Lagrangian Optics

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Lagrangian Optics

V. Lakshminarayanan,Ajoy Ghatak,K. Thyagarajan
Lagrangian Optics Book PDF

Author : V. Lakshminarayanan,Ajoy Ghatak,K. Thyagarajan
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 40,9 Mb
Release : 2013-11-27
Category : Science
ISBN : 9781461517115

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Lagrangian Optics by V. Lakshminarayanan,Ajoy Ghatak,K. Thyagarajan Pdf

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

Kurt Bernardo Wolf
Geometric Optics on Phase Space Book PDF

Author : Kurt Bernardo Wolf
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 48,8 Mb
Release : 2004-07-21
Category : Science
ISBN : 3540220399

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Geometric Optics on Phase Space by Kurt Bernardo Wolf Pdf

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

Max Born,Emil Wolf
Principles of Optics Book PDF

Author : Max Born,Emil Wolf
Publisher : CUP Archive
Page : 996 pages
File Size : 45,9 Mb
Release : 2000-02-28
Category : Science
ISBN : 0521784492

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Principles of Optics by Max Born,Emil Wolf Pdf

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

Vasudevan Lakshminarayanan,María L. Calvo,Tatiana Alieva
Mathematical Optics Book PDF

Author : Vasudevan Lakshminarayanan,María L. Calvo,Tatiana Alieva
Publisher : CRC Press
Page : 630 pages
File Size : 47,5 Mb
Release : 2018-10-08
Category : Science
ISBN : 9781439869611

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Mathematical Optics by Vasudevan Lakshminarayanan,María L. Calvo,Tatiana Alieva Pdf

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.

Geometric Optics

Antonio Romano,Roberto Cavaliere
Geometric Optics Book PDF

Author : Antonio Romano,Roberto Cavaliere
Publisher : Birkhäuser
Page : 289 pages
File Size : 49,5 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9783319437323

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Geometric Optics by Antonio Romano,Roberto Cavaliere Pdf

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.

Basic Optics

Avijit Lahiri
Basic Optics Book PDF

Author : Avijit Lahiri
Publisher : Elsevier
Page : 1010 pages
File Size : 43,8 Mb
Release : 2016-08-29
Category : Science
ISBN : 9780128093078

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Basic Optics by Avijit Lahiri Pdf

Basic Optics: Principles and Concepts addresses in great detail the basic principles of the science of optics, and their related concepts. The book provides a lucid and coherent presentation of an extensive range of concepts from the field of optics, which is of central relevance to several broad areas of science, including physics, chemistry, and biology. With its extensive range of discourse, the book’s content arms scientists and students with knowledge of the essential concepts of classical and modern optics. It can be used as a reference book and also as a supplementary text by students at college and university levels and will, at the same time, be of considerable use to researchers and teachers. The book is composed of nine chapters and includes a great deal of material not covered in many of the more well-known textbooks on the subject. The science of optics has undergone major changes in the last fifty years because of developments in the areas of the optics of metamaterials, Fourier optics, statistical optics, quantum optics, and nonlinear optics, all of which find their place in this book, with a clear presentation of their basic principles. Even the more traditional areas of ray optics and wave optics are elaborated within the framework of electromagnetic theory, at a level more fundamental than what one finds in many of the currently available textbooks. Thus, the eikonal approximation leading to ray optics, the Lagrangian and Hamiltonian formulations of ray optics, the quantum theoretic interpretation of interference, the vector and dyadic diffraction theories, the geometrical theory of diffraction, and similar other topics of basic relevance are presented in clear terms. The presentation is lucid and elegant, capturing the essential magic and charm of physics. All this taken together makes the book a unique text, of major contemporary relevance, in the field of optics. Avijit Lahiri is a well-known researcher, teacher, and author, with publications in several areas of physics, and with a broad range of current interests, including physics and the philosophy of science. Provides extensive and thoroughly exhaustive coverage of classical and modern optics Offers a lucid presentation in understandable language, rendering the abstract and difficult concepts of physics in an easy, accessible way Develops all concepts from elementary levels to advanced stages Includes a sequential description of all needed mathematical tools Relates fundamental concepts to areas of current research interest

An Introduction to Hamiltonian Optics

H. A. Buchdahl
An Introduction to Hamiltonian Optics Book PDF

Author : H. A. Buchdahl
Publisher : Courier Corporation
Page : 392 pages
File Size : 48,9 Mb
Release : 1993-01-01
Category : Science
ISBN : 0486675971

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An Introduction to Hamiltonian Optics by H. A. Buchdahl Pdf

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

Julio Chaves
Introduction to Nonimaging Optics Book PDF

Author : Julio Chaves
Publisher : CRC Press
Page : 560 pages
File Size : 46,9 Mb
Release : 2008-05-22
Category : Science
ISBN : 9781420054323

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Introduction to Nonimaging Optics by Julio Chaves Pdf

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

Linear Ray and Wave Optics in Phase Space

Amalia Torre
Linear Ray and Wave Optics in Phase Space Book PDF

Author : Amalia Torre
Publisher : Elsevier
Page : 541 pages
File Size : 49,5 Mb
Release : 2005-11-11
Category : Science
ISBN : 9780080535531

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Linear Ray and Wave Optics in Phase Space by Amalia Torre Pdf

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

The Quantum Theory of Nonlinear Optics

Peter D. Drummond,Mark Hillery
The Quantum Theory of Nonlinear Optics Book PDF

Author : Peter D. Drummond,Mark Hillery
Publisher : Cambridge University Press
Page : 385 pages
File Size : 48,8 Mb
Release : 2014-03-27
Category : Science
ISBN : 9781107004214

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The Quantum Theory of Nonlinear Optics by Peter D. Drummond,Mark Hillery Pdf

This self-contained treatment of field quantization requires no prior knowledge of nonlinear optics. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, it is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics.

Progress in Optics

Anonim
Progress in Optics Book PDF

Author : Anonim
Publisher : Elsevier
Page : 652 pages
File Size : 55,8 Mb
Release : 2002-05-17
Category : Science
ISBN : 9780080929989

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Progress in Optics by Anonim Pdf

The seven reviews articles presented in this volume cover a broad range of subjects. The first article is concerned with the use of active optics in modern, large telescopes. The second article discusses variational methods used in nonlinear fibre optics and in related fields. The article by O. Keller which follows deals with a topic of historical interest, presenting a account of researches of the Danish physicist L.V. Lorenz who in 1867 established the electrodynamic theory of light, independently of the work of James Clerk Maxwell. The fourth article is concerned with the canonical quantum description of light propagation in dielectric media. The fifth article by D. Dragoman describes the similarities and the differences between classical optics and quantum mechanics in phase space. The article by R. Boyd and D. Gauthier which follows, summarizes research on pulse propagation effects in resonant material system. The concluding article by A. Torre is concerned with the fractional Fourier transform and some of it applications in optics. It is clear that the articles in this volume cover a broad range of subjects, some of which are likely to be of interest to many scientists concerned with optical theory or with optical devices.

Introduction to Design of Optical Systems

Dimitar Popmintchev,Tenio Popmintchev
Introduction to Design of Optical Systems Book PDF

Author : Dimitar Popmintchev,Tenio Popmintchev
Publisher : Unknown
Page : 216 pages
File Size : 53,7 Mb
Release : 2018-04-10
Category : Science
ISBN : 8210379456XXX

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Introduction to Design of Optical Systems by Dimitar Popmintchev,Tenio Popmintchev Pdf

This textbook is devoted to the fundamentals of optical system design and analysis. It is part of series on applied optics covering the math and theory of the Optical phenomena. This book starts wilh short overview of the wave optics and transitions to the theory of geometric optics and its limitations. It is self-contained and only basics of Fourier optics are covered that relate to applications and design of optical and imaging systems. The third chapter covers concepts of simple imaging systems. The last fourth chapter, discusses the theory of third order aberrations. The text is more appropriate for researchers, grad students, undergrad students, with interests in the realm of Optics. The series is written in language that is accessible for large audience, however, calculus is highly recommended as it goes in depth discussing the topics. It does not cover the use of specific raytracing software for optimization. Last update: 8 January 2019 Length: 216 pages 83 figures in color

Geometric Mechanics - Part I: Dynamics And Symmetry (2nd Edition)

Holm Darryl D
Geometric Mechanics Part I Dynamics And Symmetry 2nd Edition Book PDF

Author : Holm Darryl D
Publisher : World Scientific Publishing Company
Page : 468 pages
File Size : 54,5 Mb
Release : 2011-07-13
Category : Mathematics
ISBN : 9781911298656

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Geometric Mechanics - Part I: Dynamics And Symmetry (2nd Edition) by Holm Darryl D Pdf

See also GEOMETRIC MECHANICS — Part II: Rotating, Translating and Rolling (2nd Edition) This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduates and beginning graduate students in mathematics, physics and engineering. It treats the fundamental problems of dynamical systems from the viewpoint of Lie group symmetry in variational principles. The only prerequisites are linear algebra, calculus and some familiarity with Hamilton's principle and canonical Poisson brackets in classical mechanics at the beginning undergraduate level.The ideas and concepts of geometric mechanics are explained in the context of explicit examples. Through these examples, the student develops skills in performing computational manipulations, starting from Fermat's principle, working through the theory of differential forms on manifolds and transferring these ideas to the applications of reduction by symmetry to reveal Lie-Poisson Hamiltonian formulations and momentum maps in physical applications.The many Exercises and Worked Answers in the text enable the student to grasp the essential aspects of the subject. In addition, the modern language and application of differential forms is explained in the context of geometric mechanics, so that the importance of Lie derivatives and their flows is clear. All theorems are stated and proved explicitly.The organisation of the first edition has been preserved in the second edition. However, the substance of the text has been rewritten throughout to improve the flow and to enrich the development of the material. In particular, the role of Noether's theorem about the implications of Lie group symmetries for conservation laws of dynamical systems has been emphasised throughout, with many applications./a

Singularities of Caustics and Wave Fronts

Vladimir Arnold
Singularities of Caustics and Wave Fronts Book PDF

Author : Vladimir Arnold
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 51,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789401133302

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Singularities of Caustics and Wave Fronts by Vladimir Arnold Pdf

One service mathematics has rendered the 'Et moi ...) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. ErieT. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Foundations of Optical System Analysis and Design

Lakshminarayan Hazra
Foundations of Optical System Analysis and Design Book PDF

Author : Lakshminarayan Hazra
Publisher : CRC Press
Page : 774 pages
File Size : 50,5 Mb
Release : 2022-02-07
Category : Science
ISBN : 9781498744959

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Foundations of Optical System Analysis and Design by Lakshminarayan Hazra Pdf

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.