Energetic vs Inference-Based Invisibility: Fisher-Information Analysis of Two-Layer Acoustic Near-Cloaks
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917194071277568 |
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| author | Sumaya-Martinez, J. Mulia-Rodriguez, J. |
| author_facet | Sumaya-Martinez, J. Mulia-Rodriguez, J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Energetic vs Inference-Based Invisibility: Fisher-Information Analysis of Two-Layer Acoustic Near-Cloaks Sumaya-Martinez, J. Mulia-Rodriguez, J. Optics Soft Condensed Matter Fluid Dynamics 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. |
| title | Energetic vs Inference-Based Invisibility: Fisher-Information Analysis of Two-Layer Acoustic Near-Cloaks |
| topic | Optics Soft Condensed Matter Fluid Dynamics |
| url | https://arxiv.org/abs/2601.06091 |