Lagrangian Optics

Lagrangian Optics

Author: V. Lakshminarayanan

Publisher: Springer Science & Business Media

Published: 2013-11-27

Total Pages: 230

ISBN-13: 1461517117

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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.


Principles of Optics

Principles of Optics

Author: Max Born

Publisher: CUP Archive

Published: 2000-02-28

Total Pages: 996

ISBN-13: 9780521784498

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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

Mathematical Optics

Author: Vasudevan Lakshminarayanan

Publisher: CRC Press

Published: 2018-10-08

Total Pages: 630

ISBN-13: 1439869618

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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.


Linear Ray and Wave Optics in Phase Space

Linear Ray and Wave Optics in Phase Space

Author: Amalia Torre

Publisher: Elsevier

Published: 2005-11-11

Total Pages: 541

ISBN-13: 0080535534

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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


Geometric Optics

Geometric Optics

Author: Antonio Romano

Publisher: Birkhäuser

Published: 2016-09-26

Total Pages: 289

ISBN-13: 3319437321

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This book—unique in the literature—provides readers with the mathematical background needed to design many of the optical combinations that are used in astronomical telescopes and cameras. The results presented in the work were obtained by using a different approach to third-order aberration theory as well as the extensive use of the software package Mathematica®. Replete with workout examples and exercises, Geometric Optics is an excellent reference for advanced graduate students, researchers, and practitioners in applied mathematics, engineering, astronomy, and astronomical optics. The work may be used as a supplementary textbook for graduate-level courses in astronomical optics, optical design, optical engineering, programming with Mathematica, or geometric optics.


An Introduction to Hamiltonian Optics

An Introduction to Hamiltonian Optics

Author: H. A. Buchdahl

Publisher: Courier Corporation

Published: 1993-01-01

Total Pages: 392

ISBN-13: 9780486675978

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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

Introduction to Nonimaging Optics

Author: Julio Chaves

Publisher: CRC Press

Published: 2008-05-22

Total Pages: 560

ISBN-13: 1420054325

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The world's insatiable consumption of energy must be met with new technologies that offer alternative, environmentally conscious sources of light and power. The relatively young field of nonimaging optics is an ideal tool for designing optimized solar energy collectors and illumination optics and holds great promise in the development of solid stat


Foundations of Optical System Analysis and Design

Foundations of Optical System Analysis and Design

Author: Lakshminarayan Hazra

Publisher: CRC Press

Published: 2022-02-06

Total Pages: 775

ISBN-13: 1498744958

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Since the incorporation of scientific approach in tackling problems of optical instrumentation, analysis and design of optical systems constitute a core area of optical engineering. A large number of software with varying level of scope and applicability is currently available to facilitate the task. However, possession of an optical design software, per se, is no guarantee for arriving at correct or optimal solutions. The validity and/or optimality of the solutions depend to a large extent on proper formulation of the problem, which calls for correct application of principles and theories of optical engineering. On a different note, development of proper experimental setups for investigations in the burgeoning field of optics and photonics calls for a good understanding of these principles and theories. With this backdrop in view, this book presents a holistic treatment of topics like paraxial analysis, aberration theory, Hamiltonian optics, ray-optical and wave-optical theories of image formation, Fourier optics, structural design, lens design optimization, global optimization etc. Proper stress is given on exposition of the foundations. The proposed book is designed to provide adequate material for ‘self-learning’ the subject. For practitioners in related fields, this book is a handy reference. Foundations of Optical System Analysis and Synthesis provides A holistic approach to lens system analysis and design with stress on foundations Basic knowledge of ray and wave optics for tackling problems of instrumental optics Proper explanation of approximations made at different stages Sufficient illustrations for facilitation of understanding Techniques for reducing the role of heuristics and empiricism in optical/lens design A sourcebook on chronological development of related topics across the globe This book is composed as a reference book for graduate students, researchers, faculty, scientists and technologists in R & D centres and industry, in pursuance of their understanding of related topics and concepts during problem solving in the broad areas of optical, electro-optical and photonic system analysis and design.


Engineering Optics with MATLAB®

Engineering Optics with MATLAB®

Author: Ting-Chung Poon

Publisher: World Scientific Publishing Company

Published: 2006-07-06

Total Pages: 260

ISBN-13: 9814365483

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This invaluable textbook serves two purposes. The first is to introduce some traditional topics such as matrix formalism of geometrical optics, wave propagation and diffraction, and some fundamental background on fourier optics. The second is to present the essentials of acousto-optics and electro-optics, and provide the students with experience in modeling the theory and applications using a commonly used software tool MATLAB®. The book is based on the authors' own in-class lectures as well as researches in the area.


Quantum Mechanics of Charged Particle Beam Optics: Understanding Devices from Electron Microscopes to Particle Accelerators

Quantum Mechanics of Charged Particle Beam Optics: Understanding Devices from Electron Microscopes to Particle Accelerators

Author: Ramaswamy Jagannathan

Publisher: CRC Press

Published: 2019-05-20

Total Pages: 356

ISBN-13: 1351868284

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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.