Numerical iteration method to reduce the surface shape error of a bendable mirror in synchrotron radiation

Abstract

X-ray mirrors with high focusing performance are extensively used in the synchrotron radiation field. Especially for vertical reflecting bendable mirrors, many elements such as gravity, extended parts used for the bending mechanism, etc., usually affect the surface shape precision. There are no effective methods to remove all these errors at this point. However, an iteration method can be adopted to solve this problem. In this paper, a novel, to the best of our knowledge, iteration method on decreasing the error between the practice surface shape and the desired one is proposed. Not only can the precision of the surface shape be realized by this method, but also computational efficiency. Errors induced by gravity can be compensated for by an analytical method, while errors caused by the extended parts should be eliminated by a numerical method. Therefore, two main kinds of errors—gravity and parts of clamping—can be removed by iteration. Some examples are presented to illustrate the advantages of this method by comparison with the regular one.