Estimation of Focal Length Variations of a 100-m Radio Telescope’s Main Reflector by Laser Scanner Measurements

Abstract

Due to gravitation, the main reflector of a radio telescope underlies a deformation that causes a change in focal length depending on the variations of the elevation angle of the telescope. To estimate these gravity dependent deformations of the main reflector of the 100-m radio telescope at Effelsberg, Germany, this study proposes a measurement concept based on a laser scanner being mounted upside down on the subreflector. The measurements that have been performed at seven different elevations between 90 and 7.5° are used to estimate the focal length variation of the main reflector parameterized by a rotational paraboloid. To guarantee reliability of the adjustment, this study uses an orthogonal distance regression (ODR) rather than a classical least squares adjustment in a Gauss-Helmert model and formulates the independence of the focal length estimation from the absolute position and orientation of the main reflector in space as a requirement for a reliable adjustment approach. This investigation attests that the ODR has superior reliability with regard to this criterion. A three-step adjustment procedure based on an alteration of the ODR and several outlier eliminations is used to determine the variations of the focal length due to gravitation. The estimated focal length decreases by a maximum of 12.6 mm when tilting the reflector from 90 to 7.5° elevation angle. The postfit discrepancies between the best-fit paraboloid and the reflector’s surface are Gaussian distributed within the accuracy of the measurements. This face supports the assumption of a homologous deformation of the main reflector.