Reconstructing small perturbations of scatterers from electric or acoustic far-field measurements

In this paper, we consider the problem of determining the boundary perturbations of an object from far-field electric or acoustic measurements. Assuming that the unknown scatterer boundary is a small perturbation of a circle, we develop a linearized relationship between the far-field data and the shape of the object. This relationship is used to find the Fourier coefficients of the perturbation of the shape.