Advances In Electronics And Electron Physics, Vol. 67

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This volume contains review articles covering a broad range of topics in image processing and analysis. The topics covered include image analysis - which has united and harmonized a host of heterogeneous material; contemporary approaches to the Fourier transform; number theoretic transforms, which are particularly attractive for discrete, finite signals; the use of the Wigner distribution - which encodes both spatial and spectral information, for image filtering; and applications of the concept of information energy. These up-to-date surveys are intended to provide the reader with access to the latest results in the extremely active field of image science.

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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 67 EDITOR-IN-CHIEF PETER W. HAWKES Laboratoire d Optique Electronique du Centre National de la Recherche Scienti$que Toulouse, France ASSOCIATE EDITOR-IMAGE PICK-UP AND DISPLAY BENJAMIN KAZAN Xerox Corporation Palo Alto Research Center Palo Alto, California Advances in Electronics and Electron Physics EDITEDB Y PETER W. HAWKES Laboratoire d'Optique Electronique du Centre National de la Recherche Scientifique Toulouse, France VOLUME 67 1986 ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers Orlando San Diego New York Austin Boston London Sydney Tokyo Toronto COPYRIGHT 0 1986 BY ACADEMIC PRESS. INC ALL RIGHTS RESERVED NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED I N ANY FORM OR BY ANY MEANS. ELECTRONIC OR MECHANICAL. INCLUDING PHOTOCOPY. RECORDING. OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION I N WRITING FROM THE PUBLISHER ACADEMIC PRESS, INC. Orlando, Florida 32887 Uttitrd Kingdom Edirion published by ACADEMIC PRESS INC. (LONDON) 24-28 Oval Road, London NWI 7DX LIBRARY OF CONGRESS CAT4LOG C A R D ISBN 0-12-014667-3 (alk. paper) PHINltD INTHt L I N I T I I ~ ~ T A l t S O F A M ~ H I ~ A 86 87 Rn 89 Y X 7 6 5 4 1 2 1 LTD NUMBER49-7504 CONTENTS PREFACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii The Status of Practical Fourier Phase Retrieval R . H. T. BATESand D . MNYAMA I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Phase Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV . Iterative Phase Refinement . . . . . . . . . . . . . . ................. V . Canterbury Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 14 Lie Algebraic Theory of Charged-Particle Optics and Electron Microscopes ALEXJ . DRAGTand ETIENNE FOREST I . Introduction ........................................... I1 . Lie Algebraic Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Simple Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV . Lagrangians and Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . . . . V . Liecalculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI . Paraxial Map for Solenoidal Lens . . . . . . . . . . . . . . . . . . . . . . . . . VII . Second- and Third-Order Effects for Solenoidal Lens . . . . . . . . . VIII . Spherical Aberration for a Simple Imaging System . . . . . . . . . . . IX . Correction of Spherical Aberration . . . . . . . . . . . . . . . . . . . . . . . . X . Concluding Discussion . . . . . . . . . . . . . . . . . . . . . . . . .