This book presents an in-depth look at lenses free of spherical aberrations and is provided using illustrative examples. Mathematical principles behind lenses free of spherical aberration are included with an introduction to set theory, the conics, continuity, real analysis and topology. Physical principles are covered as well as a step by step guide to mathematical model for deducing the general formula of the stigmatic lens, in order to design a singlet free of spherical aberration. Subsequently, the characteristics of these lenses and the equations that describes them are studied. Finally, several implications of these lenses are studied, such as freeform lenses, optical systems, axicons, telescopes and more. Scenarios with on-axis objects and off-axis objects are considered. Cases where the object is real or virtual, and the image is real or virtual are also presented. The book is a valuable resource for industrial specialists and academics in lens design and optics, and an insightful guide for optical physics students.
Author(s): Rafael G. Gonzalez-Acuna, Hector A. Chaparro-Romo, Julio C. Gutierrez-Vega
Series: Emerging Technologies in Optics and Photonics
Publisher: Iop Publishing
Year: 2020
Language: English
Pages: 500
City: Bristol
PRELIMS.pdf
Preface
Acknowledgements
Acknowledgements of Rafael G González-Acuña
Acknowledgements of Héctor A Chaparro-Romo
Acknowledgements of Julio C Gutiérrez-Vega
Author biographies
Rafael G González-Acuña
Héctor A Chaparro-Romo
Julio C Gutiérrez-Vega
CH001.pdf
Chapter 1 A brief history of stigmatic lens design
1.1 The rise of geometrical optics
1.2 Optics of the ancient Greeks and Arab world
1.3 Snell, Descartes, Huygens, Newton and Fermat
1.4 19th and 20th century
1.5 The computer era and the closure of a conjecture
Further reading
CH002.pdf
Chapter 2 A mathematical toolkit for stigmatic imaging
2.1 A mathematical toolkit
2.2 Set theory
2.2.1 Axiom of extension
2.2.2 Axioms of specification and pairing
2.2.3 Operations between sets
2.2.4 Relations and functions
2.2.5 Continuity
2.3 Topological spaces
2.3.1 Definition of a topological space via neighbourhoods
2.3.2 Definition of a topological space via open sets
2.3.3 Continuity and homeomorphism
2.3.4 Topological properties
2.4 Metric spaces
2.4.1 Euclidean metric
2.5 The conics
2.5.1 The parabola
2.5.2 The ellipse
2.5.3 The hyperbola
2.5.4 The circle
2.6 Geometric algebra
2.6.1 Scalars, vectors, and vector spaces
2.6.2 The inner product
2.6.3 The outer product
2.6.4 The geometric product
2.6.5 The imaginary number
2.6.6 Multiplicative inverse of a vector
2.6.7 Application of Clifford algebra in the law of sines
2.6.8 Application of Clifford algebras in the law of cosines
2.7 Conclusions
Further reading
CH003.pdf
Chapter 3 An introduction to geometrical optics
3.1 Geometrical optics
3.2 The principle of least action
3.3 Reflection
3.4 Refraction
3.5 Two-dimensional Snell’s law in geometric algebra
3.6 Three dimensions Snell’s law in geometric algebra
3.7 Stigmatism
3.8 Optical aberrations
3.8.1 Spherical aberration
3.8.2 Coma
3.8.3 Astigmatism
3.8.4 Field curvature
3.8.5 Image distortion
3.9 Conclusions
Further reading
CH004.pdf
Chapter 4 On-axis stigmatic aspheric lens
4.1 Introduction
4.2 Finite object finite image
4.2.1 Fermat’s principle
4.2.2 Snell’s law
4.2.3 Solution
4.2.4 Illustrative examples
4.3 Evolution tables of the shape of on-axis stigmatic lens
4.4 Stigmatic aspheric collector
4.4.1 Examples
4.5 Stigmatic aspheric collimator
4.5.1 Illustrative examples
4.6 The single-lens telescope
4.6.1 Examples
4.7 Conclusions
Further reading
CH005.pdf
Chapter 5 Geometry of on-axis stigmatic lenses
5.1 Introduction
5.2 Lens free of spherical aberration finite-finite case
5.2.1 The condition of maximum aperture for the finite–finite case
5.3 Lens free of spherical aberration infinite–finite case
5.3.1 The condition of maximum aperture for the infinite–finite case
5.4 Lens free of spherical aberration finite–infinite case
5.4.1 The condition of maximum aperture for finite–infinite case
5.5 Lens free of spherical aberration infinite–infinite case
5.5.1 The condition of maximum aperture for the infinite–infinite case
5.6 Conclusions
Further reading
CH006.pdf
Chapter 6 Topology of on-axis stigmatic lenses
6.1 Introduction
6.2 The topology of on-axis stigmatic lens
6.3 Example of the topological properties
6.4 Conclusions
Further reading
CH007.pdf
Chapter 7 The gaxicon
7.1 Introduction
7.2 Geometrical model
7.3 Gallery of axicons
7.4 Conclusions
Further reading
CH008.pdf
Chapter 8 On-axis spherochromatic singlet
8.1 Introduction
8.2 Mathematical model
8.3 Illustrative examples
8.4 Spherochromatic collimator
8.5 Galley of spherochromatic collimators
8.6 Discussion and conclusions
Further reading
CH009.pdf
Chapter 9 On-axis stigmatic freeform lens
9.1 Introduction
9.2 Finite image-object
9.2.1 Fermat principle
9.2.2 Snell’s law
9.2.3 Solution
9.2.4 Illustrative examples
9.3 The freeform collector lens
9.3.1 Examples
9.4 The freeform collimator lens
9.4.1 Illustrative examples
9.5 The beam-shaper
9.5.1 Illustrative example
9.6 Conclusions
Further reading
CH010.pdf
Chapter 10 On-axis astigmatic freeform lens
10.1 Introduction
10.2 Mathematical model
10.3 Galley of examples
10.4 Conclusions
Further reading
CH011.pdf
Chapter 11 On-axis sequential optical systems
11.1 Introduction
11.2 Mathematical model
11.2.1 Fermat’s principle
11.2.2 Snell’s law
11.2.3 Solution
11.2.4 Surfaces expressed in terms of the refracted rays
11.3 Illustrative examples
11.4 Conclusions
Further reading
CH012.pdf
Chapter 12 On-axis sequential refractive–reflective telescope
12.1 Introduction
12.1.1 Mathematical model
12.2 Examples
12.3 Conclusions
Further reading
CH013.pdf
Chapter 13 Off-axis stigmatic lens
13.1 Introduction
13.2 Mathematical model
13.3 Illustrative examples
13.3.1 A non symmetric solution
13.4 Mathematical implications of a non-symmetric solution
13.5 Conclusions
Further reading
CH014.pdf
Chapter 14 Aplanatic singlet lens: general setting, part 1
14.1 Introduction
14.2 Off-axis stigmatic collector lens
14.3 On-axis stigmatic lens for an arbitrary reference path
14.4 The merging of two solutions
14.5 Examples
14.6 Conclusions
Further reading
CH015.pdf
Chapter 15 Aplanatic singlet lens: general setting, part 2
15.1 Introduction
15.2 Off-axis stigmatic lens
15.3 On-axis stigmatic lens for an arbitrary reference path
15.4 The merging of two solutions
15.5 Examples
15.6 Conclusions
Further reading
APP1.pdf
Chapter
On-axis stigmatic collector singlet lens
On−axis stigmatic collimator singlet lens
On−axis stigmatic singlet lens infinite object finite image
Single−lens telescope
Gaxicon
Off−axis stigmatic singlet lens
On−axis stigmatic triplet lens
