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Optical transforms
Book
Reviews
OPTICAL TRANSFORMS (ed. by H. S. Lipson). 436 pages, diagrams, 6 x 9 in. London and New York, Academic Press, 1972. Price $17.00 (approx. $7.25).
A series of articles on a fairly wide variety of topics all loosely tied together by the fact that each involves the application of optical Fourier transforms (Fraunhofer diffraction). Each of the articles was especially commissioned for this book and is apprently intended to be a survey-review of a specific area. In reviewing a book of this kind, it is first necessary to consider the merits of the individual articles and then to evaluate how well their combination succeeds in fulfilling the overall intent of the book. A number of the articles deal with the problem of analyzing atomic structure from X-ray diffraction patterns by optical analogue techniques, employing Freunhofer diffraction from carefully constructed masks. Well-illustrated chapters on crystal structure, polymer and fiber low-energy electron structure, diffraction and experimental optical Fourier synthesis techniques are all clearly readable and leave one with a good feeling for the problems involved. In addition, the chapter on experimental techniques details methods and materials sufficiently for it to act as a not too involved manual for a student interested in performing his own experiments. The low-energy electron diffraction article was also of particular interest: simply because it is a topic on which very little has been written. The article on biological studies shows interesting results which have been obtained for optical processing of electron microscope pictures of biological specimens. Some of the techniques include direct examination of the optical transform for periodic structure; Fourier plane filtering for image enhancement or feature extraction; and, of particular interest, three-dimensional “reconstruction” from several electron micrographs taken from different angles.
However, the article on optical data rather disappointing. processing was While it gave a very nice review of basic techniques, its discussion of applications was extremely limited. With the introduction of lasers and holography, the field of optical image. processing has produced many exciting results, yet the few examples given were either out of date, well known or plainly uninteresting. Just the opposite is true of the sections on holography and optical transforms in teaching. Both are beautifully written numerous applications and contain examples. In fact, the article on holography is by far the clearest exposition on the subject this reviewer has seen. It is both concise and complete, while still being highly readable. Starting with some of the mathematics of holography, it continues with emulsion requirements, coherence requirements, recording configurations, volume holograms and so on. A detailed account of hologram interferometry is included along with briefer discussions of many other applications. The purpose of the chapter on optical transforms in teaching is to show that the cleerest way to teach Fourier theory is with optical demonstrations. To this end, a detailed plan is given, topic by topic, along with a discussion of display techniquesandmanyillustrative examples. A final chapter gives a brief discussion on a few “miscellaneous applications” though each probably could have been included in one of the earlier chapters. Overall, this is really an excellent book containing many clear, well-written articles, each richly illustrated and each with many detailed examples. Of course, a book that is a collection of separate articles has problems with redundancy, particularly with background information, and lack of cross-referencing between articles which is only partielly compensated by the subject index. Yet, despite these weaknesses, the book is worth its price for the holography article alone; or for the optics in teaching alone; or for the biological studies article and so on. Put
297
Book Reviews them together invaluable.
and
the
book
becomes
PETER NISENSON Itek Corporation Lexington, Massachusetts
CELESTIALMECHANICS, Vol. 2, Parts 1 and 2, PERTURBATION THEORY, by Yusuke Hagihara. 919 pages, diagrams, 6 x 9 in. Cambridge, Mass., The M.I.T. Press, 1971. Price $30.00 (each part) (approx. f12.10). This is the second of a planned fivevolume work in Celestial Mechanics by the author, which is sure to be the most comprehensive account of this subject so far attempted. The first volume (1970), containing six chapters, dealt exclusively with basic analyticsl dynamics and transformation theory and with the known, exact, integrals of motion of various problems, without reliance on expansion into series. The present Volume 2 takes up these expansions in considerable detail. After the opening Chap. 7, on the disturbing function and its expansion, Chap 8 takes up the classical perturbation method of Lagrange, including various methods for the calculation of secular perturbations, as well as a brief account of the general relativistic perturbation, of renewed interest in anticipation of further tests by artificial satellites of the sun. Chapter 9, which concludes part 1, is devoted to canonical perturbation theory, starting with Delauney’s lunar theory, and continuing with a variety of satellite motions. A final section takes up the formalism of canonical perturbation to any order, useful for carrying out the necessary algebra on a computer. Section 10.44 of part 2 of this volume, on the Lie transform with an application to Delaunay’s lunar theory by computer, could well have been included at the end of Chap. 9. Chapter 10, the first of two chapters comprising part 2 of this volume is entitled “absolute perturbations”, and discusses the various methods of direct calculation of the perturbations of the coordinates themselves, rather than of the
298
orbital elements. The chapter ends, however, with a number of separate and unrelated topics, i.e. comet perturbation and possible capture, interplanetary trajectories, comet disintegration, the Lie transform, Bohlin’s theory of the threebody problem and power-series attempts at the same problem. The section entitled “Interplttnetsry trajectories” is in fact mainly a discussion of the recent method of matched asymptotic expansions applied both to an earth-to-moon trajectory and to a satellite orbit near critical inclination. The concluding chapter deals with Hill’s lunar theory and an application to Jupiter’s satellites. Later volumes will be concerned with a mathematical justification for the expansions used in this volume, s,s well as with periodic, quasi-periodic and asymptotic solutions in general. A final note: as in many other works on Celestial Mechanics, rotational motion, as opposed to translational motion, receives very scsnt treatment. Apart from a section in Chap. 6, Volume 1, on Kowalewski’s top motion, there is only passing mention of a relation between the secular acceleration of the moon, tidal friction and an irregularity in the earth’s surface rotation. Topics such as the precession of the equinoxes, Cassini’s laws governing the moon’s rotation and the rotations of the planets Mercury and Venus, have not been included. JOHN V. BREA~WEU Department of Aeronautics and Astronautics Stanford, California
TECHNIQUES OF POLYMER SYNTHESES AND C~ACTERIZATIONS, by Dietrich Braun, Herald Cherdron and Werner Kern. 282 pages, diagrams, 6 x 9 in. New York, Wiley-Interscience, 1972. Price $17.95 (approx. $6.80). In their preface, Braun, Cherdron and “Although in 1961 W. Kern wrote: Sorenson and T. W. Campbell published a book on Preparative Methods of Polymer we have approached the Chemistry, subject in a different manner. We have not intended to present a comprehensive
Journal of The Franklin
Institute
Reviews
OPTICAL TRANSFORMS (ed. by H. S. Lipson). 436 pages, diagrams, 6 x 9 in. London and New York, Academic Press, 1972. Price $17.00 (approx. $7.25).
A series of articles on a fairly wide variety of topics all loosely tied together by the fact that each involves the application of optical Fourier transforms (Fraunhofer diffraction). Each of the articles was especially commissioned for this book and is apprently intended to be a survey-review of a specific area. In reviewing a book of this kind, it is first necessary to consider the merits of the individual articles and then to evaluate how well their combination succeeds in fulfilling the overall intent of the book. A number of the articles deal with the problem of analyzing atomic structure from X-ray diffraction patterns by optical analogue techniques, employing Freunhofer diffraction from carefully constructed masks. Well-illustrated chapters on crystal structure, polymer and fiber low-energy electron structure, diffraction and experimental optical Fourier synthesis techniques are all clearly readable and leave one with a good feeling for the problems involved. In addition, the chapter on experimental techniques details methods and materials sufficiently for it to act as a not too involved manual for a student interested in performing his own experiments. The low-energy electron diffraction article was also of particular interest: simply because it is a topic on which very little has been written. The article on biological studies shows interesting results which have been obtained for optical processing of electron microscope pictures of biological specimens. Some of the techniques include direct examination of the optical transform for periodic structure; Fourier plane filtering for image enhancement or feature extraction; and, of particular interest, three-dimensional “reconstruction” from several electron micrographs taken from different angles.
However, the article on optical data rather disappointing. processing was While it gave a very nice review of basic techniques, its discussion of applications was extremely limited. With the introduction of lasers and holography, the field of optical image. processing has produced many exciting results, yet the few examples given were either out of date, well known or plainly uninteresting. Just the opposite is true of the sections on holography and optical transforms in teaching. Both are beautifully written numerous applications and contain examples. In fact, the article on holography is by far the clearest exposition on the subject this reviewer has seen. It is both concise and complete, while still being highly readable. Starting with some of the mathematics of holography, it continues with emulsion requirements, coherence requirements, recording configurations, volume holograms and so on. A detailed account of hologram interferometry is included along with briefer discussions of many other applications. The purpose of the chapter on optical transforms in teaching is to show that the cleerest way to teach Fourier theory is with optical demonstrations. To this end, a detailed plan is given, topic by topic, along with a discussion of display techniquesandmanyillustrative examples. A final chapter gives a brief discussion on a few “miscellaneous applications” though each probably could have been included in one of the earlier chapters. Overall, this is really an excellent book containing many clear, well-written articles, each richly illustrated and each with many detailed examples. Of course, a book that is a collection of separate articles has problems with redundancy, particularly with background information, and lack of cross-referencing between articles which is only partielly compensated by the subject index. Yet, despite these weaknesses, the book is worth its price for the holography article alone; or for the optics in teaching alone; or for the biological studies article and so on. Put
297
Book Reviews them together invaluable.
and
the
book
becomes
PETER NISENSON Itek Corporation Lexington, Massachusetts
CELESTIALMECHANICS, Vol. 2, Parts 1 and 2, PERTURBATION THEORY, by Yusuke Hagihara. 919 pages, diagrams, 6 x 9 in. Cambridge, Mass., The M.I.T. Press, 1971. Price $30.00 (each part) (approx. f12.10). This is the second of a planned fivevolume work in Celestial Mechanics by the author, which is sure to be the most comprehensive account of this subject so far attempted. The first volume (1970), containing six chapters, dealt exclusively with basic analyticsl dynamics and transformation theory and with the known, exact, integrals of motion of various problems, without reliance on expansion into series. The present Volume 2 takes up these expansions in considerable detail. After the opening Chap. 7, on the disturbing function and its expansion, Chap 8 takes up the classical perturbation method of Lagrange, including various methods for the calculation of secular perturbations, as well as a brief account of the general relativistic perturbation, of renewed interest in anticipation of further tests by artificial satellites of the sun. Chapter 9, which concludes part 1, is devoted to canonical perturbation theory, starting with Delauney’s lunar theory, and continuing with a variety of satellite motions. A final section takes up the formalism of canonical perturbation to any order, useful for carrying out the necessary algebra on a computer. Section 10.44 of part 2 of this volume, on the Lie transform with an application to Delaunay’s lunar theory by computer, could well have been included at the end of Chap. 9. Chapter 10, the first of two chapters comprising part 2 of this volume is entitled “absolute perturbations”, and discusses the various methods of direct calculation of the perturbations of the coordinates themselves, rather than of the
298
orbital elements. The chapter ends, however, with a number of separate and unrelated topics, i.e. comet perturbation and possible capture, interplanetary trajectories, comet disintegration, the Lie transform, Bohlin’s theory of the threebody problem and power-series attempts at the same problem. The section entitled “Interplttnetsry trajectories” is in fact mainly a discussion of the recent method of matched asymptotic expansions applied both to an earth-to-moon trajectory and to a satellite orbit near critical inclination. The concluding chapter deals with Hill’s lunar theory and an application to Jupiter’s satellites. Later volumes will be concerned with a mathematical justification for the expansions used in this volume, s,s well as with periodic, quasi-periodic and asymptotic solutions in general. A final note: as in many other works on Celestial Mechanics, rotational motion, as opposed to translational motion, receives very scsnt treatment. Apart from a section in Chap. 6, Volume 1, on Kowalewski’s top motion, there is only passing mention of a relation between the secular acceleration of the moon, tidal friction and an irregularity in the earth’s surface rotation. Topics such as the precession of the equinoxes, Cassini’s laws governing the moon’s rotation and the rotations of the planets Mercury and Venus, have not been included. JOHN V. BREA~WEU Department of Aeronautics and Astronautics Stanford, California
TECHNIQUES OF POLYMER SYNTHESES AND C~ACTERIZATIONS, by Dietrich Braun, Herald Cherdron and Werner Kern. 282 pages, diagrams, 6 x 9 in. New York, Wiley-Interscience, 1972. Price $17.95 (approx. $6.80). In their preface, Braun, Cherdron and “Although in 1961 W. Kern wrote: Sorenson and T. W. Campbell published a book on Preparative Methods of Polymer we have approached the Chemistry, subject in a different manner. We have not intended to present a comprehensive
Journal of The Franklin
Institute