Foundations of Optical System Analysis and Design

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Acknowledgments
Author Brief Biography
1 Introduction
	1.1 An Early History of Optical Systems and Optics
		1.1.1 Early History of Mirrors
		1.1.2 Early History of Lenses
		1.1.3 Early History of Glass Making
		1.1.4 Ancient History of Optics in Europe, India and China
		1.1.5 Optics Activities in the Middle East in 10th Century ce
		1.1.6 Practical Optical Systems of the Early Days
		1.1.7 Reading Stones and Discovery of Eyeglasses
		1.1.8 Revival of Investigations On Optics in Europe By Roger Bacon in the 13th Century ce
		1.1.9 Optics During Renaissance in Europe
		1.1.10 Invention of Telescope and Microscope
		1.1.11 Investigations On Optics and Optical Systems By Johannes Kepler
		1.1.12 Discovery of the Laws of Refraction
		1.1.13 Discovery of the Phenomena of Diffraction, Interference and Double Refraction
		1.1.14 Newton’s Contributions in Optics and Rømer’s Discovery of Finite Speed of Light
		1.1.15 Contributions By Christian Huygens in Instrumental Optics and in Development of the Wave Theory of Light
	1.2 Metamorphosis of Optical Systems in the Late Twentieth Century
	1.3 Current Definition of Optics
	1.4 Types of Optical Systems
	1.5 Classification of Optical Systems
	1.6 Performance Assessment of Optical Systems
	1.7 Optical Design: System Design and Lens Design
	1.8 Theories of Light
	References
2 From Maxwell’s Equations to Thin Lens Optics
	2.1 Maxwell’s Equations
	2.2 The Wave Equation
	2.3 Characteristics of the Harmonic Plane Wave Solution of the Scalar Wave Equation
		2.3.1 Inhomogeneous Waves
	2.4 Wave Equation for Propagation of Light in Inhomogeneous Media
		2.4.1 Boundary Conditions
	2.5 Vector Waves and Polarization
		2.5.1 Polarization of Light Waves
	2.6 Propagation of Light in Absorbing/Semi-Absorbing Media
	2.7 Transition to Scalar Theory
	2.8 ‘Ray Optics’ Under Small Wavelength Approximation
		2.8.1 The Eikonal Equation
		2.8.2 Equation for Light Rays
	2.9 Basic Principles of Ray Optics
		2.9.1 The Laws of Refraction
			2.9.1.1 A Plane Curve in the Neighbourhood of a Point On It
			2.9.1.2 A Continuous Surface in the Neighbourhood of a Point On It
			2.9.1.3 Snell’s Laws of Refraction
		2.9.2 Refraction in a Medium of Negative Refractive Index
		2.9.3 The Case of Reflection
			2.9.3.1 Total Internal Reflection
		2.9.4 Fermat’s Principle
		2.9.5 The Path Differential Theorem
		2.9.6 Malus-Dupin Theorem
	2.10 Division of Energy of a Light Wave Incident On a Surface of Discontinuity
		2.10.1 Phase Changes in Reflected and Transmitted Waves
		2.10.2 Brewster’s Law
	2.11 From General Ray Optics to Parabasal Optics, Paraxial Optics and Thin Lens Optics
	References
3 Paraxial Optics
	3.1 Raison d’Être for Paraxial Analysis
	3.2 Imaging By a Single Spherical Interface
	3.3 Sign Convention
	3.4 Paraxial Approximation
		3.4.1 On-Axis Imaging
			3.4.1.1 Power and Focal Length of a Single Surface
		3.4.2 Extra-Axial Imaging
		3.4.3 Paraxial Ray Diagram
		3.4.4 Paraxial Imaging By a Smooth Surface of Revolution About the Axis
	3.5 Paraxial Imaging By Axially Symmetric System of Surfaces
		3.5.1 Notation
		3.5.2 Paraxial Ray Tracing
		3.5.3 The Paraxial Invariant
	3.6 Paraxial Imaging By a Single Mirror
	3.7 The General Object-Image Relation for an Axisymmetric System
		3.7.1 A Geometrical Construction for Finding the Paraxial Image
		3.7.2 Paraxial Imaging and Projective Transformation (Collineation)
	3.8 Cardinal Points in Gaussian Optics
		3.8.1 Determining Location of Cardinal Points From System Data
		3.8.2 Illustrative Cases
			3.8.2.1 A Single Refracting Surface
			3.8.2.2 A System of Two Separated Components
			3.8.2.3 A Thick Lens With Different Refractive Indices for the Object and the Image Spaces
			3.8.2.4 A Thin Lens With Different Refractive Indices for the Object and the Image Spaces
			3.8.2.5 Two Separated Thin Lenses in Air
	3.9 The Object and Image Positions for Systems of Finite Power
	3.10 Newton’s Form of the Conjugate Equation
	3.11 Afocal Systems
	3.12 Vergence and Power
	3.13 Geometrical Nature of Image Formation By an Ideal Gaussian System
		3.13.1 Imaging of a Two-Dimensional Object On a Transverse Plane
		3.13.2 Imaging of Any Line in the Object Space
		3.13.3 Suitable Values for Paraxial Angle and Height Variables in an Ideal Gaussian System
	3.14 Gaussian Image of a Line Inclined With the Axis
	3.15 Gaussian Image of a Tilted Plane: The Scheimpflug Principle
		3.15.1 Shape of the Image
	3.16 Gaussian Image of a Cube
	References
4 Paraxial Analysis of the Role of Stops
	4.1 Aperture Stop and the Pupils
		4.1.1 Conjugate Location and Aperture Stop
	4.2 Extra-Axial Imagery and Vignetting
		4.2.1 Vignetting Stop
	4.3 Field Stop and the Windows
		4.3.1 Field of View
		4.3.2 Field Stop, Entrance, and Exit Windows
			4.3.2.1 Looking at an Image Formed By a Plane Mirror
			4.3.2.2 Looking at Image Formed By a Convex Spherical Mirror
			4.3.2.3 Imaging By a Single Lens With a Stop On It
			4.3.2.4 Imaging By a Single Lens With an Aperture Stop On It and a Remote Diaphragm in the Front
			4.3.2.5 Appropriate Positioning of Aperture Stop and Field Stop
			4.3.2.6 Aperture Stop and Field Stop in Imaging Lenses With No Dedicated Physical Stop
			4.3.2.7 Imaging By a Multicomponent Lens System
			4.3.2.8 Paraxial Marginal Ray and Paraxial Pupil Ray
	4.4 Glare Stop, Baffles, and the Like
	4.5 Pupil Matching in Compound Systems
	4.6 Optical Imaging System of the Human Eye
		4.6.1 Paraxial Cardinal Points of the Human Eye
			4.6.1.1 Correction of Defective Vision By Spectacles
			4.6.1.2 Position of Spectacle Lens With Respect to Eye Lens
		4.6.2 Pupils and Centre of Rotation of the Human Eye
			4.6.2.1 Position of Exit Pupil in Visual Instruments
		4.6.3 Visual Magnification of an Eyepiece Or Magnifier
	4.7 Optical (Paraxial) Invariant: Paraxial Variables and Real Finite Rays
		4.7.1 Different Forms of Paraxial Invariant
			4.7.1.1 Paraxial Invariant in Star Space
			4.7.1.2 A Generalized Formula for Paraxial Invariant H
			4.7.1.3 An Expression for Power K in Terms of H and Angle Variables of the PMR and the PPR
		4.7.2 Paraxial Ray Variables and Real Finite Rays
			4.7.2.1 Paraxial Ray Variables in an Ideal Gaussian System
			4.7.2.2 Paraxial Ray Variables in a Real Optical System
			4.7.2.3 Choice of Appropriate Values for Paraxial Angles U and
	4.8 Angular Magnification in Afocal Systems
	4.9 F-Number and Numerical Aperture
	4.10 Depth of Focus and Depth of Field
		4.10.1 Expressions for Depth of Focus, Depth of Field, and Hyperfocal Distance for a Single Thin Lens With Stop On It
		4.10.2 General Expressions for Depth of Focus, Depth of Field, and Hyperfocal Distance for an Axisymmetric Imaging System
	4.11 Telecentric Stops
	4.12 Stops in Illumination Systems
		4.12.1 Slide Projector
		4.12.2 The Köhler Illumination System in Microscopes
	References
5 Towards Facilitating Paraxial Treatment
	5.1 Matrix Treatment of Paraxial Optics
		5.1.1 The Refraction Matrix and the Translation/Transfer Matrix
		5.1.2 The System Matrix
		5.1.3 The Conjugate Matrix
		5.1.4 Detailed Form of the Conjugate Matrix in the Case of Finite Conjugate Imaging
			5.1.4.1 Location of the Cardinal Points of the System: Equivalent Focal Length and Power
	5.2 Gaussian Brackets in Paraxial Optics
		5.2.1 Gaussian Brackets: Definition
		5.2.2 Few Pertinent Theorems of Gaussian Brackets
		5.2.3 Elements of System Matrix in Terms of Gaussian Brackets
	5.3 Delano Diagram in Paraxial Design of Optical Systems
		5.3.1 A Paraxial Skew Ray and the Diagram
		5.3.2 Illustrative Diagrams
		5.3.3 Axial Distances
		5.3.4 Conjugate Lines
		5.3.5 Cardinal Points
	References
6 The Photometry and Radiometry of Optical Systems
	6.1 Radiometry and Photometry: Interrelationship
	6.2 Fundamental Radiometric and Photometric Quantities
		6.2.1 Radiant Or Luminous Flux (Power)
		6.2.2 Radiant Or Luminous Intensity of a Source
		6.2.3 Radiant (Luminous) Emittance Or Exitance of a Source
		6.2.4 Radiance (Luminance) of a Source
			6.2.4.1 Lambertian Source
		6.2.5 Irradiance (Illuminance/Illumination) of a Receiving Surface
	6.3 Conservation of Radiance/Luminance (Brightness) in Optical Imaging Systems
	6.4 Flux Radiated Into a Cone By a Small Circular Lambertian Source
	6.5 Flux Collected By Entrance Pupil of a Lens System
	6.6 Irradiance of an Image
	6.7 Off-Axial Irradiance/Illuminance
	6.8 Irradiance/Illuminance From a Large Circular Lambertian Source
		6.8.1 Radiance (Luminance) of a Distant Source
	References
7 Optical Imaging By Real Rays
	7.1 Rudiments of Hamiltonian Optics
		7.1.1 Hamilton’s Point Characteristic Function
			7.1.1.1 Hamilton-Bruns’ Point Eikonal
		7.1.2 Point Angle Eikonal
		7.1.3 Angle Point Eikonal
		7.1.4 Angle Eikonal
		7.1.5 Eikonals and Their Uses
		7.1.6 Lagrangian Optics
	7.2 Perfect Imaging With Real Rays
		7.2.1 Stigmatic Imaging of a Point
		7.2.2 Cartesian Oval[64]
			7.2.2.1 Finite Conjugate Points
			7.2.2.2 Cartesian Mirror for Stigmatic Imaging of Finite Conjugate Points
		7.2.3 Perfect Imaging of Three-Dimensional Domain
			7.2.3.1 Sufficiency Requirements for Ideal Imaging By Maxwellian ‘Perfect’ Instrument
			7.2.3.2 Impossibility of Perfect Imaging By Real Rays in Nontrivial Cases
			7.2.3.3 Maxwell’s ‘Fish-Eye’ Lens and Luneburg Lens
		7.2.4 Perfect Imaging of Surfaces
			7.2.4.1 Aplanatic Surfaces and Points
		7.2.5 Stigmatic Imaging of Two Neighbouring Points: Optical Cosine Rule
			7.2.5.1 Abbe’s Sine Condition
			7.2.5.2 Herschel’s Condition
			7.2.5.3 Incompatibility of Herschel’s Condition With Abbe’s Sine Condition
	7.3 Real Ray Invariants
		7.3.1 Skew Ray Invariant
			7.3.1.1 A Derivation of the Skew Ray Invariance Relationship
			7.3.1.2 Cartesian Form of Skew Ray Invariant
			7.3.1.3 Other Forms of Skew Ray Invariant
			7.3.1.4 Applications of the Skew Invariant
		7.3.2 Generalized Optical Invariant
			7.3.2.1 Derivation of Generalized Optical Invariant
	7.4 Imaging By Rays in the Vicinity of an Arbitrary Ray
		7.4.1 Elements of Surface Normals and Curvature
			7.4.1.1 The Equations of the Normals to a Surface
			7.4.1.2 The Curvature of a Plane Curve: Newton’s Method
			7.4.1.3 The Curvatures of a Surface: Euler’s Theorem
			7.4.1.4 The Normals to an Astigmatic Surface
		7.4.2 Astigmatism of a Wavefront in General
			7.4.2.1 Rays in the Neighbourhood of a Finite Principal Ray in Axisymmetric Systems
			7.4.2.2 Derivation of S and T Ray Tracing Formulae
			7.4.2.3 The Sagittal Invariant
	7.5 Aberrations of Optical Systems
	References
8 Monochromatic Aberrations
	8.1 A Journey to the Wonderland of Optical Aberrations: A Brief Early History
	8.2 Monochromatic Aberrations
		8.2.1 Measures of Aberration
			8.2.1.1 Undercorrected and Overcorrected Systems
		8.2.2 Ray Aberration and Wave Aberration: Interrelationship
		8.2.3 Choice of Reference Sphere and Wave Aberration
			8.2.3.2 Effect of Change in Radius of the Reference Sphere On Wave Aberration
		8.2.4 Caustics and Aberrations
		8.2.5 Power Series Expansion of the Wave Aberration Function
			8.2.5.1 Aberrations of Various Orders
			8.2.5.2 Convergence of the Power Series of Aberrations
			8.2.5.3 Types of Aberrations
	8.3 Transverse Ray Aberrations Corresponding to Selected Wave Aberration Polynomial Terms
		8.3.1 Primary Spherical Aberration
			8.3.1.1 Caustic Surface
		8.3.2 Primary Coma
		8.3.3 Primary Astigmatism
		8.3.4 Primary Curvature
		8.3.5 Primary Distortion
		8.3.6 Mixed and Higher Order Aberration Terms
	8.4 Longitudinal Aberrations
	8.5 Aplanatism and Isoplanatism
		8.5.1 Coma-Type Component of Wave Aberration and Linear Coma
		8.5.2 Total Linear Coma From Properties of Axial Pencil
		8.5.3 Offence Against Sine Condition (OSC’)
		8.5.4 Staeble – Lihotzky Condition
	8.6 Analytical Approach for Correction of Total Aberrations
	References
9 Chromatic Aberrations
	9.1 Introduction
	9.2 Dispersion of Optical Materials
		9.2.1 Interpolation of Refractive Indices
		9.2.2 Abbe Number
		9.2.3 Generic Types of Optical Glasses and Glass Codes
	9.3 Paraxial Chromatism
		9.3.1 A Single Thin Lens: Axial Colour and Lateral Colour
		9.3.2 A Thin Doublet and Achromatic Doublets
			9.3.2.1 Synthesis of a Thin Lens of a Given Power and an Arbitrary
		9.3.3 Secondary Spectrum and Relative Partial Dispersion
		9.3.4 Apochromats and Superachromats
		9.3.5 ‘Complete’ Or ‘Total’ Achromatization
			9.3.5.1 Harting’s Criterion
		9.3.6 A Separated Thin Lens Achromat (Dialyte)
		9.3.7 A One-Glass Achromat
		9.3.8 Secondary Spectrum Correction With Normal Glasses
		9.3.9 A Thick Lens Or a Compound Lens System
	9.4 Chromatism Beyond the Paraxial Domain
	References
10 Finite Or Total Aberrations From System Data By Ray Tracing
	10.1 Evaluation of Total Or Finite Wavefront Aberration (Monochromatic)
		10.1.1 Wave Aberration By a Single Refracting Interface in Terms of Optical Path Difference (OPD)
		10.1.2 Rays’ Own Focus and Invariant Foci of Skew Rays
		10.1.3 Pupil Exploration By Ray Tracing
		10.1.4 A Theorem of Equally Inclined Chords Between Two Skew Lines
		10.1.5 Computation of Wave Aberration in an Axi-Symmetric System
		10.1.6 Computation of Transverse Ray Aberrations in an Axi-Symmetric System
	10.2 Measures for Nonparaxial Chromatism
		10.2.1 Spherochromatism
		10.2.2 Conrady Chromatic Aberration Formula
		10.2.3 Image Space Associated Rays in Conrady Chromatic Aberration Formula
		10.2.4 Evaluation of Exact Chromatic Aberration Using Object Space Associated Rays
	References
11 Hopkins’ Canonical Coordinates and Variables in Aberration Theory
	11.1 Introduction
	11.2 Canonical Coordinates: Axial Pencils
	11.3 Canonical Coordinates: Extra-Axial Pencils
	11.4 Reduced Pupil Variables
	11.5 Reduced Image Height and Fractional Distortion
	11.6 Pupil Scale Ratios
		11.6.1 Entrance Pupil Scale Ratios and
		11.6.2 Exit Pupil Scale Ratios and
	11.7 and From S and T Ray Traces
	11.8 Local Sagittal and Tangential Invariants for Extra-Axial Images
	11.9 Reduced Coordinates On the Object/Image Plane and Local Magnifications
	11.10 Canonical Relations: Generalized Sine Condition
	References
12 Primary Aberrations From System Data
	12.1 Introduction
	12.2 Validity of the Use of Paraxial Ray Parameters for Evaluating Surface Contribution to Primary Wavefront Aberration
	12.3 Primary Aberrations and Seidel Aberrations
	12.4 Seidel Aberrations in Terms of Paraxial Ray Trace Data
		12.4.1 Paraxial (Abbe’s) Refraction Invariant
		12.4.2 Seidel Aberrations for Refraction By a Spherical Interface
		12.4.3 Seidel Aberrations in an Axi-Symmetric System Consisting of Multiple Refracting Interfaces
		12.4.4 Seidel Aberrations of a Plane Parallel Plate
		12.4.5 Seidel Aberrations of a Spherical Mirror
		12.4.6 Seidel Aberrations of a Refracting Aspheric Interface
			12.4.6.1 Mathematical Representation of an Aspheric Surface
			12.4.6.2 Seidel Aberrations of the Smooth Aspheric Refracting Interface
	12.5 Axial Colour and Lateral Colour as Primary Aberrations
	References
13 Higher Order Aberrations in Practice
	13.1 Evaluation of Aberrations of Higher Orders
	13.2 A Special Treatment for Tackling Higher Order Aberrations in Systems With Moderate Aperture and Large Field
	13.3 Evaluation of Wave Aberration Polynomial Coefficients From Finite Ray Trace Data
	References
14 Thin Lens Aberrations
	14.1 Primary Aberrations of Thin Lenses
	14.2 Primary Aberrations of a Thin Lens (With Stop On It) in Object and Image Spaces of Unequal Refractive Index
	14.3 Primary Aberrations of a Thin Lens (With Stop On It) With Equal Media in Object and Image Spaces
	14.4 Primary Aberrations of a Thin Lens (With Stop On It) in Air
	14.5 Structural Aberration Coefficients
	14.6 Use of Thin Lens Aberration Theory in Structural Design of Lens Systems
	14.7 Transition From Thin Lens to Thick Lens and Vice Versa
	14.8 Thin Lens Modelling of Diffractive Lenses
	References
15 Stop Shift, Pupil Aberrations, and Conjugate Shift
	15.1 Axial Shift of the Aperture Stop
		15.1.1 The Eccentricity Parameter
		15.1.2 Seidel Difference Formula
		15.1.3 Stop-Shift Effects On Seidel Aberrations in Refraction By a Single Surface
		15.1.4 Stop-Shift Effects On Seidel Aberrations in an Axi-Symmetric System
		15.1.5 Stop-Shift Effects On Seidel Aberrations in a Single Thin Lens
		15.1.6 Corollaries
	15.2 Pupil Aberrations
		15.2.1 Relation Between Pupil Aberrations and Image Aberrations
		15.2.2 Effect of Stop Shift On Seidel Spherical Aberration of the Pupil
		15.2.3 Effect of Stop Shift On Seidel Longitudinal Chromatic Aberration of the Pupil
		15.2.4 A Few Well-Known Effects of Pupil Aberrations On Imaging of Objects [9–15]
	15.3 Conjugate Shift
		15.3.1 The Coefficients of Seidel Pupil Aberrations After Object Shift in Terms of the Coefficients of Seidel Pupil ...
		15.3.2 The Coefficients of Seidel Pupil Aberrations Before Object Shift in Terms of Coefficients of Seidel Image ...
		15.3.3 The Coefficients of Seidel Image Aberrations After Object Shift in Terms of Coefficients of Seidel Pupil Aberrations ...
		15.3.4 Effects of Conjugate Shift On the Coefficients of Seidel Image Aberrations
		15.3.5 The Bow–Sutton Conditions
	References
16 Role of Diffraction in Image Formation
	16.1 Raison d’Être for ‘Diffraction Theory of Image Formation’
		Observation I
		Observation II
		Observation III
	16.2 Diffraction Theory of the Point Spread Function
		16.2.1 The Huygens–Fresnel Principle
		16.2.2 Diffraction Image of a Point Object By an Aberration Free Axi-Symmetric Lens System
		16.2.3 Physical Significance of the Omitted Phase Term
		16.2.4 Anamorphic Stretching of PSF in Extra-Axial Case
	16.3 Airy Pattern
		16.3.1 Factor of Encircled Energy
	16.4 Resolution and Resolving Power
		16.4.1 Two-Point Resolution
		16.4.2 Rayleigh Criterion of Resolution
		16.4.3 Sparrow Criterion of Resolution
		16.4.4 Dawes Criterion of Resolution
		16.4.5 Resolution in the Case of Two Points of Unequal Intensity
		16.4.6 Resolution in the Case of Two Mutually Coherent Points
		16.4.7 Breaking the Diffraction Limit of Resolution
			16.4.7.1 Use of Phase-Shifting Mask
			16.4.7.2 Superresolution Over a Restricted Field of View
			16.4.7.3 Confocal Scanning Microscopy
			16.4.7.4 Near Field Superresolving Aperture Scanning
	References
17 Diffraction Images By Aberrated Optical Systems
	17.1 Point Spread Function (PSF) for Aberrated Systems
		17.1.1 PSF of Airy Pupil in Different Planes of Focus
		17.1.2 Distribution of Intensity at the Centre of the PSF as a Function of Axial Position of the Focal Plane
		17.1.3 Determination of Intensity Distribution in and Around Diffraction Images By Aberrated Systems
		17.1.4 Spot Diagrams
	17.2 Aberration Tolerances
		17.2.1 Rayleigh Quarter-Wavelength Rule
		17.2.2 Strehl Criterion
		17.2.3 Strehl Ratio in Terms of Variance of Wave Aberration
			17.2.3.1 Use of Local Variance of Wave Aberration
			17.2.3.2 Tolerance On Variance of Wave Aberration in Highly Corrected Systems
			17.2.3.3 Tolerance On Axial Shift of Focus in Aberration-Free Systems
			17.2.3.4 Tolerance On Primary Spherical Aberration
	17.3 Aberration Balancing
		17.3.1 Tolerance On Secondary Spherical Aberration With Optimum Values for Primary Spherical Aberration and Defect of Focus
		17.3.2 Tolerance On Primary Coma With Optimum Value for Transverse Shift of Focus
		17.3.3 Tolerance On Primary Astigmatism With Optimum Value for Defect of Focus
		17.3.4 Aberration Balancing and Tolerances On a FEE-Based Criterion
	17.4 Fast Evaluation of the Variance of Wave Aberration From Ray Trace Data
	17.5 Zernike Circle Polynomials
	17.6 Role of Fresnel Number in Imaging/Focusing
	17.7 Imaging/Focusing in Optical Systems With Large Numerical Aperture
	References
18 System Theoretic Viewpoint in Optical Image Formation
	18.1 Quality Assessment of Imaging of Extended Objects: A Brief Historical Background
	18.2 System Theoretic Concepts in Optical Image Formation
		18.2.1 Linearity and Principle of Superposition
		18.2.2 Space Invariance and Isoplanatism
		18.2.3 Image of an Object By a Linear Space Invariant Imaging System
	18.3 Fourier Analysis
		18.3.1 Alternative Routes to Determine Image of an Object
		18.3.2 Physical Interpretation of the Kernel of Fourier Transform
		18.3.3 Reduced Period and Reduced Spatial Frequency
		18.3.4 Line Spread Function
		18.3.5 Image of a One-Dimensional Object
		18.3.6 Optical Transfer Function (OTF), Modulation Transfer Function (MTF), and Phase Transfer Function (PTF)
		18.3.7 Effects of Coherence in Illumination On Extended Object Imagery
	18.4 Abbe Theory of Coherent Image Formation
	18.5 Transfer Function, Point Spread Function, and the Pupil Function
		18.5.1 Amplitude Transfer Function (ATF) in Imaging Systems Using Coherent Illumination
			18.5.1.1 ATF in Coherent Diffraction Limited Imaging Systems
			18.5.1.2 Effects of Residual Aberrations On ATF in Coherent Systems
		18.5.2 Optical Transfer Function (OTF) in Imaging Systems Using Incoherent Illumination
			18.5.2.1 OTF in Incoherent Diffraction Limited Imaging Systems
			18.5.2.2 Effects of Residual Aberrations On OTF in Incoherent Systems
			18.5.2.3 Effects of Defocusing On OTF in Diffraction Limited Systems
			18.5.2.4 OTF in Incoherent Imaging Systems With Residual Aberrations
			18.5.2.5 Effects of Nonuniform Real Amplitude in Pupil Function On OTF
			18.5.2.6 Apodization and Inverse Apodization
	18.6 Aberration Tolerances Based On OTF
		18.6.1 The Wave Aberration Difference Function
		18.6.2 Aberration Tolerances Based On the Variance of Wave Aberration Difference Function
	18.7 Fast Evaluation of Variance of the Wave Aberration Difference Function From Finite Ray Trace Data
	18.8 Through-Focus MTF
	18.9 Interrelationship Between PSF, LSF, ESF, BSF, and OTF
		18.9.1 Relation Between PSF, LSF, and OTF for Circularly Symmetric Pupil Function
		18.9.2 Relation Between ESF, LSF, and OTF
		18.9.3 BSF and OTF
	18.10 Effects of Anamorphic Imagery in the Off-Axis Region On OTF Analysis
	18.11 Transfer Function in Cascaded Optical Systems
	18.12 Image Evaluation Parameters in Case of Polychromatic Illumination
		18.12.1 Polychromatic PSF
		18.12.2 Polychromatic OTF
	18.13 Information Theoretic Concepts in Image Evaluation
	References
19 Basics of Lens Design
	19.1 Statement of the Problem of Lens Design
	19.2 Lens Design Methodology
	19.3 Different Approaches for Lens Design
	19.4 Tackling Aberrations in Lens Design
		19.4.1 Structural Symmetry of the Components On the Two Sides of the Aperture Stop
		19.4.2 Axial Shift of the Aperture Stop
		19.4.3 Controlled Vignetting
		19.4.4 Use of Thin Lens Approximations
		19.4.5 D-Number and Aperture Utilization Ratio
	19.5 Classification of Lens Systems
		19.5.1 Afocal Lenses
		19.5.2 Telephoto Lenses and Wide-Angle Lenses
		19.5.3 Telecentric Lenses
		19.5.4 Scanning Lenses
		19.5.5 Lenses With Working Wavelength Beyond the Visible Range
		19.5.6 Unconventional Lenses and Lenses Using Unconventional Optical Elements
	19.6 A Broad Classification of Lenses Based On Aperture, Field of View, Axial Location of Aperture Stop, Image Quality, ...
	19.7 Well-Known Lens Structures in Infinity Conjugate Systems
	19.8 Manufacturing Tolerances
	References
20 Lens Design Optimization
	20.1 Optimization of Lens Design: From Dream to Reality
	20.2 Mathematical Preliminaries for Numerical Optimization
		20.2.1 Newton–Raphson Technique for Solving a Nonlinear Algebraic Equation
		20.2.2 Stationary Points of a Univariate Function
		20.2.3 Multivariate Minimization
			20.2.3.1 Basic Notations
			20.2.3.2 The Method of Steepest Descent
			20.2.3.3 Newton’s Method
		20.2.4 Nonlinear Least-Squares
			20.2.4.1 The Gauss–Newton Method
			20.2.4.2 The Levenberg–Marquardt Method
		20.2.5 Handling of Constraints
	20.3 Damped Least-Squares (DLS) Method in Lens Design Optimization
		20.3.1 Degrees of Freedom
		20.3.2 Formation of the Objective Function
		20.3.3 Least-Squares Optimization With Total Hessian Matrix
		20.3.4 General Form of the Damping Factor
		20.3.5 The Scaling Damping Factor
		20.3.6 Truncated Defect Function
		20.3.7 Second-Derivative Damping Factor
		20.3.8 Normal Equations
		20.3.9 Global Damping Factor .
		20.3.10 Control of Gaussian Parameters
		20.3.11 Control of Boundary Conditions
			20.3.11.1 Edge and Centre Thickness Control
			20.3.11.2 Control of Boundary Conditions Imposed By Available Glass Types
	20.4 Evaluation of Aberration Derivatives
	References
21 Towards Global Synthesis of Optical Systems
	21.1 Local Optimization and Global Optimization: The Curse of Dimensionality
	21.2 Deterministic Methods for Global/Quasi-Global Optimization
		21.2.1 Adaptive/Dynamic Defect Function
		21.2.2 Partitioning of the Design Space
		21.2.3 The Escape Function and the ‘Blow-Up/Settle-Down’ Method
		21.2.4 Using Saddle Points of Defect Function in Design Space
		21.2.5 Using Parallel Plates in Starting Design
	21.3 Stochastic Global Optimization Methods
		21.3.1 Simulated Annealing
		21.3.2 Evolutionary Computation
		21.3.3 Neural Networks, Deep Learning, and Fuzzy Logic
		21.3.4 Particle Swarm Optimization
	21.4 Global Optimization By Nature-Inspired and Bio-Inspired Algorithms
	21.5 A Prophylactic Approach for Global Synthesis
	21.6 Multi-Objective Optimization and Pareto-Optimality
	21.7 Optical Design and Practice of Medicine
	References
Epilogue
Index