Optimization of the reflective surface shape of a variable curvature mirror

We report a computational and theoretical study of the shape of a reflective surface of a variable curvature mirror (VCM) with a different thickness distribution along the mirror radius. An analytical expression is proposed for the thickness distribution and a deviation of the reflective VCM surface shape with such a distribution from the parabolic shape is assessed in comparison with the exponential and cycloid thickness profiles known in the literature. It is shown that the use of the proposed thickness distribution can significantly reduce spherical aberration and improve the quality of the shape of the reflective VCM surface in the focal length range from 50 to 500 m. It is assumed that this VCM design can be used in an optical system for laser cutting of metal structures.