Modeling the rail surface unevenness of a high-precision radio telescope

This study proposed a coarse-fine mixed model for describing the rail surface unevenness of an ultra-large fully steerable radio telescope （Qi Tai Telescope） with a diameter of 110 meters. The rail surface unevenness includes information on error arising from two different scales, i.e., the long-period- short-change and the short-period-long-change. Consequently, in this study an idea of a mixed model was proposed, in which trigonometric and fractal functions were, respectively, used to describe infor- mation on error from two scales. Key parameters were determined by using the least squares method and the wavelet transform method, and finally, a specific mathematical expression of the model was obtained by optimization. To validate the effectiveness of the new modeling method, the mixed model was then used to describe the rails of the Green Bank Telescope, the Large Millimeter Telescope, and a radio telescope in Miyun, Beijing. A comparative study revealed that the maximum error was less than 15 %, thus the result was superior to those of existing modeling methods.