One Two
Sie sind hier: Startseite Research Focal Length Variations

Deformation analyses of radio telescopes

Examples: Effelsberg 100-m radio telescope and Onsala Space Observatory 20-m radio telescope

Radio telescope's main reflectors are affected by an elevation dependent deformation due to gravitation. We perform survey campaigns with laser scanners to detect the surface deformations of the mirror which lead to a change in focal length. Furthermore, we analyze the stability of radio telescope's reference points using laser scanner. Knowledge about an elevation dependent variation of the focal length and the reference point are essential for VLBI applications because they directly impact the time-of-flight measurements. So far, we analyzed the Effelsberg 100-m radio telescope and the Onsala space observatory 20-m radio telescope.


Teleskop          theo_defo_teleskop     theo_defo_teleskop_erkl

Due to the fact that the laser scanner was mounted head down on the sub reflector it was possible to scan nearly the whole surface. The measurements were performed at seven different elevations between 90° and 7°.


In order to estimate the deformation, the surface is parameterized by an implicit model of a best fit rotational paraboloid. The orthogonal distance regression allows an estimation of the focal length of the paraboloid. The associated adjustment process presented here is a two step modification of a classical nonlinear least squares approach: First, it is based on a linearization of the functional model directly on the estimated paraboloid itself, represented by the observed coordinates’ orthogonal contacting points on the surface. Second, the distances between the observed coordinates and the corresponding calculated orthogonal contacting points are minimized. Results have shown that these modifications in the present case add up to a focal length estimation more robust towards changes in position and orientation of the paraboloid in space.


Brennweite_Effelsberg                                      Defo_Scatter

An analysis of the estimated focal length at different elevations shows a significant elevation and consequential gravity dependent variation. The focal length decreases together with the elevation with a magnitude of about one centimeter. The discrepancies from the best-fit paraboloid follow a Gaussian distribution in first approximation.

The stability of the reference point is analyzed, e.g., for the Onsala Space Observatory 20-m radio telescope:



Contact Persons
Publications and Presentations
  • Holst, C., Nothnagel, A., Haas, R., Kuhlmann, H. (2019) Investigating the gravitational stability of a radio telescope's reference point using a terrestrial laser scanner: Case study at the Onsala Space Observatory 20-m radio telescope, ISPRS J. Photogramm., 149, 67-76, doi:
  • Holst, C., Schunck, D., Nothnagel, A., Haas, R., Wennerbäck, L., Olofsson, H., Hammargren, R., Kuhlmann, H. (2017) Terrestrial laser scanner two-face measurements for analyzing the elevation-dependent deformation of the Onsala Space Observatory 20-m radio telescope's main reflector in a bundle adjustment, Sensors, 17 (8), 1833, doi:10.3390/s17081833
  • Holst, Ch., Nothnagel, A., Blome, M., Becker, P., Eichborn, M., Kuhlmann, H. (2015) Improved area-based deformation  analysis of a radio telescope's main reflector based on terrestrial laser scanning, J. Appl. Geodesy, J. Appl. Geodesy, 9 (1), S. 1-14
  • Holst Ch, Zeimetz Ph, Nothnagel A, Schauerte W, Kuhlmann H (2012) Estimation of focal length variations of a 100-m radio telescope`s main reflector by laser scanner measurements, Journal of Surveying Engineering ASCE, 138 (3) S. 126-135
  • Holst, Ch.; Kuhlmann, H. (2011) Bestimmung der elevationsabhängigen Deformation des Hauptreflektors des 100m-Radioteleskops Effelsberg mit Hilfe von Laserscannermessungen, In: Schriftenreihe DVW, Band 66 „Terrestrisches Laserscanning - TLS 2011 mit TLS-Challenge“, S. 161-180, Wißner Verlag