Optics of the Human Eye

Description

This book describes the optical structure and optical properties of the human eye. For ease of reference, the most commonly useful topics are at the beginning and topics with narrower appeal are placed towards the end. The book is divided into five sections, covering: Basic optical structure of the eye, including the refracting components, the pupil, axes, and simple models of the eye Image formation and refraction of the eye, including refractive errors, measurement, and correction Interactions between light and the eye, considering transmission, reflection, and scatter in the media and at the fundus Aberrations and retinal image quality Depth-of-field and age-related changes in the optics of the eye There have been many developments in the field of visual optics since the first edition was published in 2000. There have been advances in instrumentation for imagery, biometry, and aberrations of the eye. The refraction anomaly of myopia has increased in prevalence throughout the world, and is getting increasing attention because of its association with ocular pathology in the middle and later years of life. Ocular aberrations are now considered in terms of Zernike polynomials rather than Taylor polynomials. Aberrations can be manipulated to better understand their effects on visual performance to improve imagery of the retina for the betterment of diagnosis of various ocular conditions, and to treat the progression of myopia in children. To deal with these developments, the section on aberrations and retinal image quality has undergone considerable revision. This book will be an invaluable purchase for all those with an interest in vision, such as optometrists, ophthalmologists, vision scientists, optical physics, and student of visual optics. An understanding of the optics of the human eye is particular important to designers of ophthalmic diagnostic equipment and visual optical systems such as telescopes. Cover Half Title Series Information Title Page Copyright Page Table of Contents Acknowledgements About the Authors Sign Convention and Symbols Introduction Section I Basic Optical Structure of the Human Eye 1 The Human Eye: An Overview 1.1 Introduction 1.2 Optical Structure and Image Formation 1.3 The Retina 1.3.1 The Optic Disc and Blind Spot 1.4 The Cardinal Points 1.5 The Equivalent Power and Focal Lengths 1.6 Axes of the Eye 1.7 Center-Of-Rotation 1.8 Field-Of-Vision 1.9 Binocular Vision and Binocular Overlap 1.9.1 Interpupillary Distance 1.9.2 Binocular Overlap 1.10 Typical Dimensions Summary of Main Symbols References 2 Refracting Components: Cornea and Lens 2.1 Introduction 2.2 The Cornea 2.2.1 Anatomical Structure 2.2.2 Refractive Index 2.2.3 Radii of Curvature, Vertex Powers, and Total Corneal Power 2.2.4 Anterior Surface Shape 2.2.4.1 Toricity 2.2.4.2 Asphericity 2.2.5 Central Thickness 2.2.6 Posterior Surface Shape 2.2.7 Short-Term Changes in the Cornea 2.2.8 Positions of the Principal Points 2.3 The Lens and Its Parameters in the Unaccommodated State 2.3.1 Surface Radii of Curvature and Shapes 2.3.2 Thickness 2.3.3 Refractive Index Distribution 2.3.4 Equivalent Refractive Index 2.3.5 Equatorial Diameter 2.3.6 Lens Power 2.3.7 Positions of Principal Points 2.4 Accommodation Summary of Main Symbols References 3 The Pupil 3.1 Introduction – the Iris 3.2 Entrance and Exit Pupils 3.2.1 Effect of Aberrations 3.2.2 Accommodation 3.2.3 The Paraxial Marginal Ray and Paraxial Pupil Ray 3.3 Pupil Centration 3.4 Pupil Size 3.4.1 Level of Illumination 3.4.2 Field Size 3.4.3 Influences of Binocular Vision and Accommodation 3.4.4 Age 3.4.5 Drugs 3.4.6 Psychological Factors 3.4.7 Combining Factors 3.5 Pupil Aberration and Shape of the Obliquely Viewed Pupil 3.6 Significance of Pupil Size 3.6.1 Depth-Of-Field 3.6.2 Retinal Light Level 3.6.3 Retinal Image Quality and Visual Performance 3.6.4 Purpose of the Pupillary Light Response 3.7 Measurement of Pupil Size (Pupillometry) 3.8 Artificial Pupils Summary of Main Symbols References 4 Axes of the Eye 4.1 Introduction 4.2 Definitions and Significance 4.2.1 Optical Axis 4.2.2 Line of Sight 4.2.3 Visual Axis 4.2.4 Pupillary Axis 4.2.5 Fixation Axis 4.2.6 Keratometric Axis 4.2.7 Pupillary Circular Axis 4.3 Locating Some Axes 4.3.1 The Line of Sight 4.3.2 The Visual Axis 4.3.3 Keratometric Axis 4.4 Angles Between Axes 4.4.1 Visual Axis and Optical Axis: The Angle Alpha (α) 4.4.2 Pupillary Axis and Line of Sight: Angle Lambda (λ) 4.4.3 Pupillary Axis and the Visual Axis: Angle κ 4.4.4 Visual Axis and Achromatic Axis: Angle Psi (Ψ) 4.4.5 Fixation Axis and Optical Axis: Angle Gamma (γ) Summary of Main Symbols References 5 Paraxial Schematic Eyes 5.1 Introduction 5.2 Development of Paraxial Schematic Eyes 5.3 Gaussian Properties and Cardinal Points 5.3.1 Equivalent Power and Cardinal Points 5.3.2 The Aperture Stop and Entrance and Exit Pupils 5.3.3 Position and Magnification of Entrance Pupil 5.3.4 Paraxial Marginal Ray and Paraxial Pupil Ray 5.3.5 Paraxial Pupil Ray Angle Ratio 5.3.6 Effect of Accommodation 5.4 “Exact” Schematic Eyes 5.4.1 Gullstrand Number 1 (Exact) Eye 5.4.2 Le Grand Full Theoretical Eye 5.5 Simplified Schematic Eyes 5.5.1 Gullstrand Number 2 (Simplified) Eye as Modified By Emsley – the Gullstrand–Emsley Eye 5.5.2 Le Grand Simplified Eye 5.5.3 Bennett and Rabbetts’ Simplified Eye 5.6 Reduced Schematic Eyes 5.6.1 Emsley’s Reduced Eye (1952) 5.6.2 Bennett and Rabbetts (1989) 5.7 Variable Accommodating Eyes 5.7.1 Equivalent Power and Positions of Cardinal Points Summary of Main Symbols References Section II Image Formation and Refraction 6 Image Formation: The Focused Paraxial Image 6.1 Introduction 6.2 The General Case 6.2.1 Retinal Image Size and Perceived Angular Size in Object Space 6.3 Eye Focused at Infinity 6.4 Binocular Vision 6.4.1 Stereopsis 6.4.2 Aniseikonia Summary of Main Symbols References 7 Refractive Anomalies 7.1 Introduction 7.2 Spherical Refractive Anomalies 7.2.1 Spherical Refractive Errors 7.2.1.1 Emmetropia (Normal Sight) 7.2.1.2 Myopia (Short Sight) 7.2.1.3 Hyperopia (Hypermetropia) 7.2.2 Presbyopia 7.3 Astigmatic Refractive Errors 7.4 Anisometropia 7.5 Distribution of Refractive Errors and Ocular Components 7.5.1 Distribution 7.5.2 Astigmatism 7.6 The Power of the Correcting Lens 7.6.1 Astigmatic Corrective Powers 7.6.2 Alternative System of Specifying Refractive Errors and Correcting Lens Powers 7.6.3 Thick Lenses and the Effect of Thickness 7.7 Effect of Parameter Changes On Refractive Errors 7.7.1 Refractive Error and Axial Length 7.7.2 Change in Corneal Curvature 7.7.3 Other Parameter Changes Summary of Main Symbols References 8 Measuring Refractive Errors 8.1 Introduction 8.2 Subjective Refraction Techniques 8.2.1 Simple Perception of Blur 8.2.1.1 Conventional Subjective Refraction Techniques 8.2.1.2 Optometers 8.2.2 Longitudinal Chromatic Aberration of the Eye 8.3 Subjective/Objective Refraction Techniques 8.3.1 Remote Refraction and Relay Systems 8.3.2 Split Image and Vernier Acuity (Coincidence Method) 8.3.3 Scheiner Principle 8.4 Objective Refraction Techniques 8.4.1 Retinoscopy 8.4.2 Parallax Movement Between Object and Image 8.4.3 Grating Focus 8.4.4 Image-Size Principle 8.4.5 Hartmann–Shack Aberrometer 8.4.6 Laser Raytracing Aberrometer 8.4.7 Photography 8.4.8 Visual Evoked Response 8.5 Accuracy and Reliability of Refraction 8.6 Factors Affecting Refraction 8.6.1 Target Factors 8.6.2 Optical Factors 8.6.3 Eccentric Viewing 8.6.4 Reference Plane 8.6.5 Site of Fundus Reflectance in Objective Refraction 8.6.6 Accommodation 8.6.7 Maximum Potential Visual Acuity 8.6.8 Discrepancies Between Subjective and Objective Refraction Summary of Main Symbols References 9 Image Formation: The Defocused Paraxial Image 9.1 Introduction 9.2 Retinal Image Size 9.2.1 The Size of the Defocused Image 9.2.2 An Eye Focused at a Finite Distance, Looking at an Object at Infinity 9.2.3 The Use of Artificial Pupils 9.3 Size of the Defocus Blur Disc 9.3.1 The Geometrical Aberration-Free Defocus Blur Disc 9.3.2 Experimentally Determined Angular Diameter of the Blur Discs 9.3.3 Defocus Ratio 9.4 Other Effects of Defocus 9.4.1 Alignment of Two Targets at Different Distances 9.4.2 Effect On Visual Acuity 9.4.2.1 The Value of K and the Corresponding Defocus Ratio Summary of Main Symbols References 10 Some Optical Effects of Ophthalmic Lenses 10.1 Introduction 10.2 Spectacle Magnification 10.3 Pupil Position and Magnification 10.3.1 Retinal Image Illuminance 10.4 Relative Spectacle Magnification 10.4.1 Axial Ametropia 10.4.2 Refractive Ametropia 10.4.3 Further Comments 10.5 Effects On Far and Near Points and Accommodative Demand 10.5.1 Accommodation Through a Correcting Lens 10.6 Rotation Magnification, Field-Of-View, and Field-Of-Vision 10.6.1 Rotational Magnification 10.6.2 Field-Of-View 10.6.3 Field-Of-Vision 10.7 Spectacle Lens Design 10.8 Contact Lens Optics 10.8.1 Over-Refraction 10.8.2 Fluid Lens 10.8.3 Spectacle Magnification 10.9 Intraocular Lens Optics Summary of Main Symbols References Section III Light and the Eye 11 Light and the Eye: Introduction 11.1 Introduction 11.2 Radiation and the Electromagnetic Spectrum 11.3 Light 11.3.1 Photopic Vision 11.3.2 Mesopic Vision 11.3.3 Scotopic Vision 11.3.4 Photopic, Mesopic, and Scotopic Limits 11.4 Photometric Quantities, Units, and Example Levels 11.4.1 Luminous Flux (F) 11.4.2 Luminous Intensity (I) 11.4.3 Luminance (L) 11.4.4 Illuminance (E) 11.5 Some Useful Relationships 11.5.1 Luminous Intensity and Illuminance: The Inverse Square Law 11.5.2 Luminance and Illuminance 11.6 Which Photometric Quantity to Use 11.6.1 Threshold Detection 11.6.2 Supra-Threshold Visibility of Sources With a Small Angular Subtense 11.6.3 Supra-Threshold Visibility of Sources With a Large Angular Subtense 11.6.4 Measurement of Ambient Light Level 11.6.5 Other Comments 11.7 Colorimetry Summary of Main Symbols References 12 Passage of Light Into the Eye 12.1 Introduction 12.2 Specular Reflection 12.2.1 Images Formed By Multiple Reflections 12.3 Transmittance 12.3.1 Spectral Transmittance of the Whole Eye 12.3.2 Spectral Transmittance of Each Ocular Component 12.3.2.1 The Cornea 12.3.2.2 The Aqueous 12.3.2.3 The Lens 12.3.2.4 The Vitreous 12.3.3 Progressive Loss of Light as It Passes Through the Eye 12.3.4 Causes of Absorption Bands 12.3.5 Luminous Transmittance 12.4 Scatter 12.4.1 Scattering Theory 12.4.2 Cornea 12.4.3 Lens 12.4.4 Iris and Sclera 12.5 Fluorescence 12.6 Birefringence 12.6.1 Cornea 12.6.2 Lens Summary of Main Symbols References 13 Light Level at the Retina 13.1 Introduction 13.2 Retinal Illuminance: Directly Transmitted Light 13.2.1 On Axis 13.2.1.1 Large Area Sources The Troland Relationship Between Troland and Lux 13.2.1.2 The Point Source – Diffraction Limited 13.2.1.3 The Point Source – Aberrated 13.2.2 Off-Axis Or Peripheral Sources 13.3 Retinal Illuminance: Scattered Light 13.3.1 Effect of Position in the Lens of a Scattering Center 13.3.2 Measurement of Angular Distribution of Scattered Light 13.3.2.1 Conventional Threshold Method 13.3.2.2 Flicker Compensation Comparison Method 13.3.2.3 Hartmann–Shack Aberrometer 13.4 Photon Density Levels 13.4.1 Blackbody 13.4.2 Real Sources 13.5 Maxwellian View 13.5.1 Equivalent Luminance of a Lambertian Source 13.5.2 Adapting Pupil Size Summary of Main Symbols References 14 Light Interaction With the Fundus 14.1 Introduction 14.1.1 Inner Limiting Membrane to Photoreceptors (Six Layers) 14.1.2 The Photoreceptors 14.1.3 The Pigment Epithelium 14.1.4 The Choroid 14.1.5 The Sclera 14.2 Fundus Reflectance 14.2.1 Polarized Light 14.2.2 Guided and Unguided Light 14.2.3 Layers Responsible for the Fundus Reflectance 14.2.4 Veiling Glare 14.3 Absorption 14.4 Birefringence 14.5 The Stiles–Crawford Effect and Retinal Directionality 14.5.1 Peak of the Stiles–Crawford Effect 14.5.2 Integrating the Stiles–Crawford Effect Across the Pupil 14.5.3 Some Factors Influencing the Stiles–Crawford Effect 14.5.3.1 Wavelength 14.5.3.2 Eccentricity 14.5.3.3 Luminance 14.5.3.4 Field Size 14.5.3.5 Refractive Errors and Aberrations 14.5.3.6 Accommodation 14.5.3.7 Eye Disease 14.5.3.8 Phototropism 14.5.4 Theory 14.5.5 Measurement 14.5.6 Role of the Stiles–Crawford Effect Summary of Main Symbols References Section IV Aberrations and Retinal Image Quality 15 Monochromatic Aberrations 15.1 Introduction 15.2 Representation of Monochromatic Aberrations 15.3 Specification of Monochromatic Aberrations – Taylor Series 15.4 Specification of Monochromatic Aberrations – Zernike Aberration System 15.4.1 Comparing Zernike and Taylor Aberration Systems 15.4.2 Right and Left Eyes 15.4.3 Using Zernike Aberrations to Determine Refraction 15.4.4 Zernike Aberrations Presented in Magnitude/Axis Format 15.4.5 Power Variation Across the Pupil 15.4.6 Other Aberration Systems 15.4.7 Reference Axis 15.4.8 Cornea and Lenticular Components of Aberrations 15.4.9 Change of Wavelength 15.4.10 Peripheral Aberrations 15.5 Techniques 15.6 Magnitudes of Aberrations 15.6.1 Central Field 15.6.2 Peripheral Field 15.6.2.1 Distortion 15.7 Influence of Monochromatic Aberrations On Visual Performance and Consequences of Correcting Them Summary of Main Symbols References 16 Monochromatic Aberrations of Optical Model Eyes 16.1 Introduction 16.2 Aberrations of Paraxial Schematic Eyes 16.2.1 On-Axis 16.2.2 Peripheral Field 16.2.3 Summary 16.3 Modeling Surface Shapes 16.3.1 Conicoid Surfaces 16.3.2 Figured Conicoid Surfaces 16.3.3 More Sophisticated Surfaces 16.3.4 Surface Types Used in Studies 16.4 Modeling the Lenticular Refractive Index Distribution 16.4.1 The Power of the Lens 16.4.1.1 Surface Powers 16.4.1.2 The Gradient Index Power 16.4.1.3 Total Lens Power and Positions of the Cardinal Points 16.5 Modeling the Retina 16.6 Survey of Finite Schematic Eyes 16.6.1 Lotmar (1971) 16.6.2 Drasdo and Fowler (1974) 16.6.3 Kooijman (1983) 16.6.4 Navarro Et Al. (1985) 16.6.5 Liou and Brennan (1997) 16.6.6 Reduced Eye Models of Thibos and Colleagues 16.7 Performance of Finite Schematic Eyes 16.7.1 On-Axis 16.7.2 Peripheral Field 16.7.3 Retinal Image Position 16.7.4 Retinal Illuminance 16.7.5 Summary 16.8 Other Optical Model Eyes, Including Customized Models 16.9 Which Eye Model to Use Summary of Main Symbols References 17 Chromatic Aberrations 17.1 Introduction 17.2 Longitudinal Chromatic Aberration 17.3 Transverse Chromatic Aberration 17.3.1 Chromatic Magnification 17.4 Measurement of Longitudinal Chromatic Aberration 17.4.1 Some Techniques 17.4.1.1 Best Focus Method 17.4.1.2 Vernier Method 17.4.1.3 Double-Pass Techniques 17.4.1.4 Chromo-Retinoscopy 17.4.1.5 Aberrometry 17.4.2 Magnitude 17.4.3 Wavelength in Focus 17.4.4 Effect of Accommodation and Refractive Error 17.5 Measurement of Transverse Chromatic Aberration 17.5.1 Technique 17.5.2 Magnitude 17.6 Effects of Chromatic Aberrations On Vision 17.6.1 Accommodation 17.6.2 Spatial Vision 17.6.3 Chromostereopsis 17.6.4 Aberrations of Ophthalmic Devices 17.7 Aberration Compensation and Correction 17.7.1 Natural Compensation Mechanism 17.7.2 Achromatizing Correcting Lenses 17.7.3 Other Compensation Methods 17.8 Modeling Chromatic Aberrations 17.8.1 Chromatic Dispersion 17.8.2 Schematic Eyes 17.8.2.1 Gaussian Properties 17.8.2.2 Chromatic Difference of Power and Chromatic Difference of Refraction 17.8.2.3 Chromatic Difference of Refraction of Reduced Schematic Eyes 17.8.2.4 Chromatic and Indiana Reduced Eyes of Thibos Et Al. (1992, 1997) 17.9 Estimating Lengths in Eyes Summary of Main Symbols References 18 Retinal Image Quality 18.1 Introduction 18.2 The Point and Line Spread Functions 18.2.1 The Diffraction-Limited PSF (Monochromatic Light) 18.2.2 The Aberrated PSF 18.2.3 The PSF and Its Use in Quantifying Image Quality 18.2.3.1 The Rayleigh Criterion (Diffraction-Limited and Monochromatic Sources) 18.2.3.2 The Half-Width 18.2.3.3 The Strehl Intensity Ratio 18.2.4 The PSF and LSF of Eyes 18.3 The Optical Transfer Function 18.3.1 The Diffraction-Limited OTF With No Stiles-Crawford Effect 18.3.2 Determination of the OTF 18.3.2.1 Determining the OTF From the Measured Wave Aberrations 18.3.2.2 Determining the OTF From the Aerial PSF 18.3.2.3 Determining the OTF From Psychophysical Comparison 18.3.3 OTF in the Presence of Defocus 18.3.3.1 The Geometrical Optical Approximation for Defocus 18.4 Retinal Image Quality 18.4.1 Central Vision 18.4.1.1 Defocus and Refraction 18.4.1.2 Polychromatic Light 18.4.1.3 The Stiles-Crawford Effect 18.4.1.4 Pupil Decentration 18.4.2 Peripheral Vision 18.5 More Image Quality Criteria – Metrics Summary of Main Symbols References Section V Miscellaneous 19 Depth-Of-Field 19.1 Introduction 19.2 Criteria for Determining Depth-Of-Field 19.2.1 Criterion 1: The Range of Focusing Errors for Which No Perceptible Blur of a Target Is Noticeable 19.2.2 Criterion 2: The Range of Focusing Errors for Which the Visual Acuity Or Contrast Sensitivity Does Not Decrease Below a Particular Level Or By More Than a Certain Amount 19.2.3 Criterion 3: The Range of Focusing Errors for Which Changes in Contrast Are Not Detected for a Target in Longitudinal Sinusoidal Motion 19.2.4 Criterion 4: The Range of Focusing Errors for Which the Accommodation Response Does Not Change 19.2.5 Criterion 5: The Range of Focusing Errors Which Degrades Retinal Image Quality Below a Particular Level Or By More Than a Certain Amount 19.3 Modeling Depth-Of-Field 19.3.1 Criterion 1: The Range of Focusing Errors for Which No Perceptible Blur of a Target Is Noticeable 19.3.1.1 Effects of Diffraction and Aberrations 19.3.1.2 Influence of Diffraction Alone at Small Pupil Diameters 19.3.1.3 Influence of Aberrations Alone at Large Pupil Diameters 19.3.1.4 More Complex Objects 19.3.2 Criterion 5: The Range of Focusing Errors, Which Degrades Retinal Image Quality Below a Particular Level Or By More Than a Certain Amount 19.4 Methods for Increasing Depth-Of-Field 19.4.1 Artificial Pupils 19.4.2 Aspheric Surfaces 19.4.3 Other Methods Summary of Main Symbols References 20 The Aging Eye 20.1 Introduction 20.2 Cornea 20.2.1 Corneal Shape 20.2.2 Corneal Thickness 20.2.3 Transmittance 20.3 Anterior Chamber 20.4 Pupil Diameter 20.5 Lens 20.5.1 Shape 20.5.2 Thickness 20.5.3 Refractive Index Distribution 20.5.4 Equivalent Refractive Index 20.5.5 Diameter 20.5.6 Lens Power 20.5.7 Lenticular Transmittance, Scatter, and Fluorescence 20.6 Vitreous Chamber 20.7 Refractive Errors and Axial Length 20.8 Accommodation and Presbyopia 20.8.1 Presbyopia Theories 20.8.1.1 Lenticular Theories – Mechanical Changes in Lens and Capsule 20.8.1.2 Lenticular Theories – Geometric Theories 20.8.1.3 Extra-Lenticular Theories – Duane’s Theory and Changes in Ciliary Muscle 20.8.1.4 Extra-Lenticular Theories – Changes in Elastic Components of Zonules And/or Ciliary Body 20.8.1.5 Summary 20.9 Aberrations 20.10 Photometry 20.10.1 Effect of Light Loss On Visual Performance 20.10.2 Stiles–Crawford Effect 20.11 Schematic Eyes Summary of Main Symbols References Appendices Appendix 1 Paraxial Optics A1.1 Introduction A1.1.1 Finite Raytracing A1.2 The Paraxial Approximations and Paraxial Rays A1.2.1 Definition of a Paraxial Ray A1.2.2 Paraxial Raytrace Equations A1.3 A Paraxial Raytracing Scheme A1.3.1 Step 1: Choosing a Ray A1.3.2 Step 2: Refraction at the Jth Surface A1.3.3 Step 3: Transfer to the Next (J + 1)th Surface A1.3.4 Image Size and Magnification A1.3.5 Special Case of the Object at Infinity A1.3.6 Choice of Ray A1.4 The Optical Invariant A1.5 Cardinal Points and Equivalent Power A1.6 The Lens Equation A1.7 Gaussian Optics Summary of Main Symbols Appendix 2 Seidel Aberration Theory A2.1 Quantification of Aberrations A2.1.1 Rays From an Axial Point A2.1.2 Rays From an Off-Axis Point A2.2 The Wave Aberration Function A2.2.1 Units of Aberrations A2.2.2 Defocus and Wave Aberration A2.2.3 Calculation of the Wave Aberration Function A2.3 Seidel Aberrations A2.3.1 Seidel Aberrations and the Primary Wave Aberration Coefficients A2.3.2 Sagittal, Tangential, and Petzval Surfaces A2.3.3 Wave Aberration Coefficients W2,0 and W2,2 A2.3.4 Modifications for a Curved Retina A2.3.5 Seidel Aberrations of a Gradient Index Medium Summary of Main Symbols References Appendix 3 Schematic Eyes A3.1 Introduction A3.1.1 Units A3.2 Paraxial Schematic Eyes A3.2.1 List of Eyes A3.2.2 Relaxed “Exact” Schematic Eyes A3.2.3 Relaxed Simplified Schematic Eyes A3.2.4 Reduced Eyes A3.2.5 Accommodated ‘Exact’ Schematic Eyes A3.2.6 Accommodated Simplified Schematic Eyes A3.3 Finite Schematic Eyes A3.3.1 List of Eyes Summary of Main Symbols References Appendix 4: Refraction Powers Across the Pupil Summary of Main Symbols Reference Appendix 5 Calculation of PSF and OTF From Aberrations of an Optical System A5.1 The Point Spread Function (PSF) A5.1.1 The Wave Aberration Function W(X, Y) A5.1.1.1 Defocus A5.1.1.2 Chromatic Aberration A5.1.1.3 Polychromatic Sources A5.1.1.4 Computation Checks A5.2 The Optical Transfer Function (OTF) Summary of Main Symbols References Index