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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
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ISBN 0-12-014667-3
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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 . . . . . . . . . . . . . . . . . . . . . . . . .