Download or read book Geometric Optics on Phase Space written by Kurt Bernardo Wolf and published by Springer Science & Business Media. This book was released on 2004-07-21 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Phase Space Optics Fundamentals and Applications written by Markus Testorf and published by McGraw Hill Professional. This book was released on 2009-09-07 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive cross section of phase-space optics This definitive volume highlights an elegant, unified approach to optical rays, waves, and system design using cutting-edge phase-space techniques. Phase-Space Optics: Fundamentals and Applications details theoretical concepts of phase space as well as novel engineering applications in specific disciplines. This authoritative guide includes full coverage of sampling, superresolution imaging, and the phase-space interpretation of ultrafast optics. Work with Wigner optics, analyze phase-space equations, develop wave propagation models, and gain a new understanding of optical sources and systems. Discover how to: Describe optical phenomena using Wigner and ambiguity functions Perform phase-space rotations using ray transformation matrices Influence the trade-off between pupil size and depth of field Analyze and design optical signals using the Radon-Wigner transform Accomplish superresolution by squeezing phase space Interpret the intimate relationship between radiometry and coherence Use basic algebra to discover self-imaging, Fresnel diffraction, and the Talbot effect Develop discrete models, sampling criteria, and interpolation formulae Work with ultrafast processes and complex space-time structures
Download or read book Linear Ray and Wave Optics in Phase Space written by Amalia Torre and published by Elsevier. This book was released on 2005-11-11 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Selected Papers on Phase space Optics written by Markus E. Testorf and published by SPIE-International Society for Optical Engineering. This book was released on 2006 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase-space methods can be traced back to early contributions in classical geometrical optics, yet it is only recently that scientists and engineers began to systematically explore the use of phase-space representations for analyzing and synthesizing optical signals. This seminal collection of 70 papers dated from 1932 through 2004 describes the spatial properties of optical signals in terms of phase-space in the classical optical fields, and sketches some of the many interesting applications of phase-space methods.
Download or read book Linear Ray and Wave Optics in Phase Space written by Amalia Torre and published by Elsevier. This book was released on 2029-01-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Ray and Wave Optics in Phase Space, Second Edition, is a comprehensive introduction to Wigner optics. The book connects 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. Analogies with other branches of classical and quantum physics-such as classical and quantum mechanics, quantum optics, signal theory and magnetic optics-are evidenced by pertinent comments and/or rigorous mathematics. Lie algebra and group methods are introduced and explained through the elementary optical systems within the ray and wave optics contexts, the former being related to the symplectic group and the latter to the metaplectic group. In a similar 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. This second edition contains 150 pages of new material on Wigner distribution functions, ambiguity functions for partially coherent beams, and phase-space picture and fast optics. All chapters are fully revised and updated. All topics have been developed to a deeper level than in the previous edition and are now supported with Mathematica and Mathcad codes. Provides powerful tools to solve problems in quantum mechanics, quantum optics and signal theory Includes numerous examples supporting a gradual and comprehensive introduction to Wigner optics Treats both ray and wave optics, resorting to Lie-algebra based methods Connects the subject with other fields, such as quantum optics, quantum mechanics, signal theory and optics of charged particles Introduces abstract concepts through concrete examples Includes logical diagrams to introduce mathematics in an intuitive way Contains 150 pages of new material on Wigner distribution functions, ambiguity functions for partially coherent beams, and phase-space picture and fast optics Supported with Mathematica and Mathcad codes
Download or read book Lagrangian Optics written by V. Lakshminarayanan and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric Optics written by J. Warren Blaker and published by . This book was released on 1971 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Optics in Phase Space written by Wolfgang P. Schleich and published by John Wiley & Sons. This book was released on 2015-12-11 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book. Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect. Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields. Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.
Download or read book Introduction to Geometrical Optics written by Milton Katz and published by World Scientific. This book was released on 2002 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the culmination of twenty-five years of teaching Geometrical Optics. The volume is organised such that the single spherical refracting surface is the basic optical element. Spherical mirrors are treated as special cases of refraction, with the same applicable equations. Thin lens equations follow as combinations of spherical refracting surfaces while the cardinal points of the thick lens make it equivalent to a thin lens. Ultimately, one set of vergence equations are applicable to all these elements.The chapters are devoted to in-depth treatments of stops, pupils and ports; magnifiers, microscopes, telescopes, and camera lenses; ophthalmic instruments; resolving power and MTF; trigonometric ray tracing; and chromatic and monochromatic aberrations. There are over 100 worked examples, 400 homework problems and 400 illustrations.First published in 1994 by Penumbra Publishing Co.
Download or read book Field Theory of Nonimaging Optics written by Angel Garcia-Botella and published by CRC Press. This book was released on 2023-07-10 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to overcome the traditional ray paradigm and provide an analytical paradigm for Nonimaging Optics based on Field Theory. As a second objective, the authors address the connections between this Field Theory of Nonimaging Optics and other radiative transfer theories. The book introduces the Field Theory of Nonimaging Optics as a new analytical paradigm, not statistical, to analyze problems in the frame of nonimaging geometrical optics, with a formulation based on field theory of irradiance vector D. This new paradigm provides new principles and tools in the optical system design methods, complementary to flowline method, overcoming the classical ray paradigm. This new Field paradigm can be considered as a generalization of the ray paradigm and new accurate and faster computation algorithms will be developed. In a parallel way, the advance in the knowledge of the principles of Field Theory of Nonimaging Optics has produced clear advances in the connection between nonimaging optics and other apparently disconnected theories of radiation transfer. The irradiance vector D can be considered as the macroscopic average of Poynting vector, with a clear connection with radiation pressure. Lorentz geometry techniques can also be applied to study irradiance vector D. There are clear thermodynamic connections between the nonimaging concentrator and Stefan-Boltzmann law of radiation. From this thermodynamic connection, nonimaging optics and irradiance vector D can also be studied from a phase space point of view. This book is intended for researchers, graduate students, academics and professionals looking to analyze, design and optimize optical systems.
Download or read book Geometrical Optics in Engineering Physics written by I︠U︡riĭ Aleksandrovich Kravt︠s︡ov and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides concise and clear coverage of modern ray theory without the need of complicated mathematics. Comprehensive coverage is given to wave problems in engineering physics, considering rays and caustics as physical objects.
Download or read book The Ray and Wave Theory of Lenses written by A. Walther and published by Cambridge University Press. This book was released on 2006-11-02 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed description of lens behaviour in real optical systems.
Download or read book Geometric Optics written by Antonio Romano and published by Birkhäuser. This book was released on 2016-09-26 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometrical Optics written by J. L. Synge and published by CUP Archive. This book was released on 1937-01-02 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is by no means easy for the applied mathematician to decide how much importance he should attach to the more abstract and aesthetic side of his work ... To all appearances, Sir William Rowan Hamilton (1850-1865) attached little importance to the practical applications of his method, and it was only with the publication of his Mathematical Papers that it was possible to form a more correct and balanced judgement of Hamilton as an applied mathematician.
Download or read book The Principles and Methods of Geometrical Optics written by James Powell Cocke Southall and published by . This book was released on 1910 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometrical Optics of Inhomogeneous Media written by Yurii Aleksandrovich Kravtsov and published by Springer. This book was released on 1990-09-10 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is concerned with the fundamentals of up-to-date geo metrical optics treated as an approximate method of wave theory. Geometrical optics has changed dramatically over the last two decades. Primarily, it has acquired a number of novel disciplines: space-time geo metrical optics, the quasi-isotropic approximation, the modern theory of caustics related to catastrophe theory, and perturbation techniques for rays, to name only a few. Another acquisition is the reliable boundaries of appli cability for geometrical optics, based upon the concept of the Fresnel volume for a ray. These recent additions to the field are the focus of dis cussion in the book. We did not attempt to separate study-oriented and illustrative material from that intended for professionals, but rather we spread it throughout the text to facilitate for the reader the mastering of this attractive, intuitively appealing and efficient ray method. In preparing the manuscript we used a set of lecture notes devised for All-Union Schools on Diffraction and Wave Propagation, published in Rus sian. Sections 2.1-4,6 and 10 result from joint efforts of both authors. The other material of the book we wrote separately. I contributed Sects. 2.5,9 and 3.17 and Chap.4; Yu.l. Orlov prepared the rest. Unfortunately, he could not take part in the preparation of the English edition, as he died in 1982 at the age of 41, on the verge of what would have been great achieve ments considering his strong and original talent.
Download or read book Encyclopedia of Modern Optics written by Bob D. Guenther and published by Academic Press. This book was released on 2018-02-14 with total page 2253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopedia of Modern Optics, Second Edition, Five Volume Set provides a wide-ranging overview of the field, comprising authoritative reference articles for undergraduate and postgraduate students and those researching outside their area of expertise. Topics covered include classical and quantum optics, lasers, optical fibers and optical fiber systems, optical materials and light-emitting diodes (LEDs). Articles cover all subfields of optical physics and engineering, such as electro-optical design of modulators and detectors. This update contains contributions from international experts who discuss topics such as nano-photonics and plasmonics, optical interconnects, photonic crystals and 2D materials, such as graphene or holy fibers. Other topics of note include solar energy, high efficiency LED’s and their use in illumination, orbital angular momentum, quantum optics and information, metamaterials and transformation optics, high power fiber and UV fiber lasers, random lasers and bio-imaging. Addresses recent developments in the field and integrates concepts from fundamental physics with applications for manufacturing and engineering/design Provides a broad and interdisciplinary coverage of specialist areas Ensures that the material is appropriate for new researchers and those working in a new sub-field, as well as those in industry Thematically arranged and alphabetically indexed, with cross-references added to facilitate ease-of-use
