This book examines the concept of stigmatism from its base to the most fundamental stigmatic systems. The book begins with Maxwell's equations, before continuing with the wave equation, the eikonal equation and the ray equation. The eikonal equation is also studied with the formalism of the calculation of variations and the concept of stigmatism. Once the foundations of stigmatism have been established, the book focuses on fundamental stigmatic systems, Cartesian ovals and stigmatic lenses. Step by step, the derivations of these systems are obtained and illustrative examples of all their cases are shown. Through the study of these systems, the uniqueness of stigmatism is formulated, and the implications of this uniqueness are presented at the end of the book. This book is an excellent guide for producers of lenses and optical products, and academics in lens design and optics.
Key Features
- Includes examples throughout
- Presents problems proposed to be solved by students as well as codes and algorithms in every chapter
- Discusses the physical concepts needed, then focuses on the mathematical tools needed to understand the eikonal and the close form solution of the stigmatic optical systems
- A great reference for research centres, optical based societies, optics journals, universities and optical based companies.
Author(s): Rafael G. González-Acuña, Hector A. Chaparro-Romo
Series: IOP Series in Emerging Technologies in Optics and Photonics
Publisher: IOP Publishing
Year: 2020
Language: English
Pages: 308
City: Bristol
PRELIMS.pdf
Preface
Series Editor’s foreword
Acknowledgements
Author biographies
Rafael G González-Acuña
Héctor A Chaparro-Romo
CH001.pdf
Chapter 1 The Maxwell equations
1.1 Introduction
1.2 Lorentz force
1.3 Electric flux
1.4 The Gauss law
1.5 The Gauss law for magnetism
1.6 Faraday’s law
1.7 Ampère’s law
1.8 The wave equation
1.9 The speed and propagation of light
1.10 Refraction index
1.11 Electromagnetic waves
1.11.1 One-dimensional way
1.11.2 Spherical coordinates
1.12 End notes
Further reading
CH002.pdf
Chapter 2 The eikonal equation
2.1 From the wave equation, through Helmholtz equation to end with the eikonal equation
2.2 The eikonal equation
2.3 The ray equation
2.3.1 n as constant
2.3.2 n(r⃗) as a function
2.4 The Snell law from eikonal
2.5 The Fermat principle from eikonal
2.6 End notes
Further reading
CH003.pdf
Chapter 3 Calculus of variations
3.1 Calculus of variations
3.2 The Euler equation
3.3 Newton’s second law
3.4 End notes
Further reading
CH004.pdf
Chapter 4 Optics of variations
4.1 Introduction
4.2 Lagrangian and Hamiltonian optics
4.3 Law of reflection
4.4 Law of refraction
4.5 The Fermat principle and Snell’s law
4.6 Malus–Dupin’s theorem
4.7 End notes
Further reading
CH005.pdf
Chapter 5 Stigmatism and stigmatic reflective surfaces
5.1 Introduction
5.2 Aberrations
5.3 Conic mirrors
5.4 Elliptic mirror
5.5 Circular mirror
5.6 Hyperbolic mirror
5.7 Parabolic mirror
5.8 End notes
Further reading
CH006.pdf
Chapter 6 Stigmatic refractive surfaces: the Cartesian ovals
6.1 Introduction
6.2 Stigmatic surfaces
6.2.1 Case I: ro=ri=0,zo→−∞ and zi=f
6.2.2 Case II: ro=ri=0,zo=f and zi→−∞
6.3 Analytical stigmatic refractive surfaces
6.3.1 Case A: ro=ri=0, zo→−∞ and zi=f
6.3.2 Case B: ro=ri=0,zo=f and zi→−∞
6.3.3 Case C: ro=ri=0,zo=∓f and zi=±f
6.3.4 Case D: ro=ri=0,zo=−αf and zi=+f
6.3.5 Case E: ro=ri=0,zo=αf and zi=−f
6.4 Conclusions
Further reading
CH007.pdf
Chapter 7 The general equation of the Cartesian oval
7.1 From Ibn Sahl to Rene Descartes
7.2 A generalized problem
7.3 Mathematical model
7.4 Illustrative examples
7.5 Collimated input rays
7.6 Illustrative examples
7.7 Collimated output rays
7.8 Illustrative examples
7.9 Reflective surface
7.9.1 Parabolic mirror
7.10 Illustrative examples
7.11 End notes
Further reading
CH008.pdf
Chapter 8 The stigmatic lens generated by Cartesian ovals
8.1 Introduction
8.2 Mathematical model
8.3 Examples
8.4 Collector
8.5 Examples
8.6 Collimator
8.7 Examples
8.8 Single-lens telescope with Cartesian ovals
8.9 Example
8.10 End notes
Further reading
CH009.pdf
Chapter 9 The general equation of the stigmatic lenses
9.1 Introduction
9.2 Finite object finite image
9.2.1 Fermat principle
9.2.2 Snell’s law
9.2.3 Solution
9.2.4 The eikonal of the stigmatic lens
9.2.5 Gallery
9.3 Stigmatic aspheric collector
9.3.1 The eikonal of the stigmatic collector
9.3.2 Gallery
9.4 Stigmatic aspheric collimator
9.4.1 The eikonal of the stigmatic collimator
9.4.2 Gallery
9.5 The single-lens telescope
9.5.1 The eikonal of the single-lens telescope
9.5.2 Gallery
9.6 End notes
Further reading
CH010.pdf
Chapter 10 The stigmatic lens and the Cartesian ovals
10.1 Introduction
10.2 Comparison between the different stigmatic lenses made by Cartesian ovals
10.3 Cartesian ovals in a parametric form
10.4 Cartesian ovals in an explicit form as a first surface and general equation of stigmatic lenses
10.5 Cartesian ovals in a parametric form as a first surface and general equation of stigmatic lenses
10.5.1 First surface
10.5.2 Second surface
10.6 Illustrative comparison
10.7 Cartesian ovals in a parametric form for an object at minus infinity
10.8 Cartesian ovals in an explicit form for an object at minus infinity
10.9 Cartesian ovals in a parametric form as a first surface and general equation of stigmatic lenses for an object at minus infinity
10.10 Illustrative comparison
10.11 Implications
10.12 End notes
Further reading
CH011.pdf
Chapter 11 Algorithms for stigmatic design
11.1 Programs for chapter 6
11.1.1 Case: real finite object—real finite image
11.1.2 Case: real infinity object—real finite image
11.1.3 Case: real infinity object—virtual finite image
11.1.4 Case: real finite object—virtual finite image
11.1.5 Case: real finite object—real infinite image
11.1.6 Case: virtual finite object—real infinite image
11.1.7 Case: virtual finite object—virtual finite image
11.2 Programs for chapter 7
11.2.1 Case 1: real finite object—real finite image
11.2.2 Case 2: real infinity object—real finite image
11.2.3 Case 3: real infinity object—virtual finite image
11.2.4 Case 4: real finite object—virtual finite image
11.2.5 Case 5: real finite object—real infinite image
11.2.6 Case 6: virtual finite object—real infinite image
11.2.7 Case 7: virtual finite object—real finite image
11.2.8 Case 8: virtual finite object—virtual finite image
11.2.9 Case 9: real infinite object—real infinite image
11.3 Programs for chapter 8
11.3.1 Case 1: real finite object—real finite image
11.3.2 Case 2: real infinity object—real finite image
11.3.3 Case 3: real infinity object—virtual finite image
11.3.4 Case 4: real finite object—virtual finite image
11.3.5 Case 5: real finite object—real infinite image
11.3.6 Case 6: virtual finite object—real infinite image
11.3.7 Case 7: virtual finite object—real finite image
11.3.8 Case 8: virtual finite object—virtual finite image
11.3.9 Case 9: real infinite object—real infinite image
11.4 Programs for chapter 9
11.4.1 Case 1: real finite object—real finite image
11.4.2 Case 2: real infinity object—real finite image
11.4.3 Case 3: real infinity object—virtual finite image
11.4.4 Case 4: real finite object—virtual finite image
11.4.5 Case 5: real finite object—real infinite image
11.4.6 Case 6: virtual finite object—real infinite image
11.4.7 Case 7: virtual finite object—real finite image
11.4.8 Case 8: virtual finite object—virtual finite image
11.4.9 Case 9: real infinite object—real infinite image
