Modelling of an inexpensive 9M satellite dish from 3D point clouds captured by terrestrial laser scanners

Abstract

This paper presents the use of Terrestrial laser scanners (TLS) to model the surface of satellite dish. In this case, the dish was an inexpensive 9m parabolic satellite dish with a mesh surface, and was to be utilised in radio astronomy. The aim of the modelling process was to determine the deviation of the surface away from its true parabolic shape, in order to estimate the surface efficiency with respect to its principal receiving frequency. The main mathematical problems were the optimal and unbiased estimation the orientation of the dish and the fitting of a parabola to the local orientation or coordinate system, which were done by both orthogonal and algebraic minimization using the least-squares method. Due to the mesh structure of the dish, a classification method was also applied to filter out erroneous points being influenced by the supporting structure behind the dish. Finally, a comparison is performed between the ideal parabolic shape, and the data collected from three different temporal intervals.