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We derive relationships between the shape deformation of an impenetrableobstacle and boundary measurements of scattering fields on the perturbed shapeitself. Our derivation is rigourous by using systematic way, based on layerpotential techniques and the field expansion (FE) method (formal derivation).We extend these techniques to derive asymptotic expansions of theDirichlet-to-Neumann (DNO) and Neumann-to-Dirichlet (NDO) operators in terms ofthe small perturbations of the obstacle as well as relationships between theshape deformation of an obstacle and boundary measurements of DNO or NDO on theperturbed shape itself. All relationships lead us to very effective algorithmsfor determining lower-order Fourier coefficients of the shape perturbation ofthe obstacle.

Reconstructing Small Perturbations of an Obstacle for Acoustic Waves from Boundary Measurements on the Perturbed Shape Itself