The scattering data of a Riemannian manifold with boundary record the incoming and outgoing directions of each geodesic passing through. We show that the scattering data of a generic Riemannian surface with no trapped geodesics and no conjugate points determine the lengths of geodesics. Counterexamples exists when trapped geodesics are allowed.

introduction: in this study, we intend to use diffuse optical tomography (dot) as a noninvasive, safe and low cost technique that can be considered as a functional imaging method and mention the importance of image reconstruction in accuracy and procession of image. one of the most important and fastest methods in image reconstruction is the boundary element method (bem). this method is introdu...