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    Optics

    Learning by Computing, with Examples Using Maple, MathCad, Mathematica, and MATLAB

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    Optics
    Learning by Computing, with Examples Using Maple, MathCad, Mathematica, and MATLAB

    Autoren:

    Verlag:
    Springer-Verlag   Weitere Titel dieses Verlages anzeigen

    Auflage: 2nd ed.
    Erschienen: August 2007
    Seiten: 454
    Sprache: Englisch
    Illustration: CD-ROM, 281 schw.-w. Abb., 13 schw.-w. Fotos, 268 schw.-w. Zeich
    Maße: 246x189x32
    Einband: Leinen (Buchleinen)
    ISBN: 0387261680
    EAN: 9780387261683

    Inhaltsverzeichnis

    Contents
    Prefacevii
    1Geometrical Optics1
    1.1Introduction1
    1.2Fermat's Principle and the Law of Refraction2
    1.3Prisms7
    1.3.1Angle of Deviation7
    1.4Convex Spherical Surfaces9
    1.4.1Image Formation and Conjugate Points9
    1.4.2Sign Convention11
    1.4.3Object and Image Distance, Object and Image Focus, Real and Virtual Objects, and Singularities11
    1.4.4Real Objects, Geometrical Constructions, and Magnification15
    1.4.5Virtual Objects, Geometrical Constructions, and Magnification17
    1.5Concave Spherical Surfaces19
    1.6Thin Lens Equation23
    1.6.1Thin Lens Equation23
    1.6.2Object Focus and Image Focus24
    1.6.3Magnification25
    1.6.4Positive Lens, Graph, Calculations of Image Positions, and Graphical Constructions of Images25
    1.6.5Negative Lens, Graph, Calculations of Image Positions, and Graphical Constructions of Images30
    1.6.6Thin Lens and Two Different Media on the Outside33
    1.7Optical Instruments35
    1.7.1Two Lens System36
    1.7.2Magnifier and Object Positions37
    1.7.3Microscope42
    1.7.4Telescope44
    1.8Matrix Formulation for Thick Lenses48
    1.8.1Refraction and Translation Matrices48
    1.8.2Two Spherical Surfaces at Distance d and Prinicipal Planes51
    1.8.3System of Lenses59
    1.9Plane and Spherical Mirrors67
    1.9.1Plane Mirrors and Virtual Images67
    1.9.2Spherical Mirrors and Mirror Equation67
    1.9.3Sign Convention69
    1.9.4Magnification69
    1.9.5Graphical Method and Graphs of xiDepending on x0 70
    1.10Matrices for a Reflecting Cavity and the Eigenvalue Problem73
    2Interference79
    2.1Introduction79
    2.2Harmonic Waves80
    2.3Superposition of Harmonic Waves82
    2.3.1Superposition of Two Waves Depending on Space and Time Coordinates82
    2.3.2Intensities86
    2.3.3Normalization88
    2.4Two-Beam Wavefront Dividing Interferometry89
    2.4.1Model Description for Wavefront Division89
    2.4.2Young's Experiment90
    2.5Two-Beam Amplitude Dividing Interferometry96
    2.5.1Model Description for Amplitude Division96
    2.5.2Plane Parallel Plate97
    2.5.3Michelson Interferometer and Heidinger and Fizeau Fringes103
    2.6Multiple Beam Interferometry110
    2.6.1Plane Parallel Plate110
    2.6.2Fabry-Perot Etalon115
    2.6.3Fabry-Perot Spectrometer and Resolution118
    2.6.4Array of Source Points121
    2.7Random Arrangement of Source Points125
    3Diffraction129
    3.1Introduction129
    3.2Kirchhoff-Fresnel Integral131
    3.2.1The Integral131
    3.2.2On Axis Observation for the Circular Opening133
    3.2.3On Axis Observation for Circular Stop135
    3.3Fresnel Diffraction, Far Field Approximation, and Fraunhofer Observation136
    3.3.1Small Angle Approximation in Cartesian Coordinates137
    3.3.2Fresnel, Far Field, and Fraunhofer Diffraction138
    3.4Far Field and Fraunhofer Diffraction139
    3.4.1Diffraction on a Slit140
    3.4.2Diffraction on a Slit and Fourier Transformation144
    3.4.3Rectangular Aperture145
    3.4.4Circular Aperture148
    3.4.5Gratings152
    3.4.6Resolution162
    3.5Babinet's Theorem166
    3.6Apertures in Random Arrangement169
    3.7Fresnel Diffraction172
    3.7.1Coordinates for Diffraction on a Slit and Fresnels Integrals172
    3.7.2Fresnel Diffraction on a Slit173
    3.7.3Fresnel Diffraction on an Edge175
    A3.1.1Step Grating178
    A3.2.1Cornu's Spiral181
    A3.2.2Babinet's Principle and Cornu's Spiral182
    4Coherence185
    4.1Spatial Coherence185
    4.1.1Introduction185
    4.1.2Two Source Points185
    4.1.3Coherence Condition189
    4.1.4Extended Source190
    4.1.5Visibility194
    4.1.6Michelson Stellar Interferometer197
    4.2Temporal Coherence200
    4.2.1Wavetrains and Quasimonochromatic Light200
    4.2.2Superposition of Wavetrains201
    4.2.3Length of Wavetrains202
    A4.1.1Fourier Tranform Spectometer and Blackbody Radiation203
    5Maxwell's Theory205
    5.1Introduction205
    5.2Harmonic Plane Waves and the Superposition Principle206
    5.2.1Plane Waves206
    5.2.2The Superposition Principle208
    5.3Differentiation Operation208
    5.3.1Differentiation "Time" d/dt208
    5.3.2Differentiation "Space" Δ = id/dx+jd/dy+ kd/dz208
    5.4Poynting Vector in Vacuum209
    5.5Electromagnetic Waves in an Isotropic Nonconducting Medium210
    5.6Fresnel ´ s Formulas211
    5.6.1Electrical Field Vectors in the Plane of Incidence (Parallel Case)211
    5.6.2Electrical Field Vector Perpendicular to the Plane of Incidence (Perpendicular Case)214
    5.6.3Fresnel's Formulas Depending on the Angle of Incidence215
    5.6.4Light Incident on a Denser Medium, n1< n2, and the Brewster Angle216
    5.6.5Light Incident on a Less Dense Medium, n1> n2, Brewster and Critical Angle219
    5.6.6Reflected and Transmitted Intensities222
    5.6.7Total Reflection and Evanescent Wave228
    5.7Polarized Light230
    5.7.1Introduction230
    5.7.2Ordinary and Extraordinary Indices of Refraction231
    5.7.3Phase Difference Between Waves Moving in the Direction of or Perpendicular to the Optical Axis232
    5.7.4Half-Wave Plate, Phase Shift of π233
    5.7.5Quarter Wave Plate, Phase Shift π/2235
    5.7.6Crossed Polarizers238
    5.7.7General Phase Shift240
    A5.1.1Wave Equation Obtained from Maxwell's Equation242
    A5.1.2The Operations Δ and Δ2 243
    A5.2.1Rotation of the Coordinate System as a Principal Axis Transformation and Equivalence to the Solution of the Eigenvalue Problem243
    A5.3.1Phase Difference Between Internally Reflected Components244
    A5.4.1Jones Vectors and Jones Matrices244
    A5.4.2Jones Matrices245
    A5.4.3Applications245
    6Maxwell II. Modes and Mode Propagation249
    6.1Introduction249
    6.2Stratified Media252
    6.2.1Two Interfaces at Distance d253
    6.2.2Plate of Thickness d = (λ/2n2)255
    6.2.3Plate of Thickness d and Index n2 256
    6.2.4Antireflection Coating256
    6.2.5Multiple Layer Filters with Alternating High and Low Refractive Index258
    6.3Guided Waves by Total Internal Reflection Through a Planar Waveguide259
    6.3.1Traveling Waves259
    6.3.2Restrictive Conditions for Mode Propagation261
    6.3.3Phase Condition for Mode Formation262
    6.3.4(TE) Modes or s-Polarization262
    6.3.5(TM) Modes or p-Polarization265
    6.4Fiber Optics Waveguides266
    6.4.1Modes in a Dielectric Waveguide266
    A6.1.1Boundary Value Method Applied to TE Modes of Plane Plate Waveguide270
    7Blackbody Radiation, Atomic Emission, and Lasers273
    7.1Introduction273
    7.2Blackbody Radiaton274
    7.2.1The Rayleigh-Jeans Law274
    7.2.2Planck's Law275
    7.2.3Stefan-Boltzmann Law277
    7.2.4Wien's Law278
    7.2.5Files of Planck's, Stefan-Boltzmann's, and Wien's Laws. Radiance, Area, and Solid Angle279
    7.3Atomic Emission281
    7.3.1Introduction281
    7.3.2Bohr's Model and the One Electron Atom282
    7.3.3Many Electron Atoms282
    7.4Bandwidth285
    7.4.1Introduction285
    7.4.2Classical Model, Lorentzian Line Shape, and Homogeneous Broadening286
    7.4.3Natural Emission Line Width, Quantum Mechanical Model289
    7.4.4Doppler Broadening (Inhomogeneous)289
    7.5Lasers291
    7.5.1Introduction291
    7.5.2Population Inversion292
    7.5.3Stimulated Emission, Spontaneous Emission, and the Amplification Factor293
    7.5.4The Fabry-Perot Cavity, Losses, and Threshold Condition294
    7.5.5Simplified Example of a Three-Level Laser296
    7.6Confocal Cavity, Gaussian Beam, and Modes297
    7.6.1Paraxial Wave Equation and Beam Parameters297
    7.6.2Fundamental Mode in Confocal Cavity299
    7.6.3Diffraction Losses and Fresnel Number302
    7.6.4Higher Modes in the Confocal Cavity303
    8Optical Constants315
    8.1Introduction315
    8.2Optical Constants of Dielectrics316
    8.2.1The Wave Equation, Electrical Polarizability, and Refractive Index316
    8.2.2Oscillator Model and the Wave Equation317
    8.3Determination of Optical Constants320
    8.3.1Fresnel' s Formulas and Reflection Coefficients320
    8.3.2Ratios of the Amplitude Reflection Coefficients321
    8.3.3Oscillator Expressions322
    8.3.4Sellmeier Formula324
    8.4Optical Constants of Metals326
    8.4.1Drude Model326
    8.4.2Low Frequency Region327
    8.4.3High Frequency Region328
    8.4.4Skin Depth331
    8.4.5Reflectance at Normal Incidence and Reflection Coefficients with Absorption333
    8.4.6Elliptically Polarized Light334
    A8.1.1Analytical Expressions and Approximations for the Detemination of n and K335
    9Fourier Transformation and FT-Spectroscopy339
    9.1Fourier Transformation339
    9.1.1Introduction339
    9.1.2The Fourier Integrals339
    9.1.3Examples of Fourier Transformations Using Analytical Functions340
    9.1.4Numerical Fourier Transformation341
    9.1.5Fourier Transformation of a Product of Two Functions and the Convolution Integral350
    9.2Fourier Transform Spectroscopy352
    9.2.1Interferogram and Fourier Transformation. Superposition of Cosine Waves352
    9.2.2Michelson Interferometer and Interferograms353
    9.2.3The Fourier Transform Integral355
    9.2.4Discrete Length and Frequency Coordinates356
    9.2.5Folding of the Fourier Transform Spectrum359
    9.2.6High Resolution Spectroscopy363
    9.2.7Apodization366
    A9.1.1Asymmetric Fourier Transform Spectroscopy370
    10Imaging Using Wave Theory375
    10.1Introduction375
    10.2Spatial Waves and Blackening Curves, Spatial Frequencies, and Fourier Transformation376
    10.3Object, Image, and the Two Fourier Transformations382
    10.3.1Waves from Object and Aperture Plane and Lens382
    10.3.2Summation Processes383
    10.3.3The Pair of Fourier Transformations385
    10.4Image Formation Using Incoherent Light386
    10.4.1Spread Function386
    10.4.2The Convolution Integral387
    10.4.3Impulse Response and the Intensity Pattern387
    10.4.4Examples of Convolution with Spread Function388
    10.4.5Transfer Function392
    10.4.6Resolution395
    10.5Image Formation with Coherent Light398
    10.5.1Spread Function398
    10.5.2Resolution399
    10.5.3Transfer Function401
    10.6Holography403
    10.6.1Introduction403
    10.6.2Recording of the Interferogram403
    10.6.3Recovery of Image with Same Plane Wave Used for Recording404
    10.6.4Recovery Using a Different Plane Wave405
    10.6.5Production of Real and Virtual Image Under an Angle405
    10.6.6Size of Hologram406
    11Aberration415
    11.1Introduction415
    11.2Spherical Aberration of a Single Refracting Surface415
    11.3Longitudinal and Lateral Spherical Aberration of a Thin Lens418
    11.4The π-σ Equation and Spherical Aberration421
    11.5Coma423
    11.6Aplanatic Lens425
    11.7Astigmatism427
    11.7.1Astigmatism of a Single Spherical Surface427
    11.7.2Astigmatism of a Thin Lens428
    11.8Chromatic Aberration and the Achromatic Doublet430
    11.9Chromatic Aberration and the Achromatic Doublet with Separated Lenses432
    Appendix A About Graphs and Matrices in Mathcad435
    Appendix B Formulas439
    References443
    Index445



    Vorwort

    Preface

    The book is for readers who want to use model computational files for fast learning of the basics of optics. In the Second Edition, Matlab, Mathematica and Maples files have been added to the Mathcad files on the CD of the First Edition. The applications, given at the end of files to suggest different points of view on the subject, are extended to home work problems and are also on the CD of the Second Edition.
    While the book is suited well for self learning, it was written over several years for a one semester course in optics for juniors and seniors in science and engineering. The applications provide a simulated laboratory where students can learn by exploration and discovery instead of passive absorption.
    The text covers all the standard topics of a traditional optics course, including: geometrical optics and aberration, interference and diffraction, coherence, Maxwell's equations, wave guides and propagating modes, blackbody radiation, atomic emission and lasers, optical properties of materials, Fourier transforms and FT spectroscopy, image formation, and holography. It contains step by step derivations of all basic formulas in geometrical and wave optics.
    The basic text is supplemented by over 170 Mathcad, Matlab, Mathematica and Maple files, each suggesting programs to solve a particular problem, and each linked to a topic in or application of optics. The computer files are dynamic, allowing the reader to see instantly the effects of changing parameters in the equations. Students are thus encouraged to ask "what... if" questions to asses the physical implications of the formulas. To integrate the files into the text, applications are listed connecting the formulas and the corresponding computer file, and problems for all 11 chapters are on the CD.
    The availability of the numerical Fourier transform makes possible an introduction to the wave theory of imaging, spatial filtering, holography and Fourier transform spectroscopy.
    The book is written for the study of particular projects but can easily be adapted to a variation of related studies. The three fold arrangement of text, applications and files makes the book suitable for "self-learning" by scientists and engineers who would like to refresh their knowledge of optics. All files are printed out and are available on a CD, (Mathcad 7) (Mathcad 2000) (Matlab 6.5) (Mathematica 4.1) (Maple 9.5) and may well serve as starting points to find solutions to more complex problems as experienced by engineers in their applications.
    The book can be used in optical laboratories with faculty-student interaction. The files may be changed and extended to study the assigned projects, and the student may be required to hand in printouts of all assigned applications and summarize what he has been learned.
    I would like to thank Oren Sternberg and Assaf Sternberg for the translation of the files into Matlab, Mathematica and Maples, Prof. Ken Chin and Prof. Haim Grebel of New Jersey Institute of Technology for continuous support, and my wife for always keeping me in good spirit.

    Newark, New Jersey
    K.D. Möller

    Klappentext

    Karl Dieter Möller

    Second Edition

    Optics

    This new edition is intended for a one semester course in optics for juniors and seniors in science and engineering; it uses scripts from Math-Cad®, MATLAB®, Mathematica®, and Maple® and provides a simulated laboratory where students can learn by exploration and discovery instead of passive absorption.


    The text covers all the standard topics of a traditional optics course, including: geometrical optics and aberration, interference and diffraction, coherence, Maxwell's equations, wave guides and propagating modes, blackbody radiation, atomic emission and lasers, optical properties of materials, Fourier transforms and FT spectroscopy, image formation, and holography. It contains step by step derivations of all basic formulas in geometrical, wave and Fourier optics.


    The basic text is supplemented by over 170 files in Math-Cad®, MATLAB®, Mathematica®, and Maple® (many of which are in the text; all scripts are included on the CD), each suggesting programs to solve a particular problem, and each linked to a topic in or application of optics. The computer files are dynamic, allowing the reader to see instantly the effects of changing parameters in the equations. Students are thus encouraged to ask "What if?" questions to asses the physical implications of the formulas. The discussion of Fourier transforms in particular is enhanced by the availability of numerical methods.
    The book is written for the study of particular projects but can easily be adapted to other situations. The threefold arrangement of text, applications, and files makes the book suitable for "self-learning" by scientists or engineers who would like to refresh their knowledge of optics.ln the classroom, the Math-Cad®, MATLAB®, Mathematka®, and Maple® scripts can serve as starting points for homework; outside, they can help find solutions to complex problems in engineering applications.


    Some praise for the previous edition:


    OPTICS AND PHOTONICS NEWS [OCTOBER 2004]
    "This book and its companion CD cover geometrical optics, electromagnetic theory, interference, diffraction and coherence theory. Chapters on optical constants, blackbody radiation, emission and absorption, lasers, holography and Fourier transform spectroscopy broaden its scope. The packet contains over 170 Math-CAD® files linked to specific topics and applications.... The main virtues of the book are the excellent photographs of basic optical phenomena. ... The index is comprehensive. ... [The book] will certainly be helpful to ... students in an introductory optics course."


    THE PHYSICIST (March/April 2004)
    "The author has developed a suite of model programs covering the whole spectrum of optics from classical geometric ray to wave and modern optics. Illustrative resonator and waveguide modes are also part of the program mix as well as introductory laser theory. In addition to an optics course, this book would be useful in a 3rd or 4th year electromagnetism course as well as an introduction to lasers and resonators. There are certainly more topics in this text than could possibly be covered in the typical 30 hour one semester course.... All formulas and diagrams are provided in Adobe .pdf files as well for transcription into other software suites or inclusion in notes.This book is a comprehensive optics text that has been written in a mode to encourage students to run the models, do the calculations and generate their own illustrations....The book would serve as an excellent text for undergraduate use and reference for laboratory simulation experiments."

    springer.com

    ISBN 978-0-387-26168-3


     

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    Index


    A

    Aberration, 415
    achromatic doublet, 432
    aplanatic lens, 425
    astigmatism of single surface, 428
    astigmatism of a thin lens, 429
    - chromatic aberration, 430
    - coma, 423
    - π-6 equation, 420
    - spherical of single surface, 415
    - spherical of thin lens, 418
    absorption, 319
    achromatic doublet, 430
    achromatic doublet with separated lenses, 432
    active medium, 295
    Airy disc, 149
    Airy function, 116
    alternating high and low refractive indices, 258
    amplitude division, 96
    amplitude grating, 152, 158, 170
    amplitude reflection coefficients, 321
    angle of deviation, 7 angular magnification, 40
    angular momentum quantum number, 282, 283
    angular quantum number, 283
    antireflection coating, 252, 256
    aperture function α(η), 385
    aperture plane, 382
    aperture in random arrangement, 169
    aplanatic lens, 425, 427
    apodization, 366, 367
    Arago, 135
    array of source points, 121
    - nonperiodic, 126
    - periodic, 121
    astigmatic difference ASD, 427, 428, 429
    astigmatism of a single spherical surface, 427
    astigmatism of a single surface, 429
    astigmatism of a thin lens, 428, 429
    asymmetric Fourier transform, 370
    atomic emission, 273
    atomic energy states, 284
    - exited states, 286
    - occupation rule, 283
    atomic polarizability, 317, 318


    B

    Babinet's theorem, 166, 168
    background spectrum, 372
    bandpass filter, 364
    bandwidth, 285, 288
    - doppler, 291
    - homogeneous, 288
    - Lorentzian, 293
    - mechanical, 291
    - natural, 291
    - quantum, 291
    beamsplitter, 104
    Bessel function, 149, 165, 166, 389, 390
    Bessel function J1(q), 151
    Bessel function as transfer function, 394
    birefringent, 231
    Blackbody radiation, 203, 273, 274
    Boltzmann's, Wien's law, 281
    - depending on frequency, 279
    - depending on wavelength, 279
    - Radiance, Area, solid angle, 281
    blackening curves, 376, 377
    blocking function, 402
    Bohr's model, 282
    buildup principle, 283
    - K-shell, 284
    - L-shell, 284
    - M-shell, 284
    boundary conditions, 254
    Brewster angle, 216, 321, 322


    C

    C-ray, 15, 36
    calcite, 232, 236
    cavity
    concentric, 77
    condition for stability, 76
    confocal, 77, 297, 299, 300, 303, 307
    - matrix for eigenvalue problem, 73
    - rectangular shaped mirrors, 303
    - stability relation, 74
    - with round mirrors, 307
    changing numbers, 435
    charge density, 206, 316
    chromatic aberrations, 430, 431, 432
    - negative, 430
    circular aperture, 148
    circular mirrors, 308, 309
    circular polarized light, 237, 240
    Clausius-Mossotti equation, 320
    coherence, 185
    condition, 189
    - extended source, 191
    - intensity fringe pattern, 187
    - interval, 195
    - length, 204
    - two source points, 185
    - visibility, 194
    - Young's experiment, 186
    coherent light, 398
    coma
    - negative coma, 424
    - positive coma, 424
    commercial microscopes, 44
    complementary screens, 166, 168
    complex efft, 380
    complex dielectric constant, 315
    complex Fourier transformation, 345, 346, 349, 370
    complex notation, 87
    complex refractive index, 315, 321, 326, 327
    concave mirror, 71
    concave spherical mirror, 70
    condition for laser action, 293
    confocal cavity, 297
    - beam parameters, 297
    - beam waist, 299-301
    - wavelength at center, 299
    - wavefront at mirror, 300
    - wavefront of beam and mirror, 299
    confocal resonator, 304, 309
    conjugate points, 9

    constructive interference, 91, 93, 94, 98, 99, 104, 113, 116
    convex single refracting surface, 12, 14
    convex spherical mirror, 72
    convex spherical surfaces, 9, 14, 19
    convex-plane lens, 67
    convolution
    - integral 350, 387
    - product of two functions, 350
    - spread function, 397
    convolution with the spread function, 397
    coordinates for the derivation of Fresnel's formulas, 212
    Cornu's spiral, 182
    critical angle
    - phase shift, 219
    - reflected and transmitted intensity, 223
    - total reflection, 227
    crossed polarizers, 238, 239, 245, 246
    current density, 326, 327
    current density vector, 206, 316
    curvature of the wavefront, 299
    cylindrical coordinates, 311
    cylindrical lens, 388


    D

    Damping term, 318
    denominator, 123
    dense medium, 216, 219, 319
    density of the oscillators, 319
    dependence on θ, 109
    destructive interference, 91, 93, 94, 98-100, 105
    dielectric circular waveguide, 268
    dielectric constant, 318
    dielectrics, 316
    differentiation, 442
    differentiation "space", 208
    differentiation "time" d/dt, 208
    differentiation operation, 208
    diffraction
    - amplitude grating, 155
    - circular aperture, 148
    - circular opening, 133
    - circular stop, 135
    - echelette grating, 159
    - on an edge, 176
    - factor, 153
    - far field, 138
    - Fraunhofer, 138
    - generated wavelets, 131
    - grating, 152
    - incident light under an angle, 158
    - Kirchhoff-Fresnel Integral, 131
    - losses, 302
    - on slit, 140-142, 144, 172, 174

    - 3-D graph of rectangular aperture, 147

    - 3-D graph of round aperture, 151
    discrete Fourier transform, 366
    discrete length coordinates, 356
    dispersion of light, 7
    Doppler broading, 393
    - line shape, 290
    - line width, 296
    double slit, 157
    double-sided step function, 344, 346, 347
    drift velocity, 326
    Drude model, 326


    E

    Echelette grating, 159, 161
    eigenvalue problem, 73
    Einstein coefficient, 289
    - coefficient of stimulated absorption, 292
    - probability coefficient, 276
    electrical field vector, 206, 316
    electrical polarizability, 316
    electromagnetic theory, 205
    ellipsometry, 335
    elliptically polarized light, 237, 240, 241, 334
    emission of light from86 Kr, 202
    energy density per frequency, 274
    energy levels, 284
    energy state, 284
    - transitions between states, 286
    evanescent wave 228, 229
    - attenuation factor, 229
    - penetration depth, 229, 331
    - and index of refraction, 232
    excited state, 286
    extended source, 191, 196
    extinction index, 318
    extraordinary indices of refraction, 231
    eye, 2


    F

    Fabry-Perot, 77, 115-117, 249
    - cavity, 294
    - etalon, 115
    - plates, 249
    - spectrometer and resolution, 118
    - transmission depending on D, 117

    far field approximation, 136
    Fast Fourier transformation, 341, 342
    Fermat's principle, 2, 5
    - law of refraction, 5
    - optimum path, 3
    - optimum time, 6
    - velocity for travel, 4
    Fiber optics waveguide, 266
    - Bessel function solution, 267
    - determination of k, 268
    - periodic exponential solution, 266
    Fizeau fringes, 106

    focal length, 34

    folding of the Fourier transform spectrum, 359

    folding of the spectrum, 360

    formula for summation, 122

    formula for the summation process, 112

    formulas, 439
    Fourier integrals, 339
    Fourier series, 378
    Fourier transform integral, 372
    Fourier transform spectrometer, 203
    Fourier transform spectroscopy, 339, 354, 355
    - apodization, 368
    folded spectrums, 364
    - high resolution, 365
    - large optical path difference, 363
    Fourier transform spectroscopy (cont.) Michelson interferometer, 355
    Fourier transformation, 144, 339, 350, 376, 392
    - asymmetric, 370
    - discrete length and frequency coordinates, 358
    fast, 343
    functions 1/(1 + x2) and π-2πv , 341
    - gauss function, 340
    - general, 351
    - numerical, 341
    - real, 352, 349, 366
    - sample interval, 358, 365
    - two transformations, 382
    Fourier transformation using analytical functions, 340
    Fraunhofer diffraction, 138, 139
    Fraunhofer observation, 136

    frequency coordinates, 356

    frequency domain, 401

    frequency spectrum, 367
    Fresnel, 95, 138
    Fresnel diffraction 136, 172
    - on an edge, 175
    - integrals, 174
    - on a slit, 173
    Fresnel number, 302
    Fresnel's double mirror experiment, 93
    Fresnel's formulas, 80, 211, 320
    - as function of angle, 215, 217
    - parallel case 211, 321
    - perpendicular case, 214
    - transmission coefficient, 218
    Fresnel's mirror, 95

    fringe pattern, 89

    fundamental mode, 299, 308

    fused quartz, 325


    G

    Gain of the beam, 294
    Galilean telescope, 46, 48
    Gauss function, 340, 350, 351
    Gaussian beam, 297
    Gaussian line shape, 290
    generated wavelet, 131
    Geometrical construction, 18
    geometrical construction, 15, 17, 18, 29, 31, 70, 72
    geometrical optics, 1
    graphical constructions, 25, 30, 36
    graphical method, 70
    graphs and matrices in Mathcad, 435
    grating, 152
    - number of lines N, 155
    - openings d, 155
    - periodicity constant, 159
    - resolution, 154
    - side maxima, 154
    - side minima, 152, 156
    Green's function, 132
    guided waves, 259


    H

    Half-wave plate, 233, 238, 245
    - phase shift 0, 233
    harmonic waves
    - phase factor, 80
    - superposition, 82, 206
    - two depending on space and time coordinates, 82
    Heidinger interference fringes, 103, 106, 107, 108
    high frequency region, 328
    high resolution spectroscopy, 363
    Holography, 403
    - different waves, 405
    hologram, 404
    - product of real image, 405
    - real image, 404
    - recovery, 404, 405
    - size of hologram, 406
    - transmission curve, 404
    - under an angle, 405
    - virtual image, 404, 405
    homogeneous equation, 327
    Huygens' principle, 129, 131
    Huygens' wavelets, 129, 375


    I

    Image of
    - one bar, 388
    - one round object, 389
    - two round objects, 390, 397
    - two bars, 388
    Image formation using wave theory, 375
    - amplitude function, 385
    - aperture function, 385
    - circular lens, 389-391
    - convolution, 387
    image formation, 386, 398
    image forming process, 382
    impulse response, 387
    - one bar, two bars as object, 389
    - one round, two round as object, 389, 390
    - pair of Fourier transformations, 385
    - resolution, 399
    - spread function, 386
    - summation process, 383, 384
    - transfer function, 401
    imaginary part, 318
    imaging with coherent light, 400
    impulse response, 387
    incident intensity, 113
    incident light under an angle Ψ , 158
    incoherent light, 386
    induced absorption, 275
    induced dipoles, 316
    induced emission, 275
    inhomogeneous equation, 327
    intensity, 87, 126
    - complex notation, 87
    - normalization, 88
    - time average, 87
    intensity fringe patterns, 187
    intensity pattern, 387
    interference, 78

    - (minima) air gaps, 100, 101
    - factor, 153
    - fringes, 113
    - maxima, minima, 83
    - pattern generated by two sources, 83
    - pattern of N sources, 124
    interferogram function S(y), 356
    interferograms, 353
    interferometry, 89
    - amplitude dividing, 96
    - Fresnel double mirror, 93
    - Lloyd, 92
    - Michelson, 103
    - model, 89
    - Newton's Rings, 101
    - plane parallel plate, 99
    - wavefront dividing, 89
    - wedge shaped, 99
    - Young, 90
    internally reflected components, 244
    inverse transformation, 342, 344, 346, 347
    inverted image, 2
    isotropic medium, 81
    isotropic nonconducting medium, 210


    J

    Jones matrices, 244, 245
    Jones vectors, 244


    K

    Kepler telescope, 45, 46, 48
    Kirchhoff-Fresnel integral, 131, 132, 139, 376
    Kramer-Kroning model, 325


    L

    Labels for energy levels, 283
    laser beam expander, 48
    lasers, 273
    - active medium, 295
    - amplification factor, 293, 294
    - gain of the beam, 294
    - spontaneous transition, 292
    - stimulated emission, 291, 292, 293
    - stimulated transition, 293
    - two-level systems, 292
    lateral magnification, 17
    lateral spherical aberration, 418, 420
    law of reflection, 2 law of refraction, 1, 2, 5, 222, 320
    left polarized light, 237
    length of wavetrains, 202
    length units, 12
    Lens
    - negative f, 31
    - plane-convex, 67
    lenses, 1
    less dense medium, 229, 317
    life-time, 286
    lifetime r, 286, 288
    linear polarized light, 240
    Lloyd's mirror, 92, 95, 96
    longitudinal modes, 295
    longitudinal spherical aberration, 415, 417, 419
    Lorentz correction, 320
    Lorentzian line shape, 286, 288, 290
    Lorentzian line width, 295
    lossless dielectrics, 336
    low frequency region, 327


    M

    Magnetic field vector, 206, 316
    magnetic quantum number and degeneracy, 282
    magnification, 17, 18, 25, 36, 37, 43, 44, 46, 69
    magnifier, 37, 47
    - angular magnification, 40
    magnifying power, 40
    - virtual image at infinity, 39, 41
    - virtual image nearpoint, 39
    magnifying power, 40, 43
    many electron atoms, 282
    Mathcad plotting a graph, 435
    matrices, 436
    matrix elements, 53
    matrix method, 49
    - application to two-and three-lens systems, 47
    - glass sphere, 58
    - hemispherical lens, 58
    - principal planes, 51
    - refraction matrix, 49
    - thick lens, 55
    - translation matrix, 49
    - two lenses in air, 59
    - two thick lenses, 62
    maxima, but only N - 2, 125
    Maxwell's equations, 205, 315, 326
    meridional (vertical) plane, 428
    Michelson interferometer, 106
    - dependence on θ, 109
    - nonnormal incidence, 106
    - nonnormal incident light, 106
    - normal incident light, 103
    - superposition of two cosine waves, 352
    Michelson's stellar interferometer, 197, 198, 199
    - two patterns, 197
    microscope, 42, 47, 48
    magnification 43
    magnifying power, 43
    - near point configuration 41-43
    - slides, 100
    - virtual image at infinity, 43
    minimum deviation, 8

    mirror equation, 68
    mirrors, 1
    mirrors for laser cavities, 252
    mode
    - in a dielectric waveguide, 266
    - formation, 262
    - number of nodes, 250
    - propagation, 249, 261
    - rectangular box, 251
    - restrictive conditions, 261
    - (TE) modes or s -polarization, 215, 262, 265
    - (TM) modes or p-polarization, 214, 262
    modes in a dielectric waveguide, 266
    modes of the rectangular box, 251
    monochromatic light, 200
    M Wilson observatory, 198
    multiple layer filters, 258
    multiple lens system, 49
    mutual orthogonal triad, 209


    N

    Natural emission line width, 289
    negative chromatic aberration, 430
    negative coma, 424
    negative crystal, 232, 236
    negative lens, 33
    Newton, 7
    Newton's rings, 101, 102
    Newton's work, 79
    node lines, 250
    noncommutation of matrices, 65
    nonconductive medium, 210
    normal and anomalous dispersion, 319
    number of nodes, 250


    O

    Object amplitude function h(y), 385
    object focus, 12, 16, 24, 32
    object point, 10
    object positions, 37
    occupation rule, 283
    one electron atom, 282
    one oscillator, 322
    one round object, 389
    optical axis, 232
    optical axis is the fast axis, 232
    optical constants, 315, 316, 326, 338, 372
    optical constants of metals, 328
    - high frequency region, 330
    - low frequency region, 329
    - skin depth, 332
    optical constants n and K, 370
    optical instruments, 1, 35
    optical materials, 231
    optical path difference
    - Fresnel's double mirror, 94
    - Lloyd's mirror, 93
    - Newton's rings, 103
    - Michelson interferometer, 104
    - plane parallel plate, 98
    - wedge, 99
    - Young's experiment, 91
    optically denser medium, 80
    order of interference, 83
    ordinary index n0 , 232
    oscillator expressions, 322
    oscillator model, 317, 318
    - damping term, 317


    P

    Pair of Fourier transform integrals, 356
    pair of Fourier transformation, 385
    paraxial approximation, 15
    paraxial theory, 1, 10
    paraxial wave equation, 297
    Pauli principle, 283
    periodic arrangement, 74
    periodic array, 126, 171
    periodic set of slits, 152
    permittivity, 206, 316, 317
    perpendicular case, 214
    PF-ray, 15, 36
    phase difference Δ, 111
    phase factor, 80
    phase jump, 80
    phase velocity, 210
    phase velocity in vacuum, 81
    planar waveguide, 259, 263
    Planck, 273
    Planck's radiation law, 275, 280, 292
    plane mirror, 67
    - virtual image, 67
    plane parallel plate, 97, 110, 113, 114
    - normal incidence, 114
    phase difference, δ, 111
    - summation of the reflected amplitude, 111
    - transmission, 113
    - transmitted amplitudes, 111
    - transmitted intensity, 114, 116
    plane plate waveguide, 270
    - characteristic determinant, 271
    - traveling waves, 259
    plane wave, 206
    - depending on space and time coordinates, 82
    plasma frequency, 318, 328
    Poisson spot, 135
    polarization, 316
    polarized light, 230
    - linear circular elliptical, 240
    population inversion, 291, 292
    positive chromatic aberration, 430
    positive coma, 424
    positive crystal, 232, 234, 236
    positive lens, 25, 28, 30
    Poynting vector S, 222
    Poynting vector in vacuum, 209
    principal angle, 321
    principal axis transformation, 243
    principal planes, 56, 60, 62, 63, 67
    principal quantum number, 282, 283
    prism, 7
    - angle of deviation, 7


    Q

    Quality factor, 288
    quantum emission, 273
    quantum mechanical model, 289
    quarter-wave plate, 239, 246
    quartz, 232, 234, 236
    quasimonochromatic light, 200


    R

    Radius of curvature, 69, 71, 300, 417
    radius of curvature p, 417
    Raleigh-Jean law, 275
    random arrangement, 169
    random arrangement of source points
    - array, 125
    - grating, 169
    random array, 170, 172
    random phase angles, 126
    randomly distributed, 126
    rate equations, 292
    ratio rs /rp , 322, 335
    Rayleigh criterion, 164, 395
    Rayleigh distance, 165, 395
    Rayleigh-Jeans law, 274, 276, 280
    Real Fourier transformation, 349
    real image, 29, 404
    real object, 16, 29, 32
    real object function, 380
    real object point, 11
    real objects, 15, 20
    recording of the interferogram, 403
    recovery of image, 404
    rectangular aperture, 145, 147
    rectangular-shaped mirrors, 303
    references, 443
    reflectance R, 226
    reflected intensity, 114, 116
    reflecting cavity, 73
    reflection, 113
    - amplitude, 111
    - intensity, 114, 116, 224, 227
    - power, 51
    reflected and transmitted, 274
    reflection coefficients, 217, 220, 320
    reflection coefficients with absorption, 333
    reflection in a mirror cavity, 74
    reflection measurements, 322
    refracting powers, 51
    refraction, 49
    refraction matrix, 50
    refractive index, 2, 4, 316
    relaxation time T, 327
    resolution
    - coherent light, 399
    - grating, 162
    - incoherent light, , 394
    resolving power, 119, 164
    resonance
    - condition, 304, 308
    - mode, 116
    - wave numbers, 323
    resonance of vibrations, 323
    resonator parameters, 74
    restricting, 284
    right polarized light, 237
    rotation, 65
    rotation of the coordinate system, 243
    round aperture, 149
    round object, 390
    round objects, 391


    S

    Sagittal (horizontal) plane, 428
    sagittal coma CS , 423, 425
    sampling interval, 359
    scalar wave equation, 79, 131
    Schawlow and Townes, 295
    selection rules, 284
    Sellmeier formula, 324
    shape factor, 421
    sign convention, 11, 69
    simulations of interferograms, 358
    sine function and apodization, 367
    single refracting surface, 415
    single surface, 416
    single-sided step function, 343, 346
    size of hologram, 406
    skin depth, 331, 333
    slow axis, 232
    small angle approximation, 10, 16, 137, 154
    solution of the eigenvalue problem, 243
    spatial coherence, 185
    - frequencies, 376
    - wavelength, 378
    - waves, 376
    spherical aberration, 415, 416, 418, 421, 422
    spherical mirrors, 68
    - concave spherical mirror, 70
    - convex spherical mirror, 72
    - graphical method, 70
    - magnification, 69
    - virtual image, 73
    spherical surfaces, 1, 9, 11, 15
    - conjugate points, 9
    - geometrical construction, 16
    - image focus, 12
    - image forming equation, 11
    - image point, 10
    - magnification, 16, 18
    - real object, 16
    sign convention, 11
    - virtual image, 16, 18, 19
    - virtual object, 17, 18, 19
    spherical thick lens, 58
    spherical wave, 80, 131
    spin states, 283
    spontaneous emission A21 , 275, 289, 293
    spread function, 386, 392, 398
    standing wave conditions, 249
    static conductivity, 327
    - gold, 330
    - lead, 330
    - nickel, 330
    silver, 330
    Stefan-Boltzmann law, 277, 278
    step function, 340
    step grating, 178
    stratified media, 252
    - antireflection coating, 258
    - plate of thickness d =η/2η2 , 257
    - two interfaces at distance d, 253
    superposition
    - of two cosine waves, 84
    - of two double slit patterns, 188
    - of wavetrains, 201
    - principle, 80, 208
    susceptibility x, 317


    T

    Tangential coma CT , 424, 425
    TE modes, 262, 270
    telescope, 44
    - Galilean, 46
    - Kepler's, 44
    temporal coherence, 200
    - length of wavetrains, 202
    - quasimonochromatic light, 200
    - superposition, 200
    - wavetrains, 200
    Theory of Color, 7

    thick lens, 51, 54
    - concentration lens, 67
    - focal length, 54
    - matrix, 51
    two hemispherical 62, 63
    two thick lenses, 61, 63
    - virtual image, 67
    thin lens, 24, 33, 53, 54, 418, 422
    - different media, 34
    - equation, 23, 30
    - image focus, 24
    - magnification, 25
    - matrix, 52
    - model, 1
    - negative lens, 31
    - object focus, 24
    - positive lens, 26
    transformation to principal planes, 54
    two different media, 33
    two thin lenses, 36
    two thin lenses in air, 59
    - virtual image, 29, 32
    - virtual object, 29, 32
    three lens system, 42
    three-level laser, 296
    threshold condition, 294-296
    time average, 87
    time-dependent, 88
    TM modes, 265
    total internal reflection, 259, 263
    total reflection, 226, 228, 229
    transmission coefficient, 221
    transfer function, 392, 401

    - function for (Bess/arg), 402

    - function for (sin x/x), 402
    translation matrices, 49, 51
    transmission intensity, 225, 227
    transmittance T, 223
    transposed matrix, 65
    trigonometric formulas, 440
    two lens system, 36
    two lenses in air, 59
    two round apertures, 391, 395
    two-level system, 292


    U

    Uniaxial crystals, 231
    unit matrix, 65


    V

    Velocity for travel, 4
    vertex of the spherical surfaces, 56
    violet catastrophe, 275
    virtual image, 16, 29, 32, 68, 404, 405
    virtual object, 30, 32
    visibility, 194-196
    visibility for two point sources, 194


    W

    Water waves, 83
    wave equation, 242, 317
    wavefront division, 89
    wavelength, 279, λ, 142
    wavetrains, 200, 287
    wedge shaped air gap, 99
    Wien's displacement law, 278


    Y

    Young's experiment, 90, 91, 96
    Young, Thomas, 79



    Reviews

    Some praise for the previous edition: OPTICS AND PHOTONICS NEWS [OCTOBER 2004] "This book cover geometrical optics, electromagnetic theory, interference, diffraction and coherence theory. Chapters on optical constants, blackbody radiation, emission and absorption, lasers, holography and Fourier transform spectroscopy broaden its scope. The packet contains over 170 MathCAD files linked to specific topics and applications. ... [T]he main virtues of the book are the excellent photographs of basic optical phenomena. ... The index is comprehensive. ... [The book] will certainly be helpful to ... students in an introductory optics course." THE PHYSICIST (March/April 2004) "The author has developed a suite of model programs covering the whole spectrum of optics from classical geometric ray to wave and modern optics. Illustrative resonator and waveguide modes are also part of the program mix as well as introductory laser theory. In addition to an optics course, this book would be useful in a 3rd or 4th year electromagnetism course as well as an introduction to lasers and resonators. There are certainly more topics in this text than could possibly be covered in the typical 30 hour one semester course. ... All formulas and diagrams are provided in Adobe .pdf files as well for transcription into other software suites or inclusion in notes. This book is a comprehensive optics text that has been written in a mode to encourage students to run the models, do the calculations and generate their own illustrations. ... The book would serve as an excellent text for undergraduate use and reference for laboratory simulation experiments." From the reviews of the second edition: "Möller (physics, NJIT) presents introductory-level coverage of the basics in optics and provides model computational files for simulation of the governing laws. ... Selected classical textbook references are listed at the end of the book. Summing Up: Recommended. Upper-division undergraduates." (O. Eknoyan, CHOICE, Vol. 45 (6), 2008) "In this book Möller presents an impressive procedure of studying optics using the computer through the packages of Algebraic Computation. ... It is very well written. ... I believe that a dedicated professor could use this book to design physics projects with his interested students. It would be a pleasure for both." (Everton Murilo C. Abreu, Mathematical Reviews, Issue 2009 c) "The book is aimed at readers who want to learn the basics of optics by using model computations. Step by step all basic formulas in geometrical, wave and Fourier optics are derived and supplemented by programs to solve a particular problem linked to a topic in optics or some application. ... The book is intended for a one semester introductory optics course, but also suitable for self-learning by scientists or engineers who would like to refresh their knowledge of optics." (Gunther Schmidt, Zentralblatt MATH, Vol. 1179, 2010)