Axisymmetric surface shape correction of optical elements by a wide-aperture ion beam

Methods for calculating the process of axisymmetric surface shape correction with a wide-aperture ion beam through a forming diaphragm for optical elements with a round and arbitrary border shape are presented. In the case of circular optical elements, an approach based on the separation of the axisymmetric component of the surface shape error from its decomposition by Zernike polynomials is used. In the case of optical elements with an arbitrary border shape (not round), an algorithm for searching the axisymmetric component of the shape error is proposed. The search criterion is to minimize the residual volume of the deviation of the surface shape from the calculated one. The proposed algorithm makes it possible to separate the axisymmetric component of the shape error relative to an arbitrary axis, including one located outside the workpiece. The results of surface treatment in accordance with the above methods are presented.