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Author: Kurt Bernardo Wolf Publisher: Springer Science & Business Media ISBN: 9783540220398 Category : Science Languages : en Pages : 400
Book Description
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.
Author: Kurt Bernardo Wolf Publisher: Springer Science & Business Media ISBN: 9783540220398 Category : Science Languages : en Pages : 400
Book Description
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.
Author: Markus Testorf Publisher: McGraw Hill Professional ISBN: 0071597999 Category : Medical Languages : en Pages : 400
Book Description
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
Author: Amalia Torre Publisher: Elsevier ISBN: 9780080535531 Category : Science Languages : en Pages : 540
Book Description
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
Author: Markus E. Testorf Publisher: SPIE-International Society for Optical Engineering ISBN: Category : Optics Languages : en Pages : 730
Book Description
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.
Author: V. Lakshminarayanan Publisher: Springer Science & Business Media ISBN: 1461517117 Category : Science Languages : en Pages : 230
Book Description
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.
Author: Angel Garcia-Botella Publisher: CRC Press ISBN: 1000873196 Category : Science Languages : en Pages : 184
Book Description
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.
Author: H. A. Buchdahl Publisher: Courier Corporation ISBN: 9780486675978 Category : Science Languages : en Pages : 392
Book Description
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.
Author: Antonio Romano Publisher: Birkhäuser ISBN: 3319437321 Category : Mathematics Languages : en Pages : 289
Book Description
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.
Author: Ernst Binz Publisher: American Mathematical Soc. ISBN: 0821844954 Category : Heisenberg uncertainty principle Languages : en Pages : 321
Book Description
"The three-dimensional Heisenberg group, being a quite simple non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered." "This book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics."--BOOK JACKET.
Author: Kurt Bernardo Wolf
Author: Kurt Bernardo Wolf
Author: Markus Testorf
Author: Amalia Torre
Author: Markus E. Testorf
Author: V. Lakshminarayanan
Author: Angel Garcia-Botella
Author: H. A. Buchdahl
Author: A. Walther
Author: Antonio Romano
Author: Ernst Binz