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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.
Excerpt from Treatise on Optics 1. When a material object is presented before us, we become by vision sensible of its existence and figure. In such a case light is said to be propagated from the object to our eyes, and the science of Optics has for its design the examination of the circumstances of such propagation. The science is divided into Geometrical and Physical Optics. In Geometrical Optics the circumstances of the transmission and modification of light are computed on certain laws established by experiment; in Physical Optics these laws are accounted for on hypotheses of the structure of bodies, and of the matter filling the space in which they are placed. In a similar manner in Geometrical Astronomy the phenomena of heavenly bodies are calculated on observed laws which their apparent motions are found to obey; in Physical Astronomy these apparent laws are shewn to result from the hypothesis of Gravitation. The former branch of the science is the subject of the present treatise, wherein from certain laws established by experiment under simple circumstances, the course of light under more complex circumstances is computed, and the results applied to the construction of Optical Instruments. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
This comprehensive and self-contained text for researchers and professionals presents a detailed account of optical imaging from the viewpoint of both ray and wave optics.
In Measuring Shadows, Raz Chen-Morris demonstrates that a close study of Kepler’s Optics is essential to understanding his astronomical work and his scientific epistemology. He explores Kepler’s radical break from scientific and epistemological traditions and shows how the seventeenth-century astronomer posited new ways to view scientific truth and knowledge. Chen-Morris reveals how Kepler’s ideas about the formation of images on the retina and the geometrics of the camera obscura, as well as his astronomical observations, advanced the argument that physical reality could only be described through artificially produced shadows, reflections, and refractions. Breaking from medieval and Renaissance traditions that insisted upon direct sensory perception, Kepler advocated for instruments as mediators between the eye and physical reality, and for mathematical language to describe motion. It was only through this kind of knowledge, he argued, that observation could produce certainty about the heavens. Not only was this conception of visibility crucial to advancing the early modern understanding of vision and the retina, but it affected how people during that period approached and understood the world around them.
Fundamentals of Photonics A complete, thoroughly updated, full-color third edition Fundamentals of Photonics, Third Edition is a self-contained and up-to-date introductory-level textbook that thoroughly surveys this rapidly expanding area of engineering and applied physics. Featuring a blend of theory and applications, coverage includes detailed accounts of the primary theories of light, including ray optics, wave optics, electromagnetic optics, and photon optics, as well as the interaction of light and matter. Presented at increasing levels of complexity, preliminary sections build toward more advanced topics, such as Fourier optics and holography, photonic-crystal optics, guided-wave and fiber optics, LEDs and lasers, acousto-optic and electro-optic devices, nonlinear optical devices, ultrafast optics, optical interconnects and switches, and optical fiber communications. The third edition features an entirely new chapter on the optics of metals and plasmonic devices. Each chapter contains highlighted equations, exercises, problems, summaries, and selected reading lists. Examples of real systems are included to emphasize the concepts governing applications of current interest. Each of the twenty-four chapters of the second edition has been thoroughly updated.
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.