Preface of the Book Series xxi Preface of the First Volume xxiii Acknowledgements xxv 1 Introduction 1 1.1 Modelling and Goal of Lens Design 2 1.2 Optical System Types and Aperture Field Classification 3 1.2.1 Selected Classes of Systems 7 References 10 2 Optical Materials 13 2.1 Introduction 13 2.2 Dispersion 14 2.2.
1 Definition 14 2.2.2 Wavelengths 15 2.2.3 Abbe Number 16 2.2.4 Dispersion of Crown and Flint Glasses 17 2.2.
5 Glass Diagram 18 2.2.6 Interpolation of the Refractive Index 18 2.2.7 Relative Partial Dispersion 20 2.2.7.1 Definition 20 2.
2.7.2 Line of Normal Dispersion 22 2.2.7.3 Anomalous Partial Dispersion 25 2.2.7.
4 Hoogland Diagram 26 2.2.7.5 The Anomalous Dispersion Representation of Münz 26 2.2.8 Generalized Mathematical Descriptions of Dispersion 29 2.2.8.
1 Introduction 29 2.2.8.2 Derivative Based Dispersion Description 31 2.2.8.3 Buchdahls Chromatical Coordinates 32 2.2.
8.4 Adaptive Dispersion Formula of Sasian 33 2.2.9 Miscellaneous 35 2.2.9.1 Dispersion of Diffractive Surfaces 35 2.2.
9.2 Dispersion of Gradient-Index Materials 36 2.3 Group Velocity Dispersion and Short Pulses 37 2.3.1 Introduction 37 2.3.2 Dispersion Coefficients 38 2.3.
3 Pulse Changes due to Dispersion 38 2.3.4 Pulse Dispersion Data of Glasses 39 2.3.4.1 Introduction 39 2.3.4.
2 Numerical Calculation of Index Derivatives 39 2.3.4.3 GVD Properties of Glasses 40 2.4 Absorption and Transmission 42 2.4.1 Complex Index of Refraction 42 2.4.
2 Lambert-Beers Law 44 2.4.3 Transmission of a Component 44 2.4.4 Transmission of Glasses 45 2.5 Thermal Properties 46 2.5.1 Thermal Expansion 46 2.
5.2 Index Change 47 2.5.3 Thermo-Optical Coefficient 48 2.5.3.1 Introduction 48 2.5.
3.2 Temperature-Dependence of Dispersion 49 2.6 Other Optical Materials 49 2.6.1 Crystal Materials for IR and UV 49 2.6.2 Plastics 53 2.6.
3 Water 54 2.6.4 Technical Liquids 54 2.6.5 Immersion Liquids 56 2.6.6 Optical Cements 57 References 57 3 Geometrical Optics 61 3.1 Introduction 61 3.
2 Law of Refraction 61 3.2.1 Introduction 61 3.2.2 Ray Bending 62 3.2.3 Description of Refraction in the k-Space 64 3.3 Fresnel Formulas 65 3.
3.1 Amplitude Coefficients 65 3.3.2 Reflectivity and Transmittivity 67 3.3.3 Transmission of Systems 68 3.3.4 Total Internal Reflection 70 3.
3.5 Reflection at Metals 73 3.4 Raytrace 74 3.4.1 Introduction 74 3.4.2 Paraxial Formulas 76 3.4.
3 Meridional Q-U Method 77 3.4.4 Three-dimensional Case 78 3.4.5 Pitfalls and Special Cases 80 3.4.6 Modelling of Mirrors 81 3.4.
7 Ray Intersection with Surfaces of Higher Order 82 3.4.8 Gradient Index Media 83 3.4.9 Differential Raytrace, Parabasal Rays and Ray Tubes 84 3.4.10 Diffractive Surfaces 86 3.4.
10.1 Introduction 86 3.4.10.2 Plane linear gratings 87 3.4.10.3 Generalized Diffractive Surfaces 88 3.
4.11 Non-Sequential Raytrace 88 3.4.12 Special Ray Types 89 3.4.13 Ray Aiming 91 3.4.13.
1 Introduction 91 3.4.13.2 Paraxial Aiming Approach 94 3.4.13.3 Real Ray Aiming 95 3.4.
13.4 General Formulation of Greynolds 97 3.4.13.5 Examples 97 3.4.14 Complex Rays 98 3.4.
14.1 Introduction 98 3.4.14.2 Gaussian Beams with Complex Source Point 99 3.4.14.3 Tracing Complex Rays 100 3.
5 Paraxial Approximation 101 3.5.1 Introduction 101 3.5.2 Abbe Invariant 104 3.5.2.1 Paraxial Definition 104 3.
5.2.2 Generalized Abbe Invariant 105 3.5.3 Superposition of Rays 105 3.5.4 Generalized Paraxiality 106 3.5.
5 Collinear Transform 107 3.6 Matrix Calculus 108 3.6.1 Introduction 108 3.6.2 Properties of the Matrices 110 3.6.3 Matrices of Simple Components 111 3.
6.4 Decompositions of an ABCD Matrix 112 3.6.4.1 Iwasawa Decomposition 112 3.6.4.2 Alternative Decompositions 113 3.
6.5 Matrices for Generalized Geometries 115 3.6.5.1 Two-dimensional 3 × 3 Matrices for Plane-Symmetric Systems 115 3.6.5.2 Centered 4 × 4 Matrices 116 3.
6.5.3 Special 4 × 4 Matrices 117 3.6.5.4 Decomposition of a 4 ×4 Matrix 118 3.6.5.
5 General 5 × 5 Matrices 119 3.7 Helmholtz-Lagrange Invariant 120 3.7.1 Introduction 120 3.7.2 Lagrange Invariant for Arbitrary z-Positions 122 3.7.3 Generalized Etendue Definitions 122 3.
7.4 Smith''s Cosine Invariant 124 3.8 Delano Diagram 124 3.8.1 Definition 124 3.8.2 Properties of the Delano Diagram 125 3.8.
3 Vignetting 127 3.8.4 Examples 128 3.9 Gaussian Brackets 131 3.9.1 Introduction 131 3.9.2 Alternative Representations 132 3.
9.3 Relation to ABCD Formalism 132 3.9.4 Applications 133 3.9.4.1 Tolerancing 133 3.9.
4.2 Achromatization 133 3.9.4.3 Zoom Systems 133 References 134 4 Optical Components 137 4.1 Overview 137 4.2 Single Refractive Spherical Surface 137 4.3 Plane Plates 138 4.
3.1 Introduction 138 4.3.2 Perpendicular Plates 139 4.3.2.1 Beam Displacement 139 4.3.
2.2 Aberrations 140 4.3.3 Tilted Plates 140 4.3.4 Non-Orthogonal Prisms 141 4.3.5 Plane-parallel Plate in a Convergent Beam 141 4.
4 Lenses 143 4.4.1 Notations 143 4.4.2 Focal Length 144 4.4.3 Principal Planes and Surfaces 146 4.4.
4 Lens Shape and Bending 147 4.4.5 Generalized Bending 151 4.4.6 Modified Bending Definition 152 4.4.7 Thick Lenses 152 4.4.
8 The Ideal Lens Dilemma 154 4.5 Mirrors 157 4.6 Aspheres 158 4.6.1 Introduction 158 4.6.2 Conic Surfaces 159 4.6.
2.1 Introduction 159 4.6.2.2 Parabolic Mirrors 161 4.6.2.3 Ellipsoidal Mirror 162 4.
6.2.4 Hyperboloidal Mirror 163 4.6.2.5 Grazing Incidence Telescopes 163 4.6.3 Cartesian Ovaloids 164 4.
6.3.1 Introduction 164 4.6.3.2 Special Case Infinity 165 4.6.3.
3 Special Case Aplanatism 167 4.6.4 Asphere with Polynomial Expansion 167 4.6.4.1 Traditional Taylor Expansion 167 4.6.4.
2 Strong Forbes Aspheres 168 4.6.4.3 Mild Forbes Aspheres 170 4.6.4.4 Superconical Surfaces 171 4.7 Freeform Surfaces 172 4.
7.1 Introduction 172 4.7.2 Basic Shape 174 4.7.3 Boundary and Projection Factor 175 4.7.4 Polynomial Functions 176 4.
7.4.1 Introduction 176 4.7.4.2 Monomials 176 4.7.4.
3 Zernike Polynomials 176 4.7.4.4 Chebyshev Polynomials 178 4.7.4.5 Legendre Polynomials 178 4.7.
4.6 Forbes Freeform Surfaces 178 4.7.5 Functional Systems with Local Support 179 4.7.5.1 Introduction 179 4.7.
5.2 Radial Basis Functions 179 4.7.5.3 Splines 182 4.7.6 Technological Constraints and Manufacturability 185 4.8 Special Component Types 185 4.
8.1 Cylindrical Lenses 185 4.8.1.1 Introduction 185 4.8.1.2 Aspherical Cylindrical Lenses 186 4.
8.1.3 Toroidal Lenses 188 4.8.1.4 Toroidal Ring Lens 188 4.8.1.
5 Combinations of Cylindrical Lenses 189 4.8.2 Fresnel Lenses 191 4.8.2.1 Introduction 191 4.8.2.
2 Basic Equations 193 4.8.2.3 Properties of Fresnel Lenses 193 4.8.3 Axicons 194 4.8.3.
1 Geometrical Concept 194 4.8.3.2 Physical Description 195 4.8.4 Variable Components 197 4.8.4.
1 Introduction 197 4.8.4.2 Electrowetting Liquid Lenses 198 4.8.4.3 Electrophoretic Liquid Lenses 199 4.8.
4.4 Hydraulic Membrane Liquid Lenses 200 4.8.4.5 Liquid Crystal Lenses 200 4.8.4.6 Deformable Mirrors 200 4.
8.4.7 Alvarez Lenses 202 4.8.5 Lenslet Arrays 202 4.8.5.1 Introduction 203 4.
8.5.2 Special Lens Arrays 203 4.8.5.3 Matrix Calculation of Arrays 204 4.8.5.
4 Applications 205 4.8.6 Digital Mirror Device 208 4.9 Gradient Index Lenses 210 4.9.1 Introduction 210 4.9.2 Quadratic Radial Index Lenses 211 4.
9.3 Axial Gradient Index Lenses 212 4.9.4 Stigmatic Imaging Gradient Index-Lenses 212 4.10 Prisms 215 4.10.1 Reflecting Prisms 215 4.10.
2 Roof Prisms 216 4.10.2.1 Description of the Geometry 216 4.10.2.2 Dimensioning of the Size 217 4.10.
2.3 Image Formation Problems Related to Roof Edges 217 4.10.3 Dispersion Prisms 218 4.10.3.1 Introduction 218 4.10.
3.2 Achromatic Prism Pairs 219 4.10.3.3 Anamorphic Prism Pair 220 4.10.3.4 Fery Prisms 221 4.
10.4 Risley Prisms 221 4.11 Diffractive Elements 223 4.11.1 Linear Gratings 223 4.11.1.1 Introduction 223 4.
11.1.2 Blazed Grating 224 4.11.2 General Diffractive Elements 226 4.11.2.1 Introduction 226 4.
11.2.2 Discretization and Quantization 230 4.11.2.3 Types of DOE 231 4.11.2.
4 Fresnel Zone Plates 232 4.11.2.5 Classical Diffractive Lens 232 4.11.2.6 Decomposition into Orders or Zones 233 4.11.
2.7 Problems of Real Diffractive Elements 234 4.11.3 Modelling DOEs by Raytrace 235 4.12 Diffusor Plates 235 4.12.1 Types of Diffusers 236 4.12.
2 Properties of Diffusers 236 4.12.3 Angle Characteristic 238 References 239 5 Imaging Systems 243 5.1 Introduction 243 5.1.1 Mathematical Description of Optic.