Table Of ContentIMAGE FORMATION FROM COHERENCE
FUNCTIONS IN ASTRONOMY
ASTROPHYSICS AND
SPACE SCIENCE LIBRARY
A SERIES OF BOOKS ON THE RECENT DEVELOPMENTS
OF SPACE SCIENCE AND OF GENERAL GEOPHYSICS AND ASTROPHYSICS
PUBLISHED IN CONNECTION WITH THE JOURNAL
SPACE SCIENCE REVIEWS
Editorial Board
J. E. BLAMONT, Laboratoire d'Aeronomie, Verrieres, France
R. L. F. BOYD, University College, London. England
L. GOLDBERG. Kitt Peak National Observatory, Tucson. Ariz. • U.S.A.
C. DE JAGER, University of Utrecht. The Netherlands
Z. KOPAL, University ofM anchester, England
G. H. LUDWIG, NOAA, National Environmental Satellitf Service, Suitland, Md., U.S.A.
R. LUST, President Max-Planck·Geselischaft zur Forderung der Wissenschaften. Miinchen. F.R. G.
B. M. McCORMAC, Lockheed Palo Alto Research Laboratory, Palo Alto. Calif. U.S.A.
H. E. NEWELL, Alexandria. Va .• U.S.A.
L. I. SEDOV, Academy of Sciences of the U.S.S.R .. Moscow, U.S.S.R.
Z. SVESTKA, University of Utrecht, The Netherlands
VOLUME 76
PROCEEDINGS
IMAGE FORMATION FROM
COHERENCE FUNCTIONS IN
ASTRONOMY
PROCEEDINGS OF IAU COLLOQUIUM NO. 49 ON THE
FORMATION OF IMAGES FROM SPATIAL COHERENCE
FUNCTIONS IN ASTRONOMY, HELD AT GRONINGEN,
THE NETHERLANDS, 10-12 AUGUST 1978
Edited by
CORNELIS VAN SCHOONEVELD
Leiden Observatory, Leiden, The Netherlands
D. REIDEL PUBLISHING COMPANY
DORDRECHT : HOLLAND / BOSTON: U.S.A.
LONDON:ENGLAND
library of Congress Cataloging in Publication Data
Image Formation from Coherence Functions in Astronomy.
(Astrophysics and space science library; v. 76)
Includes indexes.
1. Radio astronomy-Congresses. 2. Telescope-Congresses.
3. Coherence (optics)-Congresses.
1. Schooneveld, Cornelis van, 1933- II. Title: International
Astronomical Union Colloquium No. 49. III. Series.
QB475.A1I43 522'.682 79-11787
ISBN-13: 978-94-009-9451-5 e-ISBN-13: 978-94-009-9449-2
DOl: 10.1007/978-94-009-9449-2
Published by D. Reidel Publishing Company,
P. O. Box 17, Dordrecht, Holland.
Sold and distributed in the U.'S.A., Canada and Mexico
by D. Reidel Publishing Company, Inc.
Lincoln Building, 160 Old Derby Street, Hingham,
Mass. 02043, U.S.A.
All Rights Reserved
Copyright © 1979 by D. Reidel Publishing Company, Dordrecht, Holland
Softcover reprint of the hardcover I 5t edition 1979
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical
including photocopying, recording or by any informational storage and
retrieval system, without written permission from the copyright owner
TABLE OF CONTENTS
Introduction ix
Organizing Committee xi
PART I - APERTURE SYNTHESIS METHODS
E.B. FOMALONT I Fundamentals and Deficiencies of Aperture
Synthesis (Invited paper) 3
R.H. FRATER I The Two Dimensional Representation of Three
Dimensional Interferometer Measurements 19
J.P. HAMAKER I Measurement Errors in Rotational Synthesis
and their Effects in the Map Plane (Invited Paper) 27
J.P. HAMAKER I "Kneading": The Adjustment of Instrumental
Phase and Gain Parameters to Suppress Error Patterns
in a Synthesis Map 47
A.H. ROTS I A ~roposal to Obtain Short Spacing Information
by Interpolation 55
E. BAJAJA I The Short Spacings Problem in Correlation
Interferometers and a Procedure for Solving It
(Abstract) 59
R.D. EKERS and A.H. ROTS I Short Spacing Synthesis from a
Primary Beam Scanned Interferometer 61
PART II - APERTURE SYNTHESIS WITH LIMITED OR NO PHASE INFORMATION
J.E. BALDWIN and P.J. WARNER I Fundamental Aspects of
Aperture Synthesis with Limited or No Phase
Information (Invited paper) 67
P.N. WILKINSON and A.C.S. READHEAD I Map-making with
Non-phase Stable Interferometers 83
W.D. COTTON and -J.J. WITTELS I Image Reconstruction from
VLBI Amplitude and Phase Closure Data (Abstract) 93
J.C. DAINTY, M.A. FIDDY and A.H. GREENAWAY I On the
Danger of Applying Statistical Reconstruction
Methods in the Case of Missing Phase Information 95
A. OKATAN and J.P. BASART / Reduction of Phase Noise in
Interferometry with State-space Analysis 103
v
vi TABLE OF CONTENTS
PART III - PROCESSING TECHNIQUES AND DISPLAY METHODS
B.G. CLARK / Digital Processing Methods for Aperture
Synthesis Observations (Invited paper) 113
R.H. FRATER / Digital Hardware Processing of
Rotational Synthesis Data (Abstract) 121
T.W. COLE / Analogue Processing Methods for Synthesis
Observations (Invited paper) 123
R.J. ALLEN / Exploring Methods of Effective Data
Display in an Interactive Astronomical Data
processing Environment (Invited paper) 143
M. WRIGHT / Processing and Display of Spectral Line
Absorption Maps (Abstract) 157
D.J. McLEAN / A Proposed Correlator Back-end for the
Culgoora Radio-heliograph 159
K. KAI and T. KOSUGI / An Acousto-optical Image
Processor and Its Application to a 160 MHz
Interferometer 165
PART IV - OPTICAL INTERFEROMETRIC METHODS
C. RODDIER and F. RODDIER / Imaging with a Coherence
Interferometer in Optical Astronomy 175
R.H.T. BATES and M.O. MILNER / Towards Imaging of Star
Clusters by Speckle Interferometry 187
PART V - MAXIMUM ENTROPY IMAGE RECONSTRUCTION
C. van SCHOONEVELD / Resolution Enhancement: the
'Maximum Entropy Method' and the 'High
Resolution Method' (Invited paper) 197
S.F. GULL and G.J. DANIELL / The Maximum Entropy
Method (Invited paper) 219
T.J. CORNWELL / The Use of Bayesian Statistics in
Image Estimation from Interferometer Data 227
J.E.B. PONSONBY / Problems with Maximum Entropy
(Abstract) 235
J.A. HOGBOM / The Introduction of A Priori Knowledge
in Certain Processing Algorithms 237
M.M. KOMESAROFF and I. LERCHE / Extending the Fourier
Transform - The Positivity Constraint 241
P.M.W. KALBERLA / The Information of Images and Its
Dependence on Noise and Spatial Resolution 249
R. BHANDARI/Maximum Entropy Spectral Analysis - Some
Comments (Abstract) 257
PART VI - OTHER IMAGE IMPROVEMENT METHODS
U.J. SCHWARZ / The Method CLEAN - Use, Misuse and
Variations (Invited paper) 261
vii
TABLE OF CONTENTS
M. ISHIGURO and M. ISHIGURO / Fitting a Gaussian
Model to Aperture Synthesis Data by Akaike's
Information Criterion (AIC) 277
C.R. SUBRAHMANYA / An Optimum Deconvolution Method 287
P.L. BAKER / Application of the Simplex Algorithm
to Image Restoration (Abstract) 291
D.T. EMERSON and U. KLEIN / Observations of
Extended Radio Sources Using a Multiple-beam
Technique 293
Y. BlRAUD, B. ESCUDIE, A. HELLION and J. MUNIER /
Formation of Acoustic Images from Spatial Coherence
Functions: Processing by Superresolution Techniques 299
PART VII - RELEVANT INPUTS FROM OTHER FIELDS
R. GORDON / Reconstruction from Projections in Medicine
and Astronomy (Invited paper) 317
Subject index 327
Name index 333
INTRODUCTION
The IAU Colloquium No.49, on the formation of images from spatial
coherence functions in astronomy, was held at Groningen, the Netherlands,
during the period 10-12 August 1978. The colloquium was attended by 108
participants from 14 countries (U.S.A. 29, the Netherlands 20, U.K. 19,
Germany 10, France 7, Australia 5, Canada 5, Japan 4, India 2, New Zea
land 2, Sweden 2, Argentina I, Belgium I, Israel I). It was sponsored
by the Netherlands Foundation for Radio Astronomy, the International
Astronomical Union, the Department of Education and Sciences, the Union
Radio-Scientifique Internationale, the Leiden Kerkhoven-Bosscha Foundat
ion and the State University at Groningen.
This volume contains 36 of the 37 papers presented. Nearly all
papers are followed by a sununary of the discussion that took place after
their presentation. A few papers, published in full elsewhere, are given
only as abstracts.
The majority of the papers are related to aperture synthesis in
radio astronomy; a small number deal with optical astronomy and with
applications in acoustics and medicine. The presentations are divided in
7 groups: aperture synthesis and its deficiencies, the problem of limited
or missing phase information, techniques for processing and data display,
optical interferometric methods, maximum entropy image reconstruction,
other image improvement methods, and a survey of image formation from
projections. Each group contains one or two invited lectures (see Table
of Contents), intended as surveys of particular areas; on the average
they occupy twice as many pages as the other papers.
Looking at the contents as a whole, one is struck by the fact that
relatively little is said about the classic method of image formation
through straightforward fourier inversion of the visibility data. On the
other hand, many proposals are made for non-fourier techniques. They are
prompted by the wish to cope with the phase problem or by the desire to
achieve improved resolution in the image. The key to many of these methods
is a simple one: the exploitation of previously neglected a priori know
ledge of the brightness distribution and of the measurement errors. In
spite of this simplicity we are confronted by a profusion of non-fourier
image formation schemes. Some 20 different methods are listed in the
Subject Index under the heading "Image reconstruction". A comparison of
the relative performance of these methods - and of their combinations -
is at present hampered by the fact that practically none of them has a
closed form solution. 110re work is needed in the future to clarify the
ix
x INTRODUCTION
situation. Progress in this area is not only expected through astronomic
ally oriented investigations but also through contributions from geo
physics, acoustics, statistical spectrum analysis and picture processing,
where similar problems exist.
The editor gratefully acknowledges the cooperation of all authors
in preparing the typescripts and expresses his gratitude to Hrs. }1. H.
van Haaster for her assistance with editing the book.
C. van SCHOONEVELD
ORGANIZING COHUITTEE
SCIENTIFIC LOCAL
W.N. Brouw (Netherlands) E. Raimond (Netherlands)
E. Blum (France) J.P. Hamaker (Netherlands)
H.H. Cohen (U.S.A.) R.H. Harten (Netherlands)
T.W. Cole (Australia) R.S. Ie Poole (Netherlands)
R.D. Ekers (Netherlands) U.J. Schwarz (Netherlands)
E.B. Fomalont (U.S.A.)
EDITOR
11. Ishiguro (Japan)
G.G. Pooley (U.K.) C. van Schooneveld (Netherlands)
