Abstract
This front matter contains an introduction, table of contents, and symbol glossary.

Library of Congress Cataloging-in-Publication Data

Schwiegerling, Jim.

Field guide to visual and opththalmic optics / Jim Schwiegerling.

p. cm.

Includes bibliographical references and index.

ISBN 0-8194-5628-4

1. Physiological optics. I. Title.

QP475.S385 2004

612.8′4--dc22 2004020668

Published by

SPIE—The International Society for Optical Engineering

P.O. Box 10

Bellingham, Washington 98227-0010 USA

Phone: +1360 676 3290

Fax: +1360 647 1445

Email: spie@spie.org

Web: http://spie.org

The content of this book reflects the work and thought of the author(s). Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon.

Printed in the United States of America.

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Introduction to the Series

Welcome to the SPIE Field Guides! This volume is one of the first in a new 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

Field Guide to Visual and Ophthalmic Optics

Visual optics is a scientific field that brings together many disciplines. Optical engineering and biology are interwoven to produce the most sophisticated imaging system known. The human visual system functions over a broad range of conditions, adapts to its surroundings and is capable of quickly processing complex visual information at enviable speeds. Many of the great names of optical physics such as Newton, Maxwell, Young, Helmholtz, and Alvarez have all made significant contributions to the field of visual optics. This book assembles much of the anatomy, physiology, and functioning of the eye, as well as the engineering and design of a wide assortment of tools for measuring, photographing and characterizing properties of the surfaces and structures of the eye. Finally, descriptions of our attempts to correct vision, reverse the aging process, and improve on Mother Nature are given.

I would like to express my gratitude to several colleagues for their help with this book. First, I’d like to thank John Greivenkamp for granting the opportunity to write this book and for his mentoring and friendship. Second, I’d like to thank Joseph Miller, whose enthusiasm for engineering is contagious, and whose ideas are always elegant. Finally, I’d like to thank Charlie Campbell for passing on a bit of his wisdom and knowledge and for providing an outlet for my babbling about Zernike polynomials.

This book is dedicated to my wonderful wife Diana, my son Max, and my daughter Marie.

Jim Schwiegerling

Dept. of Ophthalmology and Optical

Sciences Center, University of Arizona

Table of Contents

Glossary x

Ocular Function 1

Eyeball 1

Cornea 2

Retina 3

Photoreceptors 4

Retinal Landmarks 5

Properties of Ocular Components 6

Accommodation 7

Pupil Size and Dark Adaptation 8

Transmission and Reflectance 9

Axes of the Eye 10

Stiles-Crawford Effect 11

Photopic V(λ) and Scotopic V′(λ) Response 12

Eye Movements 13

Vergence 14

Paraxial Schematic Eye 15

Arizona Eye Model 16

Aberrations 17

Visual Acuity 19

Visual Acuity and Eye Charts 20

Contrast Sensitivity Function (CSF) 21

Emmetropia and Ametropia 23

Far and Near Points 24

Presbyopia 25

Correction of Ocular Errors 26

Spectacles: Single Vision 26

Spectacle Lenses 27

Lensmeter 28

Spherical and Cylindrical Refractive Error 29

Prismatic Error 30

Astigmatic Decomposition 31

Special Ophthalmic Lenses 32

Variable Prisms and Lenses 33

Contact Lenses 34

Radiuscope 35

Spectacle and Contact Lens Materials 36

Surgical Correction of Refractive Error 37

Cataract Surgery 38

Ophthalmic Instrumentation and Metrology 39

Purkinje Images 39

Fluorescein Imaging 40

Indocyanine Green Imaging 41

Keratometry 42

Corneal Topography 43

Corneal Topography: Axial Power 44

Corneal Topography: Instantaneous Power 45

Anterior Segment Imaging 46

Wavefront Sensing: Shack-Hartmann Sensing 47

Wavefront Sensing: Tscherning Aberrometry 48

Wavefront Sensing: Retinal Raytracing 49

Wavefront Sensing: Spatially Resolved Refractometry 50

Wavefront Sensing: Reconstruction 51

Zernike Polynomials: Wavefront Sensing Standard 53

Zernike Polynomials: Cartesian Coordinates 54

Zernike Polynomials: Useful Formulas 55

Ophthalmoscopy 57

Retinal Imaging 58

Field of View and Perimetry 59

Retinoscopy 60

Autorefraction 61

Badal Optometer and Maxwellian View 62

Common Ophthalmic Lasers 63

Eye Safety: Laser Sources 64

Eye Safety: Non-laser Sources 65

Color 66

Photometry 66

Colorimetry: RGB and CIE XYZ Systems 67

Colorimetry: Chromaticity Diagram 68

Colorimetry: Primaries and Gamut 69

Colorimetry: CIELUV Color Space 70

Colorimetry: CIELAB Color Space 71

Chromatic Adaptation 72

L, M, and S Cone Fundamentals 73

Appendices 74

Aspheric and Astigmatic Surfaces 74

Differential Geometry 75

Trigonometric Identities 76

CIE Photopic V(λ) and Scotopic V′(λ) Response 77

1931 CIE 2° Color Matching Functions 78

1964 CIE 10° Color Matching Functions 80

Stockman & Sharpe 2° Cone Fundamentals 82

Incoherent Retinal Hazard Functions 85

Zernike Polynomials: Table in Polar Coordinates 87

Zernike Polynomials: Table in Cartesian Coordinates 88

Equation Summary 89

Bibliography 99

Index 105

Glossary

A

Accommodation

A

A-constant

α*

Color coordinate in CIELAB space

A(λ)

Aphakic & infant retinal hazard function

A(θ)

Oblique astigmatism

ACD

Anterior chamber depth

AK

Astigmatic keratotomy

ARMD

Age-related macular degeneration

ArF

Argon fluoride

Axis

Cylinder axis

B

Blue channel in RGB space

b*

Color coordinate in CIELAB space

B(λ)

Blue light retinal hazard function

b¯(λ)

Color matching function in CIE RGB space

BD

Base down

BI

Base in

BO

Base out

BU

Base up

CA, CB, Cc

Constants for laser exposure calculations

C*uv, C*ab

Chroma

cd

Units of candelas

CIE

Commission Internationale de l’Eclairage

CK

Conductive keratoplasty

CMF

Color matching function

CSF

Contrast sensitivity function

Cyl

Cylinder power

D

Units of diopters (inverse meters)

D

Pupil diameter

d

Distance

dϕ

Power error

D65

6500° K reference white light source

E

Component of the first fundamental form

Ev

Illuminance

F

Component of the first fundamental form

f

Focal length

fo

Spatial frequency

FOV

Field of view

G

Green channel in RGB Space

G

Component of the first fundamental form

g¯(λ)

Color matching function in CIE RGB space

H

Mean curvature

hab, huv

Hue

HDTV

High-definition television

Iv

Luminous intensity

ICG

Indocyanine green

IOL

Intraocular lens

J0

Horizontal crossed cylinder

J45

Oblique crossed cylinder

JCC

Jackson crossed cylinder

K

Conic constant

K

Keratometry values

K

Gaussian curvature

L

Luminance

L

Axial length

L

Component of the second fundamental form

L*, Lv, Lλ

Luminance

L(λ)

Long-wavelength cone fundamental

LA

LogMAR acuity

LASEK

Laser epithelial keratomileusis

LASIK

Laser in situ keratomileusis

LOS

Line of sight

LCA

Longitudinal chromatic aberration

lm

Units of lumens

LSA

Longitudinal spherical aberration

LTK

Laser thermal keratoplasty

lux

Units of lumens/m2

M

Spherical equivalent power

M

Component of the second fundamental form

M(λ)

Middle-wavelength cone fundamental

MPE

Maximum permissible exposure

N

Component of the second fundamental form

n,n′

Index of refraction

nk

Keratometric index of refraction

OCT

Optical coherence tomography

OD

Oculus dexter (right eye)

OS

Oculus sinister (left eye)

OU

Oculus uterque (both eyes)

P

Prism power

PI-PIV

Purkinje images

PAL

Progressive addition lens

PD

Interpupillary distance

PIOLs

Phakic intraocular lenses

PMMA

Polymethylmethacrylate

PRK

Photorefractive keratectomy

q

Center of rotation of the eye

R

Radius of curvature

R

Red channel in RGB space

r

Radial position in polar coordinates

Rx, Ry

Radii of curvature along the x and y axes

R(λ)

Thermal retinal hazard function

r¯(λ)

Color matching function in CIE RGB space

RGP

Rigid gas permeable

RK

Radial keratotomy

ROC

Radius of curvature

S

Snellen fraction

S(λ)

Short-wavelength cone fundamental

SEP

Spherical equivalent power

SF

Surgeon factor

SLO

Scanning laser ophthalmoscope

SLT

Selective laser trabeculoplasty

Sph

Spherical power

t

Thickness

t

Exposure time

Td

Units of troland

U

Object vergence

u*,u

Color coordinates in CIELUV space

V

Image vergence

υ*, υ′

Color coordinates in CIELUV space

V(λ)

CIE photopic response

V’(λ)

CIE scotopic response

V*(λ)

Stockman & Sharpe corrected photopic response

W

Wavefront error

X

Tristimulus value in CIE XYZ space

x

Chromaticity coordinate in CIE XYZ space

x

Horizontal Cartesian coordinate

x¯(λ)

Color matching function in CIE XYZ space

Y

Tristimulus value in CIE XYZ space

y

Chromaticity coordinate in CIE XYZ space

y

Vertical Cartesian coordinate

y¯(λ)

Color matching function in CIE XYZ space

Z

Tristimulus value in CIE XYZ space

z

Chromaticity coordinate in CIE XYZ space

z

Axial Cartesian coordinate

z¯(λ)

Color matching function in CIE XYZ space

Znm(ρ,θ)

Zernike polynomial

Δ

Units of prism diopters

ΔE

Color difference in CIELAB and CIELUV spaces

Δλ

Wavelength interval

Δx, Δy, Δz

Translation along Cartesian axes

Φ,ϕ

Power

Φa

Axial power

Φi

Instantaneous power

Φv

Luminous flux

Φ(λ)

Radiometric power

κ1, κ2

Principal curvatures

λ

Wavelength

θ

Angle in polar coordinates

ρ

Normalized radial position in polar coordinates

τ

Transmission

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