Handbook of Optical Systems

Edited by

Herbert Cross

Volume 1: Fundamentals of Technical OpticsHerbert Gross

WILEY-VCH

WILEY-VCH Verlag GmbH & Co. KGaA

VII

Contents

Preface

1

22.12.1.12.1.22.1.32.1.42.1.52.1.62.1.72.22.2.12.2.22.2.32.32.3.12.3.22.3.32.3.42.3.52.42.4.12.4.22.52.5.12.5.22.5.32.5.42.5.52.6

V

Introduction 1

Paraxial Imaging 5General Remarks 7Paraxial Approximation 7Linear Collineation 9Image Locations 10Magnification 14Lens Equation 25Newtons Equation 19Three-dimensional Systems 20Single Surface 21Refracting Plane Surface 21Refractive Spherical Surface 22Mirror Surface 23Single Lens 24Parameters of a Lens 24Cardinal Elements 25Thin Lens 28Thick Lens 29Graphical Image Construction 32Multiple-component Systems 33System Consisting of Two Thin Components 33Systems Consisting of Several Thin Lenses 36Invariants 36Helmholtz-Lagrange Invariant 36Abbe Invariant Q 39Paraxial Invariant 39Further Invariants 40Matrix Form of the Helmholtz Invariant 40Matrix Calculus 41

Handbook of Optical Systems: Vol. 1. Fundamentals of Technical Optics. H. GrossCopyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 3-527-40377-9

VIII Contents

2.6.12.6.22.6.32.6.42.6.52.72.7.12.7.22.7.32.8

33.13.1.13.1.23.1.33.23.2.13.2.23.2.33.2.43.2.53.2.63.2.73.2.83.2.93.2.103.33.3.13.3.23.43.4.13.4.23.4.33.4.43.53.5.13.5.23.63.6.13.6.23.6.33.6.43.6.53.7

Paraxial ABCD Matrices 41Properties of the Matrices 44Matrices of Simple Components 45Finite Imaging with an Afocal System 48Decompositions of an ABCD Matrix 49Matrices Describing a More General Geometry 51Two-dimensional 3X3 Matrices 51Centered 4X4 Matrices 54General 5x5 Matrices 58Literature 59

Interfaces 62Basics 62Boundary Conditions 62The Law of Refraction 63The Law of Reflection 66The Fresnel Equations 67Definition of the Amplitude Coefficients 67Reflection 67Transmission 69Properties of the Fresnel Equations 69Stokes Relations 72Azimuthal Angle 74Reflectivity and Transmirtivity 75Phase Changes 79Description of the Refraction in the k-Space 80Reflection Losses in Optical Systems 82Polarization Effects at Interfaces 84Brewster Angle 84Degree of Polarization 86Evanescent Waves 88Total Internal Reflection 88Evanescent Surface Waves 92Damped Total Internal Reflection 94Frustrated Total Internal Reflection 95Non-geometrical Effects at Reflection 96The Goos-Haenchen Effect 96Total Internal Reflection of a Gaussian Beam 100Absorbing Media 102Complex Refractive Index 102Lambert-Beer Law 103Reflection at an Absorbing Medium 104Metals 105Reflection at Metals 105Literature 209

44.14.1.14.1.24.1.34.24.2.14.2.24.2.34.2.44.2.54.2.64.2.74.34.3.14.3.24.3.34.3.44.3.54.44.4.14.4.24.4.34.54.5.14.5.24.5.34.5.44.5.54.5.64.5.74.5.84.5.94.5.104.64.6.14.6.24.74.7.14.7.24.7.34.84.8.14.8.24.9

Contents IX

Materials 111Basics 113Introduction 113Optical Parameters 113Non-optical Properties 114Dispersion 114Definition 114Wavelengths 116Characterizing the Dispersion 117Optical Crowns and Flints 118Interpolation of the Refractive Index 120Dispersion of the Group Velocity 123Chromatic Coordinates According to Buchdahl 124Relative Partial Dispersion 125Definition 125Line of Normal Dispersion 228Glasses with Anomalous Partial Dispersion 230Relative Partial Dispersion in the Glass diagram 232Hoogland Diagram 133Transmission 134Transmission and Internal Transmission 234Transmission Edge 236Transmission of Glasses and Plastics 237Glasses 239General Remarks 239Glass Diagram 239Glass Ranges 242Thermal Properties 243Data Sheet 246Mechanical Properties of Glass 247Chemical Properties of Glass 249Deliverable Forms of Glass 249Practical Aspects of the Choice of Glass in Optical Design 249Special Glasses 250Crystals and Special Materials 252Materials for IR and UV 152Quartz 254Plastics 257General Properties 257Optical Properties 258Transmission 260Gases 262General Remarks 161Air 262Liquids and Cements 162

X Contents

4.9.14.9.24.9.34.9.44.104.10.14.10.24.11

55.15.25.35.3.15.3.25.3.35.3.45.3.55.3.65.3.75.45.4.15.4.25.4.35.4.45.4.55.4.65.4.75.55.5.15.5.25.5.35.5.45.65.6.15.6.25.6.35.6.45.75.7.15.7.25.8

Water 162Technical Liquids 163Immersion Oils 166Optical Cements 267Metals 168Optical Parameters 168Reflectivity of Metallic Mirrors 169Literature 171

Raytracing 173The Meaning of Raytracing 174Raytracing Scheme 174Raytracing Formula Sets 178General Remarks 178Paraxial y-u-Method 178Paraxial s-h- Method 179Meridional S-U-Method 180Meridional Q-U-Method 182Set of Vector Formulas 182Iterative Calculation of the Intersection Point for Aspherical Surfaces 186Raytracing in Optical Systems 189Description of the Geometry 189Types of Surface 194Particular Properties 206Output Quantities 207Errors 208Apodization 208Polarization Raytracing 209Special Components 220Ideal Lens 220Raytracing in GRIN media 211Raytracing for Diffractive Elements 215Knife-edge Diffraction Model in Raytracing 219Differential Rays 220General Remarks 220Coddington Equations 220General Differential Rays 222Ray Tubes 223Non-sequential Raytracing 224General Remarks 224Monte-Carlo Raytracing 226Literature 227

66.16.1.16.1.26.1.36.1.46.1.56.1.66.1.76.1.86.1.96.1.106.1.116.26.2.16.2.26.36.3.16.3.26.3.36.3.46.46.4.16.4.26.4.36.4.46.4.56.4.66.56.5.16.5.26.5.36.6

77.17.1.17.1.27.1.37.1.47.1.57.27.2.17.2.27.2.3

Radiometry 229

Introduction 230General Remarks 230Definition of the Radiometric Quantities 230Photometric Quantities 232Radiometric and Photometric Quantities 233Solid Angle 233Differential Flux 235Fundamental Law of Radiometry 235Projection of the Irradiance 236Irradiance 237Spectral Densities of Quantities 237Energy, Power and Photons 238Lambertian Radiator 239Classical Lambertian Radiator 239General Lambertian Radiator 240Radiation Transfer 241General Remarks 241Point Source of Light 242Radiation Transfer between Surfaces 244Numerical Radiation Transfer 247Radiometry of Optical Systems 248Optical System 248Radiation Transport with Interaction 249Aplanatic Systems 250Natural Vignetting 252Radiometry in Real Optical Systems 259Ray Tube Model 260Description of Radiation Transport in the Phase Space 263Helmholtz - Lagrange Invariant 263Phase Space Coordinates 264Phase Space Representation of Radiation Transport 265Literature 267

Light Sources 269

Introduction 271Classification 271Efficiency 271Electromagnetic Spectrum 273Standard Light Sources 275Daylight and Sunlight 276Thermal Radiators 278Plancks Formula 278Optical Efficiency 281Radiation Temperature 282

Contents XI

XII Contents

7.2.4 Wiens Displacement Law 2837.2.5 Stefan-Boltzmann Law 2847.2.6 Rayleigh-Jeans Radiation Formula 2847.2.7 Wiens Law of Radiation 2857.3 Classical Lamps 2857.3.1 Incandescent Bulbs 2857.3.2 Halogen Lamps 2887.3.3 Electrical Arc Lamps / Discharge Lamps 2887.3.4 Xenon Lamps 2907.3.5 Mercury-Xenon Lamps 2917.3.6 High-pressure Mercury Lamps 2917.4 Diodes 2927.4.1 Types of Light Emitting Diodes 2927.4.2 Organic Light Emitting Diodes 2947.4.3 Spectra of Light Emitting Diodes 2957.4.4 Emission Characteristic of LEDs 2977.4.5 White Light Emitting Diodes 2997.5 Laser Light Sources 3007.5.1 Overview 3007.5.2 Comparison of Lasers with Classical Light Sources7.5.3 Semiconductor Laser 3037.5.4 Gas Laser 3097.5.5 Solid State Laser 3097.5.6 Excimer Laser 3117.6 Model Descriptions of Radiation Sources 3147.6.1 Models of Light Sources 3147.6.2 Characterization of the Spatial Emission 3157.6.3 Spectral Characteristic 3187.6.4 Raytracing Model Description of Sources 3197.7 Literature 321

8 Sensor Technology and Signal Processing 323

8.1 Introduction 3258.1.1 Signal Chain 3258.1.2 Information Transfer in Optics 3258.1.3 Adjustment of the Beam 3278.1.4 Information Gain 328

8.1.5 Spatial Discretization and Resolution 3318.1.6 Discretization of the Signal Strength 3338.2 Sensor Characteristics 3358.2.1 General Remarks 3358.2.2 Signal-to-noise Ratio 3368.2.3 Precision of a Sensor 3378.2.4 Dynamic Range 3398.2.5 Time Behavior 340

300

8.2.68.2.78.38.3.18.3.28.3.38.3.48.3.58.48.4.18.4.28.4.38.4.48.58.5.18.5.28.5.38.5.48.5.58.68.6.18.6.28.6.38.6.48.78.7.18.7.28.8

99.19.29.2.19.2.29.2.39.2.49.39.3.19.3.29.3.39.3.49.3.59.49.4.19.4.2

Directional Sensitivity 342Detection of Color Signals 343Special Types of Sensor 345Classification 345Photoconductive Detector 346CCD Arrays 348Avalanche Photodiodes 354Photographic Film 354Sampling 357Fourier Transformation 357Sampling Theorem 358Sampling of a Band-limited Signal 362Detector Sampling 362Signal Processing 364General Remarks 364Point Operations 364Nearest-neighbor Operations 365Fourier Filter 365Savitzky-Golay Filter 368Noise 370Introduction 370Types of Noise 372Frequency-Dependence of the Noise 374Correction of the Background Noise 375Special Methods of Detection 376Heterodyne Detection 376Lock-in Principle 377Literature 378

Theory of Color Vision 379Introduction 380Color Vision of the Human Eye 380Spectral Sensitivity of the Eye 380Transmission of the Eye 383Bezold Effect and Restimulation 385Physiological Chromatic Sensation 386Phenomenologcal Theory of Color Vision 387Grassmanns Basic Laws 387Light and Body Color 388Additive Color Mixture 390Three-color Mixture 390Maxwells Color Triangle 391Colorimetry 394General Remarks 394Spectral Matching Functions 394

Contents XIII

XIV I Contents

9.4.3 Conversion Matrices 3989.4.4 Standard Spectral Value Functions of the CIE Standard System 3999.4.5 Normalized Color Coordinates 4009.5 Color Triangle 4029.5.1 Basic Properties 4029.5.2 Complementary Colors 4039.5.3 Color Saturation 4059.5.4 Helmholtz Color Values 4089.5.5 Mixture of Colors in the Color Triangle 4099.5.6 Classical Color Terms 4109.5.7 Color Temperature 4129.5.8 Brightness 4149.5.9 Color Body 4159.5.10 Color Differences 4169.6 Alternative Basic Systems 4179.6.1 RGB Primary Colors 4179.6.2 IHS Color Representation According to Munsell 4219.6.3 u' v´-Chromatiriry Chart 4239.7 Literature 424

10 Optical Systems 425

10.1 Special Properties of Lenses 42610.1.1 Bending of Lenses 42610.1.2 Position Parameter 42910.1.3 Ideal Lens 43010.1.4 Volume of a Lens 43110.2 Special Rays in Optical Systems 43210.2.1 Numerical Aperture and Stop Number 43210.2.2 Canonical Coordinates 43410.2.3 Bundles and Ray Fans 43810.2.4 Special Rays 43910.2.5 Principal Planes 44110.3 Pupils 44210.3.1 Diaphragms 44210.3.2 Definition of Pupils 44410.3.3 Spherical Pupils 44610.3.4 Pupil Sampling 44810.3.5 Vignetting 45210.3.6 Variable Pupil Position 45410.3.7 Special Stop Positions 45510.3.8 Interlinked Bundles 45810.3.9 Perspective 45810.4 Delano Diagram 46310.4.1 Definition 46310.4.2 Properties of the Delano Diagram 464

'.

•

10.4.310.4.410.510.5.110.5.210.5.310.5.410.6

1111.111.211.311.3.111.3.211.3.311.3.411.3.511.411.511.5.111.5.211.5.311.5.411.611.6.111.6.211.6.311.711.811.8.111.8.211.911.1011.1111.1211.13

1212.112.1.112.1.212.1.312.1.412.1.5

Examples 468Vignetting 472Special Aspects 474Curved Objects 474Scheimpflug Imaging 475Anamorphotic Imaging 479Introduction of thick lenses 480Literature 483

Aberrations 485

General Considerations 486Description of Aberrations 487Ray Aberrations 490Longitudinal Aberrations 490Transverse Aberrations 491Spot Diagrams 492Caustics 493Seidel Aberrations 494The Sine Condition 495Wave Aberrations 497Definition 497Tilt 499Defocus 500Zernike Polynomials 501Spherical Aberration 506Introduction 506Aplanatic Surfaces 507Aplanatic Lenses 509Astigmatism 510Field Curvature 511Image Surfaces 511Petzval Theorem 523Coma 524Distortion 526Chromatic Longitudinal Aberrations 528Chromatic Transverse Aberrations 520Literature 522

Wave Optics 523

Basic Principles 524Wave Equation 524TEA and LPIA Approximations for Thin Components 525Kirchhoff Integral 527Fresnel Approximation 530Fraunhofer Integral 532

Contents XV

XVI Contents

12.1.6 Fresnel Number 53212.1.7 Diffraction of an Aperture 53312.1.8 Paraxial Approximation 53512.1.9 Model Approximations for the Description of Optical Systems12.1.10 Spot Model Calculations 53812.2 Point-spread Function 53912.2.1 Ideal Point Image 53912.2.2 Scaling Factors 54212.2.3 Transverse Airy Distribution 54312.2.4 Axial Distribution 54512.2.5 Point-spread Function and Aberrations 54612.3 Fourier Theory of Image Formation 54812.3.1 Spatial Frequency and Expansion in Plane Waves 54812.3.2 Plane Wave Representation 54912.3.3 Phase Effect of a Lens 55012.3.4 Resolution Model 55112.3.5 4-f-Fourier Model 55412.3.6 Complete 6-f-Fourier Model 55712.3.7 Coherent Image Formation 55912.3.8 Incoherent Image Formation 56012.4 Transfer Functions 56212.4.1 Definition 56212.4.2 OTF of Ideal Systems 56412.4.3 Contrast Transfer 56512.4.4 Sagittal and Tangential Structures 56612.5 Literature 568

13 Piano-optical Components

13.1 Plane-parallel plates 57113.1.1 Beam Displacement 57113.1.2 Aberrations 57213.1.3 Plane-parallel Plate in a Convergent Beam 57413.1.4 Reflections at Plane-parallel Plates 57613.2 Dispersion Prisms 57613.2.1 General Considerations 57713.2.2 Dispersion by a Prism 57813.2.3 Thin-prism Approximation 57913.2.4 Symmetric Prisms 58013.2.5 Prism Magnification 58013.2.6 Astigmatism of a Wedge Prism 58213.2.7 Curved Spectral Lines Produced by a Prism 58213.2.8 Variable-angle Prisms 58313.2.9 Achromatic Prism Pairs 58413.2.10 Direct-vision Prisms 58513.2.11 Double Amici Prisms 586

536

13.2.1213.2.1313.2.1413.313.3.113.3.213.3.313.3.413.3.513.3.613.3.713.3.813.413.4.113.4.213.4.313.513.5.113.5.213.5.313.5.413.5.513.613.6.113.6.213.6.313.6.413.6.513.7

1414.114.214.2.114.2.214.2.314.2.414.2.514.2.614.314.3.114.3.214.3.314.3.414.4

Wernicke-type Direct-vision Prisms 587Wadsworth Prism Mounting 588Fery Prisms 589Reflection Prisms 590Function of Reflection Prisms 590The Tunnel Diagram 591Dimensioning of Prisms 592Total Internal Reflection 595Image Reorientation 596Matrix Calculations for Reflection Prisms 599Roof Prisms 601Classification of the Reflection Prisms 604Construction Designs for Reflection Prisms 605General Consideration 605Single Prism Types 606Composite Prisms 624Prism Systems 630Sliding Prism Pair 630Scanning by Rotating Wedge Pair 632Anamorphotic Prism Pair 632Double Dove Prism 633Beam Splitters 635Filters 639General Principles of Operation 639Characterization of Filters 640Filter Types 643Interference Filters 644Absorption Filters 645Literature 645

Gratings 647Diffraction by a Slit 648Diffraction Gratings 651General Considerations 651Interference Function 652Diffraction by a Grating 655Width of the Diffraction Orders 658Grating Dispersion 659Grating Efficiency 662Blazed Gratings 663The Concept of Blazing 663Particular Case of Normal Incidence 666Littrow Arrangement 667Real Blazed Gratings 668Fourier Theory of the Grating Diffraction 669

Contents XVII

XVIII Contents

14.4.114.4.214.4.314.4.414.514.5.114.5.214.5.314.614.6.114.6.214.6.314.6.414.6.514.6.614.714.814.8.114.8.214.9

15

15.115.1.115.1.215.1.315.1.415.1.515.215.2.115.2.215.2.315.2.415.315.3.115.415.515.5.115.5.215.615.6.115.6.215.6.315.715.7.1

Ewald Model of the Grating Diffraction 669Rectangular Amplitude Grating 671Grating Structure Function 672Fourier Optics of the Blazed Grating 672Transmission Gratings 673Blaze Condition 673Carpenter Prisms 674Diffractive Lenses 675Types of Grating 677Classification 677Sine Phase Gratings 679Laminary Reflection Gratings 680Echelette Gratings 681Ronchi Gratings 682Damman Gratings 684Gratings in Image Formation Systems 686Diffraction by a Grating in the General Case 688Non-paraxial Diffraction by a Grating 688Conical Diffraction by a Grating 690Literature 692

Special Components 693Aspherical Devices 695Introduction 695Conic Sections 695Polynomial Aspherical Surfaces 700Conical Surfaces 703Parameters for Aspherical Surfaces 704Gradient-index Lenses 705Parabolic Lateral Gradient-index 705Axial Linear Gradient-index Media 707Gradium Media 708Spherically Corrected Gradient-index Lenses 711Diffusing Disks 714Description of the Effect of a Diffusing Disk 714Cylinder Lenses 717Simple Cylinder Lenses 717Rotatable Pair of Cylinder Lenses 71 7Alvarez Lens 728Dynamic Light Modulators 719General Remarks 719Digital Mirror Device 720Liquid Crystal Devices 722Fresnel Lenses 729Principle 729

15.7.215.7.315.7.415.7.515.7.615.7.715.815.8.115.8.215.8.315.915.9.115.9.215.9.315.9.415.10

1616.116.216.2.116.2.216.316.3.116.3.216.3.316.416.4.116.4.216.4.316.516.5.116.5.216.616.6.116.6.216.6.316.716.7.116.7.216.7.316.7.416.816.8.116.8.2

Basic Equations 730Total Internal Reflection 731Aberrations 732Stray Light 733Applications 734Radiometric Aspects 735Light Pipes 737Light-guiding Rods 737Slab Homogenizer 738Tapers 747Axicons 751Refractive Axicons 751Refractive Axicon with Lens 752Reflective Axicons 753Axicon for an Axial Profile Formation 755Literature 757

Optical Measurement and Testing Techniques 759

Overview 761Measurement of the Focal Length 761Measurement with a Collimator 761Gauss Method 762Measurement of Angles 763Autocollimator 763Interferometric Test of Prism Angles 764Alignment Telescope 768Centering 769Measuring Centering in Reflection 769Measuring Centering in Transmission 770Interference Method 771Measuring the Index of Refraction 773Refractometer 773Toeplers Schlieren Method 775Surface-shape Measurement 776Triangulation 776Fringe Projection 776Optical Coherence Tomography 778Testing of Surface Radii and Shapes 780Newton Interferometer 780Twyman-Green Interferometer 782Fizeau Interferometer 784Evaluation of the Fringes 785Measuring Wavefronts 786Hartmann-Shack Wavefront Sensor 786Hartmann Test 790

Contents XIX

XX. Contents

16.9 Measurement of the Optical Transfer Function 79316.9.1 General Considerations 79316.9.2 Measurement by Edge Imaging 79416.9.3 Measurement by Line Imaging 79616.9.4 Measurement of Grating Structures 79716.10 Beam-quality Measurement 79916.10.1 Overview 79916.10.2 Knife-edge Method 80016.10.3 Scanning-slit Method 80216.10.4 Ronchi Test 80316.11 Coherence Measurement 80716.11.1 Youngs Experiment 80716.12 Polarization Measurement 80816.13 Stray-light Measurement 81016.14 Color Measurement 81116.14.1 Overview 81116.14.2 Spectral Photometry 81216.15 Literature 813

Index 815