Far-Field Sensitivity to Local Boundary Perturbations in 2D Wave Scattering

We numerically investigate the sensitivity of the scattered wave field to perturbations in the shape of a scattering body illuminated by an incident plane wave. This study is motivated by recent work on the inverse problem of reconstructing a scatterer shape from measurements of the scattered wave at large distances from the scatterer. For this purpose we consider star-shaped scatterers represented using cubic splines, and our approach is based on a Nystr\"om method-based discretisation of the shape derivative. Using the singular value decomposition, we identify fundamental geometric modes that most strongly influence the scattered wave, providing insight into the most visible boundary features in scattering data.