# OPTICS Learning by Computing with Examples Using Matlab, Mathcad, Mathematica, and Maple

by admin in on June 5, 2019

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.

Newark, New Jersey K.D. M’oller

### Contents

1 Geometrical Optics 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Fermat’s Principle and the Law of Refraction . . . . . . . . . . . . . . . 2
1.3 Prisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Convex Spherical Surfaces . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Concave Spherical Surfaces . . . . . . . . . . . . . . . . . . . . . . . . 19
1.6 Thin Lens Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.7 Optical Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.8 Matrix Formulation for Thick Lenses . . . . . . . . . . . . . . . . . . . 48
1.9 Plane and Spherical Mirrors . . . . . . . . . . . . . . . . . . . . . . . . 67
1.10 Matrices for a Reflecting Cavity and the Eigenvalue Problem . . . . . . 73
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.2 Harmonic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.3 Superposition of Harmonic Waves . . . . . . . . . . . . . . . . . . . . 82
2.4 Two-Beam Wave front Dividing Interferometry . . . . . . . . . . . . . . 89
2.5 Two-Beam Amplitude Dividing Interferometry . . . . . . . . . . . . . . 96
2.6 Multiple Beam Interferometry . . . . . . . . . . . . . . . . . . . . . . . 110
2.7 Random Arrangement of Source Points . . . . . . . . . . . . . . . . . . 125
3 Diffraction 129
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.2 Kirchhoff–Fresnel Integral . . . . . . . . . . . . . . . . . . . . . . . . 131
3.3 Fresnel Diffraction, Far Field Approximation, and Fraunhofer Observation . . . 136
3.4 Far Field and Fraunhofer Diffraction . . . . . . . . . . . . . . . . . . . 139
3.5 Babinet’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
3.6 Apertures in Random Arrangement . . . . . . . . . . . . . . . . . . . . 169
3.7 Fresnel Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
4.1 Spatial Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
4.2 Temporal Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
5 Maxwell’s Theory 205
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
5.2 Harmonic Plane Waves and the Superposition Principle . . . . . . . . . 206
5.3 Differentiation Operation . . . . . . . . . . . . . . . . . . . . . . . . . 208
5.4 Poynting Vector in Vacuum . . . . . . . . . . . . . . . . . . . . . . . . 209
5.5 Electromagnetic Waves in an Isotropic Nonconducting Medium . . . . . 210
5.6 Fresnel’s Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
5.7 Polarized Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
6 Maxwell II. Modes and Mode Propagation 249
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
6.2 Stratified Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
Refractive Index . . . . . . . . . . . . . . . . . . . . . . . . . . 258
6.3 Guided Waves by Total Internal Reflection Through a Planar Waveguide . . . . 259
6.4 Fiber Optics Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . 266
7 Blackbody Radiation, Atomic Emission, and Lasers 273
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
7.2 Blackbody Radiaton . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
7.3 Atomic Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
7.4 Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
7.5 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
7.6 Confocal Cavity, Gaussian Beam, and Modes . . . . . . . . . . . . . . . 297
8 Optical Constants 315
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
8.2 Optical Constants of Dielectrics . . . . . . . . . . . . . . . . . . . . . . 316
8.3 Determination of Optical Constants . . . . . . . . . . . . . . . . . . . . 320
8.4 Optical Constants of Metals . . . . . . . . . . . . . . . . . . . . . . . . 326
9 Fourier Transformation and FT-Spectroscopy 339
9.1 Fourier Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 339
9.2 Fourier Transform Spectroscopy . . . . . . . . . . . . . . . . . . . . . 352
10 Imaging UsingWave 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
10.4 Image Formation Using Incoherent Light . . . . . . . . . . . . . . . . . 386
10.5 Image Formation with Coherent Light . . . . . . . . . . . . . . . . . . 398
10.6 Holography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
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
11.8 Chromatic Aberration and the Achromatic Doublet . . . . . . . . . . . . 430
11.9 Chromatic Aberration and the Achromatic Doublet with Separated Lenses . . . 432
Appendix B Formulas 439

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June 5, 2019

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June 5, 2019