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This section contains the title pages, CIP page, introduction to the series, titles in the series, preface, table of contents, and the glossary of symbols and acronyms.

Library of Congress Cataloging-in-Publication Data

Bentley, Julie (Julie L.)

Field guide to lens design / Julie Bentley, Craig Olson.

pages cm. – (The field guide series)

Includes bibliographical references and index.

ISBN 978-0-8194-9164-0

1. Lenses--Design and construction. I. Olson, Craig 1971-II. Title.

QC385.B43 2012

681'.423--dc23

2012035700

Published by

SPIE

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Introduction to the Series

Welcome to the SPIE Field Guides—a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series.

Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights, and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships, and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field.

The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be easily updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at fieldguides@SPIE.org.

John E. Greivenkamp, Series Editor

Optical Sciences Center

The University of Arizona

The Field Guide Series

Keep information at your fingertips with all of the titles in the Field Guide Series:

Adaptive Optics, Second Edition, Robert Tyson & Benjamin Frazier

Atmospheric Optics, Larry Andrews

Binoculars and Scopes, Paul Yoder, Jr. & Daniel Vukobratovich

Diffractive Optics, Yakov Soskind

Geometrical Optics, John Greivenkamp

Illumination, Angelo Arecchi, Tahar Messadi, & John Koshel

Image Processing, Khan M. Iftekharuddin & Abdul Awwal

Infrared Systems, Detectors, and FPAs, Second Edition, Arnold Daniels

Interferometric Optical Testing, Eric Goodwin & Jim Wyant

Laser Pulse Generation, Rüdiger Paschotta

Lasers, Rüdiger Paschotta

Microscopy, Tomasz Tkaczyk

Optical Fabrication, Ray Williamson

Optical Fiber Technology, Rüdiger Paschotta

Optical Lithography, Chris Mack

Optical Thin Films, Ronald Willey

Optomechanical Design and Analysis, Katie Schwertz & James Burge

Polarization, Edward Collett

Probability, Random Processes, and Random Data Analysis, Larry Andrews

Radiometry, Barbara Grant

Special Functions for Engineers, Larry Andrews

Spectroscopy, David Ball

Terahertz Sources, Detectors, and Optics, Créidhe O’Sullivan & J. Anthony Murphy

Visual and Ophthalmic Optics, Jim Schwiegerling

Field Guide to Lens Design

Optical design has a long and storied history, from the magnifiers of antiquity, to the telescopes of Galileo and Newton at the onset of modern science, to the ubiquity of modern advanced optics. The process for designing lenses is often considered both an art and a science. While advancements in the field over the past two centuries have done much to transform it from the former category to the latter, much of the lens design process remains encapsulated in the experience and knowledge of industry veterans. This Field Guide provides a working reference for practicing physicists, engineers, and scientists for deciphering the nuances of basic lens design. Because the optical design process is historically (and quite practically) closely related to ray optics, this book is intended as a companion to the Field Guide to Geometrical Optics, in which first-order optics, thin lenses, and basic optical systems are treated in more detail. Note that this compact reference is not a substitute for a comprehensive technical library or the experience gained by sitting down and designing lenses.

This material was developed over the course of several years for undergraduate and graduate lens design classes taught at the University of Rochester. It begins with an outline of the general lens design process before delving into aberrations, basic lens design forms, and optimization. An entire section is devoted to techniques for improving lens performance. Sections on tolerancing, stray light, and optical systems are followed by an appendix covering related topics such as optical materials, nonimaging concepts, designing for sampled imaging, and ray tracing fundamentals, among others.

Thanks to both of our families—Danielle, Alison, Ben, Sarah, Julia, and especially our spouses, Jon and Kelly. The cats will now get fed, and all soccer parents beware!

Julie Bentley

University of Rochester

Craig Olson

L-3 Communications

Table of Contents

Glossary of Symbols and Acronyms xi

Fundamentals of Optical Design 1

Sign Conventions 1

Basic Concepts 2

Optical Design Process 3

Aperture and Wavelength Specifications 4

Resolution and Field of View 5

Packaging and Environment 6

Wave Aberration Function 7

Third-Order Aberration Theory 8

Spot Diagram and Encircled Energy 9

Transverse Ray Plot 10

Wavefront or OPD Plots 11

Point Spread Function and Strehl Ratio 12

MTF Basics 13

Using MTF in Lens Design 14

Defocus 15

Wavefront Tilt 16

Spherical Aberration 17

Coma 18

Field Curvature 19

Petzval Curvature 20

Astigmatism 21

Distortion 22

Primary Color and Secondary Color 23

Lateral Color and Spherochromatism 24

Higher-Order Aberrations 25

Intrinsic and Induced Aberrations 26

Design Forms 27

Selecting a Design Form: Refractive 27

Selecting a Design Form: Reflective 28

Singlets 29

Achromatic Doublets 30

Airspaced Doublets 31

Cooke Triplet 32

Double Gauss 33

Petzval Lens 34

Telephoto Lenses 35

Retrofocus and Wide-Angle Lenses 36

Refractive versus Reflective Systems 37

Obscurations 38

Newtonian and Cassegrain 39

Gregorian and Schwarzschild 40

Catadioptric Telescope Objectives 41

Unobscured Systems: Aperture Clearance 42

Unobscured Systems: Field Clearance 43

Three-Mirror Anastigmat 44

Reflective Triplet 45

Wide-Field Reflective Design Forms 46

Zoom Lens Fundamentals 47

Zoom Lens Design and Optimization 48

Improving a Design 49

Techniques for Improving an Optical Design 49

Angle of Incidence and Aplanatic Surfaces 50

Splitting and Compounding 51

Diffraction-Limited Performance 52

Thin Lens Layout 53

Lens Bending 54

Material Selection 55

Controlling the Petzval Sum 56

Stop Shift and Stop Symmetry 57

Telecentricity 58

Vignetting 59

Pupil Aberrations 60

Aspheres: Design 61

Aspheres: Fabrication 62

Gradient Index Materials 63

Diffractive Optics 64

Optimization 65

Optimization 65

Damped Least Squares 66

Global Optimization 67

Merit Function Construction 68

Choosing Effective Variables 69

Solves and Pickups 70

Defining Field Points 71

Pupil Sampling 72

Tolerancing 73

Tolerancing 73

Design Margin and Performance Budgets 74

Optical Prints 75

Radius of Curvature Tolerances 76

Surface Irregularity 77

Center Thickness and Wedge Tolerances 78

Material and Cosmetic Tolerances 79

Lens Assembly Methods 80

Assembly Tolerances 81

Compensators 82

Probability Distributions 83

Sensitivity Analysis 84

Performance Prediction 85

Monte Carlo Analysis 86

Environmental Analysis 87

Athermalization 88

Stray Light 89

Stray Light Analysis 89

Stray Light Reduction 90

Antireflection (AR) Coatings 91

Ghost Analysis 92

Cold Stop and Narcissus 93

Nonsequential Ray Tracing 94

Scattering and BSDF 95

Optical Systems 96

Photographic Lenses: Fundamentals 96

Photographic Lenses: Design Constraints 97

Visual Instruments and the Eye 98

Eyepiece Fundamentals 99

Eyepiece Design Forms 100

Telescopes 101

Microscopes 102

Microscope Objectives 103

Relays 104

Appendix: Optical Fundamentals 105

Index of Refraction and Dispersion 105

Optical Materials: Glasses 106

Optical Materials: Polymers/Plastics 107

Optical Materials: Ultraviolet and Infrared 108

Snell’s Law and Ray Tracing 109

Focal Length, Power, and Magnification 110

Aperture Stop and Field Stop 111

Entrance and Exit Pupils 112

Marginal and Chief Rays 113

Zernike Polynomials 114

Conic Sections 115

Diffraction Gratings 116

Optical Cements and Coatings 117

Detectors: Sampling 118

Detectors: Resolution 119

The Lagrange Invariant and Étendue 120

Illumination Design 121

Equation Summary 122

Biography 127

Index 129

Glossary of Symbols and Acronyms

A

Area

AOI

Angle of incidence

AR

Antireflection

BBAR

Broadband antireflection coating

BFL

Back focal length

BFS

Best fit sphere

BRDF

Bidirectional reflectance distribution function

BSDF

Bidirectional scattering distribution function

BTDF

Bidirectional transmittance distribution function

c

Surface curvature

C

Lens conjugate factor

CA

Clear aperture

CCD

Charge-coupled device

CDF

Cumulative distribution function

CGH

Computer-generated hologram

CMOS

Complementary metal-oxide semiconductor

CRA

Chief ray angle

CT

Center thickness

CTE

Coefficient of thermal expansion

CTF

Contrast transfer function

d

Airspace

d

Thickness

DLS

Damped least squares

d n/d T

Thermo-optic coefficient

DOE

Diffractive optical element

EFL

Effective focal length

EPD

Entrance pupil diameter

ESF

Edge-spread function

ETD

Edge thickness difference

f

Focal length

f/#

f-number or relative aperture

FEA

Finite-element analysis

FFL

Front focal length

FFOV

Full field of view

FFT

Fast Fourier transform

FOV

Field of view

GQ

Gaussian quadrature

GRIN

Gradient index

h, h

Object/image height

H

Lagrange invariant

H

Normalized field coordinate

HFOV

Half field of view

HO

Higher order

HOE

Holographic optical element

HR

High-reflection

i, i

Angle of incidence w.r.t. surface normal

i, ia

Marginal ray angle w.r.t. surface normal

i¯, ib

Chief ray angle w.r.t. surface normal

ID

Inner diameter of a lens barrel or mount

IR

Infrared

L

Radiance

LOS

Line of sight

LR

Limiting resolution

LSF

Line spread function

LWIR

Long-wave infrared

m

Diffraction order

m

Magnification

MP

Magnifying power (magnifier or telescope)

MTF

Modulation transfer function

MWIR

Midwave infrared

n, n

Index of refraction

n(z), n(r)

Gradient index profile function

NA

Numerical aperture

NITD

Narcissus-induced temperature difference

NRT

Nonsequential ray tracing

NUC

Nonuniformity correction

OAP

Off-axis parabola

OAR

Off-axis rejection

OD

Outer diameter (of a lens)

OPD

Optical path difference

OTF

Optical transfer function

p

Pixel pitch in sampled detector arrays

P

Partial dispersion

PDF

Probability distribution function

PSF

Point spread function

PSNIT

Point-source normalized irradiance transmittance

PST

Point-source transmittance

P–V

Peak to valley

Q

Sampling ratio

r

Radial surface coordinate

R, ROC

Radius of curvature

RI

Relative illumination

RMS

Root mean square

RSS

Root sum square

RT

Reflective triplet

s, s

Object/image distance

SA

Spherical aberration

SLR

Single-lens reflex

t

Thickness or airspace

T

Temperature

TIR

Total indicator runout

TIR

Total internal reflection

TIS

Total integrated scatter

TMA

Three-mirror anastigmat

TML

Three mirror long

u, u

Paraxial ray angles w.r.t. optical axis

u, ua

Marginal ray angle w.r.t. optical axis

u¯, ub

Chief ray angle w.r.t. optical axis

UV

Ultraviolet

V

Abbe number

W

Wave aberration function

Wi jk

Wavefront aberration coefficient

WD

Working distance

y, ya

Marginal ray height at a surface

y¯, yb

Chief ray height at a surface

z

Optical axis

z(r)

Surface sag/profile function

Zn

Zernike polynomial coefficient

β

Lens shape factor

Δλ

Wavelength range or bandwidth

δz

Defocus

ε

Obscuration ratio

ε, εx , εy

Transverse ray error

θ, θ

Angle of incidence/refraction

θ

Half field of view

θ

Pupil azimuthal coordinate

κ

Conic constant

λ

Wavelength

λ0

Center wavelength

ρ, ρx , ρy

Normalized radial pupil coordinate

Φ

System power

ϕ

Element or surface power

ϕ

Merit or penalty function

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