We solve the inverse scattering problem for a surface profile by measuring the intensity of the scattered near field. It was shown numerically [Opt. Lett. 20, 949 (1995)] that the image produced by the superposition of different images taken with all possible angles of incidence closely follows the surface profile. We establish a rigorous analysis of this method based on perturbation theory. Furthermore, we prove that the procedure is equivalent to illuminating the surface with incoherent light and thus has broad experimental applications.
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