Simulation of local error correction of the surface shape by a low-dimensional ion beam

We propose an algorithm for solving the problem of local error correction of the surface shape by a low-dimensional ion beam. The algorithm presumes successive sampling running over protrusions relative to the average height aimed at searching for the optimal etching point satisfying the criterion for the reduction of the sum of derivative moduli on the etching spot. It is shown that the new approach makes it possible to considerably extend the range of spatial frequencies accessible to the action for a given dimension of an ion beam.