Small defects reconstruction in waveguides from multifrequency one-side scattering data

Angèle Niclas (1, 2, 3, 4) , L. Seppecher (1, 2, 3, 4) , Eric Bonnetier (5) , Grégory Vial (4, 3, 2, 1)

1 UCBL - Université Claude Bernard Lyon 1
2 MMCS - Modélisation mathématique, calcul scientifique
3 ICJ - Institut Camille Jordan
4 ECL - École Centrale de Lyon
5 IF - Institut Fourier

Localization and reconstruction of small defects in acoustic or electromagnetic waveguides is of crucial interest in nondestructive evaluation of structures. The aim of this work is to present a new multi-frequency inver- sion method to reconstruct small defects in a 2D waveguide. Given one-side multi-frequency wave field measurements of propagating modes, we use a Born approximation to provide a L2-stable reconstruction of three types of defects: a local perturbation inside the waveguide, a bending of the waveguide, and a localized defect in the geometry of the waveguide. This method is based on a mode-by-mode spacial Fourier inversion from the available partial data in the Fourier domain. Indeed, in the available data, some high and low spa- tial frequency information on the defect are missing. We overcome this issue using both a compact support hypothesis and a minimal smoothness hypoth- esis on the defects. We also provide a suitable numerical method for efficient reconstruction of such defects and we discuss its applications and limits.

Domaines: Mathématiques [math]

Angèle Niclas, L. Seppecher, Eric Bonnetier, Grégory Vial. Small defects reconstruction in waveguides from multifrequency one-side scattering data. Inverse Problems and Imaging , 2022, 16 (2), pp.417-450. ⟨10.3934/ipi.2021056⟩. ⟨hal-03130533⟩