The history of the quantum phase problem, characterized by renewed interest in the solution to the problem, is included and brought up to date.

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

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

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.

Fiber-optic communication systems have revolutionized our telecommunication infrastructures – currently, almost all telephone land-line, cellular, and internet communications must travel via some form of optical fibers. In these transmission systems, neither the phase nor frequency of the optical signal carries information – only the intensity of the signal is used. To transmit more information in a single optical carrier, the phase of the optical carrier must be explored. As a result, there is renewed interest in phase-modulated optical communications, mainly in direct-detection DPSK signals for long-haul optical communication systems. When optical amplifiers are used to maintain certain signal level among the fiber link, the system is limited by amplifier noises and fiber nonlinearities. Phase-Modulated Optical Communication Systems surveys this newly popular area, covering the following topics: - The transmitter and receiver for phase-modulated coherent lightwave systems - Method for performance analysis of phase-modulated optical signals - Direct-detection DPSK signal with fiber nonlinearities, degraded by nonlinear phase noise and intrachannel effects - Wavelength-division-multiplexed direct-detection DPSK signals - Multi-level phase-modulated optical signals, such as the four-phase DQPSK signal. Graduate students, professional engineers, and researchers will all benefit from this updated treatment of an important topic in the optical communications field.

Generalized Phase Contrast elevates the phase contrast technique not only to improve phase imaging but also to cross over and interface with diverse and seemingly disparate fields of contemporary optics and photonics. This book presents a comprehensive introduction to the Generalized Phase Contrast (GPC) method including an overview of the range of current and potential applications of GPC in wavefront sensing and phase imaging, structured laser illumination and image projection, optical trapping and manipulation, and optical encryption and decryption. The GPC method goes further than the restrictive assumptions of conventional Zernike phase contrast analysis and achieves an expanded range of validity beyond weak phase perturbations. The generalized analysis yields design criteria for tuning experimental parameters to achieve optimal performance in terms of accuracy, fidelity and light efficiency. Optimization can address practical issues, such as finding an optimal spatial filter for the chosen application, and can even enable a Reverse Phase Contrast mode where intensity patterns are converted into a phase modulation.

This book has been prompted by our des ire to share with others our apprecia tion of the harmony and beauty in a particular sphere of modern optics known as "optical phase conjugation". Practical applications of the phase conjugated wave are likely to be far-reaching. Optical phase conjugation (OPC) combines in itself aesthetic and pragmatic attractiveness, a synthesis that has made OPC a subject of general attention. The figure presents the ap proximate rate of publications (number of articles per year) on OPC in the world literature for recent years, the lower curve denoting the work carried out in the USSR. The efforts of a large unofficial international collective have yielded an impressive result. 150 100 50 1975 1980 At present, the physical pro ces ses underlying various OPC methods are quite understandable, and it is the physics of OPC to which our book is devoted. Practical and scientific applications of phase-conjugated waves, which are of no less interest, have been touched upon in short, as major achievements in this sphere are a matter of the future. Today there are two main methods of OPC: i) by backward stimulated light scattering, ii) by four-wave mixing. Naturally, much attention is given to these methods in our book which, after the introductory Chap. 1, can be divided into two almost independent parts - Chaps. 2 - 5, and Chaps. 6 - 8.

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.

This guide provides extensive coverage of microscopic imaging principles. After reviewing the main principles of image formation, diffraction, interference, and polarization used in microscopy, this guide describes the most widely applied microscope configurations and applications. It also covers major system components, including light sources, illumination layouts, microscope optics, and image detection electronics. This guide also provides a comprehensive overview of microscopy techniques, including bright field and dark field imaging, contrast enhancement methods (such as phase and amplitude contrast), DIC, polarization, and fluorescence microscopy. In addition, it describes scanning techniques (such as confocal and multiphoton imaging points); new trends in super-resolution methods (such as 4Pi microscopy, STED, STORM, and structured illumination); and array microscopy, CARS, and SPIM.

This tutorial introduces the theory and applications of MTF, used to specify the image quality achieved by an imaging system. It covers basic linear systems theory and the relationship between impulse response, resolution, MTF, OTF, PTF, and CTF. Practical measurement and testing issues are discussed.