Table Of ContentSpringer Series in Optical Sciences 183
Chris Velzel
A Course in
Lens Design
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Max-Planck-InstitutfürQuantenoptik OptischesInstitut
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Chris Velzel
A Course in Lens Design
123
Chris Velzel
Deurne
The Netherlands
ISSN 0342-4111 ISSN 1556-1534 (electronic)
ISBN 978-94-017-8684-3 ISBN 978-94-017-8685-0 (eBook)
DOI 10.1007/978-94-017-8685-0
Springer Dordrecht Heidelberg New YorkLondon
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Preface
Lenses play an important role in our life. Our eyes make images of the world
around us and are sometimes aided by spectacle glasses or contact lenses.
IndailylifeweuselensesinCD-drives,inwebcamsandcellphones,incameras
forphotographyandobservation,infilmprojectorsandsearchlights,inbinoculars
for looking at birds, or other far-away objects. Scientific applications of lenses
(and mirrors) are found in microscopes and astronomical telescopes. And
machines for the production of integrated circuits use huge lens (or mirror)
systems to project very tiny details. Lenses are everywhere.
The book presented here has the title ‘‘A Course in Lens Design.’’ This title
should be understood as follows: the design of lenses is a complicated activity,
because it comprises the design of an optical system that performs a desired
function, but also the design of the mechanical parts in which the optics are
mounted (and sometimes also electronics and software). Moreover, the design
must result in a product that can be manufactured by existing technology.
Becauseopticalsystemdesignisthefirstinthischainofactivities,thesuccess
of later stages depends on its performance. This book is limited to lens design in
the sense of design of a suitable optical system for a given application.
As‘‘ACourseinLensDesign’’isaimedatuserswhohave littleknowledgeof
the subject (an elementary optics course would be helpful, but is not strictly
required), it is limited in treatment to the essentials, as will be seen from the
description of its contents below.
As in many research and development activities (and in society as a whole) in
thesecondhalfofthetwentieth-century,the‘‘artandscience’’oflensdesignwas
revolutionized by the coming of the computer.
Inthepastittookanaccomplishedopticaldesignerseveralminutestocalculate
thepath ofaraythroughaspherical surface.Withthecomputerthis‘‘ray-surface
time interval’’ was reduced to parts of microseconds. In the beginning there was
the hope that the design of lenses could be automated completely with the aid of
computers.Aftersometimeitbecameclearthatthiswasanillusion;thedesignof
lenses makes in many of its stages decisions of the designer necessary. Never-
theless,theuseofdesignsoftwareonthecomputersavesthedesigneralotoftime
and effort.
It remains true that one needs a certain level of expertise to profit from the
expertisestoredinlensdesignsoftwareprograms.Thiscourseisintendedtobuild
v
vi Preface
upthisexpertise;itbringsthebeginnertoapointwherehe/shecandesignavariety
of lenses and will be able to use a software program with success.
Comingfromacareerasanopticalscientist,Itaughtmyselfthesubjectoflens
design; with this book I want to share this experience with the reader.
Ifoundthatmostbooksonlensdesigneithergavemoreattentiontotheresults
thantotheprocessoflensdesign,ordrownedthedesignprocessinaseaofdetails
on physics, mechanics, and production technology.Thatdoes notmeanthat these
booksarenotuseful;whenyouhavemasteredtheprocessoflensdesign,theycan
provide awiderand/ormoredetailed viewofthesubject.WiththisbookIoffera
complete method of lens design that is neither too simple nor too detailed. For a
wider perspective the book refers to the literature. As one of my professors said:
we want to spare the wolf, the goat, and the cabbage.
The book is divided in six chapters.
Chapter 1 contains a short introduction to geometrical optics. The image for-
mation by spherical mirrors, refractive surfaces, and lenses is described. The thin
lens is introduced as a useful and simple model of a real lens. An algorithm is
given for tracing rays through optical systems in the paraxial approximation.
Finally,definitionandfunctionofstopsandpupilsarediscussed.Theconceptsand
tools prepared in this chapter are used continuously in the rest of the book.
Chapter 2 gives a description of important categories of optical instruments:
cameras,magnifiers,microscopes,telescopes,andoftheoptics ofthehumaneye.
This is useful to understand the function of lenses used in optical instruments.
In Chaps. 1 and 2, the paraxial approximation of geometrical optics is used
throughout. It is a simple, but very useful method to describe centered optical
systems. In this book, we do not treat the design of noncentered systems.
In Chap. 3, the description of optical systems is made more accurate by con-
sidering third-order aberrations. The relation between wavefront errors in the exit
pupilandaberrationsintheimageplaneisshown.Theformulasforthecalculation
of aberration coefficients are given and discussed. The aberration coefficients
depend on the position of the stop; stop shift equations are given that quantify
these effects.
Chapter 4 describes the processes of lens design.
InSect.4.1,systemspecificationistreated;alsoareviewofexistinglenstypes
is given.
InSect.4.2,theparaxiallayoutofthesystemstobedesignedisdescribed.The
number, powers, and positions of components are determined. The primary
chromaticaberrationsarecorrected.Thecomponentsaredescribedbythinlenses.
InSect.4.3,theformulasfortheaberrationsofathinlensatthestoparegiven.
The stop shift equations are used to determine the coefficients of system compo-
nents. A procedure for the correction of the aberrations of the thin lens model is
described that, with some variations, is used in the design examples of Chap. 6.
InSect.4.4,aprocedureisgiventoconvertthethinlenspredesigntoa‘‘surface
model’’ by giving thickness. After this the third-order aberrations of the surface
model can be calculated.
Preface vii
In Sect. 4.5, the optimization of the design is discussed. Topics of this section
are: construction of merit functions, aberration balancing and fifth order aberra-
tions, the mathematics of optimization and the analysis of the optimized design.
In Sect. 4.6, the sensitivity of the design to fabrication errors is considered; a
method of calculation of the system tolerances is presented.
InSect. 4.7,we derive someresultsfromdiffractiontheorythatcan beusedin
lensdesign,viz.pointspreadfunction(PSF),modulationtransferfunction(MTF),
Strehl’s number, and Airy radius.
InChap.5,thestrategiesoflensdesignarereviewed.Weconsiderfivefieldsof
application: color correction (with a section on optical materials), degrees of
freedom, symmetries, stops and pupils, and correction offield aberrations.
Chapter6containsthedetaileddescriptionsofthedesignofavarietyoflenses.
Thisbeginswiththedesignofthinsystems(singletsanddoublets),followedbythe
design of a telescope, asymmetric two-component systems, triplets and triplet
variants, symmetric four-component systems, micro-objectives, and a section on
the application of aspheric surfaces with a postscript on diffractive optics.
The book is addressed primarily to beginners in lens design; for instance,
people with an education in applied physics or engineering, or students of tech-
nical optics.
When you want to learn lens design, it is not enough to read this book. You
should begin to design lenses yourself. The book contains 21 exercises that are
meant for that purpose. By completing these you will find that, step-by-step, you
will become able to make your own designs. In the beginning this will take some
time, because you have to do calculations with pen and paper (and a calculator).
By using the spreadsheet facility on your computer you can speed up these cal-
culations.Whenyouhavemasteredthefirststagesofthelensdesignprocess,you
can use lens design software tooptimize the design. With the designs of Chap. 6,
the Zemax(cid:3) software was used for this purpose.
In most of this book the mathematics is limited to algebra. In some sections
mathematicsofahigherlevelisused.Thesesectionsprovidebackgroundmaterial
andcanbeskippedifnecessary.PartofSect.4.5andallofSect.4.7belongtothis
category, marked by an asterisk.
Deurne, 2013 Chris Velzel
Acknowledgments
Many people helped me to produce this book.
Fromthebeginning,BogusiaDubiksupportedmebytypingthemanuscript.In
alater stage, Ariadne Tenner took careofthe lay-out,the figures,andthe version
management.
The photograph on page 329 (About the Author) was made by Paul Keizer.
Harry Kessels, Michiel van Rijnbach, and Jørgen van der Veen helped to for-
mulate the contents of the course by discussions.
Abdel Boujnane and Elena Sokolova gave their support by checking the cal-
culations and exercises.
Anearly version ofthe manuscript was read byLeo Beckmann, Peter Nuyens,
BeateMitchunas,andWolfgangVollrath.Thefinalmanuscriptprofitedfromtheir
criticism.
Iam mostthankfultoLeonoor,who supported me duringthe 3yearsinwhich
the book grew.
November 2013 Chris Velzel
ix
Contents
1 Geometrical Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Principles of Geometrical Optics. . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Paraxial Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 The Concave Mirror . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 The Spherical Refractive Surface. . . . . . . . . . . . . . . . . 7
1.2.3 Prisms and Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Optical Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 The Single Lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.2 Thin Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Paraxial Raytracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.1 The Optical Invariant. . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4.2 Ray Tracing with Thin Lenses . . . . . . . . . . . . . . . . . . 18
1.5 Stops and Pupils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5.1 Telecentric Stop . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.5.2 Adding Rays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2 Optical Instruments (Paraxial Approximation) . . . . . . . . . . . . . . . 25
2.1 Camera. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1.1 Camera Obscura . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2 Human Eye. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.1 Nodal Points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.2 Exercise 4, Nodal Points of the Eye. . . . . . . . . . . . . . . 29
2.3 Magnifier and Microscope . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.1 Maximum Magnification . . . . . . . . . . . . . . . . . . . . . . 31
2.4 Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5 Illumination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 Aberrations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1 Wavefronts and Aberrations . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.1 First Order Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1.2 The Third Order Aberrations. . . . . . . . . . . . . . . . . . . . 43
3.1.3 Spherical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
xi
