Layer Acoustic Near-Cloaks",
"url": "https://arxiv.org/abs/2601.06091",
"version": "v1"
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