The Adam Hilger Series on Optics and OptoelectronicsSeries Editors:E R Pike FRS,B E A Saleh and the late W T Welford FRsOther books in the seriesLaser Damage in Optical MaterialsR M WoodWaves in Focal RegionsJ J StamnesLaser Analytical Spectrochemistryedited by V S LetokhovLaser Picosecond Spectroscopy and Photochemistry of Biomoleculesedited by V S LetokhovCutting and Polishing Optical and Electronic MaterialsG W Fynn and W J A PowellPrism and Lens MakingF TwymanThe Optical Constaats of Bnlk Materials and FilmsL WardInfrared Optical FibersT Katsuyama and H MatsumuraSolar Cells and Optics for Photovoltaic ConcentrationA LuqueThe Fabry-Perot InterferometerJ M VaughanInterferometry of Fibrons MaterialsN Barakat and AA HamzaPhysics and Chemistry of Crystalline Lithium NiobateA M Prokhorov and Yu S Kuz'minovLaser Heating of MetalsA M Prokhorov,V I Konov,I Ursu and I N MihailescuKDP-family Single CrystalsL N RashkovichThe Adam Hilger Series on Optics and OptoelectronicsAberrations ofOptical SystemsW T Welford FRSThe Blackett Laboratory,Imperial College of Science and Technology,University of LondonAdamHilgerAdam HilgerBristol,Philadelphia and New YorkIOP Publishing Ltd 1986All rights reserved.No part of this publication may be reproduced,storedin a retrievalsystem or transmitted in any form or by any means,electronic,mechanical,photocopying,recording or otherwise,without the prior permission of the publisher.Multiple copying is only permitted under the termsof the agreement between the Committee of Vice-Chancellors and Principalsand the Copyright Licensing Agency.British Library Cataloguing in Publication DataWelford.W.T.Aberrations of optical systems.1.Optics,Geometrical 2.AberrationI.Title535'.32QC381ISBN0-85274-564-8Library of Congress Cataloging-in-Publication DataWelford,W.T.Aberrations of optical systems/W.T.Welford.p.cm.-(The Adam Hilger series on optics andoptoelectronics)Bibliography:p.Includes indexes1.Optical instruments-Design and construction.2.Aberration.3.Optics,Geometrical.I.Title.II.Series.QC372.2.D4W43198989-1675535'.33dc19CIPFirst published 1986Reprinted with minor corrections 1989Amended reprint 1991Published under the Adam Hilger imprint by IOP Publishing LtdTechno House,Redcliffe Way,Bristol BS1 6NX,England335 East 45th Street,New York,NY 10017-3483,USAUS Editorial Office:1411 Walnut Street,Philadelphia,PA 19102Printed in Great Britain by J W Arrowsmith Ltd,Bristol