LEADER 04677nam 2200589Ia 450 001 9910830948603321 005 20230829003132.0 010 $a1-280-72360-2 010 $a9786610723607 010 $a3-527-60817-6 010 $a3-527-60829-X 035 $a(CKB)1000000000377389 035 $a(EBL)482317 035 $a(OCoLC)609855581 035 $a(SSID)ssj0000302755 035 $a(PQKBManifestationID)11947569 035 $a(PQKBTitleCode)TC0000302755 035 $a(PQKBWorkID)10274704 035 $a(PQKB)11271799 035 $a(MiAaPQ)EBC482317 035 $a(EXLCZ)991000000000377389 100 $a20040206d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe mathematics of geometrical and physical optics$b[electronic resource] $ethe k-function and its ramifications /$fOrestes N. Stavroudis 210 $aWeinheim $cWiley-VCH$dc2006 215 $a1 online resource (242 p.) 300 $aDescription based upon print version of record. 311 $a3-527-40448-1 320 $aIncludes bibliographical references and index. 327 $aThe 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 327 $a2.6 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 327 $a5.7 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 327 $a7.6 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 327 $a9.7 Conclusions 330 $aIn 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 606 $aGeometrical optics$xMathematics 606 $aPhysical optics$xMathematics 615 0$aGeometrical optics$xMathematics. 615 0$aPhysical optics$xMathematics. 676 $a535.32 700 $aStavroudis$b O. N$g(Orestes Nicholas),$f1923-$027009 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830948603321 996 $aThe mathematics of geometrical and physical optics$93922492 997 $aUNINA