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R Hanbury Brown FRS THE INTENSITY INTERFEROMETER its Application to Astronomy R. HANBURY BROWN, F.R.S. Professor of Physics (Astronomy) Unfrersity of Sydney TAYLOR & FRANCIS LTD 10-14 Macklin Street London \\\W H 1974 First published 1974 by Taylor & Francis Ltd 10-14 Macklin Street, London WC2B 5NF © 1974 R. Hanbury Brown All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the copyright owner ISBN 0 85066 072 6 Printed and bound in Great Britain by Taylor & Francis Ltd 10-14 Macklin Street, London WC2B 5NF Distributed in the United States of America and its territories by Halsted Press (a division of John Wiley & Sons Inc.) 605, Third Avenue, New York, NY 10016 List of Symbols .-l area of light detector or mirror a( i·) amplitude of Fourier component of light wave a fraction of photomultiplier anode current due to stray light and dark current B apparent blue magnitude of star Bo bandwidth of light (eqn. (5.2)) b,. electrical bandwidth (eqn. (5.10)) c wlocity of light c(d) correlation observed in 100 s at a baseline d c (d) obsen·ed correlation corrected for zero-drift ( eqn. ( 10.1)) 0 c,(d) normalized correlation ( eqn. ( 10.f)) Cs zero-baseline correlation normalized to nlue expected for a single unresoh-ed star D zero-drift of correlator d baseline length E amplitude of electric wctor of light waw e charge on the electron voltages voltage gain at frequency f .\bsolute monochromatic flux emitted per unit area of stellar surface at wawlength ,\ f frequency of electric current or voltage f1 absolute monochromatic flux recei\·ed from a star at wawkngth ,\ Gr electrical gain of correlator G(1·) mutual spectral density of two light beams (eqn. (3.12)) g(1·) transmittance of optical system at frequency v lz the Planck constant I liaht intensitv l(S) li~ht intensit;· per unit area of source i (§ f) angle of inclination of orbital plane of a binary star 11· 12 electric currents IX Preface· In this book I have tried to write a history of the intensity interferometer together with a brief account 0f the theory, practice and application of this new instrument to a classical problem in astronomy-the measurement of the apparent angular diameters of stars. Much of the scientific material has already appeared in print but it is scattered through more than twenty years of scientific literature. My aim has been to collect it into one book and to tell how and why the work came to be done. There are at least three good reasons for doing this. Firstly, the intensity interferometer has proved to be of lively interest to physicists and incomprehensible to astronomers; there should be a single written account appropriate to both groups. Secondly, the measurements of the angular diameters of stars made at Narrabri Observatory have been widely used by astrophysicists and there is no other existing instrument capable of checking them. It is therefore doubly important that there should be a detailed account of exactly how the observations were made and analysed so that their credibility can be assessed. Finally, I want to preserve our experience so that other groups, perhaps in the Northern Hemisphere, will one day follow our lead. Those of us who have tried to build on the experience gained with the unsuccessful 50 ft. stellar interferometer built at Mount Wilson by Hale and Pease have found that although there are descriptions of the v instrument, like so many scientific papers, they don't tell us all we need to know-what checks were made and what went wrong. With this in mind I hope the reader will excuse some of the details in this book which, at first sight, may seem unnecessary. During my life I have been fortunate to take part in two other scientific adventures: the early work on radar and the beginnings of radio-astronomy. Books about those pioneering days have always seemed to me to leave out the essential ingredient of such adventures-the sense of purpose and excitement which transfigures the hardest work and dullest routine. Telling my own story has made me well aware that a lifetime of writing scientific papers is not a good training for conveying that same sense of ad,·enture which was felt by all who helped t0 build the stellar interferometer at Narrabri. If only for one moment I could take you into the great plains of northern New South Wales and show you this elegant instrument looking at the stars, I believe you would understand what is missing from my book. Not only was the work we did at Narrahri worth while in strictly scientific terms, but in personal terms it was exciting, exhausting and profoundly rewarding. The success of a project lasting more than two decades has involved the help and support of many people over the years. Much of the work described in this book has been done by my colleagues, Dr R. Q. Twiss, Dr J. Davis and Dr L. R. Allen. VI Others who have "done time" at Narrabri are Dr D. Herbison-Evans and Dr C. Hazard and a small galaxy of postgraduate students: Dr M. J. Yerbury, Mr J.M. Rome, Mr R. J. W. Lake, Mr D. W. Keenan, Dr R. J. Webb and Mr R. K. Outhred. Mr Gifford has taken care of the maintenance of the Observatory for ten years, Mr S. Owens has looked after the electronics and Miss V. Raymond has been throughout, secretary to the Department of Astronomy in the University of Sydney. The original design of the instrument owes much to the staff of Dunford and Elliott (Sheffield), Mullard Ltd. (Salford) and MacDonald, Wagner and Priddle (North Sydney). The financial support was provided by the Department of Scientific and Industrial Research (now the Science Research Council), the Nuclear Research Foundation (now the Foundation for Research in Physics) within the University of Sydney, the Office of Scientific Research of the United States Air Force, the Australian Research Grants Committee and the Research Grants Committee of the University of Sydney. I am grateful to Sir Bernard Lovell for giving the original work at Jodrell Bank his support and to Professor Harry Messel who, as Head of the School of Physics in the University of Sydney, has always supported us with characteristic enthusiasm. Among our many friends overseas, I must mention vii Dr D. M. Popper of U.C.L.A., Dr E. P. Ney of the University of Michigan and Dr D. C. Morton of Princeton, all of whom have worked at Narrabri. Finally I thank my wife Heather for making our life in the bush so happy and for her help with everything described in this book except the mathematics. Narrabri Observatory R. HANBURY BROWN New South Wales Australia June 1973 Ylll Jc wave noise (eqn. (4.18)) Jn shot noise (eqn. (4.19)) k the Boltzmann constant lo coherence length of light (eqn. (3.33)) N,n number of counts of pulses N(T) r.m.s. noise or uncertainty after a time T n(v) number of photons per unit time, per unit area, per unit light bandwidth at frequency v R radius of star Ri> R distances from observer to points on a light source 2 (S/N) signal to noise ratio T,t time Te effective temperature of a star u limb-darkening coefficient (eqn. (10.12)) v apparent visual magnitude of star V(d) fringe visibility with baseline d V(t) electric vector of light wave W(f) spectral density of electrical fluctuations z (§ 5.6) zenith angle, (§ 5.8) coordinate parallel to line from observer to source quantum efficiency ratio of brightness of components of binary star polarization factor (eqn. (5.7)) normalized correlation factor ( eqn. (5.8)) mutual coherence function (eqn. (3.16)) complex degree of coherence (eqn. (3.18)) partial coherence factor ( eqn. (5.11)) difference in brightness of components of a binary star light bandwidth electrical bandwidth intensity fluctuation x