The Optics of Rays, Wavefronts, and Caustics

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