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| Contents | ||||||
| Preface | vii | |||||
| 1 | Geometrical Optics | 1 | ||||
| 1.1 | Introduction | 1 | ||||
| 1.2 | Fermat's Principle and the Law of Refraction | 2 | ||||
| 1.3 | Prisms | 7 | ||||
| 1.3.1 | Angle of Deviation | 7 | ||||
| 1.4 | Convex Spherical Surfaces | 9 | ||||
| 1.4.1 | Image Formation and Conjugate Points | 9 | ||||
| 1.4.2 | Sign Convention | 11 | ||||
| 1.4.3 | Object and Image Distance, Object and Image Focus, Real and Virtual Objects, and Singularities | 11 | ||||
| 1.4.4 | Real Objects, Geometrical Constructions, and Magnification | 15 | ||||
| 1.4.5 | Virtual Objects, Geometrical Constructions, and Magnification | 17 | ||||
| 1.5 | Concave Spherical Surfaces | 19 | ||||
| 1.6 | Thin Lens Equation | 23 | ||||
| 1.6.1 | Thin Lens Equation | 23 | ||||
| 1.6.2 | Object Focus and Image Focus | 24 | ||||
| 1.6.3 | Magnification | 25 | ||||
| 1.6.4 | Positive Lens, Graph, Calculations of Image Positions, and Graphical Constructions of Images | 25 | ||||
| 1.6.5 | Negative Lens, Graph, Calculations of Image Positions, and Graphical Constructions of Images | 30 | ||||
| 1.6.6 | Thin Lens and Two Different Media on the Outside | 33 | ||||
| 1.7 | Optical Instruments | 35 | ||||
| 1.7.1 | Two Lens System | 36 | ||||
| 1.7.2 | Magnifier and Object Positions | 37 | ||||
| 1.7.3 | Microscope | 42 | ||||
| 1.7.4 | Telescope | 44 | ||||
| 1.8 | Matrix Formulation for Thick Lenses | 48 | ||||
| 1.8.1 | Refraction and Translation Matrices | 48 | ||||
| 1.8.2 | Two Spherical Surfaces at Distance d and Prinicipal Planes | 51 | ||||
| 1.8.3 | System of Lenses | 59 | ||||
| 1.9 | Plane and Spherical Mirrors | 67 | ||||
| 1.9.1 | Plane Mirrors and Virtual Images | 67 | ||||
| 1.9.2 | Spherical Mirrors and Mirror Equation | 67 | ||||
| 1.9.3 | Sign Convention | 69 | ||||
| 1.9.4 | Magnification | 69 | ||||
| 1.9.5 | Graphical Method and Graphs of xiDepending on x0 | 70 | ||||
| 1.10 | Matrices for a Reflecting Cavity and the Eigenvalue Problem | 73 | ||||
| 2 | Interference | 79 | ||||
| 2.1 | Introduction | 79 | ||||
| 2.2 | Harmonic Waves | 80 | ||||
| 2.3 | Superposition of Harmonic Waves | 82 | ||||
| 2.3.1 | Superposition of Two Waves Depending on Space and Time Coordinates | 82 | ||||
| 2.3.2 | Intensities | 86 | ||||
| 2.3.3 | Normalization | 88 | ||||
| 2.4 | Two-Beam Wavefront Dividing Interferometry | 89 | ||||
| 2.4.1 | Model Description for Wavefront Division | 89 | ||||
| 2.4.2 | Young's Experiment | 90 | ||||
| 2.5 | Two-Beam Amplitude Dividing Interferometry | 96 | ||||
| 2.5.1 | Model Description for Amplitude Division | 96 | ||||
| 2.5.2 | Plane Parallel Plate | 97 | ||||
| 2.5.3 | Michelson Interferometer and Heidinger and Fizeau Fringes | 103 | ||||
| 2.6 | Multiple Beam Interferometry | 110 | ||||
| 2.6.1 | Plane Parallel Plate | 110 | ||||
| 2.6.2 | Fabry-Perot Etalon | 115 | ||||
| 2.6.3 | Fabry-Perot Spectrometer and Resolution | 118 | ||||
| 2.6.4 | Array of Source Points | 121 | ||||
| 2.7 | Random Arrangement of Source Points | 125 | ||||
| 3 | Diffraction | 129 | ||||
| 3.1 | Introduction | 129 | ||||
| 3.2 | Kirchhoff-Fresnel Integral | 131 | ||||
| 3.2.1 | The Integral | 131 | ||||
| 3.2.2 | On Axis Observation for the Circular Opening | 133 | ||||
| 3.2.3 | On Axis Observation for Circular Stop | 135 | ||||
| 3.3 | Fresnel Diffraction, Far Field Approximation, and Fraunhofer Observation | 136 | ||||
| 3.3.1 | Small Angle Approximation in Cartesian Coordinates | 137 | ||||
| 3.3.2 | Fresnel, Far Field, and Fraunhofer Diffraction | 138 | ||||
| 3.4 | Far Field and Fraunhofer Diffraction | 139 | ||||
| 3.4.1 | Diffraction on a Slit | 140 | ||||
| 3.4.2 | Diffraction on a Slit and Fourier Transformation | 144 | ||||
| 3.4.3 | Rectangular Aperture | 145 | ||||
| 3.4.4 | Circular Aperture | 148 | ||||
| 3.4.5 | Gratings | 152 | ||||
| 3.4.6 | Resolution | 162 | ||||
| 3.5 | Babinet's Theorem | 166 | ||||
| 3.6 | Apertures in Random Arrangement | 169 | ||||
| 3.7 | Fresnel Diffraction | 172 | ||||
| 3.7.1 | Coordinates for Diffraction on a Slit and Fresnels Integrals | 172 | ||||
| 3.7.2 | Fresnel Diffraction on a Slit | 173 | ||||
| 3.7.3 | Fresnel Diffraction on an Edge | 175 | ||||
| A3.1.1 | Step Grating | 178 | ||||
| A3.2.1 | Cornu's Spiral | 181 | ||||
| A3.2.2 | Babinet's Principle and Cornu's Spiral | 182 | ||||
| 4 | Coherence | 185 | ||||
| 4.1 | Spatial Coherence | 185 | ||||
| 4.1.1 | Introduction | 185 | ||||
| 4.1.2 | Two Source Points | 185 | ||||
| 4.1.3 | Coherence Condition | 189 | ||||
| 4.1.4 | Extended Source | 190 | ||||
| 4.1.5 | Visibility | 194 | ||||
| 4.1.6 | Michelson Stellar Interferometer | 197 | ||||
| 4.2 | Temporal Coherence | 200 | ||||
| 4.2.1 | Wavetrains and Quasimonochromatic Light | 200 | ||||
| 4.2.2 | Superposition of Wavetrains | 201 | ||||
| 4.2.3 | Length of Wavetrains | 202 | ||||
| A4.1.1 | Fourier Tranform Spectometer and Blackbody Radiation | 203 | ||||
| 5 | Maxwell's Theory | 205 | ||||
| 5.1 | Introduction | 205 | ||||
| 5.2 | Harmonic Plane Waves and the Superposition Principle | 206 | ||||
| 5.2.1 | Plane Waves | 206 | ||||
| 5.2.2 | The Superposition Principle | 208 | ||||
| 5.3 | Differentiation Operation | 208 | ||||
| 5.3.1 | Differentiation "Time" d/dt | 208 | ||||
| 5.3.2 | Differentiation "Space" Δ = id/dx+jd/dy+ kd/dz | 208 | ||||
| 5.4 | Poynting Vector in Vacuum | 209 | ||||
| 5.5 | Electromagnetic Waves in an Isotropic Nonconducting Medium | 210 | ||||
| 5.6 | Fresnel ´ s Formulas | 211 | ||||
| 5.6.1 | Electrical Field Vectors in the Plane of Incidence (Parallel Case) | 211 | ||||
| 5.6.2 | Electrical Field Vector Perpendicular to the Plane of Incidence (Perpendicular Case) | 214 | ||||
| 5.6.3 | Fresnel's Formulas Depending on the Angle of Incidence | 215 | ||||
| 5.6.4 | Light Incident on a Denser Medium, n1< n2, and the Brewster Angle | 216 | ||||
| 5.6.5 | Light Incident on a Less Dense Medium, n1> n2, Brewster and Critical Angle | 219 | ||||
| 5.6.6 | Reflected and Transmitted Intensities | 222 | ||||
| 5.6.7 | Total Reflection and Evanescent Wave | 228 | ||||
| 5.7 | Polarized Light | 230 | ||||
| 5.7.1 | Introduction | 230 | ||||
| 5.7.2 | Ordinary and Extraordinary Indices of Refraction | 231 | ||||
| 5.7.3 | Phase Difference Between Waves Moving in the Direction of or Perpendicular to the Optical Axis | 232 | ||||
| 5.7.4 | Half-Wave Plate, Phase Shift of π | 233 | ||||
| 5.7.5 | Quarter Wave Plate, Phase Shift π/2 | 235 | ||||
| 5.7.6 | Crossed Polarizers | 238 | ||||
| 5.7.7 | General Phase Shift | 240 | ||||
| A5.1.1 | Wave Equation Obtained from Maxwell's Equation | 242 | ||||
| A5.1.2 | The Operations Δ and Δ2 | 243 | ||||
| A5.2.1 | Rotation of the Coordinate System as a Principal Axis Transformation and Equivalence to the Solution of the Eigenvalue Problem | 243 | ||||
| A5.3.1 | Phase Difference Between Internally Reflected Components | 244 | ||||
| A5.4.1 | Jones Vectors and Jones Matrices | 244 | ||||
| A5.4.2 | Jones Matrices | 245 | ||||
| A5.4.3 | Applications | 245 | ||||
| 6 | Maxwell II. Modes and Mode Propagation | 249 | ||||
| 6.1 | Introduction | 249 | ||||
| 6.2 | Stratified Media | 252 | ||||
| 6.2.1 | Two Interfaces at Distance d | 253 | ||||
| 6.2.2 | Plate of Thickness d = (λ/2n2) | 255 | ||||
| 6.2.3 | Plate of Thickness d and Index n2 | 256 | ||||
| 6.2.4 | Antireflection Coating | 256 | ||||
| 6.2.5 | Multiple Layer Filters with Alternating High and Low Refractive Index | 258 | ||||
| 6.3 | Guided Waves by Total Internal Reflection Through a Planar Waveguide | 259 | ||||
| 6.3.1 | Traveling Waves | 259 | ||||
| 6.3.2 | Restrictive Conditions for Mode Propagation | 261 | ||||
| 6.3.3 | Phase Condition for Mode Formation | 262 | ||||
| 6.3.4 | (TE) Modes or s-Polarization | 262 | ||||
| 6.3.5 | (TM) Modes or p-Polarization | 265 | ||||
| 6.4 | Fiber Optics Waveguides | 266 | ||||
| 6.4.1 | Modes in a Dielectric Waveguide | 266 | ||||
| A6.1.1 | Boundary Value Method Applied to TE Modes of Plane Plate Waveguide | 270 | ||||
| 7 | Blackbody Radiation, Atomic Emission, and Lasers | 273 | ||||
| 7.1 | Introduction | 273 | ||||
| 7.2 | Blackbody Radiaton | 274 | ||||
| 7.2.1 | The Rayleigh-Jeans Law | 274 | ||||
| 7.2.2 | Planck's Law | 275 | ||||
| 7.2.3 | Stefan-Boltzmann Law | 277 | ||||
| 7.2.4 | Wien's Law | 278 | ||||
| 7.2.5 | Files of Planck's, Stefan-Boltzmann's, and Wien's Laws. Radiance, Area, and Solid Angle | 279 | ||||
| 7.3 | Atomic Emission | 281 | ||||
| 7.3.1 | Introduction | 281 | ||||
| 7.3.2 | Bohr's Model and the One Electron Atom | 282 | ||||
| 7.3.3 | Many Electron Atoms | 282 | ||||
| 7.4 | Bandwidth | 285 | ||||
| 7.4.1 | Introduction | 285 | ||||
| 7.4.2 | Classical Model, Lorentzian Line Shape, and Homogeneous Broadening | 286 | ||||
| 7.4.3 | Natural Emission Line Width, Quantum Mechanical Model | 289 | ||||
| 7.4.4 | Doppler Broadening (Inhomogeneous) | 289 | ||||
| 7.5 | Lasers | 291 | ||||
| 7.5.1 | Introduction | 291 | ||||
| 7.5.2 | Population Inversion | 292 | ||||
| 7.5.3 | Stimulated Emission, Spontaneous Emission, and the Amplification Factor | 293 | ||||
| 7.5.4 | The Fabry-Perot Cavity, Losses, and Threshold Condition | 294 | ||||
| 7.5.5 | Simplified Example of a Three-Level Laser | 296 | ||||
| 7.6 | Confocal Cavity, Gaussian Beam, and Modes | 297 | ||||
| 7.6.1 | Paraxial Wave Equation and Beam Parameters | 297 | ||||
| 7.6.2 | Fundamental Mode in Confocal Cavity | 299 | ||||
| 7.6.3 | Diffraction Losses and Fresnel Number | 302 | ||||
| 7.6.4 | Higher Modes in the Confocal Cavity | 303 | ||||
| 8 | Optical Constants | 315 | ||||
| 8.1 | Introduction | 315 | ||||
| 8.2 | Optical Constants of Dielectrics | 316 | ||||
| 8.2.1 | The Wave Equation, Electrical Polarizability, and Refractive Index | 316 | ||||
| 8.2.2 | Oscillator Model and the Wave Equation | 317 | ||||
| 8.3 | Determination of Optical Constants | 320 | ||||
| 8.3.1 | Fresnel' s Formulas and Reflection Coefficients | 320 | ||||
| 8.3.2 | Ratios of the Amplitude Reflection Coefficients | 321 | ||||
| 8.3.3 | Oscillator Expressions | 322 | ||||
| 8.3.4 | Sellmeier Formula | 324 | ||||
| 8.4 | Optical Constants of Metals | 326 | ||||
| 8.4.1 | Drude Model | 326 | ||||
| 8.4.2 | Low Frequency Region | 327 | ||||
| 8.4.3 | High Frequency Region | 328 | ||||
| 8.4.4 | Skin Depth | 331 | ||||
| 8.4.5 | Reflectance at Normal Incidence and Reflection Coefficients with Absorption | 333 | ||||
| 8.4.6 | Elliptically Polarized Light | 334 | ||||
| A8.1.1 | Analytical Expressions and Approximations for the Detemination of n and K | 335 | ||||
| 9 | Fourier Transformation and FT-Spectroscopy | 339 | ||||
| 9.1 | Fourier Transformation | 339 | ||||
| 9.1.1 | Introduction | 339 | ||||
| 9.1.2 | The Fourier Integrals | 339 | ||||
| 9.1.3 | Examples of Fourier Transformations Using Analytical Functions | 340 | ||||
| 9.1.4 | Numerical Fourier Transformation | 341 | ||||
| 9.1.5 | Fourier Transformation of a Product of Two Functions and the Convolution Integral | 350 | ||||
| 9.2 | Fourier Transform Spectroscopy | 352 | ||||
| 9.2.1 | Interferogram and Fourier Transformation. Superposition of Cosine Waves | 352 | ||||
| 9.2.2 | Michelson Interferometer and Interferograms | 353 | ||||
| 9.2.3 | The Fourier Transform Integral | 355 | ||||
| 9.2.4 | Discrete Length and Frequency Coordinates | 356 | ||||
| 9.2.5 | Folding of the Fourier Transform Spectrum | 359 | ||||
| 9.2.6 | High Resolution Spectroscopy | 363 | ||||
| 9.2.7 | Apodization | 366 | ||||
| A9.1.1 | Asymmetric Fourier Transform Spectroscopy | 370 | ||||
| 10 | Imaging Using Wave Theory | 375 | ||||
| 10.1 | Introduction | 375 | ||||
| 10.2 | Spatial Waves and Blackening Curves, Spatial Frequencies, and Fourier Transformation | 376 | ||||
| 10.3 | Object, Image, and the Two Fourier Transformations | 382 | ||||
| 10.3.1 | Waves from Object and Aperture Plane and Lens | 382 | ||||
| 10.3.2 | Summation Processes | 383 | ||||
| 10.3.3 | The Pair of Fourier Transformations | 385 | ||||
| 10.4 | Image Formation Using Incoherent Light | 386 | ||||
| 10.4.1 | Spread Function | 386 | ||||
| 10.4.2 | The Convolution Integral | 387 | ||||
| 10.4.3 | Impulse Response and the Intensity Pattern | 387 | ||||
| 10.4.4 | Examples of Convolution with Spread Function | 388 | ||||
| 10.4.5 | Transfer Function | 392 | ||||
| 10.4.6 | Resolution | 395 | ||||
| 10.5 | Image Formation with Coherent Light | 398 | ||||
| 10.5.1 | Spread Function | 398 | ||||
| 10.5.2 | Resolution | 399 | ||||
| 10.5.3 | Transfer Function | 401 | ||||
| 10.6 | Holography | 403 | ||||
| 10.6.1 | Introduction | 403 | ||||
| 10.6.2 | Recording of the Interferogram | 403 | ||||
| 10.6.3 | Recovery of Image with Same Plane Wave Used for Recording | 404 | ||||
| 10.6.4 | Recovery Using a Different Plane Wave | 405 | ||||
| 10.6.5 | Production of Real and Virtual Image Under an Angle | 405 | ||||
| 10.6.6 | Size of Hologram | 406 | ||||
| 11 | Aberration | 415 | ||||
| 11.1 | Introduction | 415 | ||||
| 11.2 | Spherical Aberration of a Single Refracting Surface | 415 | ||||
| 11.3 | Longitudinal and Lateral Spherical Aberration of a Thin Lens | 418 | ||||
| 11.4 | The π-σ Equation and Spherical Aberration | 421 | ||||
| 11.5 | Coma | 423 | ||||
| 11.6 | Aplanatic Lens | 425 | ||||
| 11.7 | Astigmatism | 427 | ||||
| 11.7.1 | Astigmatism of a Single Spherical Surface | 427 | ||||
| 11.7.2 | Astigmatism of a Thin Lens | 428 | ||||
| 11.8 | Chromatic Aberration and the Achromatic Doublet | 430 | ||||
| 11.9 | Chromatic Aberration and the Achromatic Doublet with Separated Lenses | 432 | ||||
| Appendix A About Graphs and Matrices in Mathcad | 435 | |||||
| Appendix B Formulas | 439 | |||||
| References | 443 | |||||
| Index | 445 | |||||
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
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
Index
AAberration, 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
BBabinet'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
CC-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, 9constructive 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
DDamping 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
EEchelette 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
FFabry-Perot, 77, 115-117, 249
- cavity, 294
- etalon, 115
- plates, 249
- spectrometer and resolution, 118
- transmission depending on D, 117far 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, 106focal 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, 136frequency 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, 95fringe pattern, 89
fundamental mode, 299, 308
fused quartz, 325
GGain 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
HHalf-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
IImage 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
JJones matrices, 244, 245
Jones vectors, 244
KKepler telescope, 45, 46, 48
Kirchhoff-Fresnel integral, 131, 132, 139, 376
Kramer-Kroning model, 325
LLabels 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
MMagnetic 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, 8mirror 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
NNatural 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
OObject 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
PPair 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
QQuality factor, 288
quantum emission, 273
quantum mechanical model, 289
quarter-wave plate, 239, 246
quartz, 232, 234, 236
quasimonochromatic light, 200
RRadius 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
SSagittal (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
TTangential 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, 7thick 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
UUniaxial crystals, 231
unit matrix, 65
VVelocity 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
WWater 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
YYoung's experiment, 90, 91, 96
Young, Thomas, 79
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)