Geometric Optics (eBook)

Preface 6
Contents 9
1 Fermat's Principle and General Considerations Regarding Centered Optical Systems 13
1.1 An Introduction to Fermat's Principle 13
1.2 Forming an Image 17
1.3 Axial Chromatic Aberrations 21
1.4 Monochromatic Aberrations 22
1.5 Surfaces of Revolution 24
1.6 Ray Tracing in Axially Symmetric Systems 28
1.7 Exercises 31
2 Gaussian Optics 34
2.1 Gaussian Approximation for a Single Surface 34
2.2 Compound Systems 38
2.3 Useful Decompositions of Matrix mathbbT 40
2.4 Principal Planes and Focal Lengths 43
2.5 Stops and Pupils 45
2.6 Some Gaussian Optical Invariants 47
2.7 Gaussian Analysis of Compound Systems 49
2.8 A Graphical Method 53
2.9 Thick and Thin Lenses 54
2.10 A Different Approach to Gaussian Optics 56
2.11 Exercises 59
3 Fermat's Principle and Third-Order Aberrations 63
3.1 Introduction 63
3.2 The Aberration Function 64
3.3 A New Aberration Function 68
3.4 The Aberration Function ? for a Single Surface 72
3.5 The Total Aberration Function for a Compound System 77
3.6 Analysis of Third-Order Aberrations 82
3.7 Petzval's Theorem 86
3.8 Aberration Formulae 88
3.9 Combined Effect of Third-Order Aberrations 89
3.10 Primary or Axial Chromatic Aberrations 90
3.11 Third-Order Aberrations in the Exit Pupil 93
3.12 Plate with Parallel Plane Faces 98
4 About Higher Order Aberrations 100
4.1 Aplanatism and Sine Condition 100
4.2 Aplanatic Refractive Surfaces 104
4.3 Introduction to Fifth-Order Aberrations 105
4.4 Meaning of the Terms of (4.33), (4.34) 109
4.5 The Light Diffraction and the Airy Disk 111
5 Newtonian and Cassegrain Telescopes 115
5.1 The Newtonian Telescope 115
5.2 Location and Dimension of Flat Mirror 118
5.3 Newtonian Telescope with Spherical Primary Mirror 120
5.4 Cassegrain Telescopes 121
5.5 Spherical Aberration and Coma in Cassegrain Telescopes 123
5.6 Concluding Remarks 124
5.7 Examples 125
6 Cameras for Astronomy 127
6.1 Introduction 127
6.2 Aberrations for a Single Mirror 128
6.3 Schmidt's Camera 129
6.4 Examples of Schimdt's Camera 133
6.5 Wright's Camera 135
6.6 Houghton's Camera 137
6.7 Examples 146
6.8 Maksutov Camera 147
6.9 Examples 151
7 Compound Cassegrain Telescopes 153
7.1 Introduction to Cassegrain Telescopes 153
7.2 Schmidt--Cassegrain Telescopes 155
7.3 Examples 156
7.4 Houghton--Cassegrain Telescopes 159
7.5 Examples 162
7.6 Maksutov--Cassegrain Telescopes 165
7.7 Examples 167
7.8 Final Remarks 169
8 Doublets and Triplets 170
8.1 Achromatic Doublets 170
8.2 Elimination of Spherical Aberration and Coma 172
8.3 Examples 174
8.4 Triplets 177
8.5 Examples 178
9 Other Optical Combinations 181
9.1 Schmidt--Cassegrain Telescope with Spherical Surfaces 181
9.2 The Flat-field Baker--Schmidt Camera 183
9.3 Cassegrain Telescope with the Corrector at the Prime Focus 186
9.4 The Klevtsov Telescope 188
9.5 A First Analysis of the Meniscus 189
9.6 Analysis of Mangin Mirror 190
9.7 Buchroeder's Camera 191
9.8 The Baker--Nunn Camera 193
9.9 Houghton--Cassegrain Telescope with Sub-Aperture Corrector 196
9.10 Petzval's Objective 199
10 Fermat's Principle and Wave Fronts 202
10.1 Fermat's Principle 202
10.2 The Boundary Value Problem 211
10.3 Maupertuis' Principle 213
10.4 Fermat's Principle and the Formation of Mirages 215
10.5 Rotational Symmetry and Lagrange's invariant 217
10.6 Wave Fronts and Fermat's Principle 220
10.7 Huygens' Principle 224
11 Hamiltonian Optics 226
11.1 Hamilton's Equations in Geometric Optics 226
11.2 Hamilton's Principal Functions 228
11.3 Symmetries and Characteristic Functions 232
11.4 Lagrange's Optical Invariant for Axially Symmetric Systems 234
11.5 Hamiltonian Equations and Primary Aberrations 235
11.6 Equations of Primary Aberrations 239
11.7 The Case of Spherical Surfaces 243
11.8 Recalls of Symplectic Mechanics 244
11.9 Symplectic Optics 249
12 Principal Functions and Primary Aberrations 251
12.1 Introduction to Third-Order Aberrations 251
12.2 Third-Order Aberrations via Angular Function 252
12.3 Reduced Coordinates 255
12.4 Schwarzschild's eikonal 257
12.5 Addition Theorem for Third-Order Aberrations 260
12.6 Fourth-Order Expansion of Angular Function 262
12.7 Aberrations of Axially Symmetric Systems 265
13 Introduction to Optics in Anisotropic Media 268
13.1 Maxwell's Equations in Anisotropic Media 268
13.2 Refractive Index in Anisotropic Media 270
13.3 Fermat's Principle in Anisotropic Media 273
Appendix A First-Order PDE 275
Appendix B Symplectic Vector Spaces 282
References 285
Index 287