# GEOMETRICAL OPTICS AND OPTICAL DESIGN

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1 GEOMETRICAL OPTICS AND OPTICAL DESIGN Pantazis Mouroulis Associate Professor Center for Imaging Science Rochester Institute of Technology John Macdonald Senior Lecturer Physics Department University of Reading New York Oxford OXFORD UNIVERSITY PRESS 1997

2 Contents Rays and the Foundations of Geometrical Optics 1.1. Waves, Wavefronts, and Rays The Pinhole Camera Propagation of Wavefronts, Reflection, Refraction Fermat's Principle Irradiance and the Inverse-Square Law The Basic Postulates of Geometrical Optics 15 Review of Elementary Ray Optics Plane Surfaces Reflecting Surfaces Refracting Surfaces Curved Surfaces: Focusing Focusing in the Paraxial Region Graphical Ray Tracing for Thin Lenses Graphical Ray Tracing for Mirrors 31 Imagery by a Single Surface and a Thin Lens The Sign Convention The Paraxial Approximation 39

3 x CONTENTS 3.3. Imagery by a Single Surface The Conjugate Equation Power and Focal Lengths of a Surface Mirrors Imagery by a Thin Lens Thin Lens Conjugate Equation Power of a Thin Lens in Air Focal Lengths of a Thin Lens Thin Lens Refraction: The General Case Many Surfaces in Contact Throw Imagery of an Extended Object. Magnification The One-Component Design Problem Other Types of Magnification The Angular Size of an Object Visual Magnification Longitudinal Magnification. Imagery of a Volume Gaussian Optics The Paraxial Height and Angle Variables Paraxial Ray Tracing for Systems of Many Surfaces Notation Magnification Paraxial Ray Tracing through Many Surfaces The Optical Invariant Principal Planes 70 AAA. Definition and Properties of the Principal Planes Power and Focal Lengths of a General System Reference to an Arbitrary Set of Conjugates Afocal Systems Location of Principal Planes Power and Principal Planes of a System of Two Separated Components Thick Lenses: Power and Location of Principal Planes Nodal Points, Measurement of Focal Length Additional Topics in Gaussian Optics Newton's Form of the Conjugate Equation Imagery of a Tilted Plane Summary of Gaussian Optics The Two-Component Design Problem 88

4 5. Putting It All Together Stops and Pupils Entrance and Exit Pupils Numerical Aperture, F Number Depth of Focus, Depth of Field Pupils: Off-Axis Imagery Pupil Matching Paraxial Marginal and Pupil Rays How to Find the Stops Size of a Lens or Surface (Clear Aperture) Two-Ray Forms of Я Significance and Use of the Marginal and Pupil Rays Connecting Paraxial and Finite Optics The Sine Condition The Tangent Condition Gaussian Predesign The Two-Lens System with Fixed Pupil Positions The y-y Diagram Light Flux Transmission through Optical Systems Radiometry versus Photometry Radiometric (Photometric) Quantities and Units Flux Emitted into a Cone by a Lambertian Source Flux Collected by a Lens Irradiance of an Image Radiance (Luminance) of an Aerial Image Photometry of Illumination Systems Off-Axis Illumination Illuminance from a Large Source Luminance of a Distant Source 132 CONTENTS xi 6. Gaussian Optics of Optical Instruments and Components The Telescope Visual Telescopes Astronomical Telescopes and Resolution Information Capacity of an Optical System Laser Beam Expander The Microscope Magnifying Power and Resolution Microscope Illumination Systems Projection Systems The Overhead Projector Aspherics in Illumination Systems Other Projection Systems The Eye Basic Anatomy Geometrical Parameters 152

5 xii CONTENTS Scene Luminance and Retinal Illuminance Refractive Effects and Accommodation Resolution and Acuity Contrast Sensitivity Reflecting Prisms Geometrical Aspects of Reflection Tunnel Diagram. Effect of a Plane Block of Glass Common Prism Types Some Instrumental Applications of Reflecting Prisms Cylindrical and Anamorphic Optics Image of a Point through a Cylindrical Lens Image Illuminance through a Cylindrical Lens Gradient Index Optics Snell's Law The Parabolic Index Profile Paraxial Ray Tracing for Gradient Index Media Gaussian Constants of GRIN Rods The Optical Invariant Diffractive Optics The Diffraction Grating Holographic Optical Elements Binary Optics Introduction to Aberrations Chromatic Aberration Characterization of Dispersion Chromatic Effects for a Thin Lens The Achromatic Doublet and Related Concepts Secondary Spectrum. Apochromatic Correction Introduction to Monochromatic Aberrations The Origin of Monochromatic Aberrations Wavefront and Ray Aberrations Canonical Coordinates The Wave Aberration Function. Classification of Aberrations The Wave Aberration Polynomial for Rotationally Symmetric Systems Classical Aberration Types Ray Intersection Patterns and Spot Diagrams Longitudinal Aberration Aberration Tolerances Example: Computation of Wave and Ray Aberration Computation of Primary Aberrations The Seidel Aberration Coefficients The Paraxial Refraction Invariants 227

6 CONTENTS xiii Surface Contribution to the Wavefront Aberration The Seidel Aberration Formulae Special Aberration-Free Cases. The Aplanatic Meniscus Chromatic Aberrations Design Example: A Simple Camera Objective Astigmatism and Field Curvature Primary Aberrations of a Reflecting Prism (Plane-Parallel Plates) Primary Aberrations of a Spherical Mirror Aberrations of a Thin Lens in Air Central Aberrations (Stop at the Lens) Shape-Independent Aberrations The Shape Factor and the Magnification Parameter Shape-Dependent Aberrations The Corrected Doublet A Practical Aberration Primer Thin-Lens Aberrations with a Remote Stop The Eccentricity Parameter Stop-Shift Effects for a Single Surface Stop-Shift Effects for a General System and a Thin Lens Stop-Shift Theorems Example: The Petzval Projection Lens The Two- and Three-Component Solution with Fixed ЪК The Two-Component Solution The Three-Component Solution The Cooke Triplet Optical Design The Optical Design Process Making the System Real: Thickening, Total Aberration Design Example: Operating Spectacles Optimization Pupils and Pupil Imagery Pupil Aberration Off-Axis Pupil Shape and Vignetting Off-Axis Image Formation and Canonical Coordinates Aspherics A Brief Guide to Optical Design Software 289

7 xiv CONTENTS Appendix 1. Matrix Methods in Paraxial Optics 294 Al.l. The Conjugate Matrix 296 A 1.2. Relation between A,B,C,D and 5,5',К 298 Appendix 2. Gaussian Beam Ray Tracing 300 A2.1. Basic Characteristics of Gaussian Beams 300 A2.2. Paraxial Equations for Gaussian Beams 303 A2.3. Thin Lens in Air 306 A2.4. The General System: Principal Planes 308 A2.5. Two-Ray Formulation of Gaussian Beams 311 Appendix 3. Finite Ray Tracing 317 A3.1. Vector Form of Snell's Law 318 A3.2. The Surface Equation and the Surface Normal 318 A3.3. Surface Transfer 319 A3.4. Refraction 320 Appendix 4. Shift of Focus 322 A4.1. Longitudinal Focal Shift 322 A4.2. Transverse Focal Shift 324 Appendix 5. Two Computer Programs 327 A5.1. Thin Aplanatic Doublet Design (Stop at the Lens) 327 A5.2. Paraxial Ray Tracing and Seidel Aberration Computation 331 Appendix 6. Thin-Lens Bending Program 341 Bibliography 349 Index 351

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