AN ELEMENTARY TREATISE ON OPTICS
I Basic properties of the electromagnetic field 11 The electromagnetic field 111 Maxwell's equations 1 112 Material equations 2 113 Boundary conditions at a surface of discontinuity 4 114 The energy law of the electromagnetic field 7 12 The wave equation and the velocity of light 11 13 Scalar waves 14 131 Plane waves 15 132 Spherical waves 16 16 133 Harmonic waves The phase velocity 19 134 Wave packets The group velocity 24 14 Vector waves 141 The general electromagnetic plane wave 24 142 The harmonic electromagnetic plane wave 25 (a) Elliptic polarization 25 (b) Linear and circular polarization 29 (c) Characterization of the state of polarization by Stokes parameters 31 143 Harmonic vector waves of arbitrary form 33 15 Reflection and refraction of a plane wave 38 151 The laws of reflection and refraction 38 152 Fresnel formulac 40 153 The reflectivity and transmissivity; polarization on reflection and refraction 43 154 Total reflection 49 16 Wave propagation in a stratified medium Theory of dielectric films 54 161 The basic differential equations 55 162 The characteristic matrix of a stratified medium 58 (a) A homogeneous dielectric film 61 (b) A stratified medium as a pile of thin homogeneous films 62 163 The reflection and transmission coefficients 63 164 A homogeneous dielectric film 64 165 Periodically stratified media 70 II Electromagnetic potentials and polarization 75 21 The electrodynamic potentials in the vacuum 1 76 211 The vector and scalar potentials 212 Retarded potentials 22 Polarization and magnetization 221 The potentials in terms of polarization and magnetization 222 Hertz vecto 223 The field of a linear electric dipole 23 The Lorentz-Lorenz formula and elementary dispersion theory 231 The dielectric and magnetic susceptibilities 232 The effective field 233 The mean polarizability: the Lorentz-Lorenz fommula 234 Elementary theory of dispersion 108 24 Propagation of electromagnetic waves treated by integral equations 104 241 The basic integral equation 242 The Ewald-Oseen extinction theorem and a rigorous derivation of the Lorentz-Lorenz formula 105 243 Refinction and reflection of a plane wave, teated with the help of the Ewald-Oneen extinction theorem 130 III Foundations of geometrical opties 116 31 Approximation the very short wavelengths 116 311 Dervation of the eikonal equation 117 312 The light rays and the intensity law of geometrical optics 120 313 Propagation of the amplitude vectors 125 314 Geneind lzations and the limits of validity of geometrical optics 127 129 32 General properties of mys 129 321 The differential equation of light says 132 322 The laws of refraction and reflection 134 323 Raycongruences and their focal properties 135 33 Other basic theorems of geometrical optics 135 331 lagrange's integral invariant 90 92 95 136 332 The principle of Femmat 139 IV Geometrical theory of optical imaging 333 The theorem of Malus and Dupin and some related theorems 142 41 The characteristic functions of Hamilton 142 411 The point characteristic 142 412 The mised chance distic 144 413 The angle chamcteristic 146 414 Approximate form of the angle characteristic of a re fracting surface of revolution 147 415 Approximate form of the angle chamcteristic of a reflecting surface of revolution 151 159 42 Perfect imaging 152 421 Geneal theorems 157 422 Maxwell "fish-eye 159 423 Stigmatic imaging of surfaces 160 43 Projective tansformation (collineation) with axial symmetry 166 431 Geneal forde 164 432 The telescopic case 165 433 Classification of projective transdemations 166 44 Gaussian optics 434 Combination of projective transfomations 167 441 Refiacting surface of evolution 167 442 Reflecting surface of revolution 443 The thick lens 444 The thin lens 445 The general centred system 45 Stigmatic imaging with wide-angle pencils 451 The sine condition 452 The Herschel condition 46 Astigmatic pencils of raya 170 171 174 175 178 179 180 181 461 Focal properties of a thin pencil 181 462 Refraction of a thin pencil 182 47 Chromatic alteration Dispersion by a priam 186 471 Chromatic aberation 186 472 Dispersion by a priam 190 48 Radiometry and apertures 193 481 Basic concepts of indiometry 194 482 Stops and pupils 199 483 Brightnessand il lamination of images 201 49 Raytracing 204 491 Oblique meridional rays 204 492 Panxial aya 207 493 Skew mys 208 410 Design of aspheric surfaces 211 4101 Artainment of axial stigmatisme 211 4102 Attainment of aplanation 214 411 Image-reconstruction from projections (computerized tomography) 217 4111 Introduction 217 4112 Beam propagation in an absorbing medium 218 4113 Ray integrals and projections 219 4114 The N-dimensional Radontiansfores 221 4115 Reconstruction of cross-sections and the projection-ice theorem of computerized tomography 223 V Geometrical theory of aberra?ons 228 51 Wave and ray aberrations, the aberation function 229 52 The perturbation eikonal of Schwarzschild 233 53 The primary (Seidel) ale mations 236 (4) Spherical alberation (80) 238 (b) Coma (F? 238 (c) Astigmatism (C0) and curvature of field (D+0) 240 (4) Distortion (E+0) 243 54 Addition theorem for the primary aberations 244 55 The primary alberintion coefficients of a general centred lens system 246 551 The Seidel formulae in terms of two paraxial rays 246 552 The Seidel formulae in terms of one paraxial ray 553 Petzval's theorem 251 253 56 Example: The primary allerntions of a thin lens 254 57 The clunatic aberration of a general cented lens system 257 VI Image-forming instruments 261 61 The eye 261 62 The camera 263 63 The refacting telescope 267 64 The reflecting telescope 274 651ments of umimtion 279 66 The microscope 282 VII Elements of the theory of interference and interferometers 71 Introduction 286 72 1terference of two monochromatic waves 286 73 Two-beam interference division of wave-front 287 731 Young's experiment 290 732 Presnel's mimos and similar anangements 290 733 Pringes with quasi-monochromatic and white light 292 734 Use of slit sources, visibility of fit ages 296 295 735 Application to the measurement of optical path difference: the Rayleigh Intermeter 299 736 Application to the measurement of angular dimensions of sources: the Michelson stellar interferometer 302 74 Standing waves 308 75 Two-beam interference: division of amplitude 313 751 Pringes with a plane-parallel plate 313 752 Pringes with thin films, the Fizeau interferometer 318 753 Localization of fringes 325 754 The Michelson interferometer 334 755 The Twyman Green and related interferometer 336 756 Fringes with two identical plates: the Jamin interferometer and Interference microscopes 341 757 The Mach-Zehnder interferometer, the Bates wave-front shearing intes ferometer 348 758 The coherence length the application of two-beam interference to the study of the fine structure of spectral lines 352 76 Multiple-beam interference 359 761 Multiple-beam firinges with a plane-parallel plate 360 762 The Fabry-Perot interferometer 366 763 The application of the Fabry-Perot interferometer to the study of the fine structure of spectisi lines 370 764 The application of the Fabry Perot interferometer to the comparison of wavelengths 377 765 The Lummer-Gebroke interferometer 380 766 Interference filters 386 767 Multiple-heam firinges with this films 39% 768 Multiple-beam fringes with two plane-parallel plates 400 (a) Fringes with monochromatic and quasi-monochromatic light 400 (b) Fringes of superposition 405 77 The comparison of wavelengths with the standard mete 409