Stigmatic Optics.
González-Acuña, Rafael G.
Stigmatic Optics. - 1st ed. - 1 online resource (277 pages) - IOP Series in Emerging Technologies in Optics and Photonics Series . - IOP Series in Emerging Technologies in Optics and Photonics Series .
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 concept of stigmatism from its base to the most fundamental stigmatic systems. It is an excellent guide for producers of lenses and optical products, and academics in lens design and optics.
9780750334631
Optical physics.
Electronic books.
Z286.O68 G669 2020
070.50285
Stigmatic Optics. - 1st ed. - 1 online resource (277 pages) - IOP Series in Emerging Technologies in Optics and Photonics Series . - IOP Series in Emerging Technologies in Optics and Photonics Series .
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 concept of stigmatism from its base to the most fundamental stigmatic systems. It is an excellent guide for producers of lenses and optical products, and academics in lens design and optics.
9780750334631
Optical physics.
Electronic books.
Z286.O68 G669 2020
070.50285