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Lens DesignAutomatic and quasi-autonomous computational methods and techniques

IOP Series: Emerging Technologies in Optics and Photonics

Series EditorR Barry Johnson a Senior Research Professor at Alabama A&MUniversity, has been involved for over 40 years in lens design,optical systems design, electro-optical systems engineering, andphotonics. He has been a faculty member at three academicinstitutions engaged in optics education and research, employedby a number of companies, and provided consulting services.

Dr Johnson is an SPIE Fellow and Life Member, OSA Fellow, and was the 1987President of SPIE. He serves on the editorial board of Infrared Physics &Technology and Advances in Optical Technologies. Dr Johnson has been awardedmany patents, has published numerous papers and several books and book chapters,and was awarded the 2012 OSA/SPIE Joseph WGoodman BookWriting Award forLens Design Fundamentals, Second Edition. He is a perennial co-chair of the annualSPIE Current Developments in Lens Design and Optical Engineering Conference.

ForewordUntil the 1960s, the field of optics was primarily concentrated in the classical areas ofphotography, cameras, binoculars, telescopes, spectrometers, colorimeters, radio-meters, etc. In the late 1960s, optics began to blossom with the advent of new types ofinfrared detectors, liquid crystal displays (LCD), light emitting diodes (LED), chargecoupled devices (CCD), lasers, holography, fiber optics, new optical materials,advances in optical and mechanical fabrication, new optical design programs, andmany more technologies. With the development of the LED, LCD, CCD and otherelecto-optical devices, the term ‘photonics’ came into vogue in the 1980s to describethe science of using light in development of new technologies and the performance ofa myriad of applications. Today, optics and photonics are truly pervasive throughoutsociety and new technologies are continuing to emerge. The objective of this series isto provide students, researchers, and those who enjoy self-teaching with a wide-ranging collection of books that each focus on a relevant topic in technologies andapplication of optics and photonics. These books will provide knowledge to preparethe reader to be better able to participate in these exciting areas now and in the future.The title of this series is Emerging Technologies in Optics and Photonics where‘emerging’ is taken to mean ‘coming into existence,’ ‘coming into maturity,’ and‘coming into prominence.’ IOP Publishing and I hope that you find this Series ofsignificant value to you and your career.

Lens DesignAutomatic and quasi-autonomous computational methods and techniques

Donald DilworthOptical Systems Design, Inc.

IOP Publishing, Bristol, UK

ª IOP Publishing Ltd 2018

All rights reserved. No part of this publication may be reproduced, stored in a retrieval systemor transmitted in any form or by any means, electronic, mechanical, photocopying, recordingor otherwise, without the prior permission of the publisher, or as expressly permitted by law orunder terms agreed with the appropriate rights organization. Multiple copying is permitted inaccordance with the terms of licences issued by the Copyright Licensing Agency, the CopyrightClearance Centre and other reproduction rights organisations.

Permission to make use of IOP Publishing content other than as set out above may be soughtat permissions@iop.org.

Donald Dilworth has asserted his right to be identified as the author of this work in accordancewith sections 77 and 78 of the Copyright, Designs and Patents Act 1988.

ISBN 978-0-7503-1611-8 (ebook)ISBN 978-0-7503-1609-5 (print)ISBN 978-0-7503-1610-1 (mobi)

DOI 10.1088/978-0-7503-1611-8

Version: 20180701

IOP Expanding PhysicsISSN 2053-2563 (online)ISSN 2054-7315 (print)

British Library Cataloguing-in-Publication Data: A catalogue record for this book is availablefrom the British Library.

Published by IOP Publishing, wholly owned by The Institute of Physics, London

IOP Publishing, Temple Circus, Temple Way, Bristol, BS1 6HG, UK

US Office: IOP Publishing, Inc., 190 North Independence Mall West, Suite 601, Philadelphia,PA 19106, USA

I cannot help fearing that men may reach a point where they look on every new theoryas a danger, every innovation as a toilsome trouble, … and that they may absolutely

refuse to move at all for fear of being carried off their feet.

—Alexis de Tocqueville, 1840

Contents

Foreword xii

Series Editor’s foreword xiv

Preface xviii

Acknowledgements xxi

Author biography xxii

1 Preliminaries 1-1

1.1 Why is lens design hard? 1-3

1.1.1 The lens design landscape 1-3

1.1.2 Simulated annealing 1-5

1.1.3 Global optimization 1-5

1.1.4 Chaos in lens design 1-6

1.2 How to use this book 1-7

2 Fundamentals 2-1

2.1 Paraxial optics 2-1

2.2 Lagrange invariant, thin-lens equation 2-6

2.3 Pupils 2-7

3 Aberrations 3-1

3.1 Ray-fan curves 3-2

3.2 Abbe sine condition 3-8

3.3 Higher-order aberrations 3-10

3.4 Spot diagrams 3-12

3.5 Wavefronts and aberrations: the OPD 3-14

3.5.1 Image analysis 3-16

3.6 Chromatic aberration 3-22

3.6.1 Cemented doublets 3-25

3.6.2 Secondary color 3-26

4 Using a modern lens design code 4-1

4.1 Using the software 4-1

4.1.1 Wide-angle pupil options 4-3

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4.1.2 Ray aiming 4-3

4.1.3 Paraxial solves 4-4

4.1.4 The WorkSheet 4-5

4.2 The process of lens design 4-6

5 The singlet lens 5-1

5.1 Entering data for the singlet 5-1

6 Achromatizing the lens 6-1

7 PSD optimization 7-1

8 The amateur telescope 8-1

8.1 The Newtonian telescope 8-1

8.2 The Schmidt–Cassegrain telescope 8-7

8.3 The relay telescope 8-15

8.4 How good is good enough? 8-17

9 Improving a lens designed using a different lensdesign program

9-1

10 Third-order aberrations 10-1

10.1 Tolerance desensitization 10-4

11 The in and out of vignetting 11-1

12 The apochromat 12-1

13 Tolerancing the apochromatic objective 13-1

13.1 Fabrication adjustment 13-7

13.2 Transferring tolerances to element drawings 13-12

14 A near-infrared lens example 14-1

14.1 Design approach 14-1

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15 A laser beam shaper, all spherical 15-1

16 A laser beam shaper, with aspherics 16-1

17 A laser beam expander with kinoform lenses 17-1

18 A more challenging optimization challenge 18-1

18.1 Glass absorption 18-5

19 Real-world development of a lens 19-1

20 A practical camera lens 20-1

20.1 Reusing dialog commands 20-14

21 An automatic real-world lens 21-1

22 What is a good pupil? 22-1

22.1 Which way is up? 22-6

23 Using DOEs in modern lens design 23-1

24 Designing aspheres for manufacturing 24-1

24.1 Adding unusual requirements to the merit function with CLINK 24-4

24.2 Defining an aberration with COMPOSITE 24-8

25 Designing an athermal lens 25-1

26 Using the SYNOPSYS glass model 26-1

27 Chaos in lens optimization 27-1

28 Tolerance example with clocking of element wedge errorsand AI analysis of an image error

28-1

29 Tips and tricks of a power user 29-1

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30 FLIR design, the narcissus effect 30-1

30.1 Narcissus correction 30-4

31 Understanding artificial intelligence 31-1

31.1 Error correction 31-5

31.2 MACro loops 31-5

32 The Annotation Editor 32-1

33 Understanding Gaussian beams 33-1

33.1 Gaussian beams in SYNOPSYS 33-1

33.2 Complications 33-3

33.3 Beam profile 33-5

33.4 Effect on image 33-5

34 The superachromat 34-1

35 Wide-band superachromat microscope objective 35-1

35.1 Vector diffraction, polarization 35-9

36 Ghost hunting 36-1

37 Importing a Zemax file into SYNOPSYS 37-1

38 Improving a Petzval lens 38-1

39 Athermalizing an infrared lens 39-1

40 Edges 40-1

40.1 A mirror example 40-5

41 A 90 degree eyepiece with field stop correction 41-1

42 A zoom lens from scratch 42-1

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43 Designing a free-form mirror system 43-1

44 An aspheric camera lens from scratch 44-1

44.1 Encore 44-6

44.2 Coda 44-11

44.3 Tolerancing the aspheric lenses 44-14

45 Designing a very wide-angle lens 45-1

46 A complex interferometer 46-1

47 A four-element astronomical telescope 47-1

48 A sophisticated merit function 48-1

49 When automatic methods do not apply 49-1

49.1 The ‘final exam’ problem 49-1

49.2 The solution 49-3

50 Other automatic methods 50-1

50.1 Testplate matching 50-1

50.2 Automatic thin-film design 50-2

50.3 Automatic clocking of wedge errors 50-5

Appendices

A A brief history of computer-aided lens design A-1

B Optimization methods B-1

C The mathematics of lens tolerances C-1

D Things every lens designer should understand D-1

E Useful formulas E-1

Bibliography 56-1

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Foreword

The use of computers in lens design dates back over 60 years. In that time,computers have increased in speed by many orders of magnitude and in memorycapacity by even more. This has led to enormous improvements in the capabilities oflens design programs. Analysis of lens performance has not changed significantly forseveral decades, but optimization has—and this book is, at its root, aboutoptimization.

Optimization algorithms may be divided into three categories: local, regional andglobal. The first of these categories refers to algorithms that proceed from the givenstarting point to the nearest local minimum. Regional algorithms attempt to escapefrom this local minimum and find a nearby one that is better. As the name implies,global algorithms attempt to search the entire design space and provide a solutionthat is better than any other alternative.

Don Dilworth has made significant contributions to all three categories ofoptimization algorithms which are included in his program, SYNOPSYS. Hisadvance over damped-least-squares (DLS) is called the pseudo second derivative(PSD) approach. This algorithm uses consecutive derivative matrices to approx-imate the second derivative matrix and uses this to calculate an improved dampingfactor for each variable. The result is a tremendous increase in convergence speedfrom initial designs that are far from optimal. Dilworth’s program also has analgorithm that is often able to start with a lens that does not pass all the requiredrays and tweak it until it does before starting optimization.

In the regional optimization category, SYNOPSYS starts with a standardsimulated annealing algorithm, but combines it with PSD to make it far moreeffective than simulated annealing is in other programs. Masaki Isshiki’s globaloptimization with escape function algorithm is also implemented, but this reviewerdoes not have sufficient experience with other programs’ implementations to offer acomparison. Regional optimization features unique to SYNOPSYS are ‘automaticelement insertion’ and ‘automatic element deletion’, which either insert or delete alens element at the optimal location. The former algorithm can be run in a way thatis very similar to Florian Bociort’s saddle point algorithm.

New global optimization algorithms, DSEARCH and ZSEARCH, whichDilworth has recently added to SYNOPSYS, are most impressive. DSEARCHstarts from a very rough description of a lens (the object, wavelengths, F/#, andnumber of elements) along with any other required constraints, and produces severalcandidate designs that are often close to final designs. ZSEARCH does the samething for zoom lenses. Both algorithms can provide lens designs even if the designerhas no idea of what an initial configuration might look like. Dilworth has publisheda paper with Dave Shafer, a renowned lens designer, comparing the results ofDSEARCH with Dave Shafer’s design of a well-designed eleven-element lens. Thepaper is an entertaining discussion of man versus machine. DSEARCH was able toquickly find solutions with eleven, ten, nine, and, remarkably, only eight elements.Once he knew that there was a potential solution space having fewer elements,

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Shafer was also able to find designs, but took much more time to do so. He foundone design that DSEARCH missed (with default options), but the algorithm cameup with several other designs which surpassed those of this famous lens designer.

One could say a lot more about optimization in general, and Dilworth’scontributions in particular, but this should be enough to give you a flavor.Reading this book will teach you more design tricks and insights. Many examplesare provided that readers can run on their own computer and experiment with bychanging parameters and other commands. I am certain that you will enjoy andprofit from this book.

Dr Steve EckhardtEckhardt Optics LLCWhite Bear Lake, MN

March 2018

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Series Editor’s foreword

Mr Donald C Dilworth began developing in the late 1960s a lens design and analysissoftware package called SYNthesis of OPtical SYStems (SYNOPSYS™). Over thepast 50 years, by himself, he created, developed, and has continued to improve andexpand the capabilities of this program to meet the demanding needs of lens designprofessionals throughout the world. During this period, other lens design programswere developed for both internal corporate use and general use by the opticscommunity. Many of these programs left the marketplace while a modest few havestood the test of time. All current commercial lens design programs have excellentcapabilities that meet the general needs of the optical designer; however, over thepast couple of decades, optics has become broadly pervasive, and the demand forpeople capable of accomplishing optical design rapidly outstripped the supply oftrained and talented lens designers. To overcome this lack of supply, lens designsoftware providers worked hard to make it easier for essentially untrained people touse their programs and obtain meaningful designs. One important capability thathas been explored by the software providers is to incorporate a means to allow theuser to input basic parameters of the optical system and then allow the softwareprogram to attempt to create design(s) that meet the designer’s requirements. In thisbook, Mr Dilworth presents how to design and analyze lens systems, and hisinnovative and unique developments in automated lens design that have had, andwill continue to have, significant utility in mitigating the growing lack of profes-sional lens designers as well as improving the efficiency and creativity of theprofessional lens designers. Achieving the goal of autonomous optical designcontinues to be an emerging technology for lens design software providers; however,Mr Dilworth has made great strides to accomplish quasi-autonomous lens design.

Arguably, during the 1960s and 1970s Berlyn Brixner (Los Alamos NationalLaboratory) was the first to suggest and demonstrate starting a design using just flatplates and allow the program to ‘explore’ alternative paths to generate a designsolution. As computer power became available at affordable costs and research inoptimization techniques evolved, lens design program developers began to incor-porate what is commonly called global optimization. The objective is to allow theprogram to search for a solution that is hopefully superior to that following normaloptimization methods. Indeed, the various approaches often did find better designsand often new design forms the human designer had not envisioned. Such a searchprocess is quite time- and resource-consuming, with the result potentially being adesign that is not practical. Nevertheless, the global optimization tool has been ofgreat benefit to the beginning lens designer as well as the professional. Furtherrefinement of potential designs can be obtained by using the simulated annealingfeature available in all current programs.

While lens design software developers focused on methods to improve globaloptimization along similar lines, Mr Dilworth additionally explored and exploitedseveral ‘out-of-the-box’ approaches to achieving, what might be called, quasi-autonomous lens design. There are four such innovations that provide lens designers

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additional tools that have the potential to create solutions to their design require-ments in less time, with more ease, and by exploring new configurations theSYNOPSYS program produces.

The first two innovations to aid the designer were developed initially about 1990,and provided artificial intelligence (AI) capabilities utilizing natural languageprocessing and expert systems. The natural language AI feature provides a veryflexible way to interact with SYNOPSYS, and to perform certain tasks not readilyaccomplished with the normal command syntax or spreadsheet input. Among thesetasks are displaying and changing certain lens parameters, defining new commandsor character strings, and obtaining plotted parametric curves involving up to threedifferent quantities. The input consists of English sentences comprising subjects,verbs, and conditions. The vocabulary contains many hundreds of words and theflexibility for the user is vast. This is a very powerful and useful tool for designers.

In general, an ‘expert systems’ program is one that employs a tree-structured logicwherein decisions are derived from the responses of a number of experts in aparticular field to a lengthy debriefing. Remarkable performance has been achievedin some areas, rivaling that of a human expert. In contrast, the SYNOPSYSprogram takes a somewhat different approach in that the expert system feature(XSYS) is presented with a number of finished lens designs that are the products ofexpert designers and represent the state-of-the-art. Using these lenses as models, theprogram analyzes the optical properties in great detail, determining for each lens thefirst and higher-order properties, and the aberrations that are present in the beambefore and after each element. In so doing, the program ‘learns’ how a particularoptical problem was solved by its designer. The more examples provided to XSYS,the more it learns. When presented with a new problem or a lens that is not wellcorrected, XSYS can determine if the current problem resembles one for which itknows a solution and then attempts to use bits and pieces of lenses in its expert-designed-lenses library to create various potential configurations for the user toreview, select one to optimize, and then analyze. This feature is very creative andoften finds unexpected configurations that work better than having followed aconventional design path. Of course, not having a library of relevant lenses willmitigate the utility of XSYS. However, if it is available, XSYS can provide the lensdesigner with a powerful tool to identify potential lens configurations for furtheroptimization and analysis.

As mentioned previously, a bit over a quarter of a century ago, as computerresources became more capable, the search for the optimum solution of a lens designmoved from optimizing a ‘point’ design to allowing the software program to explorean enormous variety of possible configurations in solution space. Such a searchprocess takes, in general, a huge amount of time in contrast to point designoptimization. This is known as global optimization and often includes simulatedannealing. A variety of approaches have been developed by researchers to locate the‘true’ global optimum solution (minimum merit function) while at the same timeminimizing the convergence time. Arguably, progress has been made, but the timeneeded for finding candidate solutions often remains excessive. Early in the currentdecade, in an effort to dramatically reduce the search time for candidate design

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solutions, Mr Dilworth developed a quasi-autonomous method to search forcandidate fix-focused lens configurations which he named DSEARCH™ (DesignSEARCH). This method is not intended to produce a finished lens design; itspurpose is to identify attractive starting points, and each of the designs can then besubjected to further optimization, first with transverse intercepts, then with OPDtargets, and lastly with MTF targets in the merit function. Although the solutions liein a multidimensional hyperspace that cannot be visualized, it is common tovisualize the solution space as a rough mountain range where the highest peakcorresponds to a flat-plate starting design. The objective is to find the lowest valley,which is certainly a challenge. Since any direction from the mountain peak isdownward, the question is which direction to go. Mr Dilworth reckoned that anefficient selection of directions to try would be a ‘binary’ approach where the flat-plate lenses are assigned either a positive or negative power. For an N element lens,this implies 2N starting optical configurations or directions to consider. When thevalley in a particular direction is found, the question still remains: is the this the bestsolution in this direction? To overcome this, simulated annealing is used to explorethe surrounding hyperspace to determine if a lower valley exists. Of course, aRANDOM mode can be used to attempt to find the best solution, but it can be farmore demanding of time. If the initial flat-plate design is specified to have Nelements, and in the event that the best solutions found are not good enough, anautomatic element insertion option is available and the prior solution lenses can bereprocessed. Should the solutions be ‘too good’, an automatic element deletionoption can be used to reprocess the lenses to look for adequate solutions having N−1elements.

The final innovation to mention is the evolution of DSEARCH to accomplishfinding potential solutions for zoom lenses. The design of zoom lenses is significantlymore challenging than the design of fixed-focused lenses. Mr Dilworth named thisnew feature ZSEARCH™ (Zoom SEARCH) and it was presented at the 2016 SPIEMeeting in San Diego, CA. ZSEARCH works essentially like DSEARCH exceptthat the searching process is much more complex, and the results are rather amazing.

Mr Dilworth continues to develop improvements in his quest for quasi-autonomouslens design to address the issue of the growing dearth of experienced lens designers.The inclusion of additional features in the search and final design selection processthat consider manufacturability and cost of the candidate lenses should be mostbeneficial to lens designers and their employers.

Working alone on his SYNOPSYS program for the past half century,Mr Dilworth has made exceptional contributions in computer-based optical designsoftware, which is used worldwide, and in his development of the aforementionedinnovations to assist both novice and expert designers in their work to design high-performance optical systems in minimal time.

Those learning lens design will find the material in this book helpful in masteringhow to design lens systems regardless of which lens design software is used. Allreaders should benefit from the knowledge and wisdom Mr Dilworth has gainedover the past half-century. Unlike the traditional books on lens design, theinteractive nature of this book provides readers with an unprecedented opportunity

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to work examples themselves and further explore what happens if they modify theexamples while using a provided version of SYNOPSYS. This is an excellent methodto learn the subject and sharpen one’s skills. Optics has become pervasive through-out most technological areas, and the design and manufacture of optical systems isthe fundamental foundation.

R Barry Johnson, DSc, FInstP, FOSA, FSPIESeries Editor, Emerging Technologies in Optics and Photonics

Huntsville, AL

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Preface

Why this book? A new paradigm. The lens design landscape. The lens design tree.When a friend suggested I write a book about lens design, my first reaction was:

Why? There are a number of excellent books out there already. Who needs anotherone?

My second thought was: Why me? I have never taken a course in optics or lensdesign, and (I hate to admit it) I have never even read most of the aforesaid books.What can I possibly add to the corpus?

My friend pointed out that I have been designing lenses for more than 50 years,and it is likely I have picked up a few pointers along the way. True enough.

That led to my third thought: this might be a very short book. I picked up one ofthe best of the current texts, Lens Design Fundamentals by Rudolph Kingslake andR Barry Johnson (2010, Bellingham, WA: SPIE), and read descriptions of how onedoes certain tasks that you do not have to do anymore. The classic authors anddesigners had to make do with very primitive tools and were faced with a staggeringamount of manual labor. So they devised shortcuts, found insights where they could,and invented ways to obtain an approximate answer with relatively little work.What I mean by ‘little’ can be understood in the context of Kingslake’s comment:

When someone applied for a position in our department at Kodak, I wouldask him if he could contemplate pressing the buttons of a desk calculator forthe next forty years, and if he said ‘yes’, I would hire him.

In this computer age, most of those tools and shortcuts are no longer needed. Infact, some of them actually get in the way and are better avoided. The classic textswill not tell you that. This book will.

When I first entered this field, there were no books on computer-aided lens design.I first traced rays on a computer filled with vacuum tubes. I had to figure everythingout for myself. This turns out to be an advantage, it puts me in a position to ask:what do you really need to know in order to design lenses? Not all that much, it turnsout. Certainly, you do not need all the primitive tools used by the old masters, and ifI had to use those tools and do all that manual labor, I would have left thisrewarding field years ago. Some will be offended that I give little ink to thosetechniques in this book—but I want to teach what is useful today, not what peoplehad to learn a generation ago.

Today we live in a new world. I estimate that perhaps 90% of what I read in theclassic texts is now irrelevant. I could write on two pages most of what one needs toknow when designing lenses, assuming one has a modern PC and the most powerfulof today’s lens design programs (and a basic understanding of math and physics). Agood friend, who teaches lens design at a major university, once boasted that herstudent could design a five-element lens in only five days. Modern software can

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design a seven-element lens in less than one second. My friend did not know that.Things are changing.

Many brilliant minds have contributed to this field, and prudence says we shouldnot just discard the knowledge and skills handed down to us by the old masters. Sohow can I justify saying that very little of that knowledge is relevant today? Here ishow: I challenged my friend to design a 90-degree eyepiece, essentially perfect, withthe classic tools she had long mastered. She gave up after 100 h of work. Usingsoftware that I have developed over more than 50 years, I was able to solve thatproblem in only 15 minutes—using almost none of those tools. I think experiencespeaks for itself. We are thinking out of the box here, and the results are wonderful.This is a game-changer.

Before I go too far, however, I have to caution the reader that learning to use lensdesign software is not for everyone. For one thing, it requires some familiarity withoptics and physics. The software is not going to anticipate and solve every problemfor you. The aptitude necessary to become a good engineer is not to be found inevery human head, which is why engineering schools have entrance exams. You willbe obliged to read the instruction manuals and make an effort to understand them. Isometimes receive questions from very naïve beginners showing they are startingwithout this familiarity and are confused by many of the concepts presented in themanuals and in this book. There is a reason people attend college and obtain adegree in the sciences. With that background, those concepts are simple and clearenough. I urge those without a technical education to take steps to acquire it beforediving into this fascinating field.

Some will object that the methods I present in this book rely too much on chance.A throw of the dice. Trial and error. They want the process to be deterministic,guided at every turn by expert knowledge. There is much to be said for that point ofview—but consider a conversation I once had with Kingslake (an expert if ever therewas one):

I said: ‘In your book, you show how one could alter a certain radius ofcurvature in steps and plot an aberration curve, then change a certain thicknessand plot a second curve. Where those curves cross is a better design—but howdid you know you should change this radius and that thickness?’

He replied: ‘That’s the only thing that worked. I tried everything else.’

It seems that even the experts had to resort to trial and error much of the time, ifone makes an objective appraisal of how they worked. What I have done is to makeit work much better and much faster. How much better? A colleague oncevolunteered, ‘These search methods work so well it’s scary!’ He knew what hewas talking about; he had tried them himself.

But, wait a minute. Two pages? A friend objected: ‘We cannot just teach thestudents to push a button!’ True enough. There is a whole lot of optics written

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between the lines on those pages, and the student really should know what happenswhen you push it. Kingslake observed:

‘We are losing the ability to design a lens through an effort of the intellect.’

He is right1. Grab a qualified person off the street, sit him in front of a modernlens design program, and ask: what does he need to know in order to use iteffectively? I hope to put the answers on the pages of this book.

1But we have also lost the ability to make flint arrowheads and ride horses, and I do not care.

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Acknowledgements

I want to thank the many loyal and very smart customers using my lens designprogram who have suggested new features and improvements. Together, we aremore effective than I could be by myself.

I especially want to thank Dr R Barry Johnson, whose encouragement and abilityto see outside the box has been instrumental in the progress of my career and led meto write this book.

Lastly, I wish to thank my wife Sarah, who, despite knowing nothing aboutoptics, continues to believe that what I am doing has merit.

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Author biography

Donald C Dilworth

Mr Dilworth has been designing lenses since 1961, when heparticipated in the development of the optical navigation system forthe Apollo project, the American program to land men on theMoon. He is a graduate of MIT, where he majored in physics, but isself-taught in the fields of optical engineering and lens design. Hislater work includes designing one of the spy cameras that flew overthe Soviet Union during the Cold War, and he has worked in

industry for many years, designing infrared FLIR systems (which can see in totaldarkness), and numerous kinds of lens systems including a submarine periscope. Heformed his own company, Optical Systems Design, Inc. in 1976 and has beendeveloping and marketing the lens design program SYNOPSYS™ (SYNthesis ofOPtical SYStems) ever since.

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