Localization and reconstruction of defects in waveguides is of crucial interest in nondestructive evaluation of structures. This work aims to present a new multi-frequency inversion method to image shape variations in slowly varying waveguides. Contrary to previous works done on this field, I choose to take advantage of the near resonance frequencies of the waveguide, where the Helmholtz problem is known to be ill conditioned. At these frequencies, a phenomenon close to the tunnel effect in quantum mechanics can be observed and resonant modes propagate in the waveguide. These resonant modes are very sensitive to width variations, and measuring their amplitude enables to reconstruct the local variations of the waveguide shape with very high sensibility. Given wave field measurements for a range of near resonance frequencies, I provide a stable reconstruction of the width of a slowly varying waveguide. I also provide a suitable numerical method for efficient reconstruction of such width variations, and apply it to defects like dilation or shrinkage of a waveguide.
