Advertisement

Journal of Geodesy

, Volume 88, Issue 12, pp 1145–1161 | Cite as

A complete VLBI delay model for deforming radio telescopes: the Effelsberg case

  • T. ArtzEmail author
  • A. Springer
  • A. Nothnagel
Original Article

Abstract

Deformations of radio telescopes used in geodetic and astrometric very long baseline interferometry (VLBI) observations belong to the class of systematic error sources which require correction in data analysis. In this paper we present a model for all path length variations in the geometrical optics of radio telescopes which are due to gravitational deformation. The Effelsberg 100 m radio telescope of the Max Planck Institute for Radio Astronomy, Bonn, Germany, has been surveyed by various terrestrial methods. Thus, all necessary information that is needed to model the path length variations is available. Additionally, a ray tracing program has been developed which uses as input the parameters of the measured deformations to produce an independent check of the theoretical model. In this program as well as in the theoretical model, the illumination function plays an important role because it serves as the weighting function for the individual path lengths depending on the distance from the optical axis. For the Effelsberg telescope, the biggest contribution to the total path length variations is the bending of the main beam located along the elevation axis which partly carries the weight of the paraboloid at its vertex. The difference in total path length is almost \(-\)100 mm when comparing observations at 90\(^\circ \) and at 0\(^\circ \) elevation angle. The impact of the path length corrections is validated in a global VLBI analysis. The application of the correction model leads to a change in the vertical position of \(+120\) mm. This is more than the maximum path length, but the effect can be explained by the shape of the correction function.

Keywords

VLBI Signal path variation Antenna deformation  Delay correction Ray tracing Terrestrial reference frames 

Notes

Acknowledgments

The investigations described in this publication make extensive use of observations acquired with the Effelsberg 100 m radio telescope of the Max Planck Institute for Radio Astronomy in Bonn, Germany. We thank the IVS for providing the VLBI observation data.

References

  1. Abbondanza C, Sarti P (2010) Effects of illumination functions on the computation of gravity-dependent signal path variation models in primary focus and Cassegrainian VLBI telescopes. J Geod 84(8):515–525. doi: 10.1007/s00190-010-0389-z CrossRefGoogle Scholar
  2. Altamimi Z, Collilieux X, Métivier L (2010) ITRF2008: an improved solution of the international terrestrial reference frame. J Geod 85(8):457–473. doi: 10.1007/s00190-011-0444-4 CrossRefGoogle Scholar
  3. Baars JWM (2007) The paraboloidal reflector antenna in radio astronomy and communication, vol. 348. Springer, New York. doi: 10.1007/978-0-387-69734-5, ISSN 0067-0057
  4. Bach U, Kraus A, Fürst E, Polatidis A (2007) First report about the commissioning of the new Effelsberg sub-reflector. Effelsberg memo series. http://www3.mpifr-bonn.mpg.de/div/effelsberg/EffMemo/12092007_memo.pdf
  5. Carter E, Rogers AEE, Counselman CC, Shapiro II (1980) Comparison of geodetic and radio interferometric measurements of the Haystack–Westford base line vector. J Geophys Res 85:2685–2687CrossRefGoogle Scholar
  6. Cha AG (1987) Phase and frequency stability of Cassegrain antennas. Radio Sci 22:156–166CrossRefGoogle Scholar
  7. Clark TA, Thomsen P (1988) Deformations in VLBI antennas. Technical report 100696. NASA, GreenbeltGoogle Scholar
  8. Dawson J, Sarti P, Johnston G, Vittuari L (2007) Indirect approach to invariant point determination for SLR and VLBI systems: an assessment. J Geod 81(6–8):433–441. doi: 10.1007/s00190-006-0125-x CrossRefGoogle Scholar
  9. Dutescu E, Heunecke O, Krack K (2009) Formbestimmung bei Radioteleskopen mittels Terrestrischem Laserscanning. Allgem Verm Nachr 6:239–245Google Scholar
  10. Fey A, Gordon D, Jacobs CS (2009) The second realization of the international celestial reference frame by very long baseline interferometry. IERS Technical Note No 35. Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am MainGoogle Scholar
  11. Holst C, Zeimetz P, 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. J Surv Eng 138(3):126–135. doi: 10.1061/(ASCE)SU.1943-5428.0000082 CrossRefGoogle Scholar
  12. Jacobs CS, Rius A (1989) VLBI Surveying between DSS63 and DSS65. In: Rius A (ed) Proceedings of the 7th working meeting on European VLBI for geodesy and astrometry. Universidad Complutense De Madrid, Madrid, pp 64–67Google Scholar
  13. Johannson LA, Stodne F, Wolf S (1996) The Pisa project, variations in the height of the foundation of the 20 meter radio telescope. Onsala Space Observatory, Chalmers University of Technology, Research Report No 178, GöteborgGoogle Scholar
  14. Ma C, Sauber JM, Clark TA, Ryan JW, Bell LJ, Gordon D, Himwich WE (1990) Measurement of horizontal motions in Alaska using very long baseline interferometry. J Geophys Res 95(B13):21991–22011. doi: 10.1029/JB095iB13p21991 CrossRefGoogle Scholar
  15. Miebach P, Werntgen HJ (1980) Untersuchungen zur Stabilität des Achsenpunktes am Effelsberger Radioteleskop. Diploma thesis, Geodetic Institut of the University of BonnGoogle Scholar
  16. Napier PJ (1999) The primary antenna elements. In: Taylor GB, Carilli CL, Perley RA (eds) Synthesis imaging in radio astronomy II, vol 180. Astronomical Society of the Pacific Conference Series, pp 37–56Google Scholar
  17. Nothnagel A (2002) Local Telescope displacements at Effelsberg. In: Campbell J, Haas R, Nothnagel A (eds) Measurement of vertical crusal motion in Europe. TMR Network FMRX-CT96-0071 Scientific Report 1996–2001, Bonn, pp 62–67Google Scholar
  18. Nothnagel A (2009) Conventions on thermal expansion modelling of radio telescopes for geodetic and astrometric VLBI. J Geod 83(9):787–792. doi: 10.1007/s00190-008-0284-z CrossRefGoogle Scholar
  19. Nothnagel A, Eichborn M, Holst C (2013) Improved focal length results of the Effelsberg 100 m radio telescope. In: Proceedings of the 21st meeting of the European VLBI group for geodesy and astrometry, Helsinki, pp 55–59Google Scholar
  20. Otoshi TY, Young LE (1982) An experimental investigation of the changes of VLBI time delays due to antenna structural deformations. TDA progress report 42–41, Pasadena, pp 218–225Google Scholar
  21. Rochblatt DJ, Hoppe D, Imbriale W, Franco M, Richter P, Withington P, Jackson H (2000) A Methodology for the open loop calibration of a deformable flat plate on a 70-meter antenna. In: Proceedings of the millennium conference on antennas and propagation AP2000, Davos, pp 9–14. http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/18718/1/99-2202.pdf
  22. Sarti P, Vittuari L, Abbondanza C (2009a) Laser scanner and terrestrial surveying applied to gravitational deformation monitoring of large VLBI telescopes’ primary reflector. J Surv Eng 135(4):136–148. doi: 10.1061/(ASCE)SU.1943-5428.0000008 CrossRefGoogle Scholar
  23. Sarti P, Abbondanza C, Vittuari L (2009b) Gravity-dependent signal path variation in a large VLBI telescope modelled with a combination of surveying methods. J Geod 83(11):1115–1126. doi: 10.1007/s00190-009-0331-4 CrossRefGoogle Scholar
  24. Sarti P, Abbondanza C, Petrov L, Negusini M (2011) Height bias and scale effect induced by antenna gravitational deformations in geodetic VLBI data analysis. J Geod 85(1):1–8CrossRefGoogle Scholar
  25. Schuh H, Behrend D (2012) VLBI: a fascinating technique for geodesy and astrometry. J Geodyn 61:68–80. doi: 10.1016/j.jog.2012.07.007 CrossRefGoogle Scholar
  26. Sovers OJ, Fanselow JL, Jacobs CS (1998) Astrometry and geodesy with radio interferometry: experiments, models, results. Rev Mod Phys 70(4):1393–1454CrossRefGoogle Scholar
  27. Whitney AR, Rogers AEE, Hinteregger HF, Knight CA, Levine JL, Lippincott S, Clark TA, Shapiro II, Robertson DS (1976) A very-long-baseline interferometer system for geodetic applications. Radio Sci 11(5):421–432CrossRefGoogle Scholar
  28. Wolf H (1968) Ausgleichungsrechnung nach der Methode der kleinsten Quadrate. Ferdinand Dümmlers Verlag, BonnGoogle Scholar
  29. Zernecke R (1999) Seasonal variations in height demonstrated at the radiotelescope reference point. In: Schlüter W, Hase H (eds) Proceedings of the 13th working meeting on European VLBI for geodesy and astrometry, Viechtach/Wettzell. Bundesamt für Kartographie und Geodäsie, Fundamentalstation Wettzell, pp 15–18Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute of Geodesy and GeoinformationUniversity of BonnBonnGermany

Personalised recommendations