Analytical Lens Design.

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 -- Further reading -- 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 -- 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 -- 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 -- 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 -- Chapter 7 The gaxicon -- 7.1 Introduction -- 7.2 Geometrical model -- 7.3 Gallery of axicons -- 7.4 Conclusions -- Further reading -- 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 -- Further reading -- Chapter 10 On-axis astigmatic freeform lens -- 10.1 Introduction -- 10.2 Mathematical model -- 10.3 Galley of examples -- 10.4 Conclusions -- Further reading -- 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 -- Chapter 12 On-axis sequential refractive-reflective telescope -- 12.1 Introduction -- 12.1.1 Mathematical model -- 12.2 Examples -- 12.3 Conclusions -- Further reading -- 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 -- 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 -- 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 -- 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.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.