The paraboloidal reflector antenna in radio astronomy and communication : theory and practice

267 Pages·2007·9.261 MB·English

by  J W M Baars

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.
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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
Contents xi
4. Antenna characteristics in practical applications ......................... 55
4.1. Introduction ............................................................................................. 55
4.2. Illumination efficiency, beam width, sidelobe level ............................... 57
4.2.1. Illumination efficiency ("taper") ...................................................... 57
4.2.2. Beamwidth, sidelobe level and taper ................................................ 61
4.3. Axial defocus ........................................................................................... 66
4.3.1. Gain function with axial defocus ..................................................... 68
4.3.2. Beamwidth and sidelobe variation with axial defocus ........................ 70
4.3.3. Depth of focus in prime focus and Cassegrain configuration .............. 73
4.4. Lateral defocus - Coma, Beam-Deviation-Factor ................................... 74
4.4.1. Off-axis beam function - Coma ....................................................... 74
4.4.2. Gain and sidelobe level for off-axis beam ......................................... 78
4.4.3. Beam Deviation Factor (BDF) ........................................................ 80
4.5. Aperture blocking .................................................................................... 82
4.5.1. The variables and equations ............................................................ 83
4.5.2. Gain loss and sidelobe level increase due to blockage ....................... 86
4.6. Reflector shape deviations - "surface tolerance theory" ......................... 87
4.6.1. Random surface deviation ............................................................... 87
4.6.2. Numerical results with Mathematica ................................................ 90
4.6.3. Large scale deformations - Astigmatism .......................................... 93
4.7. The Mathematica Routines ..................................................................... 96
References ............................................................................................. 107
5. Measurement of antenna parameters ...............................................109
5.1. Global antenna parameters ..................................................................... 109
5.2. Response of an antenna to a source distributed in space ......................... 112
5.3. Efficiencies and Corrections for finite source size .................................. 114
5.3.1. Aperture and Beam Efficiency ........................................................ 114
5.3.2. Convolution of the beam with a source of finite size ......................... 116
5.3.3. Beam efficiency and intensity calibration ......................................... 122
5.4. Sidelobe level and error pattern .............................................................. 124
5.4.1. Diffraction beam sidelobes ............................................................. 124
5.4.2. Error pattern due to random surface errors ....................................... 125
5.5. Pointing and focus corrections and optimisation .................................... 130
5.5.1. Pointing aspects of defocus ............................................................. 131
5.5.2. General pointing model of the antenna ............................................. 131
5.5.3. Measurement of the optimum focus ................................................. 136
5.6. On pointing and surface error calculation from FEA ............................. 138
5.7. Antenna gain and radio source flux calibration ...................................... 141
5.7.1. Determining the absolute gain of the antenna .................................... 142
5.7.2. Extraterrestrial sources as test transmitters ....................................... 143
xii Contents
5.8. The Mathematica routines ....................................................................... 146
References ............................................................................................. 149
6. Miscellaneous subjects ............................................................................ 152
6.1. Holographic measurement of reflector surface contour .......................... 152
6.1.1. Introduction ................................................................................... 152
6.1.2. The mathematical basis of Radio Holography ................................... 154
6.1.3. Details of the mathematics of nearfield holography ........................... 155
6.1.4. Aspects of the practical realisation - examples of results .................... 161
6.1.5. Alternative methods of reflector shape measurement ......................... 165
6.2. Far sidelobes, Gain calibration ................................................................ 168
6.2.1. Far sidelobes and stray radiation correction ...................................... 168
6.2.2. Absolute gain calibration with an interferometer ............................... 171
6.3. Chromatism, Off-set aperture ................................................................ 173
6.3.1. Chromatism - "baseline ripple" ........................................................ 173
6.3.2. Unblocked aperture - Offset antenna ................................................ 176
6.4. Atmospheric fluctuations and dual-beam observing ............................... 178
6.4.1. Introduction ................................................................................... 178
6.4.2. Atmospheric emission and attenuation ............................................. 181
6.4.3. Atmospheric refraction ................................................................... 182
6.4.4. Signal fluctuations due to atmospheric turbulence ............................. 184
6.4.5. Observing methods to cancel atmospheric fluctuations. ..................... 189
6.4.6. Beam overlap in the Fresnel region of the antenna ............................ 192
6.5. The Mathematica routines ....................................................................... 195
References ............................................................................................. 196
7. Design features of some radio telescopes ...................................... 201
7.1. Introduction ............................................................................................. 201
7.2. The homologous design method ............................................................. 203
7.3. The Westerbork Synthesis Radio Telescope (WSRT) ............................ 207
7.4. The Effelsberg 100-m radio telescope ................................................... 213
7.5. The IRAM 30-m Millimeter Radio Telescope (MRT) ........................... 218
7.6. The Heinrich Hertz Submillimeter Telescope (HHT) ............................. 225
7.7. The Large Millimeter Telescope (LMT) ................................................. 229
7.8. The ALMA Prototype Antennas ............................................................. 235
7.8.1. The VertexRSI design .................................................................... .237
7.8.2. The Alcatel-EIE-Consortium (AEC) design ...................................... .239
7.8.3. Performance evaluation of the ALMA prototype antennas ................. .240
7.9. Conclusion ............................................................................................... 242
References ............................................................................................. .243
Name Index ......................................................................................................... 247
Subject Index ...................................................................................................... 249