On the inversion of the atomic beam scattering data in the Eikonal approximation

The inversion method of Celli, Garcia and Rieder requires some a-priori knowledge about the phases of the dominant scattering amplitudes. A perturbational method will be introduced here which is evaluated in the Eikonal approximation, but can in principle be extended to the Helmholtz equation. It is based on the observation that the expansion coefficients PG(n) of the scattering intensities with respect to ki, the incident wave vector, are functions of the corrugation amplitudes and phase differences and fulfill certain sum rules. If these coefficients are determined by several measurements with varying scattering parameters, then the lowest PG(n) for n = 2,3.4 are sufficient for finding the essentially unique surface profile function. As an example, simulated surface domain structure scattering data will be inverted. © 1989.