Analytical Lens Design

277 Pages·2020·34.023 MB·English

by  Rafael G. Gonzalez-Acuna, Hector A. Chaparro-Romo, Julio C. Gutierrez-Vega

Analytical Lens Design
IOP Series in Emerging Technologies in Optics and Photonics
Series Editor
R Barry Johnson a Senior Research Professor at Alabama A&M
University, has been involved for over 50 years in lens design,
optical systems design, electro-optical systems engineering, and
photonics. He has been a faculty member at three academic
institutions engaged in optics education and research, employed
by a number of companies, and provided consulting services.
DrJohnsonisanIOPFellow,SPIEFellowandLifeMember,OSAFellow,andwas
the 1987 President of SPIE. He serves on the editorial board of Infrared Physics &
Technology and Advances in Optical Technologies. Dr Johnson has been awarded
manypatents,haspublishednumerouspapersandseveralbooksandbookchapters,
andwasawardedthe2012OSA/SPIEJosephWGoodmanBookWritingAwardfor
LensDesignFundamentals,SecondEdition.Heisaperennialco-chairoftheannual
SPIE Current Developments in Lens Design and Optical Engineering Conference.
Foreword
Untilthe1960s,thefieldofopticswasprimarilyconcentratedintheclassicalareasof
photography, cameras, binoculars, telescopes, spectrometers, colorimeters, radio-
meters,etc.Inthelate1960s,opticsbegantoblossomwiththeadventofnewtypesof
infrareddetectors,liquidcrystaldisplays(LCD),lightemittingdiodes(LED),charge
coupled devices (CCD), lasers, holography, fiber optics, new optical materials,
advances in optical and mechanical fabrication, new optical design programs, and
many more technologies.With thedevelopment ofthe LED,LCD, CCD and other
electo-optical devices, the term ‘photonics’ came into vogue in the 1980s to describe
thescienceofusinglightindevelopmentofnewtechnologiesandtheperformanceof
amyriadofapplications.Today,opticsandphotonicsaretrulypervasivethroughout
societyandnewtechnologiesarecontinuingtoemerge.Theobjectiveofthisseriesis
to 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 and
applicationofopticsand photonics.Thesebookswill provideknowledgetoprepare
thereadertobebetterabletoparticipateintheseexcitingareasnowandinthefuture.
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 of
significant value to you and your career.
Analytical Lens Design
Rafael G Gonza´lez-Acun˜a
Tecnológico de Monterrey, Garza Sada 2501, Monterrey 64849, México
He´ctor A Chaparro-Romo
Independent Researcher, Alcanfores 8, Lazaro Cárdenas, Tultitlán 54916, México
Julio C Gutie´rrez-Vega
Tecnológico de Monterrey, Garza Sada 2501, Monterrey 64849, México
IOP Publishing, Bristol, UK
ªIOPPublishingLtd2020
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ISBN 978-0-7503-3167-8(ebook)
ISBN 978-0-7503-3165-4(print)
ISBN 978-0-7503-3168-5(myPrint)
ISBN 978-0-7503-3166-1(mobi)
DOI 10.1088/978-0-7503-3167-8
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Contents
Preface xiii
Acknowledgements xiv
Author biographies xvi
Part I A historical, mathematical and optical introduction
1 A brief history of stigmatic lens design 1-1
1.1 The rise of geometrical optics 1-1
1.2 Optics of the ancient Greeks and Arab world 1-3
1.3 Snell, Descartes, Huygens, Newton and Fermat 1-8
1.4 19th and 20th century 1-12
1.5 The computer era and the closure of a conjecture 1-14
Further reading 1-15
2 A mathematical toolkit for stigmatic imaging 2-1
2.1 A mathematical toolkit 2-1
2.2 Set theory 2-1
2.2.1 Axiom of extension 2-2
2.2.2 Axioms of specification and pairing 2-3
2.2.3 Operations between sets 2-4
2.2.4 Relations and functions 2-7
2.2.5 Continuity 2-8
2.3 Topological spaces 2-9
2.3.1 Definition of a topological space via neighbourhoods 2-9
2.3.2 Definition of a topological space via open sets 2-10
2.3.3 Continuity and homeomorphism 2-10
2.3.4 Topological properties 2-12
2.4 Metric spaces 2-13
2.4.1 Euclidean metric 2-14
2.5 The conics 2-15
2.5.1 The parabola 2-15
2.5.2 The ellipse 2-16
2.5.3 The hyperbola 2-17
2.5.4 The circle 2-19
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AnalyticalLensDesign
2.6 Geometric algebra 2-20
2.6.1 Scalars, vectors, and vector spaces 2-20
2.6.2 The inner product 2-21
2.6.3 The outer product 2-22
2.6.4 The geometric product 2-24
2.6.5 The imaginary number 2-25
2.6.6 Multiplicative inverse of a vector 2-26
2.6.7 Application of Clifford algebra in the law of sines 2-26
2.6.8 Application of Clifford algebras in the law of cosines 2-27
2.7 Conclusions 2-28
Further reading 2-28
3 An introduction to geometrical optics 3-1
3.1 Geometrical optics 3-1
3.2 The principle of least action 3-3
3.3 Reflection 3-4
3.4 Refraction 3-4
3.5 Two-dimensional Snell’s law in geometric algebra 3-5
3.6 Three dimensions Snell’s law in geometric algebra 3-7
3.7 Stigmatism 3-8
3.8 Optical aberrations 3-12
3.8.1 Spherical aberration 3-12
3.8.2 Coma 3-13
3.8.3 Astigmatism 3-15
3.8.4 Field curvature 3-15
3.8.5 Image distortion 3-17
3.9 Conclusions 3-17
Further reading 3-18
Part II Stigmatic singlets
4 On-axis stigmatic aspheric lens 4-1
4.1 Introduction 4-1
4.2 Finite object finite image 4-7
4.2.1 Fermat’s principle 4-8
4.2.2 Snell’s law 4-9
4.2.3 Solution 4-13
4.2.4 Illustrative examples 4-15
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AnalyticalLensDesign
4.3 Evolution tables of the shape of on-axis stigmatic lens 4-16
4.4 Stigmatic aspheric collector 4-24
4.4.1 Examples 4-27
4.5 Stigmatic aspheric collimator 4-29
4.5.1 Illustrative examples 4-30
4.6 The single-lens telescope 4-31
4.6.1 Examples 4-33
4.7 Conclusions 4-34
Further reading 4-34
5 Geometry of on-axis stigmatic lenses 5-1
5.1 Introduction 5-1
5.2 Lens free of spherical aberration finite-finite case 5-2
5.2.1 The condition of maximum aperture for the finite–finite case 5-3
5.3 Lens free of spherical aberration infinite–finite case 5-5
5.3.1 The condition of maximum aperture for the infinite–finite case 5-6
5.4 Lens free of spherical aberration finite–infinite case 5-8
5.4.1 The condition of maximum aperture for finite–infinite case 5-9
5.5 Lens free of spherical aberration infinite–infinite case 5-10
5.5.1 The condition of maximum aperture for the 5-11
infinite–infinite case
5.6 Conclusions 5-11
Further reading 5-12
6 Topology of on-axis stigmatic lenses 6-1
6.1 Introduction 6-1
6.2 The topology of on-axis stigmatic lens 6-3
6.3 Example of the topological properties 6-7
6.4 Conclusions 6-9
Further reading 6-9
7 The gaxicon 7-1
7.1 Introduction 7-1
7.2 Geometrical model 7-1
7.3 Gallery of axicons 7-6
7.4 Conclusions 7-8
Further reading 7-8
ix