Handbook of Optical Systems

Transcription

1 Handbook of Optical Systems Edited by Herbert Cross Volume 1: Fundamentals of Technical Optics Herbert Gross WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA

2 VII Contents Preface V Introduction 1 Paraxial Imaging 5 General Remarks 7 Paraxial Approximation 7 Linear Collineation 9 Image Locations 10 Magnification 14 Lens Equation 25 Newtons Equation 19 Three-dimensional Systems 20 Single Surface 21 Refracting Plane Surface 21 Refractive Spherical Surface 22 Mirror Surface 23 Single Lens 24 Parameters of a Lens 24 Cardinal Elements 25 Thin Lens 28 Thick Lens 29 Graphical Image Construction 32 Multiple-component Systems 33 System Consisting of Two Thin Components 33 Systems Consisting of Several Thin Lenses 36 Invariants 36 Helmholtz-Lagrange Invariant 36 Abbe Invariant Q 39 Paraxial Invariant 39 Further Invariants 40 Matrix Form of the Helmholtz Invariant 40 Matrix Calculus 41 Handbook of Optical Systems: Vol. 1. Fundamentals of Technical Optics. H. Gross Copyright 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN:

3 VIII Contents Paraxial ABCD Matrices 41 Properties of the Matrices 44 Matrices of Simple Components 45 Finite Imaging with an Afocal System 48 Decompositions of an ABCD Matrix 49 Matrices Describing a More General Geometry 51 Two-dimensional 3X3 Matrices 51 Centered 4X4 Matrices 54 General 5x5 Matrices 58 Literature 59 Interfaces 62 Basics 62 Boundary Conditions 62 The Law of Refraction 63 The Law of Reflection 66 The Fresnel Equations 67 Definition of the Amplitude Coefficients 67 Reflection 67 Transmission 69 Properties of the Fresnel Equations 69 Stokes Relations 72 Azimuthal Angle 74 Reflectivity and Transmirtivity 75 Phase Changes 79 Description of the Refraction in the k-space 80 Reflection Losses in Optical Systems 82 Polarization Effects at Interfaces 84 Brewster Angle 84 Degree of Polarization 86 Evanescent Waves 88 Total Internal Reflection 88 Evanescent Surface Waves 92 Damped Total Internal Reflection 94 Frustrated Total Internal Reflection 95 Non-geometrical Effects at Reflection 96 The Goos-Haenchen Effect 96 Total Internal Reflection of a Gaussian Beam 100 Absorbing Media 102 Complex Refractive Index 102 Lambert-Beer Law 103 Reflection at an Absorbing Medium 104 Metals 105 Reflection at Metals 105 Literature 209

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

5 X Contents Water 162 Technical Liquids 163 Immersion Oils 166 Optical Cements 267 Metals 168 Optical Parameters 168 Reflectivity of Metallic Mirrors 169 Literature 171 Raytracing 173 The Meaning of Raytracing 174 Raytracing Scheme 174 Raytracing Formula Sets 178 General Remarks 178 Paraxial y-u-method 178 Paraxial s-h- Method 179 Meridional S-U-Method 180 Meridional Q-U-Method 182 Set of Vector Formulas 182 Iterative Calculation of the Intersection Point for Aspherical Surfaces 186 Raytracing in Optical Systems 189 Description of the Geometry 189 Types of Surface 194 Particular Properties 206 Output Quantities 207 Errors 208 Apodization 208 Polarization Raytracing 209 Special Components 220 Ideal Lens 220 Raytracing in GRIN media 211 Raytracing for Diffractive Elements 215 Knife-edge Diffraction Model in Raytracing 219 Differential Rays 220 General Remarks 220 Coddington Equations 220 General Differential Rays 222 Ray Tubes 223 Non-sequential Raytracing 224 General Remarks 224 Monte-Carlo Raytracing 226 Literature 227

6 Contents XI Radiometry 229 Introduction 230 General Remarks 230 Definition of the Radiometric Quantities 230 Photometric Quantities 232 Radiometric and Photometric Quantities 233 Solid Angle 233 Differential Flux 235 Fundamental Law of Radiometry 235 Projection of the Irradiance 236 Irradiance 237 Spectral Densities of Quantities 237 Energy, Power and Photons 238 Lambertian Radiator 239 Classical Lambertian Radiator 239 General Lambertian Radiator 240 Radiation Transfer 241 General Remarks 241 Point Source of Light 242 Radiation Transfer between Surfaces 244 Numerical Radiation Transfer 247 Radiometry of Optical Systems 248 Optical System 248 Radiation Transport with Interaction 249 Aplanatic Systems 250 Natural Vignetting 252 Radiometry in Real Optical Systems 259 Ray Tube Model 260 Description of Radiation Transport in the Phase Space 263 Helmholtz - Lagrange Invariant 263 Phase Space Coordinates 264 Phase Space Representation of Radiation Transport 265 Literature 267 Light Sources 269 Introduction 271 Classification 271 Efficiency 271 Electromagnetic Spectrum 273 Standard Light Sources 275 Daylight and Sunlight 276 Thermal Radiators 278 Plancks Formula 278 Optical Efficiency 281 Radiation Temperature 282

7 XII Contents Wiens Displacement Law Stefan-Boltzmann Law Rayleigh-Jeans Radiation Formula Wiens Law of Radiation Classical Lamps Incandescent Bulbs Halogen Lamps Electrical Arc Lamps / Discharge Lamps Xenon Lamps Mercury-Xenon Lamps High-pressure Mercury Lamps Diodes Types of Light Emitting Diodes Organic Light Emitting Diodes Spectra of Light Emitting Diodes Emission Characteristic of LEDs White Light Emitting Diodes Laser Light Sources Overview Comparison of Lasers with Classical Light Sources Semiconductor Laser Gas Laser Solid State Laser Excimer Laser Model Descriptions of Radiation Sources Models of Light Sources Characterization of the Spatial Emission Spectral Characteristic Raytracing Model Description of Sources Literature Sensor Technology and Signal Processing Introduction Signal Chain Information Transfer in Optics Adjustment of the Beam Information Gain Spatial Discretization and Resolution Discretization of the Signal Strength Sensor Characteristics General Remarks Signal-to-noise Ratio Precision of a Sensor Dynamic Range Time Behavior 340

8 Contents XIII Directional Sensitivity 342 Detection of Color Signals 343 Special Types of Sensor 345 Classification 345 Photoconductive Detector 346 CCD Arrays 348 Avalanche Photodiodes 354 Photographic Film 354 Sampling 357 Fourier Transformation 357 Sampling Theorem 358 Sampling of a Band-limited Signal 362 Detector Sampling 362 Signal Processing 364 General Remarks 364 Point Operations 364 Nearest-neighbor Operations 365 Fourier Filter 365 Savitzky-Golay Filter 368 Noise 370 Introduction 370 Types of Noise 372 Frequency-Dependence of the Noise 374 Correction of the Background Noise 375 Special Methods of Detection 376 Heterodyne Detection 376 Lock-in Principle 377 Literature 378 Theory of Color Vision 379 Introduction 380 Color Vision of the Human Eye 380 Spectral Sensitivity of the Eye 380 Transmission of the Eye 383 Bezold Effect and Restimulation 385 Physiological Chromatic Sensation 386 Phenomenologcal Theory of Color Vision 387 Grassmanns Basic Laws 387 Light and Body Color 388 Additive Color Mixture 390 Three-color Mixture 390 Maxwells Color Triangle 391 Colorimetry 394 General Remarks 394 Spectral Matching Functions 394

9 XIV I Contents Conversion Matrices Standard Spectral Value Functions of the CIE Standard System Normalized Color Coordinates Color Triangle Basic Properties Complementary Colors Color Saturation Helmholtz Color Values Mixture of Colors in the Color Triangle Classical Color Terms Color Temperature Brightness Color Body Color Differences Alternative Basic Systems RGB Primary Colors IHS Color Representation According to Munsell u' v -Chromatiriry Chart Literature Optical Systems Special Properties of Lenses Bending of Lenses Position Parameter Ideal Lens Volume of a Lens Special Rays in Optical Systems Numerical Aperture and Stop Number Canonical Coordinates Bundles and Ray Fans Special Rays Principal Planes Pupils Diaphragms Definition of Pupils Spherical Pupils Pupil Sampling Vignetting Variable Pupil Position Special Stop Positions Interlinked Bundles Perspective Delano Diagram Definition Properties of the Delano Diagram 464

10 Contents XV Examples 468 Vignetting 472 Special Aspects 474 Curved Objects 474 Scheimpflug Imaging 475 Anamorphotic Imaging 479 Introduction of thick lenses 480 Literature 483 Aberrations 485 General Considerations 486 Description of Aberrations 487 Ray Aberrations 490 Longitudinal Aberrations 490 Transverse Aberrations 491 Spot Diagrams 492 Caustics 493 Seidel Aberrations 494 The Sine Condition 495 Wave Aberrations 497 Definition 497 Tilt 499 Defocus 500 Zernike Polynomials 501 Spherical Aberration 506 Introduction 506 Aplanatic Surfaces 507 Aplanatic Lenses 509 Astigmatism 510 Field Curvature 511 Image Surfaces 511 Petzval Theorem 523 Coma 524 Distortion 526 Chromatic Longitudinal Aberrations 528 Chromatic Transverse Aberrations 520 Literature 522 Wave Optics 523 Basic Principles 524 Wave Equation 524 TEA and LPIA Approximations for Thin Components 525 Kirchhoff Integral 527 Fresnel Approximation 530 Fraunhofer Integral 532

11 XVI Contents Fresnel Number Diffraction of an Aperture Paraxial Approximation Model Approximations for the Description of Optical Systems Spot Model Calculations Point-spread Function Ideal Point Image Scaling Factors Transverse Airy Distribution Axial Distribution Point-spread Function and Aberrations Fourier Theory of Image Formation Spatial Frequency and Expansion in Plane Waves Plane Wave Representation Phase Effect of a Lens Resolution Model f-Fourier Model Complete 6-f-Fourier Model Coherent Image Formation Incoherent Image Formation Transfer Functions Definition OTF of Ideal Systems Contrast Transfer Sagittal and Tangential Structures Literature Piano-optical Components 13.1 Plane-parallel plates Beam Displacement Aberrations Plane-parallel Plate in a Convergent Beam Reflections at Plane-parallel Plates Dispersion Prisms General Considerations Dispersion by a Prism Thin-prism Approximation Symmetric Prisms Prism Magnification Astigmatism of a Wedge Prism Curved Spectral Lines Produced by a Prism Variable-angle Prisms Achromatic Prism Pairs Direct-vision Prisms Double Amici Prisms 586

12 Contents XVII Wernicke-type Direct-vision Prisms 587 Wadsworth Prism Mounting 588 Fery Prisms 589 Reflection Prisms 590 Function of Reflection Prisms 590 The Tunnel Diagram 591 Dimensioning of Prisms 592 Total Internal Reflection 595 Image Reorientation 596 Matrix Calculations for Reflection Prisms 599 Roof Prisms 601 Classification of the Reflection Prisms 604 Construction Designs for Reflection Prisms 605 General Consideration 605 Single Prism Types 606 Composite Prisms 624 Prism Systems 630 Sliding Prism Pair 630 Scanning by Rotating Wedge Pair 632 Anamorphotic Prism Pair 632 Double Dove Prism 633 Beam Splitters 635 Filters 639 General Principles of Operation 639 Characterization of Filters 640 Filter Types 643 Interference Filters 644 Absorption Filters 645 Literature 645 Gratings 647 Diffraction by a Slit 648 Diffraction Gratings 651 General Considerations 651 Interference Function 652 Diffraction by a Grating 655 Width of the Diffraction Orders 658 Grating Dispersion 659 Grating Efficiency 662 Blazed Gratings 663 The Concept of Blazing 663 Particular Case of Normal Incidence 666 Littrow Arrangement 667 Real Blazed Gratings 668 Fourier Theory of the Grating Diffraction 669

13 XVIII Contents Ewald Model of the Grating Diffraction 669 Rectangular Amplitude Grating 671 Grating Structure Function 672 Fourier Optics of the Blazed Grating 672 Transmission Gratings 673 Blaze Condition 673 Carpenter Prisms 674 Diffractive Lenses 675 Types of Grating 677 Classification 677 Sine Phase Gratings 679 Laminary Reflection Gratings 680 Echelette Gratings 681 Ronchi Gratings 682 Damman Gratings 684 Gratings in Image Formation Systems 686 Diffraction by a Grating in the General Case 688 Non-paraxial Diffraction by a Grating 688 Conical Diffraction by a Grating 690 Literature 692 Special Components 693 Aspherical Devices 695 Introduction 695 Conic Sections 695 Polynomial Aspherical Surfaces 700 Conical Surfaces 703 Parameters for Aspherical Surfaces 704 Gradient-index Lenses 705 Parabolic Lateral Gradient-index 705 Axial Linear Gradient-index Media 707 Gradium Media 708 Spherically Corrected Gradient-index Lenses 711 Diffusing Disks 714 Description of the Effect of a Diffusing Disk 714 Cylinder Lenses 717 Simple Cylinder Lenses 717 Rotatable Pair of Cylinder Lenses 71 7 Alvarez Lens 728 Dynamic Light Modulators 719 General Remarks 719 Digital Mirror Device 720 Liquid Crystal Devices 722 Fresnel Lenses 729 Principle 729

14 Contents XIX Basic Equations 730 Total Internal Reflection 731 Aberrations 732 Stray Light 733 Applications 734 Radiometric Aspects 735 Light Pipes 737 Light-guiding Rods 737 Slab Homogenizer 738 Tapers 747 Axicons 751 Refractive Axicons 751 Refractive Axicon with Lens 752 Reflective Axicons 753 Axicon for an Axial Profile Formation 755 Literature 757 Optical Measurement and Testing Techniques 759 Overview 761 Measurement of the Focal Length 761 Measurement with a Collimator 761 Gauss Method 762 Measurement of Angles 763 Autocollimator 763 Interferometric Test of Prism Angles 764 Alignment Telescope 768 Centering 769 Measuring Centering in Reflection 769 Measuring Centering in Transmission 770 Interference Method 771 Measuring the Index of Refraction 773 Refractometer 773 Toeplers Schlieren Method 775 Surface-shape Measurement 776 Triangulation 776 Fringe Projection 776 Optical Coherence Tomography 778 Testing of Surface Radii and Shapes 780 Newton Interferometer 780 Twyman-Green Interferometer 782 Fizeau Interferometer 784 Evaluation of the Fringes 785 Measuring Wavefronts 786 Hartmann-Shack Wavefront Sensor 786 Hartmann Test 790

15 XX. Contents 16.9 Measurement of the Optical Transfer Function General Considerations Measurement by Edge Imaging Measurement by Line Imaging Measurement of Grating Structures Beam-quality Measurement Overview Knife-edge Method Scanning-slit Method Ronchi Test Coherence Measurement Youngs Experiment Polarization Measurement Stray-light Measurement Color Measurement Overview Spectral Photometry Literature 813 Index 815