Lens Design for Imaging
- Nyhet
Volume 1: Fundamentals of Optical Systems
Inbunden, Engelska, 2025
Av Herbert Gross, Germany) Gross, Herbert (Carl Zeiss AG, Oberkochen
2 319 kr
Kommande
Produktinformation
- Utgivningsdatum2025-12-10
- Mått216 x 276 x undefined mm
- FormatInbunden
- SpråkEngelska
- SerieLens Design
- Antal sidor640
- FörlagWiley-VCH Verlag GmbH
- ISBN9783527414567
Tillhör följande kategorier
- Preface of the Book Series xxiPreface of the First Volume xxiiiAcknowledgements xxv1 Introduction 11.1 Modelling and Goal of Lens Design 21.2 Optical System Types and Aperture Field Classification 31.2.1 Selected Classes of Systems 7References 102 Optical Materials 132.1 Introduction 132.2 Dispersion 142.2.1 Definition 142.2.2 Wavelengths 152.2.3 Abbe Number 162.2.4 Dispersion of Crown and Flint Glasses 172.2.5 Glass Diagram 182.2.6 Interpolation of the Refractive Index 182.2.7 Relative Partial Dispersion 202.2.7.1 Definition 202.2.7.2 Line of Normal Dispersion 222.2.7.3 Anomalous Partial Dispersion 252.2.7.4 Hoogland Diagram 262.2.7.5 The Anomalous Dispersion Representation of Münz 262.2.8 Generalized Mathematical Descriptions of Dispersion 292.2.8.1 Introduction 292.2.8.2 Derivative Based Dispersion Description 312.2.8.3 Buchdahls Chromatical Coordinates 322.2.8.4 Adaptive Dispersion Formula of Sasian 332.2.9 Miscellaneous 352.2.9.1 Dispersion of Diffractive Surfaces 352.2.9.2 Dispersion of Gradient-Index Materials 362.3 Group Velocity Dispersion and Short Pulses 372.3.1 Introduction 372.3.2 Dispersion Coefficients 382.3.3 Pulse Changes due to Dispersion 382.3.4 Pulse Dispersion Data of Glasses 392.3.4.1 Introduction 392.3.4.2 Numerical Calculation of Index Derivatives 392.3.4.3 GVD Properties of Glasses 402.4 Absorption and Transmission 422.4.1 Complex Index of Refraction 422.4.2 Lambert–Beers Law 442.4.3 Transmission of a Component 442.4.4 Transmission of Glasses 452.5 Thermal Properties 462.5.1 Thermal Expansion 462.5.2 Index Change 472.5.3 Thermo-Optical Coefficient 482.5.3.1 Introduction 482.5.3.2 Temperature-Dependence of Dispersion 492.6 Other Optical Materials 492.6.1 Crystal Materials for IR and UV 492.6.2 Plastics 532.6.3 Water 542.6.4 Technical Liquids 542.6.5 Immersion Liquids 562.6.6 Optical Cements 57References 573 Geometrical Optics 613.1 Introduction 613.2 Law of Refraction 613.2.1 Introduction 613.2.2 Ray Bending 623.2.3 Description of Refraction in the k-Space 643.3 Fresnel Formulas 653.3.1 Amplitude Coefficients 653.3.2 Reflectivity and Transmittivity 673.3.3 Transmission of Systems 683.3.4 Total Internal Reflection 703.3.5 Reflection at Metals 733.4 Raytrace 743.4.1 Introduction 743.4.2 Paraxial Formulas 763.4.3 Meridional Q–U Method 773.4.4 Three-dimensional Case 783.4.5 Pitfalls and Special Cases 803.4.6 Modelling of Mirrors 813.4.7 Ray Intersection with Surfaces of Higher Order 823.4.8 Gradient Index Media 833.4.9 Differential Raytrace, Parabasal Rays and Ray Tubes 843.4.10 Diffractive Surfaces 863.4.10.1 Introduction 863.4.10.2 Plane linear gratings 873.4.10.3 Generalized Diffractive Surfaces 883.4.11 Non-Sequential Raytrace 883.4.12 Special Ray Types 893.4.13 Ray Aiming 913.4.13.1 Introduction 913.4.13.2 Paraxial Aiming Approach 943.4.13.3 Real Ray Aiming 953.4.13.4 General Formulation of Greynolds 973.4.13.5 Examples 973.4.14 Complex Rays 983.4.14.1 Introduction 983.4.14.2 Gaussian Beams with Complex Source Point 993.4.14.3 Tracing Complex Rays 1003.5 Paraxial Approximation 1013.5.1 Introduction 1013.5.2 Abbe Invariant 1043.5.2.1 Paraxial Definition 1043.5.2.2 Generalized Abbe Invariant 1053.5.3 Superposition of Rays 1053.5.4 Generalized Paraxiality 1063.5.5 Collinear Transform 1073.6 Matrix Calculus 1083.6.1 Introduction 1083.6.2 Properties of the Matrices 1103.6.3 Matrices of Simple Components 1113.6.4 Decompositions of an ABCD Matrix 1123.6.4.1 Iwasawa Decomposition 1123.6.4.2 Alternative Decompositions 1133.6.5 Matrices for Generalized Geometries 1153.6.5.1 Two-dimensional 3 × 3 Matrices for Plane-Symmetric Systems 1153.6.5.2 Centered 4 × 4 Matrices 1163.6.5.3 Special 4 × 4 Matrices 1173.6.5.4 Decomposition of a 4 ×4 Matrix 1183.6.5.5 General 5 × 5 Matrices 1193.7 Helmholtz–Lagrange Invariant 1203.7.1 Introduction 1203.7.2 Lagrange Invariant for Arbitrary z-Positions 1223.7.3 Generalized Etendue Definitions 1223.7.4 Smith’s Cosine Invariant 1243.8 Delano Diagram 1243.8.1 Definition 1243.8.2 Properties of the Delano Diagram 1253.8.3 Vignetting 1273.8.4 Examples 1283.9 Gaussian Brackets 1313.9.1 Introduction 1313.9.2 Alternative Representations 1323.9.3 Relation to ABCD Formalism 1323.9.4 Applications 1333.9.4.1 Tolerancing 1333.9.4.2 Achromatization 1333.9.4.3 Zoom Systems 133References 1344 Optical Components 1374.1 Overview 1374.2 Single Refractive Spherical Surface 1374.3 Plane Plates 1384.3.1 Introduction 1384.3.2 Perpendicular Plates 1394.3.2.1 Beam Displacement 1394.3.2.2 Aberrations 1404.3.3 Tilted Plates 1404.3.4 Non-Orthogonal Prisms 1414.3.5 Plane-parallel Plate in a Convergent Beam 1414.4 Lenses 1434.4.1 Notations 1434.4.2 Focal Length 1444.4.3 Principal Planes and Surfaces 1464.4.4 Lens Shape and Bending 1474.4.5 Generalized Bending 1514.4.6 Modified Bending Definition 1524.4.7 Thick Lenses 1524.4.8 The Ideal Lens Dilemma 1544.5 Mirrors 1574.6 Aspheres 1584.6.1 Introduction 1584.6.2 Conic Surfaces 1594.6.2.1 Introduction 1594.6.2.2 Parabolic Mirrors 1614.6.2.3 Ellipsoidal Mirror 1624.6.2.4 Hyperboloidal Mirror 1634.6.2.5 Grazing Incidence Telescopes 1634.6.3 Cartesian Ovaloids 1644.6.3.1 Introduction 1644.6.3.2 Special Case Infinity 1654.6.3.3 Special Case Aplanatism 1674.6.4 Asphere with Polynomial Expansion 1674.6.4.1 Traditional Taylor Expansion 1674.6.4.2 Strong Forbes Aspheres 1684.6.4.3 Mild Forbes Aspheres 1704.6.4.4 Superconical Surfaces 1714.7 Freeform Surfaces 1724.7.1 Introduction 1724.7.2 Basic Shape 1744.7.3 Boundary and Projection Factor 1754.7.4 Polynomial Functions 1764.7.4.1 Introduction 1764.7.4.2 Monomials 1764.7.4.3 Zernike Polynomials 1764.7.4.4 Chebyshev Polynomials 1784.7.4.5 Legendre Polynomials 1784.7.4.6 Forbes Freeform Surfaces 1784.7.5 Functional Systems with Local Support 1794.7.5.1 Introduction 1794.7.5.2 Radial Basis Functions 1794.7.5.3 Splines 1824.7.6 Technological Constraints and Manufacturability 1854.8 Special Component Types 1854.8.1 Cylindrical Lenses 1854.8.1.1 Introduction 1854.8.1.2 Aspherical Cylindrical Lenses 1864.8.1.3 Toroidal Lenses 1884.8.1.4 Toroidal Ring Lens 1884.8.1.5 Combinations of Cylindrical Lenses 1894.8.2 Fresnel Lenses 1914.8.2.1 Introduction 1914.8.2.2 Basic Equations 1934.8.2.3 Properties of Fresnel Lenses 1934.8.3 Axicons 1944.8.3.1 Geometrical Concept 1944.8.3.2 Physical Description 1954.8.4 Variable Components 1974.8.4.1 Introduction 1974.8.4.2 Electrowetting Liquid Lenses 1984.8.4.3 Electrophoretic Liquid Lenses 1994.8.4.4 Hydraulic Membrane Liquid Lenses 2004.8.4.5 Liquid Crystal Lenses 2004.8.4.6 Deformable Mirrors 2004.8.4.7 Alvarez Lenses 2024.8.5 Lenslet Arrays 2024.8.5.1 Introduction 2034.8.5.2 Special Lens Arrays 2034.8.5.3 Matrix Calculation of Arrays 2044.8.5.4 Applications 2054.8.6 Digital Mirror Device 2084.9 Gradient Index Lenses 2104.9.1 Introduction 2104.9.2 Quadratic Radial Index Lenses 2114.9.3 Axial Gradient Index Lenses 2124.9.4 Stigmatic Imaging Gradient Index-Lenses 2124.10 Prisms 2154.10.1 Reflecting Prisms 2154.10.2 Roof Prisms 2164.10.2.1 Description of the Geometry 2164.10.2.2 Dimensioning of the Size 2174.10.2.3 Image Formation Problems Related to Roof Edges 2174.10.3 Dispersion Prisms 2184.10.3.1 Introduction 2184.10.3.2 Achromatic Prism Pairs 2194.10.3.3 Anamorphic Prism Pair 2204.10.3.4 Fery Prisms 2214.10.4 Risley Prisms 2214.11 Diffractive Elements 2234.11.1 Linear Gratings 2234.11.1.1 Introduction 2234.11.1.2 Blazed Grating 2244.11.2 General Diffractive Elements 2264.11.2.1 Introduction 2264.11.2.2 Discretization and Quantization 2304.11.2.3 Types of DOE 2314.11.2.4 Fresnel Zone Plates 2324.11.2.5 Classical Diffractive Lens 2324.11.2.6 Decomposition into Orders or Zones 2334.11.2.7 Problems of Real Diffractive Elements 2344.11.3 Modelling DOEs by Raytrace 2354.12 Diffusor Plates 2354.12.1 Types of Diffusers 2364.12.2 Properties of Diffusers 2364.12.3 Angle Characteristic 238References 2395 Imaging Systems 2435.1 Introduction 2435.1.1 Mathematical Description of Optical Systems 2435.1.2 System Notations 2435.1.3 System Layout 2445.1.4 Terms of Performance Evaluation 2465.2 Geometrical Imaging 2475.2.1 Introduction 2475.2.2 Lens Makers’ Formula 2485.2.3 Paraxial Formulas 2515.2.4 Imaging Transfer Length 2515.2.5 Principal Planes 2525.2.5.1 Principal Planes of Compound Systems 2525.2.5.2 Principal Planes of Two-Lens Systems 2535.2.6 Multi-Lens Systems 2555.3 Magnification, Field of View, Aperture and Vergence 2575.3.1 Introduction 2575.3.2 Numerical Aperture and F-Number 2575.3.3 Generalized F-number 2595.3.4 Effective Aperture 2595.3.5 Magnification 2595.3.5.1 Finite Systems 2595.3.5.2 Influence of the Pupil Upon the Magnification 2605.3.5.3 Magnification of Afocal Systems 2635.3.5.4 Depth Magnification 2635.3.6 Vergence 2635.4 Pupil 2645.4.1 Introduction 2645.4.2 Pupil Matching in Composed Systems 2665.4.3 Field Lenses 2665.4.4 Pupil and Perspective 2695.5 Vignetting 2695.5.1 Introduction 2695.5.2 Photometric Natural Vignetting 2715.5.3 Artificial Geometrical Vignetting 2725.5.3.1 Introduction 2725.5.3.2 Approximation of the Pupil by an Ellipse 2745.5.3.3 Analytical Approach in the Infinity case 2745.5.3.4 Definition of Vignetting Coefficients 2765.5.3.5 Paraxial Vignetting Calculation 2775.5.3.6 Vignetting for Complicated Pupil Shapes 2795.5.3.7 Vignetting Inside a Gradient index Lens 2795.5.3.8 Vignetting in Phase Space 2795.6 Infinity Cases for Field and Pupil 2815.6.1 Overview 2815.6.2 Afocal Imaging 2825.6.2.1 Introduction 2825.6.2.2 Relay Imaging with Afocals 2835.6.2.3 Applications and Examples 2845.6.3 Telecentricity 2845.6.3.1 Introduction 2845.6.3.2 Examples 2865.7 Imaging with Mirrors 2875.7.1 Introduction 2875.7.2 Centred Two-Mirror Setups 2885.7.3 Obscuration-Free Two-Mirror Systems 2905.7.4 Three-Mirror Setups 2915.8 Imaging Without Rotational Symmetry 2925.8.1 Anamorphic Systems 2925.8.1.1 Introduction 2925.8.1.2 Classes of Anamorphic Systems 2945.8.1.3 Anamorphic Imaging Systems 2955.8.1.4 Refractive Anamorphic Systems 2965.8.1.5 Reflective Anamorphic Systems 2975.8.2 Scheimpflug Imaging 2975.8.2.1 Introduction 2975.8.2.2 Keystone Distortion 2995.8.2.3 Generalized Scheimpflug Setup 2995.8.3 General Skew Imaging 3015.8.4 Image Plane Tilt 3025.8.4.1 Introduction 3025.8.4.2 Plane Symmetric Systems and the Scheimpflug Condition 3025.8.4.3 Tilt of a Skew Spherical Surface 3035.8.4.4 Tilt of a Skew Conical Mirror Surface 3035.8.4.5 Prism Systems 3055.9 Miscellaneous 3055.9.1 Herzberger’s Diapoints 3055.9.2 Canonical Coordinates 3055.9.2.1 Axis Case 3055.9.2.2 Off-Axis Case 3075.9.3 Imaging of Curved Objects 308References 3096 Diffraction and Point Spread Function 3116.1 Diffraction Phenomena 3116.1.1 Introduction 3116.1.2 Fresnel Number 3116.1.3 Huygens Principle 3156.2 Calculation of Diffraction Effects 3166.2.1 Introduction 3166.2.2 Levels of Modelling 3176.2.3 Wave Equation 3186.2.4 Green’s Theorem 3186.2.5 Alternative Formulations of Diffraction Integrals 3196.2.5.1 Introduction 3196.2.5.2 Kirchhoff Integral 3206.2.5.3 Rayleigh–Sommerfeld Diffraction Integrals 3216.2.5.4 Angular Spectrum of PlaneWaves 3226.2.5.5 Convolution Formulation 3226.2.5.6 Fresnel Approximation 3236.2.5.7 Fraunhofer Far-field 3246.2.5.8 Debye Diffraction Integral 3256.2.5.9 Collins Integral 3256.2.6 Numerical Computation of Diffraction Integrals 3276.2.6.1 Introduction 3276.2.6.2 The Phase Oscillation Problem 3276.2.6.3 Sampling in Diffraction Calculations 3286.2.6.4 Removal of Parabolic Curvature 3306.2.6.5 Sinc-based Algorithm 3336.2.6.6 Boundary and Sampling Problems 3356.2.6.7 Phase Masks: TEA-, LPI- and LSI Approximations 3366.3 Point Spread Function in Optical Systems 3376.3.1 Hybrid Model of the Diffraction Calculation in Optical Systems 3376.3.2 Ideal point spread function 3386.3.2.1 Introduction 3386.3.2.2 Airy Pattern 3406.3.2.3 Axial Distribution 3416.4 PSF in Case of Apodization 3436.4.1 Apodization Effects 3436.4.2 Super-Gaussian Profile 3456.5 Focusing at Low Fresnel Numbers 3476.5.1 Introduction 3476.5.2 Focal Shift 3496.6 Focusing at High Numerical Aperture 3506.6.1 Introduction 3506.6.2 Scalar Apodization Effects 3516.6.3 Natural Mapping Function 3546.6.4 Vectorial Diffraction Integral 3556.6.4.1 Introduction 3556.6.4.2 Richards–Wolf Integral 3566.6.4.3 Cartesian Debye Integral Formulation 3576.6.4.4 Formulation of Mansuripur 3586.6.4.5 Relative Size of Vectorial Effects 3586.6.4.6 Example Calculation 3596.7 PSF for Compound Systems 3596.7.1 Introduction 3616.7.2 Coherent Field Propagation Through a Single Thin Lens 3616.7.3 Coherent Propagation Through a Cascaded System 3626.8 Cascaded Diffraction in Optical Systems 3656.8.1 Introduction 3656.8.2 System Model 3666.8.3 Examples 3696.8.3.1 Diffraction of a Gaussian Beam 3696.8.3.2 Double Gauss Camera Lens 3726.9 Miscellaneous 3746.9.1 Polychromatic PSF 3746.9.2 Line of Sight 3756.9.3 Extended Zernike Approach 3776.9.3.1 Introduction 3776.9.3.2 Properties of the Extended Zernike Approach 3786.9.4 Encircled Energy 3796.9.5 Fresnel Edge Diffraction 3806.9.6 Line Spread Function 3816.9.7 Slit Diffraction 3836.10 Field in a Tilted Plane 3846.10.1 Introduction 3846.10.2 Analysis of the Geometry 3856.10.3 z-Rotation by Shear Transform 3856.10.4 Calculation of the x-Rotation 3866.10.5 Run Time Performance 3886.10.6 Examples 388References 3907 Optical Transfer Function 3957.1 Spatial Frequency Concept 3957.2 Optical Transfer Function 3987.2.1 Introduction 3987.2.2 Duffieux Representation of the OTF 4007.2.3 Contrast and Resolution 4017.2.4 Ideal MTF 4027.2.5 Phase Transfer Function 4057.2.6 Coherent Transfer Function (CTF) 4057.2.7 Geometrical Approximated Transfer Function (GTF) 4077.2.8 Connection Between OTF and PSF 4077.2.9 Three-Dimensional Coherent Transfer Function 4097.3 Miscellaneous 4107.3.1 Non-Isotropic Point Spread Function 4107.3.2 Properties of MTF Curves 4107.3.3 MTF for Defocused Systems 4127.3.3.1 Introduction 4127.3.3.2 Approximations of the MTF 4137.3.3.3 The Ambiguity Function 4137.3.4 MTF for Special Pupil Shapes 4147.3.4.1 MTF for a Square Pupil Shape 4147.3.4.2 MTF of a Ring Pupil 4157.3.4.3 MTF for Systems with Apodization 4177.3.5 Relationships of System Response Functions 4177.3.6 Imaging of Phase Structures 4187.4 OTF of Cascaded Systems 4207.4.1 Introduction 4207.4.2 Coherent Cascaded Systems 4207.4.3 Incoherent Cascaded Systems 4217.4.3.1 Introduction 4217.4.3.2 Simple Case of Two Gaussian PSFs 4227.4.4 MTF of a Complete Signal Chain 422References 4238 Gaussian Beams 4258.1 Introduction 4258.1.1 Definition of Basic Properties 4258.1.2 Amplitude and Intensity Distributions 4278.1.3 Complex Representation and Collins Chart 4278.2 Gaussian Beam Transformation 4298.2.1 Transform By a Lens 4298.2.2 Beam Transform Through Afocal Telescopes 4308.2.3 Transform by an ABCD-Segment 4328.2.4 Matching of Beams 4338.2.4.1 Introduction 4338.2.4.2 Given Incoming and Outgoing Gaussian Beams 4338.2.4.3 Given Gaussian Beam, Lens and Size of the New Beam 4348.2.4.4 Given Gaussian Beam, Lens and New Waist Position 4348.2.4.5 Given Gaussian Beam, Lens Location and Size of the New Beam 4348.2.4.6 LargestWaist Distance 4348.2.4.7 Minimal Beam Size in a Certain Distance 4358.2.4.8 Coupling of Two TEMoo-Beams 4368.3 Astigmatic Beams 4378.3.1 Orthogonal Astigmatic Gaussian Beams 4378.3.2 General Astigmatic Gaussian Beams 4388.4 Ray Equivalent of Gaussian Beams 4408.4.1 Principle 4408.4.2 Ray Equivalent in Three Dimensions 4428.4.3 Selecting General Reconstruction Rays 4438.4.4 Numerical Reconstruction of ABCD by Parabasal Rays 4448.5 Truncated Gaussian Beams 4458.5.1 One-dimensional Beam 4458.5.2 Circular Symmetric Beam 4468.5.2.1 Introduction 4468.5.2.2 Exact Field Calculation 4468.5.2.3 General Properties 4478.6 Gaussian Beams Beyond the Paraxial Approximation 4498.6.1 Introduction 4498.6.2 Exact Solution of theWave Equation 4498.6.3 Taylor Expansion of the Complex Field 4508.6.4 Angle Expansion of Higher Order Modes 4508.6.5 Off-axis-Focusing 4518.7 Gaussian Beam with Spherical Aberration 4528.7.1 Introduction 4528.7.2 Intensity on Axis 4528.7.3 Aberration Balancing 4538.7.4 Numerical Example Calculations 4538.8 Single Mode Fibre Coupling with Gaussian Beam 4548.8.1 Basic Fibre Parameters 4548.8.2 Fundamental Mode Shape 4558.8.3 Calculation of Fibre Radiation Mode 4558.9 Partial Coherent Gauss–Schell Beams 4568.9.1 Introduction 4568.9.2 Simple Gauss–Schell Beams 4568.9.3 Propagation of Gauss-Schell Beams 4588.9.3.1 Initial Values 4588.9.3.2 Free-Space Propagation 4588.9.3.3 ABCD-Propagation 459References 4599 Photometry and Radiometry 4639.1 Introduction 4639.1.1 General Remarks 4639.1.2 Definition of the Radiometric Quantities 4639.1.3 Photometric Quantities 4649.1.4 Comparison of Quantities 4649.1.5 Energy, Power and Photons 4649.1.6 Solid Angle 4669.2 Lambertian Source 4669.2.1 Classical Lambertian Radiator 4669.2.2 Generalized Lambertian Radiator 4679.3 Radiometric Transfer of Energy 4679.3.1 Radiance and Irradiance 4679.3.2 Radiometric Flux Transfer 4689.3.3 Analytical Solutions for Simple Geometries 4699.3.3.1 Surface Element Illuminated by a Point Source 4699.3.3.2 Circular Plane Surface Illuminated by a Point Source 4699.3.3.3 Parallel Surface Elements 4709.3.3.4 Circular Lambertian Source and Point-Like Receiver 4709.3.3.5 Circular Lambertian Source and Circular Receiver 4709.3.4 Numerical Radiation Transfer 4719.3.4.1 Introduction 4719.3.4.2 Monte-Carlo Raytracing Approach 4729.3.4.3 Source Modelling 4739.3.4.4 Evaluation of the Detector Irradiance 4749.3.4.5 Examples 4749.3.5 Radiation Transport with Interaction 4759.3.6 Ray Tube Model 4769.4 Radiometry of Optical Systems 4779.4.1 Introduction 4779.4.2 Sine Condition and Photometry 4789.4.3 Aplanatic Systems 4799.4.4 Natural Vignetting 4809.4.4.1 General Case Free of Vignetting 4809.4.4.2 Formulation With Entrance and Exit Pupil 4819.4.4.3 Monocentric and Telecentric 4-f -Systems 4829.4.4.4 System With Rear Stop 4829.4.4.5 System with Front Stop 4849.5 Radiometry with Partial Coherent Light 4859.5.1 Introduction 4859.5.2 Partial Coherent Light 4869.5.3 Generalized Radiance 4869.5.4 Propagation of the Generalized Radiance 4879.5.4.1 Introduction 4879.5.4.2 Example Lambertian Source 487References 48810 Phase Space Representation 49110.1 General Aspects 49110.1.1 Motivation 49110.1.2 Legendre Transform and Equation of Motion 49210.1.3 Uncertainty Relation 49410.1.4 Analogy to Mechanics 49510.2 Geometrical Ray Model 49510.2.1 Introduction 49510.2.2 Phase Space Representation of Ray Bundle Transport 49610.2.3 Ray Aberrations 49910.3 Wigner Distribution Function 50010.3.1 Introduction 50110.3.2 Theory of the Wigner Function 50210.3.3 Wigner Function of Gaussian Beams 50310.3.4 Wigner Function of a Decomposed Field 50310.3.5 Propagation of the Wigner Function 50510.3.6 Transfer Through Thin Masks 50610.3.7 Wigner Function of a Slit 50610.3.8 Wigner Function for Gauss–Schell Beams 50710.3.9 Examples 50810.4 Photometry in Phase Space 50810.4.1 Introduction 50810.4.2 Conservation of Energy 51010.4.3 Vignetting 51110.4.4 Fibre Illumination 51210.4.5 Further Examples 51310.5 Miscellaneous 51510.5.1 Caustic in Phase Space 51510.5.2 Phase Space Discussion of Sampling 51510.5.3 Phase Space Analyzer 51710.5.4 Fractional Fourier Transform 51810.5.4.1 Definition 51810.5.4.2 Fresnel Integral and Fractional Fourier Transform 51910.5.4.3 Gradient Index Lenses 52010.5.5 Linear Canonical Transform 520References 52111 Computation and Digital Processing of Images 52311.1 Introduction 52311.2 Image Computation 52311.2.1 Introduction 52311.2.2 Ray Based Image Calculation 52411.2.3 Physical Model of Image Formation 52611.2.3.1 Introduction 52611.2.3.2 Image Formation According to Fourier and Abbe 52711.2.3.3 4-f -Fourier Imaging Model 52811.2.3.4 Complete 6-f -Fourier Model 53011.2.3.5 Coherent Image Formation 53111.2.3.6 Incoherent Image Formation 53211.2.3.7 Isoplanatic Condition 53211.2.3.8 Multifocal Visual Perception 53411.2.3.9 Image Computation Examples 53511.3 Confocal Imaging 53811.3.1 Introduction 53811.3.2 Scanning Options 54011.3.3 Image Model 54011.3.4 Influence of Pinhole Size and Aberrations 54211.4 Anisoplanatic Imaging 54311.4.1 Introduction 54311.4.2 Interpolation of Zernikes 54611.4.3 Spatially Variant Convolution 54711.4.4 Interpolation by Principal Components 54911.4.5 Taylor Expansion of the PSF 55111.4.6 Distortion 55211.4.7 Special Varying Blur Types 55211.5 Digital Imaging Processing 55411.5.1 Introduction 55411.5.2 Spatial Discretization and Resolution 55511.5.3 Management of Image Colour 55811.6 Image Quality Metrics 55911.6.1 Introduction 55911.6.2 MSE Criterion 56011.6.3 SSim Criterion 56111.6.3.1 Introduction 56111.6.3.2 Definition and Computation 56111.6.3.3 Examples 56211.7 Digital Image Restoration 56311.7.1 Introduction 56311.7.2 Deconvolution 56511.7.2.1 Wiener Method 56511.7.2.2 Algebraic Deconvolution 56511.7.2.3 Further Methods 56711.7.2.4 Examples 56711.7.3 Denoising 56811.8 Plenoptical Imaging 56911.8.1 Introduction 56911.8.2 Model of the Plenoptical Camera 1.0 57211.8.3 Phase Space Discussion 57311.8.4 Digital Refocusing 57511.8.5 Depth of Focus 57511.8.6 Examples 57811.9 Digital Phase Imaging 57911.9.1 Introduction 57911.9.2 Coherent Diffraction Imaging 58011.9.3 Transport of Intensity Approach 58111.9.4 Ptychography 58211.10 Extended Depth of Focus 58311.10.1 Introduction 58311.10.2 Toraldo Phase Mask 58611.10.3 Cubic Phase Plate 586References 58812 Mathematical Appendix 59112.1 Fourier Transform and Related 59112.1.1 Fourier Series 59112.1.2 Fourier Transform 59112.1.3 Discrete Fourier Transform 59212.1.3.1 Definition 59212.1.3.2 Sampling and Aliasing 59312.1.3.3 Leakage 59412.1.3.4 Zero padding and Balanced Sampling 59612.1.4 Chirp-z-Transform 59712.1.5 Semi-Analytical Fourier Transform 60012.1.6 Non-Uniform Fourier Transform 60112.1.7 Special Fourier Related Operations 60312.1.7.1 Convolution Integral 60312.1.7.2 Auto-Correlation 60412.1.7.3 Cross Correlation and Covariance 60412.1.8 Fourier Slice Theorem and Radon Transform 60512.2 Miscellaneous 60612.2.1 Singular Value Decomposition 60612.2.2 Principal Component Analysis and Karhunen–Loeve Transform 60712.2.3 Quasi-Random Sampling 60812.2.4 Window Functions 60912.2.5 Fresnel Integrals 61012.2.6 Method of Stationary Phase 61212.2.6.1 Introduction 61212.2.6.2 One-Dimensional Case 61312.2.6.3 Two-Dimensional Case 613References 614Index 615