The mathematics of geometrical and physical optics [[electronic resource] ] : the k-function and its ramifications / / Orestes N. Stavroudis

• Autore: Stavroudis O. N (Orestes Nicholas), <1923->
• Pubblicazione: Weinheim, : Wiley-VCH, c2006
• Descrizione fisica: 1 online resource (242 p.)
• Disciplina: 535.32
• Soggetto topico: Geometrical optics - Mathematics; Physical optics - Mathematics
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: The Mathematics of Geometrical and Physical Optics; Acknowledgements; Introduction; Contents; Part I Preliminaries; 1 Fermat's Principle and the Variational Calculus; 1.1 Rays in Inhomogeneous Media; 1.2 The Calculus of Variations; 1.3 The Parametric Representation; 1.4 The Vector Notation; 1.5 The Inhomogeneous Optical Medium; 1.6 The Maxwell Fish Eye; 1.7 The Homogeneous Medium; 1.8 Anisotropic Media; 2 Space Curves and Ray Paths; 2.1 Space Curves; 2.2 The Vector Trihedron; 2.3 The Frenet-Serret Equations; 2.4 When the Parameter is Arbitrary; 2.5 The Directional Derivative ; 2.6 The Cylindrical Helix2.7 The Conic Section; 2.8 The Ray Equation; 2.9 More on the Fish Eye; 3 The Hilbert Integral and the Hamilton-Jacobi Theory; 3.1 A Digression on the Gradient; 3.2 The Hilbert Integral. Parametric Case; 3.3 Application to Geometrical Optics; 3.4 The Condition for Transversality; 3.5 The Total Differential Equation; 3.6 More on the Helix; 3.7 Snell's Law; 3.8 The Hamilton-Jacobi Partial Differential Equations; 3.9 The Eikonal Equation; 4 The Differential Geometry of Surfaces.; 4.1 Parametric Curves; 4.2 Surface Normals; 4.3 The Theorem of Meusnier ; 5.7 The Eikonal Equation. The Complete Integral5.8 The Eikonal Equation. The General Solution; 5.9 The Eikonal Equation. Proof of the Pudding; Part II The k-function; 6 The Geometry of Wave Fronts; 6.1 Preliminary Calculations; 6.2 The Caustic Surface; 6.3 Special Surfaces I: Plane and Spherical Wavefronts; 6.4 Parameter Transformations; 6.5 Asymptotic Curves and Isotropic Directions; 7 Ray Tracing: Generalized and Otherwise; 7.1 The Transfer Equations; 7.2 The Ancillary Quantities; 7.3 The Refraction Equations; 7.4 Rotational Symmetry; 7.5 The Paraxial Approximation ; 7.6 Generalized Ray Tracing - Transfer7.7 Generalized Ray Tracing - Preliminary Calculations; 7.8 Generalized Ray Tracing - Refraction; 7.9 The Caustic; 7.10 The Prolate Spheroid; 7.11 Rays in the Spheroid; 8 Aberrations in Finite Terms; 8.1 Herzberger's Diapoints; 8.2 Herzberger's Fundamental Optical Invariant; 8.3 The Lens Equation; 8.4 Aberrations in Finite Terms; 8.5 Half-Symmetric, Symmetric and Sharp Images; 9 Refracting the k-Function; 9.1 Refraction; 9.2 The Refracting Surface; 9.3 The Partial Derivatives; 9.4 The Finite Object Point; 9.5 The Quest for C; 9.6 Developing the Solution ; 9.7 Conclusions
• Sommario/riassunto: In this sequel to his book, ""The Optics of Rays, Wavefronts, and Caustics,"" Stavroudis not only covers his own research results, but also includes more recent developments. The book is divided into three parts, starting with basic mathematical concepts that are further applied in the book. Surface geometry is treated with classical mathematics, while the second part covers the k-function, discussing and solving the eikonal equation as well as Maxwell equations in this context. A final part on applications consists of conclusions drawn or developed in the first two parts of the book, discussi
• Titolo autorizzato: The mathematics of geometrical and physical optics
• ISBN: 1-280-72360-2; 9786610723607; 3-527-60817-6; 3-527-60829-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910830948603321
• Lo trovi qui: Univ. Federico II