Optics: learning by computing with examples using MathCAD

Contents......Page 10
Preface......Page 8
1.1 Introduction......Page 18
1.2 Fermat’s Principle and the Law of Refraction......Page 19
1.3.1 Angle of Deviation......Page 24
1.4.1 Image Formation and Conjugate Points......Page 26
1.4.3 Object and Image Distance, Object and Image Focus, Real and Virtual Objects, and Singularities......Page 28
1.4.4 Real Objects, Geometrical Constructions, and Magnification......Page 32
1.4.5 Virtual Objects, Geometrical Constructions, and Magnification......Page 34
1.5 Concave Spherical Surfaces......Page 36
1.6.1 Thin Lens Equation......Page 40
1.6.2 Object Focus and Image Focus......Page 41
1.6.4 Positive Lens, Graph, Calculations of Image Positions, and Graphical Constructions of Images......Page 42
1.6.5 Negative Lens, Graph, Calculations of Image Positions, and Graphical Constructions of Images......Page 47
1.6.6 Thin Lens and Two Different Media on the Outside......Page 50
1.7 Optical Instruments......Page 52
1.7.1 Two Lens System......Page 53
1.7.2 Magnifier and Object Positions......Page 54
1.7.3 Microscope......Page 59
1.7.4 Telescope......Page 61
1.8.1 Refraction and Translation Matrices......Page 65
1.8.2 Two Spherical Surfaces at Distance d and Prinicipal Planes......Page 68
1.8.3 System of Lenses......Page 76
1.9.1 Plane Mirrors and Virtual Images......Page 83
1.9.2 Spherical Mirrors and Mirror Equation......Page 84
1.9.4 Magnification......Page 85
1.9.5 Graphical Method and Graphs of x[sub(i)] Depending on x[sub(o)]......Page 86
1.10 Matrices for a Reflecting Cavity and the Eigenvalue Problem......Page 89
2.1 Introduction......Page 94
2.2 Harmonic Waves......Page 95
2.3.1 Superposition of Two Waves Depending on Space and Time Coordinates......Page 97
2.3.2 Intensities......Page 101
2.3.3 Normalization......Page 103
2.4.1 Model Description for Wavefront Division......Page 104
2.4.2 Young’s Experiment......Page 105
2.5.1 Model Description for Amplitude Division......Page 111
2.5.2 Plane Parallel Plate......Page 112
2.5.3 Michelson Interferometer and Heidinger and Fizeau Fringes......Page 118
2.6.1 Plane Parallel Plate......Page 125
2.6.2 Fabry–Perot Etalon......Page 130
2.6.3 Fabry–Perot Spectrometer and Resolution......Page 133
2.6.4 Array of Source Points......Page 136
2.7 Random Arrangement of Source Points......Page 140
3.1 Introduction......Page 144
3.2.1 The Integral......Page 146
3.2.2 On Axis Observation for the Circular Opening......Page 148
3.2.3 On Axis Observation for Circular Stop......Page 150
3.3 Fresnel Diffraction, Far Field Approximation, and Fraunhofer Observation......Page 151
3.3.1 Small Angle Approximation in Cartesian Coordinates......Page 152
3.3.2 Fresnel, Far Field, and Fraunhofer Diffraction......Page 153
3.4 Far Field and Fraunhofer Diffraction......Page 154
3.4.1 Diffraction on a Slit......Page 155
3.4.2 Diffraction on a Slit and Fourier Transformation......Page 159
3.4.3 Rectangular Aperture......Page 160
3.4.4 Circular Aperture......Page 163
3.4.5 Gratings......Page 167
3.4.6 Resolution......Page 177
3.5 Babinet’s Theorem......Page 181
3.6 Apertures in Random Arrangement......Page 184
3.7.1 Coordinates for Diffraction on a Slit and Fresnels Integrals......Page 187
3.7.2 Fresnel Diffraction on a Slit......Page 188
3.7.3 Fresnel Diffraction on an Edge......Page 190
A3.1.1 Step Grating......Page 193
A3.2.1 Cornu’s Spiral......Page 196
A3.2.2 Babinet’s Principle and Cornu’s Spiral......Page 197
4.1.2 Two Source Points......Page 200
4.1.3 Coherence Condition......Page 204
4.1.4 Extended Source......Page 206
4.1.5 Visibility......Page 209
4.1.6 Michelson Stellar Interferometer......Page 212
4.2.1 Wavetrains and Quasimonochromatic Light......Page 215
4.2.2 Superposition of Wavetrains......Page 216
4.2.3 Length of Wavetrains......Page 217
A4.1.1 Fourier Tranform Spectometer and Blackbody Radiation......Page 218
5.1 Introduction......Page 220
5.2.1 Plane Waves......Page 221
5.3.2 Differentiation \"Space\" ∇=i∂/∂x+j∂/∂y+k∂/∂z......Page 223
5.4 Poynting Vector in Vacuum......Page 224
5.5 Electromagnetic Waves in an Isotropic Nonconducting Medium......Page 225
5.6.1 Electrical Field Vectors in the Plane of Incidence (Parallel Case)......Page 226
5.6.2 Electrical Field Vector Perpendicular to the Plane of Incidence (Perpendicular Case)......Page 229
5.6.3 Fresnel’s Formulas Depending on the Angle of Incidence......Page 230
5.6.4 Light Incident on a Denser Medium, n[sub(1)] < n[sub(2)], and the Brewster Angle......Page 231
5.6.5 Light Incident on a Less Dense Medium, n[sub(1)] > n[sub(2)], Brewster and Critical Angle......Page 234
5.6.6 Reflected and Transmitted Intensities......Page 237
5.6.7 Total Reflection and Evanescent Wave......Page 243
5.7.1 Introduction......Page 245
5.7.2 Ordinary and Extraordinary Indices of Refraction......Page 246
5.7.3 Phase Difference Between Waves Moving in the Direction of or Perpendicular to the Optical Axis......Page 247
5.7.4 Half-Wave Plate, Phase Shift of π......Page 248
5.7.5 Quarter Wave Plate, Phase Shift π/2......Page 250
5.7.6 Crossed Polarizers......Page 253
5.7.7 General Phase Shift......Page 255
A5.1.1 Wave Equation Obtained from Maxwell’s Equation......Page 257
A5.2.1 Rotation of the Coordinate System as a Principal Axis Transformation and Equivalence to the Solution of the Eigenvalue Problem......Page 258
A5.4.1 Jones Vectors and Jones Matrices......Page 259
A5.4.3 Applications......Page 260
6.1 Introduction......Page 262
6.2 Stratified Media......Page 265
6.2.1 Two Interfaces at Distance d......Page 266
6.2.2 Plate of Thickness d = (λ/2n[sub(2)]......Page 268
6.2.4 Antireflection Coating......Page 269
6.2.5 Multiple Layer Filters with Alternating High and Low Refractive Index......Page 271
6.3.1 Traveling Waves......Page 272
6.3.2 Restrictive Conditions for Mode Propagation......Page 274
6.3.4 (TE) Modes or s-Polarization......Page 275
6.3.5 (TM) Modes or p-Polarization......Page 278
6.4.1 Modes in a Dielectric Waveguide......Page 279
A6.1.1 Boundary Value Method Applied to TE Modes of Plane Plate Waveguide......Page 283
7.1 Introduction......Page 286
7.2.1 The Rayleigh–Jeans Law......Page 287
7.2.2 Planck’s Law......Page 288
7.2.3 Stefan–Boltzmann Law......Page 290
7.2.4 Wien’s Law......Page 291
7.2.5 Files of Planck’s, Stefan–Boltzmann’s, and Wien’s Laws. Radiance, Area, and Solid Angle......Page 292
7.3.1 Introduction......Page 294
7.3.3 Many Electron Atoms......Page 295
7.4.1 Introduction......Page 298
7.4.2 Classical Model, Lorentzian Line Shape, and Homogeneous Broadening......Page 299
7.4.4 Doppler Broadening (Inhomogeneous)......Page 302
7.5.1 Introduction......Page 304
7.5.2 Population Inversion......Page 305
7.5.3 Stimulated Emission, Spontaneous Emission, and the Amplification Factor......Page 306
7.5.4 The Fabry–Perot Cavity, Losses, and Threshold Condition......Page 307
7.5.5 Simplified Example of a Three-Level Laser......Page 309
7.6.1 Paraxial Wave Equation and Beam Parameters......Page 310
7.6.2 Fundamental Mode in Confocal Cavity......Page 312
7.6.3 Diffraction Losses and Fresnel Number......Page 315
7.6.4 Higher Modes in the Confocal Cavity......Page 316
8.1 Introduction......Page 326
8.2.1 The Wave Equation, Electrical Polarizability, and Refractive Index......Page 327
8.2.2 Oscillator Model and the Wave Equation......Page 328
8.3.1 Fresnel’s Formulas and Reflection Coefficients......Page 331
8.3.2 Ratios of the Amplitude Reflection Coefficients......Page 332
8.3.3 Oscillator Expressions......Page 333
8.3.4 Sellmeier Formula......Page 335
8.4.1 Drude Model......Page 337
8.4.2 Low Frequency Region......Page 338
8.4.3 High Frequency Region......Page 339
8.4.4 Skin Depth......Page 342
8.4.5 Reflectance at Normal Incidence and Reflection Coefficients with Absorption......Page 344
8.4.6 Elliptically Polarized Light......Page 345
A8.1.1 Analytical Expressions and Approximations for the Detemination of n and K......Page 346
9.1.2 The Fourier Integrals......Page 348
9.1.3 Examples of Fourier Transformations Using Analytical Functions......Page 349
9.1.4 Numerical Fourier Transformation......Page 350
9.1.5 Fourier Transformation of a Product of Two Functions and the Convolution Integral......Page 359
9.2.1 Interferogram and Fourier Transformation. Superposition of Cosine Waves......Page 361
9.2.2 Michelson Interferometer and Interferograms......Page 362
9.2.3 The Fourier Transform Integral......Page 364
9.2.4 Discrete Length and Frequency Coordinates......Page 365
9.2.5 Folding of the Fourier Transform Spectrum......Page 368
9.2.6 High Resolution Spectroscopy......Page 372
9.2.7 Apodization......Page 375
A9.1.1 Asymmetric Fourier Transform Spectroscopy......Page 379
10.1 Introduction......Page 384
10.2 Spatial Waves and Blackening Curves, Spatial Frequencies, and Fourier Transformation......Page 385
10.3.1 Waves from Object and Aperture Plane and Lens......Page 391
10.3.2 Summation Processes......Page 392
10.3.3 The Pair of Fourier Transformations......Page 394
10.4.1 Spread Function......Page 395
10.4.3 Impulse Response and the Intensity Pattern......Page 396
10.4.4 Examples of Convolution with Spread Function......Page 397
10.4.5 Transfer Function......Page 401
10.4.6 Resolution......Page 404
10.5.1 Spread Function......Page 407
10.5.2 Resolution......Page 408
10.5.3 Transfer Function......Page 410
10.6.2 Recording of the Interferogram......Page 412
10.6.3 Recovery of Image with Same Plane Wave Used for Recording......Page 413
10.6.5 Production of Real and Virtual Image Under an Angle......Page 414
10.6.6 Size of Hologram......Page 415
11.2 Spherical Aberration of a Single Refracting Surface......Page 422
11.3 Longitudinal and Lateral Spherical Aberration of a Thin Lens......Page 425
11.4 The π–σ Equation and Spherical Aberration......Page 428
11.5 Coma......Page 430
11.6 Aplanatic Lens......Page 432
11.7.1 Astigmatism of a Single Spherical Surface......Page 434
11.7.2 Astigmatism of a Thin Lens......Page 435
11.8 Chromatic Aberration and the Achromatic Doublet......Page 437
11.9 Chromatic Aberration and the Achromatic Doublet with Separated Lenses......Page 439
Appendix A: About Graphs and Matrices in Mathcad......Page 442
Appendix B: Formulas......Page 446
References......Page 450
Index......Page 452