  We study the inverse backscattering problem for the Schr\"odinger equation in
two dimensions. We prove that, for a non-smooth potential in 2D the main
singularities up to 1/2 of the derivative of the potential are contained in the
Born approximation (Diffraction Tomography approximation) constructed from the
backscattering data. We measure singularities in the scale of Hilbertian
Sobolev spaces.
