Analytical Lens Design / Rafael G González-Acuña, Héctor A. Chaparro-Romo, and Julio C. Gutiérrez-Vega.

Format:

Book

Author/Creator:

González-Acuña, Rafael G., author.

Chaparro-Romo, Hector A., author.

Gutiérrez-Vega, Julio C., author.

Series:

IOP series in emerging technologies in optics and photonics.

IOP Series in Emerging Technologies in Optics and Photonics Series

Language:

English

Subjects (All):

Lenses--Design and construction.

Lenses.

Optical physics.

Physical Description:

1 online resource (277 pages)

Edition:

First edition.

Place of Publication:

Bristol, England : IOP Publishing, [2020]

Summary:

This book examines the problem of designing an on-axis stigmatic lens, a lens free of spherical aberration, using two postulates: the Fermat principle and Snell's Law. It is a valuable resource for industrial specialists and academics in lens design and optics, and is an insightful guide for optical physics students.

Contents:

Intro

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

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

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

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

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

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

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

Chapter 7 The gaxicon

7.1 Introduction

7.2 Geometrical model

7.3 Gallery of axicons

7.4 Conclusions

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

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

Chapter 10 On-axis astigmatic freeform lens

10.1 Introduction

10.2 Mathematical model

10.3 Galley of examples

10.4 Conclusions

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

Chapter 12 On-axis sequential refractive-reflective telescope

12.1 Introduction

12.1.1 Mathematical model

12.2 Examples

12.3 Conclusions

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

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

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

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.

Notes:

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Includes bibliographical references.

ISBN:

0-7503-4154-8