Lagrangian Optics
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Lagrangian Optics
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Author : V. Lakshminarayanan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Lagrangian Optics written by V. Lakshminarayanan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Science categories.
Ingeometrical optics, light propagation is analyzed in terms of light rays which define the path of propagation of light energy in the limitofthe optical wavelength tending to zero. Many features oflight propagation can be analyzed in terms ofrays,ofcourse, subtle effects near foci, caustics or turning points would need an analysis based on the wave natureoflight. Allofgeometric optics can be derived from Fermat's principle which is an extremum principle. The counterpart in classical mechanics is of course Hamilton's principle. There is a very close analogy between mechanics ofparticles and optics oflight rays. Much insight (and useful results) can be obtained by analyzing these analogies. Asnoted by H. Goldstein in his book Classical Mechanics (Addison Wesley, Cambridge, MA, 1956), classical mechanics is only a geometrical optics approximation to a wave theory! In this book we begin with Fermat's principle and obtain the Lagrangian and Hamiltonian pictures of ray propagation through various media. Given the current interest and activity in optical fibers and optical communication, analysis of light propagation in inhomogeneous media is dealt with in great detail. The past decade has witnessed great advances in adaptive optics and compensation for optical aberrations. The formalism described herein can be used to calculate aberrations ofoptical systems. Toward the end of the book, we present application of the formalism to current research problems. Of particular interest is the use of dynamic programming techniques which can be used to handle variational/extremum problems. This method has only recently been applied to opticalproblems.
Geometric Optics On Phase Space
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Author : Kurt Bernardo Wolf
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-07-21
Geometric Optics On Phase Space written by Kurt Bernardo Wolf and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-21 with Science categories.
Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional Fourier transform currently used for image processing. The reader will appreciate the beautiful similarities between Hamilton's mechanics and this approach to optics. The appendices link the geometry thus introduced to wave optics through Lie methods. The book addresses researchers and graduate students.
Principles Of Optics
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Author : Max Born
language : en
Publisher: CUP Archive
Release Date : 2000-02-28
Principles Of Optics written by Max Born and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-28 with Science categories.
Principles of Optics is one of the classic science books of the twentieth century, and probably the most influential book in optics published in the past 40 years. The new edition is the first ever thoroughly revised and expanded edition of this standard text. Among the new material, much of which is not available in any other optics text, is a section on the CAT scan (computerized axial tomography), which has revolutionized medical diagnostics. The book also includes a new chapter on scattering from inhomogeneous media which provides a comprehensive treatment of the theory of scattering of scalar as well as of electromagnetic waves, including the Born series and the Rytov series. The chapter also presents an account of the principles of diffraction tomography - a refinement of the CAT scan - to which Emil Wolf, one of the authors, has made a basic contribution by formulating in 1969 what is generally regarded to be the basic theorem in this field. The chapter also includes an account of scattering from periodic potentials and its connection to the classic subject of determining the structure of crystals from X-ray diffraction experiments, including accounts of von Laue equations, Bragg's law, the Ewald sphere of reflection and the Ewald limiting sphere, both generalized to continuous media. These topics, although originally introduced in connection with the theory of X-ray diffraction by crystals, have since become of considerable relevance to optics, for example in connection with deep holograms. Other new topics covered in this new edition include interference with broad-band light, which introduces the reader to an important phenomenon discovered relatively recently by Emil Wolf, namely the generation of shifts of spectral lines and other modifications of spectra of radiated fields due to the state of coherence of a source. There is also a section on the so-called Rayleigh-Sommerfield diffraction theory which, in recent times, has been finding increasing popularity among optical scientists. There are also several new appendices, including one on energy conservation in scalar wavefields, which is seldom discussed in books on optics. The new edition of this standard reference will continue to be invaluable to advanced undergraduates, graduate students and researchers working in most areas of optics.
Mathematical Optics
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Author : Vasudevan Lakshminarayanan
language : en
Publisher: CRC Press
Release Date : 2018-10-08
Mathematical Optics written by Vasudevan Lakshminarayanan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Science categories.
Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field. Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing. Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical waveguides. Part II explores solutions to paraxial, linear, and nonlinear wave equations. Part III discusses cutting-edge areas in transformation optics (such as invisibility cloaks) and computational plasmonics. Part IV uses Lorentz groups, dihedral group symmetry, Lie algebras, and Liouville space to analyze problems in polarization, ray optics, visual optics, and quantum optics. Part V examines the role of coherence functions in modern laser physics and explains how to apply quantum memory channel models in quantum computers. Part VI introduces super-resolution imaging and differential geometric methods in image processing. As numerical/symbolic computation is an important tool for solving numerous real-life problems in optical science, many chapters include Mathematica® code in their appendices. The software codes and notebooks as well as color versions of the book’s figures are available at www.crcpress.com.
An Introduction To Hamiltonian Optics
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Author : H. A. Buchdahl
language : en
Publisher: Courier Corporation
Release Date : 1993-01-01
An Introduction To Hamiltonian Optics written by H. A. Buchdahl and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Science categories.
Accessible study provides detailed account of the Hamiltonian treatment of aberration theory in geometrical optics. Many classes of optical systems defined in terms of their symmetries. Detailed solutions. 1970 edition.
Introduction To Nonimaging Optics
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Author : Julio Chaves
language : en
Publisher: CRC Press
Release Date : 2017-12-19
Introduction To Nonimaging Optics written by Julio Chaves and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Science categories.
Introduction to Nonimaging Optics covers the theoretical foundations and design methods of nonimaging optics, as well as key concepts from related fields. This fully updated, revised, and expanded Second Edition: Features a new and intuitive introduction with a basic description of the advantages of nonimaging optics Adds new chapters on wavefronts for a prescribed output (irradiance or intensity), infinitesimal étendue optics (generalization of the aplanatic optics), and Köhler optics and color mixing Incorporates new material on the simultaneous multiple surface (SMS) design method in 3-D, integral invariants, and étendue 2-D Contains 21 chapters, 24 fully worked and several other examples, and 1,000+ illustrations, including photos of real devices Addresses applications ranging from solar energy concentration to illumination engineering Introduction to Nonimaging Optics, Second Edition invites newcomers to explore the growing field of nonimaging optics, while providing seasoned veterans with an extensive reference book.
Engineering Optics With Matlab Second Edition
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Author : Ting-chung Poon
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-10-10
Engineering Optics With Matlab Second Edition written by Ting-chung Poon and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-10 with Technology & Engineering categories.
This invaluable second edition provides more in-depth discussions and examples in various chapters. Based largely on the authors' own in-class lectures as well as research in the area, the comprehensive textbook serves two purposes. The first introduces some traditional topics such as matrix formalism of geometrical optics, wave propagation and diffraction, and some fundamental background on Fourier optics. The second presents the essentials of acousto-optics and electro-optics, and provides the students with experience in modeling the theory and applications using a commonly used software tool MATLAB®.
Linear Ray And Wave Optics In Phase Space
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Author : Amalia Torre
language : en
Publisher: Elsevier
Release Date : 2005-11-11
Linear Ray And Wave Optics In Phase Space written by Amalia Torre and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-11 with Science categories.
Ray, wave and quantum concepts are central to diverse and seemingly incompatible models of light. Each model particularizes a specific ''manifestation'' of light, and then corresponds to adequate physical assumptions and formal approximations, whose domains of applicability are well-established. Accordingly each model comprises its own set of geometric and dynamic postulates with the pertinent mathematical means.At a basic level, the book is a complete introduction to the Wigner optics, which bridges between ray and wave optics, offering the optical phase space as the ambience and the Wigner function based technique as the mathematical machinery to accommodate between the two opposite extremes of light representation: the localized ray of geometrical optics and the unlocalized wave function of wave optics.At a parallel level, the analogies with other branches of both classical and quantum physics, like classical and quantum mechanics, quantum optics, signal theory as well as magnetic optics, are evidenced by pertinent comments and/or rigorous mathematics. So, the Lie algebra and group methods are introduced and explained through the elementary optical systems within both the ray and wave optics contexts, the former being related to the symplectic group and the latter to the metaplectic group. In a like manner, the Wigner function is introduced by following the original issue to individualize a phase space representation of quantum mechanics, which is mirrored by the issue to individualize a local frequency spectrum within the signal theory context. The basic analogy with the optics of charged particles inherently underlying the ray-optics picture in phase space is also evidenced within the wave-optics picture in the Wigner phase space.· amalgamation of a great deal of contributions having witnessed the phase space picture of optics over the past 30 years· introduces abstract concepts through concrete systems· hosts of figures and logical diagrams to favour intuition and to introduce mathematics· emphasis on the interrelations with quantum optics, signal theory and magnetic optics · feeds a feeling for genuine issues in higher mathematics and theoretical physics
Contemporary Optics
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Author : A. Ghatak
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Contemporary Optics written by A. Ghatak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
With the advent of lasers, numerous applications of it such as optical information processing, holography, and optical communication have evolved. These applications have made the study of optics essential for scientists and engineers. The present volume, intended for senior under graduate and first-year graduate students, introduces basic concepts neces sary for an understanding of many of these applications. The book has grown out of lectures given at the Master's level to students of applied optics at the Indian Institute of Technology, New Delhi. Chapters 1-3 deal with geometrical optics, where we develop the theory behind the tracing of rays and calculation of aberrations. The formulas for aberrations are derived from first principles. We use the method in volving Luneburg's treatment starting from Hamilton's equations since we believe that this method is easy to understand. Chapters 4--8 discuss the more important aspects of contemporary physical optics, namely, diffraction, coherence, Fourier optics, and holog raphy. The basis for discussion is the scalar wave equation. A number of applications of spatial frequency filtering and holography are also discussed. With the availability of high-power laser beams, a large number of nonlinear optical phenomena have been studied. Of the various nonlinear phenomena, the self-focusing (or defocusing) of light beams due to the nonlinear dependence of the dielectric constant on intensity has received considerable attention. In Chapter 9 we discuss in detail the steady-state self-focusing of light beams.
Quantum Mechanics Of Charged Particle Beam Optics
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Author : Ramaswamy Jagannathan
language : en
Publisher: CRC Press
Release Date : 2019-05-20
Quantum Mechanics Of Charged Particle Beam Optics written by Ramaswamy Jagannathan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-20 with Science categories.
Classical Charged Particle Beam Optics used in the design and operation of all present-day charged particle beam devices, from low energy electron microscopes to high energy particle accelerators, is entirely based on classical mechanics. A question of curiosity is: How is classical charged particle beam optics so successful in practice though the particles of the beam, like electrons, are quantum mechanical? Quantum Mechanics of Charged Particle Beam Optics answers this question with a comprehensive formulation of ‘Quantum Charged Particle Beam Optics’ applicable to any charged particle beam device.