THE PARABOLOIDAL REFLECTOR ANTENNA IN RADIO ASTRONOMY AND COMMUNICATION ASTROPHYSICS AND SPACE SCIENCE LIBRARY VOLUME348 EDITORIALBOARD Chairman W.B.BURTON,NationalRadioAstronomyObservatory,Charlottesville,Virginia,U.S.A. ([email protected]);UniversityofLeiden,TheNetherlands([email protected]) MEMBERS F.Bertola,UniversityofPadu,Italy; J.P.Cassinelli,UniversityofWisconsin,Madison,USA; C.J.Cesarsky,EuropeanSouthernObservatory,GarchingbeiMu¨nchen,Germany; P.Ehrenfreund,LeidenUniversity,TheNetherlands; O.Engvold,UniversityofOslo,Norway; A.Heck,StrasbourgAstronomicalObservatory,France; E.P.J.vandenHeuvel,UniversityofAmsterdam,TheNetherlands; V.M.Kaspi,McGillUniversity,Montreal,Canada; J.M.E.Kuijpers,UniversityofNijmegen,TheNetherlands; H.vanderLaan,UniversityofUtrecht,TheNetherlands; P.G.Murdin,InstituteofAstronomy,Cambridge,UK; F.Pacini,IstitutoAstronomiaArcetri,Firenze,Italy; V.Radhakrishnan,RamanResearchInstitute,Bangalore,India; B.V.Somov,AstronomicalInstitute,MoscowStateUniversity,Russia; R.A.Sunyaev,SpaceResearchInstitute,Moscow,Russia THE PARABOLOIDAL REFLECTOR ANTENNA IN RADIO ASTRONOMY AND COMMUNICATION Theory and Practice JACOBW.M.BAARS EuropeanSouthernObservatory Swisttal /Bonn, Germany JacobW.M.Baars EuropeanSouthernObservatory Swisttal /Bonn, G ermany [email protected] Cover illustration: The APEX Submillimeter Telescope of the Max-Planck-Institut für Radioastronomie on Llano de Chajnantor, Chile. Photo: Arnaud Belloche, Max-Planck-Institut für Radioastronomie, Bonn, Germany. Frontispiece: Specchi Ustori di Archimede (Archimedé Burning Glasses), Giulio Pangi (attr.) 1599. Courtesy of Galleria degli Uffizi, Polo Museale, Firenze, Italia. LibraryofCongressControlNumber:2006940784 ISBN-10:0-387-69733-0 e-ISBN-10:0-387-69734-9 ISBN-13:978-0-387-69733-8 e-ISBN-13:978-0-387-69734-5 Printedonacid-freepaper. (cid:1)C 2007SpringerScience+BusinessMedia,LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnection withanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjectto proprietaryrights. 9 8 7 6 5 4 3 2 1 springer.com Dedication To Dave Heeschen, who enabled me to jump in the water, Peter Mezger, who taught me to swim, the memory of Ben Hooghoudt, who showed me how to manage the waves, Richard Kurz, who saved me from drowning in the "Mexican Gulf". and My wife Marja, for love and patiently keeping me afloat throughout. Preface The paraboloidal (often called parabolic) reflector is one of the most versatile and widely used antenna types for the transmission and reception of electro-magnetic waves in the microwave and millimeter wavelength domain of the electro-magnetic spectrum. The development of large and highly accurate reflectors has mainly been carried out at radio astronomy observatories. The emergence of satellite communica- tion and deep-space research with satellites necessitated the use of such large reflec- tors as ground stations for the communication with the satellites and space-probes. Over the years radio astronomers have developed the techniques of calibration of large antennas with radio astronomical methods. These are often the only way to characterise the antenna, because the farfield distance precludes an earth-bound test transmitter and the antennas are too big for nearfield scanning test ranges. The general theory of the reflector antenna has been presented quite completely in the classic book by Silver (1949) in the MIT Radiation Laboratory Series. Modern approaches of computer-aided analysis and design were discussed by Rusch and Potter (1970). With the current methods of analysis, like the geometrical theory of diffraction and fast algorithms of surface current integration, the analysis of the detailed behaviour of the radiation characteristics can be realised. Nevertheless these methods are laborious and often not suitable for the accurate prediction of the detailed antenna behaviour under non-ideal conditions, as mechanical distortions under gravity, temperature gradients and wind forces. Here a combination of approxi- mate theoretical analysis and measurement of antenna parameters is often the best approach to characterise the antenna. The techniques developed by radio astronomers for the characterisation of large reflector antennas has not been described comprehensively in the open literature. An early effort in this area is "Radioastronomical Methods of Antenna Measurements" by Kuz'min and Salomonovich (1966). Since then these methods have been further developed and a considerable body of experience is now available, which however has only been sparsely published in readily accessible form. It is the purpose of this book to fill part of this gap. The book is neither a replacement for antenna theory texts like Silver or Rusch and Potter, nor a substitute for books on radio astronomy techniques like Kraus (1966), Rohlfs and Wilson (1996) or Thompson, Moran and Swenson (2001). It is less general than the book "Radiotelescopes" by Christiansen and Högbom (1969). Structural and mechanical aspects of large reflector antennas have been presented in Mar and Leibovich (1969) and by Levy (1996). Here we are mainly concerned with electromagnetic aspects and concentrate on a discussion of the paraboloidal reflector antenna in a practical approach. The theory is developed with this in mind and considerable attention is given to the treatment of viii Preface non-ideal situations and the calibration of antenna parameters. While the parabolic reflector is the most used antenna, much of the discussion applies mutatis mutandis to spherical and elliptical reflectors, as well as to so-called "shaped" systems. The general subject of "Instrumentation and Techniques for Radio Astronomy" is well illustrated by the articles in the selected reprints volume of this title, collected and commented by Goldsmith (1988). Because of its usefulness, we shall indicate the presence of particular references in this volume next to their original source in our chapter reference lists as [Gold, pp]. We omit a treatment of polarisation. While control of cross-polarisation is certainly of importance in communication systems and in a limited, but important part of radio astronomy observations, its full discus- sion is beyond the aims set for this text. A complete treatment of polarisation can be found in a book by Tinbergen (1996). Basic and practical aspects of polarisation in radio interferometry are described by Morris et al.(1964) and Weiler (1973). An original matrix treatment of radio interferometric polarimetry is presented in a series of three papers by Hamaker, Bregman and Sault (1996). All calculations and results in the form of tables and figures have been made with the aid of the software package Mathematica from Wolfram Research (Wolfram, 1999). The Mathematica instructions and expressions can be used directly by the reader with access to Mathematica for the implementation of his own input data. In order not to break the flow of the text, the routines are assembled at the end of each chapter. In the text they are identified in blue print as [Mat.x.y]. Actually, the entire book has been written as a Mathematica Notebook using the excellent editorial capabilities of the program. It is hoped that the availability of the Mathematica routines will contribute to the usefulness of the book in daily use. The routines are being made available for download on the Springer Website. The reference lists are not exhaustive. We provide references of a historical nature, original work used in the text and selected references for further study of details. We aim to address the needs of observational radio astronomers and microwave communication engineers. The book should be of use to all who are involved in the design, operation and calibration of large antennas, like ground station managers and engineers, practicing radio astronomers and graduate students in radio astronomy and communication technology. Acknowledgement. The material assembled in this book has been part of my work for more than 40 years. It is clear that over such a time span I have been influenced by and have used contributions from numerous colleagues to whom I owe my debt. They are too numerous to list, but I have endeavoured to give them proper credit in the references. A few of them must be mentioned because of their decisive influence on my work and interests. Peter Mezger introduced me to the subject of antenna calibration and guided me through my early efforts. John Findlay was a great source of inspiration in the early years. The long and close collaboration with Albert Greve and Jeffrey Mangum is reflected in the text at many places. I also thank both of them for a valuable scrutiny of the draft text. Swisttal / Bonn, October 2006 Jacob W.M. Baars Preface ix Bibliography Christiansen, W.N. and J.A. Högbom, Radiotelescopes, Cambridge, University Press, 1969. Goldsmith, P.F. (Ed.), Instrumentation and Techniques for Radio Astronomy, New York, IEEE Press, 1988. [Referred to as "Gold, pp" for individual articles.] Hamaker, J.P., J.D. Bregman and R.J. Sault, Understanding radio polarimetry, Astronomy and Astrophysics Sup.117, 137-147, 149-159, 161-165 (3 papers), 1996. Kraus, J.D., Radio Astronomy, New York, McGraw-Hill, 1966; 2nd Ed., Powel OH, Cygnus-Quasar Books, 1986. Kuz'min, A.D. and A.E. Salomonovich, Radioastronomical Methods of Antenna Measurements, New York, Academic Press, 1966. Levy, R., Structural Engineering of Microwave Antennas, New York, IEEE Press, 1996. Mar, J.W. and H. Liebowitz (Eds.), Structures Technology for large Radio and Radar Telescope Systems, Cambridge MA, MIT Press, 1969. Morris, D., V. Radhakrishnan and G.A. Seielstad, On the Measurement of Polariza- tion Distribution over Radio Sources, Astrophys. J.139, 551-559, 1964. Rohlfs, K. and T.L. Wilson, Tools of Radio Astronomy, 2nd Ed., Berlin, Springer, 1996. Rusch, W.V.T. and P.D. Potter, Analysis of Reflector Antennas, New York, Aca- demic Press, 1970. Silver, S., Microwave Antenna Theory and Design, MIT Rad. Lab Series 12, New York, McGraw-Hill,1949. Tinbergen, J., Astronomical Polarimetry, Cambridge, University Press, 1996. Thompson, A.R., J.M. Moran and G.W. Swenson, Interferometry and Synthesis in Radio Astronomy, New York, Wiley, 2001. Weiler, K.W., The Synthesis Radio Telescope at Westerbork, Methods of Polariza- tion Measurements, Astron. Astrophys.26, 403-407, 1973. Wolfram, S., The Mathematica Book, 4th Ed., Wolfram Media/ Cambridge Univer- sity Press, 1999. Contents Preface ................................................................................................................... vii Bibliography ............................................................................................. ix List of Figures and Tables............................................................................. xiii Definition of Symbols........................................................................................ xvii 1. Introduction and historical development .......................................... 1 1.1. Some history of the parabolic reflector antenna ...................................... 1 1.2. Measuring antenna parameters with cosmic radio sources ...................... 9 References .............................................................................................. 12 2. Geometry of reflector antennas ............................................................ 14 2.1. Geometrical relations of the dual reflector system .................................. 14 2.2. Geometry of aberrations .......................................................................... 21 2.2.1. Lateral defocus .............................................................................. 21 2.2.2. Axial defocus ................................................................................ 25 2.3. The Mathematica Routines ..................................................................... 29 References ............................................................................................. 30 3. Electromagnetic theory of the reflector antenna .......................... 31 3.1. Basic theory - Maxwell's equations ......................................................... 31 3.2. The primary source and surface current density ..................................... 34 3.3. Surface current integration ...................................................................... 35 3.4. Aperture integration, Kirchhoff-Helmholtz diffraction .......................... 39 3.5. The far-field approximation (Fraunhofer region) .................................... 41 3.6. The near-field approximation (Fresnel region) ....................................... 46 3.7 The Fourier Transformation relationship ................................................. 50 3.8. Relation between far-field and focal region field .................................... 52 3.9. The Mathematica Routines ..................................................................... 52 References ............................................................................................. 54