The optics of rays, wavefronts, and caustics
著者
書誌事項
The optics of rays, wavefronts, and caustics
（Pure and applied physics : a series of monographs and textbooks, v. 38）
Academic Press, 1972
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注記
Includes bibliographies
内容説明・目次
内容説明
The Optics of Rays, Wavefronts, and Caustics presents the fundamental principles of geometrical optics and its unique role in modern technology. It also discusses the procedures used in optical design, which are based on geometrical optics. Organized into 16 chapters, this volume begins with an overview of the underlying general mathematical facts, which constitute the substance of geometrical optics. It then presents the various techniques used to solve the ray and wavefront problems in general inhomogeneous medium. Other chapters consider the concept of ray tracing as a tool for calculating the principal curvatures of a wavefront as it propagates through a lens. In addition, the book tackles several topics, including the aspects of lens design, as well as a system of equations that are similar to the Maxwell equations. The last chapter deals with orthotomic systems of rays. Optical designers, optical physicists, theoretical physicists, and mathematicians will find the information and methods in this book extremely useful.
目次
PrefaceAcknowledgmentsI Introduction The Seventeenth Century Descartes Newton and Fermat Huygens The Nineteenth Century The Brachistochrone ReferencesII The Calculus of Variations The Statement of the Problem The Problem in Three Dimensions The Shortest Distance between Two Points The Problem in Parametric Form The Application to Geometrical Optics ReferencesIII Space Curves The Frenet Equations The Cylindrical Helix The Osculating Sphere Optical Applications The Directional Derivative ReferencesIV Applications Maxwell's Fish Eye The Heated Window The Brachistochrone ReferencesV The Hubert Integral The Hubert Integral Defined A Lemma The Main Theorem An Illustration The Parametric Case Snell's Law Wavefronts and Caustics ReferencesVI Ray Tracing Refraction Reflection Transfer The Sphere Conic Surfaces Transfer for Conic Surfaces The Cylindrical Lens Cartesian Ovals ReferencesVII Orthotomic Systems of Ray The Total Differential Equation Exactness and Integrability Orthotomic Systems Some Properties The Orthogonal Surface Canonical Variables and the Hamilton-Jacobi Equations The Application to Geometrical Optics The Theorem of Malus ReferencesVIII Wavefronts The Nonlinear, First-Order Equation The Bracket The Complete Integral The Eikonal Equation The Singular and General Integrals The General Integral for Homogeneous Media ReferencesIX Surfaces The Theorems of Meusner and Gauss The Weingarten Equations Transformation of the Parameters Generalized Ray Tracing Caustic Surfaces ReferencesX Generalized Ray Tracing Spherical Refracting Surfaces The General Rotationally Symmetric Surface Conic Surfaces The Plane Refracting Surface The in-the-Large Problem ReferencesXI The Inhomogeneous Medium Geodesic Curves Some Vector Identities Geodesies on a Wavefront More on the Fish Eye The Pseudo-Maxwell Equations ReferencesXII Classical Aberration Theory The Point Eikonal The Angle Eikonal The Rotationally Symmetric System The First Order: Gaussian Optics Some Practical Formulas Pupil Planes The Third Order The Seidel Aberrations Herzberger's Diapoint Theory The Convergence Problem ReferencesXIII The Fundamental Optical Invariant The Inhomogeneous Medium The Lens Equation The Rotationally Symmetric System A General Solution The Residual Equations A Change of Variables The Final Factorization ReferencesXIV The Lens Equation The Transfer Matrix The Refraction Matrix The Refraction Calculations The Perfect Lens ReferencesXV The Lens Group The Full Linear Group The Lie Group Subgroups The Optical Application Essential Parameters Generators Further Optical Applications The Paraxial Case ReferencesXVI ConclusionIndex
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