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Copyrighted Material k v Contents Preface xxi Glossary xxv About the Companion Website xxix 1 Geometrical Optics 1 1.1 Geometrical Optics – Ray and Wave Optics 1 1.2 Fermat’s Principle and the Eikonal Equation 2 1.3 Sequential Geometrical Optics – A Generalised Description 3 1.3.1 Conjugate Points and Perfect Image Formation 4 1.3.2 Infinite Conjugate and Focal Points 4 1.3.3 Principal Points and Planes 5 k 1.3.4 System Focal Lengths 6 k 1.3.5 Generalised Ray Tracing 6 1.3.6 Angular Magnification and Nodal Points 7 1.3.7 Cardinal Points 8 1.3.8 Object and Image Locations - Newton’s Equation 8 1.3.9 Conditions for Perfect Image Formation – Helmholtz Equation 9 1.4 Behaviour of Simple Optical Components and Surfaces 10 1.4.1 General 10 1.4.2 Refraction at a Plane Surface and Snell’s Law 10 1.4.3 Refraction at a Curved (Spherical) Surface 11 1.4.4 Refraction at Two Spherical Surfaces (Lenses) 12 1.4.5 Reflection by a Plane Surface 13 1.4.6 Reflection from a Curved (Spherical) Surface 14 1.5 Paraxial Approximation and Gaussian Optics 15 1.6 Matrix Ray TracingCOPYRIGHTED16 MATERIAL 1.6.1 General 16 1.6.2 Determination of Cardinal Points 18 1.6.3 Worked Examples 18 1.6.4 Spreadsheet Analysis 21 Further Reading 21 2 Apertures Stops and Simple Instruments 23 2.1 Function of Apertures and Stops 23 2.2 Aperture Stops, Chief, and Marginal Rays 23 2.3 Entrance Pupil and Exit Pupil 25 2.4 Telecentricity 27 2.5 Vignetting 27 2.6 Field Stops and Other Stops 28 k k vi Contents 2.7 Tangential and Sagittal Ray Fans 28 2.8 Two Dimensional Ray Fans and Anamorphic Optics 28 2.9 Optical Invariant and Lagrange Invariant 30 2.10 Eccentricity Variable 31 2.11 Image Formation in Simple Optical Systems 31 2.11.1 Magnifying Glass or Eye Loupe 31 2.11.2 The Compound Microscope 32 2.11.3 Simple Telescope 34 2.11.4 Camera 35 Further Reading 36 3 Monochromatic Aberrations 37 3.1 Introduction 37 3.2 Breakdown of the Paraxial Approximation and Third Order Aberrations 37 3.3 Aberration and Optical Path Difference 41 3.4 General Third Order Aberration Theory 46 3.5 Gauss-Seidel Aberrations 47 3.5.1 Introduction 47 3.5.2 Spherical Aberration 48 3.5.3 Coma 49 3.5.4 Field Curvature 51 3.5.5 Astigmatism 53 3.5.6 Distortion 54 3.6 Summary of Third Order Aberrations 55 k k 3.6.1 OPD Dependence 56 3.6.2 Transverse Aberration Dependence 56 3.6.3 General Representation of Aberration and Seidel Coefficients 57 Further Reading 58 4 Aberration Theory and Chromatic Aberration 59 4.1 General Points 59 4.2 Aberration Due to a Single Refractive Surface 60 4.2.1 Aplanatic Points 61 4.2.2 Astigmatism and Field Curvature 63 4.3 Reflection from a Spherical Mirror 64 4.4 Refraction Due to Optical Components 67 4.4.1 Flat Plate 67 4.4.2 Aberrations of a Thin Lens 69 4.4.2.1 Conjugate Parameter and Lens Shape Parameter 70 4.4.2.2 General Formulae for Aberration of Thin Lenses 71 4.4.2.3 Aberration Behaviour of a Thin Lens at Infinite Conjugate 72 4.4.2.4 Aplanatic Points for a Thin Lens 75 4.5 The Effect of Pupil Position on Element Aberration 78 4.6 Abbe Sine Condition 81 4.7 Chromatic Aberration 83 4.7.1 Chromatic Aberration and Optical Materials 83 4.7.2 Impact of Chromatic Aberration 84 4.7.3 The Abbe Diagram for Glass Materials 87 4.7.4 The Achromatic Doublet 87 4.7.5 Optimisation of an Achromatic Doublet (Infinite Conjugate) 89 k k Contents vii 4.7.6 Secondary Colour 90 4.7.7 Spherochromatism 92 4.8 Hierarchy of Aberrations 92 Further Reading 94 5 Aspheric Surfaces and Zernike Polynomials 95 5.1 Introduction 95 5.2 Aspheric Surfaces 95 5.2.1 General Form of Aspheric Surfaces 95 5.2.2 Attributes of Conic Mirrors 96 5.2.3 Conic Refracting Surfaces 98 5.2.4 Optical Design Using Aspheric Surfaces 99 5.3 Zernike Polynomials 100 5.3.1 Introduction 100 5.3.2 Form of Zernike Polynomials 101 5.3.3 Zernike Polynomials and Aberration 103 5.3.4 General Representation of Wavefront Error 107 5.3.5 Other Zernike Numbering Conventions 108 Further Reading 109 6 Diffraction, Physical Optics, and Image Quality 111 6.1 Introduction 111 6.2 The Eikonal Equation 112 k 6.3 Huygens Wavelets and the Diffraction Formulae 112 k 6.4 Diffraction in the Fraunhofer Approximation 115 6.5 Diffraction in an Optical System – the Airy Disc 116 6.6 The Impact of Aberration on System Resolution 120 6.6.1 The Strehl Ratio 120 6.6.2 The Maréchal Criterion 121 6.6.3 The Huygens Point Spread Function 122 6.7 Laser Beam Propagation 123 6.7.1 Far Field Diffraction of a Gaussian Laser Beam 123 6.7.2 Gaussian Beam Propagation 124 6.7.3 Manipulation of a Gaussian Beam 126 6.7.4 Diffraction and Beam Quality 127 6.7.5 Hermite Gaussian Beams 128 6.7.6 Bessel Beams 129 6.8 Fresnel Diffraction 130 6.9 Diffraction and Image Quality 132 6.9.1 Introduction 132 6.9.2 Geometric Spot Size 133 6.9.3 Diffraction and Image Quality 134 6.9.4 Modulation Transfer Function 135 6.9.5 Other Imaging Tests 137 Further Reading 138 7 Radiometry and Photometry 139 7.1 Introduction 139 7.2 Radiometry 139 k k viii Contents 7.2.1 Radiometric Units 139 7.2.2 Significance of Radiometric Units 140 7.2.3 Ideal or Lambertian Scattering 141 7.2.4 Spectral Radiometric Units 142 7.2.5 Blackbody Radiation 142 7.2.6 Étendue 145 7.3 Scattering of Light from Rough Surfaces 146 7.4 Scattering of Light from Smooth Surfaces 147 7.5 Radiometry and Object Field Illumination 151 7.5.1 Köhler Illumination 151 7.5.2 Use of Diffusers 151 7.5.3 The Integrating Sphere 152 7.5.3.1 Uniform Illumination 152 7.5.3.2 Integrating Sphere Measurements 154 7.5.4 Natural Vignetting 154 7.6 Radiometric Measurements 155 7.6.1 Introduction 155 7.6.2 Radiometric Calibration 156 7.6.2.1 Substitution Radiometry 156 7.6.2.2 Reference Sources 156 7.6.2.3 Other Calibration Standards 157 7.7 Photometry 158 7.7.1 Introduction 158 k 7.7.2 Photometric Units 158 k 7.7.3 Illumination Levels 160 7.7.4 Colour 161 7.7.4.1 Tristimulus Values 161 7.7.4.2 RGB Colour 163 7.7.5 Astronomical Photometry 164 Further Reading 166 8 Polarisation and Birefringence 169 8.1 Introduction 169 8.2 Polarisation 170 8.2.1 Plane Polarised Waves 170 8.2.2 Circularly and Elliptically Polarised Light 170 8.2.3 Jones Vector Representation of Polarisation 172 8.2.4 Stokes Vector Representation of Polarisation 172 8.2.5 Polarisation and Reflection 175 8.2.6 Directional Flux – Poynting Vector 178 8.3 Birefringence 178 8.3.1 Introduction 178 8.3.2 The Index Ellipsoid 180 8.3.3 Propagation of Light in a Uniaxial Crystal – Double Refraction 182 8.3.4 ‘Walk-off’ in Birefringent Crystals 184 8.3.5 Uniaxial Materials 186 8.3.6 Biaxial Crystals 187 8.4 Polarisation Devices 187 8.4.1 Waveplates 187 k k Contents ix 8.4.2 Polarising Crystals 188 8.4.3 Polarising Beamsplitter 190 8.4.4 Wire Grid Polariser 190 8.4.5 Dichroitic Materials 191 8.4.6 The Faraday Effect and Polarisation Rotation 191 8.5 Analysis of Polarisation Components 191 8.5.1 Jones Matrices 191 8.5.2 Müller Matrices 195 8.6 Stress-induced Birefringence 196 Further Reading 197 9 Optical Materials 199 9.1 Introduction 199 9.2 Refractive Properties of Optical Materials 200 9.2.1 Transmissive Materials 200 9.2.1.1 Modelling Dispersion 200 9.2.1.2 Temperature Dependence of Refractive Index 203 9.2.1.3 Temperature Coefficient of Refraction for Air 205 9.2.2 Behaviour of Reflective Materials 206 9.2.3 Semiconductor Materials 210 9.3 Transmission Characteristics of Materials 212 9.3.1 General 212 9.3.2 Glasses 213 k 9.3.3 Crystalline Materials 213 k 9.3.4 Chalcogenide Glasses 214 9.3.5 Semiconductor Materials 214 9.3.6 Polymer Materials 214 9.3.7 Overall Transmission Windows for Common Optical Materials 215 9.4 Thermomechanical Properties 215 9.4.1 Thermal Expansion 215 9.4.2 Dimensional Stability Under Thermal Loading 216 9.4.3 Annealing 216 9.4.4 Material Strength and Fracture Mechanics 217 9.5 Material Quality 219 9.5.1 General 219 9.5.2 Refractive Index Homogeneity 220 9.5.3 Striae 220 9.5.4 Bubbles and Inclusions 220 9.5.5 Stress Induced Birefringence 220 9.6 Exposure to Environmental Attack 221 9.6.1 Climatic Resistance 221 9.6.2 Stain Resistance 221 9.6.3 Resistance to Acid and Alkali Attack 221 9.7 Material Processing 221 Further Reading 222 10 Coatings and Filters 223 10.1 Introduction 223 10.2 Properties of Thin Films 223 k k x Contents 10.2.1 Analysis of Thin Film Reflection 223 10.2.2 Single Layer Antireflection Coatings 225 10.2.3 Multilayer Coatings 226 10.2.4 Thin Metal Films 229 10.2.5 Protected and Enhanced Metal Films 231 10.3 Filters 232 10.3.1 General 232 10.3.2 Antireflection Coatings 233 10.3.3 Edge Filters 233 10.3.4 Bandpass Filters 236 10.3.5 Neutral Density Filters 237 10.3.6 Polarisation Filters 238 10.3.7 Beamsplitters 240 10.3.8 Dichroic Filters 241 10.3.9 Etalon Filters 241 10.4 Design of Thin Film Filters 244 10.5 Thin Film Materials 246 10.6 Thin Film Deposition Processes 247 10.6.1 General 247 10.6.2 Evaporation 248 10.6.3 Sputtering 248 10.6.4 Thickness Monitoring 249 Further Reading 250 k k 11 Prisms and Dispersion Devices 251 11.1 Introduction 251 11.2 Prisms 251 11.2.1 Dispersive Prisms 251 11.2.2 Reflective Prisms 254 11.3 Analysis of Diffraction Gratings 257 11.3.1 Introduction 257 11.3.2 Principle of Operation 258 11.3.3 Dispersion and Resolving Power 259 11.3.4 Efficiency of a Transmission Grating 261 11.3.5 Phase Gratings 262 11.3.6 Impact of Varying Angle of Incidence 262 11.3.7 Reflection Gratings 264 11.3.8 Impact of Polarisation 268 11.3.9 Other Grating Types 269 11.3.9.1 Holographic Gratings 269 11.3.9.2 Echelle Grating 270 11.3.9.3 Concave Gratings – The Rowland Grating 270 11.3.9.4 Grisms 271 11.4 Diffractive Optics 273 11.5 Grating Fabrication 274 11.5.1 Ruled Gratings 274 11.5.2
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