Abstract
A non-iterative topological sensitivity framework for guaranteed far field detection of a dielectric inclusion is presented. The cases of single and multiple measurements of the electric far field scattering amplitude at a fixed frequency are taken into account. The performance of the algorithm is analyzed theoretically in terms of resolution, stability, and signal-to-noise ratio.
Highlights
The cases of single and multiple measurements of the electric far field scattering amplitude at a fixed frequency are taken into account
A thriving interest has been shown in topological sensitivity frameworks to procure solutions of assorted inverse problems especially for detecting small inhomogeneities and cracks embedded in homogeneous media [2, 7, 9, 10]
Our aim is to design and debate a far field detection algorithm based on topological sensitivity of small dielectric inclusion Dρ := zD + ρOD ⊂ R3 with position zD, scale factor ρ and a smooth bounded domain OD ⊂ R3
Summary
A thriving interest has been shown in topological sensitivity frameworks to procure solutions of assorted inverse problems especially for detecting small inhomogeneities and cracks embedded in homogeneous media [2, 7, 9, 10]. Since jn(kr) = O(1/kr) as kr → ∞ and jn(kr) = O((kr)n) as kr → 0, the functional zS → ∂T J [E0](zS ) rapidly decays for zS away from zD and has a sharp peak when zS → zD with a focal spot size of half a wavelength of the incident wave. It synthesizes the sensitivity of J [E0](zS ) relative to the insertion of an inclusion at zS ∈ Ω. Theorem 2.4 substantiates that ∂T J (zS) ∝ Im {Γ(zS , zD)} and has a peak (sharper than that of ∂T J [E0]) when zS → zD (see Remark 2.3)
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