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Format: 1 Online-Resource

ISBN: 9780750331678 , 9780750331661 , 9780750331685

Series Statement: IOP series in emerging technologies in optics and photonics

Content: 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. Part of IOP Series in Emerging Technologies in Optics and Photonics.

Note: "Version: 20200401"--Title page verso. - Includes bibliographical references. - Title from PDF title page (viewed on May 6, 2020) , Mode of access: World Wide Web. , System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

Additional Edition: ISBN 9780750331654

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9780750331654

Additional Edition: Erscheint auch als Druck-Ausgabe González-Acunã, Rafael G. Analytical lens design Bristol, UK : IOP Publishing, 2020 ISBN 9780750331654

Additional Edition: ISBN 0750331658

Additional Edition: ISBN 9780750331685

Additional Edition: ISBN 0750331682

Language: English

Keywords: Linse

DOI: 10.1088/978-0-7503-3167-8

URL: Volltext  (lizenzpflichtig)

URL: lizenzpflichtig

UID:

Format: 1 online resource (277 pages)

Edition: 1st ed.

ISBN: 9780750341547

Series Statement: IOP Series in Emerging Technologies in Optics and Photonics Series

Content: 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.

Note: 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.

Additional Edition: Print version: González-Acuña, Rafael G Analytical Lens Design Bristol : Institute of Physics Publishing,c2020 ISBN 9780750331685

Language: English

Keywords: Electronic books.

URL: Click to View

UID:

Format: 1 online resource (various pagings) : , illustrations (some color).

ISBN: 9780750331678 , 9780750331661

Series Statement: IOP ebooks. [2020 collection]

Content: 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. Part of IOP Series in Emerging Technologies in Optics and Photonics.

Note: "Version: 20200401"--Title page verso. , part I. A historical, mathematical and optical introduction. 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 , 2. A mathematical toolkit for stigmatic imaging -- 2.1. A mathematical toolkit -- 2.2. Set theory -- 2.3. Topological spaces -- 2.4. Metric spaces -- 2.5. The conics -- 2.6. Geometric algebra -- 2.7. Conclusions , 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 -- 3.9. Conclusions , part II. Stigmatic singlets. 4. On-axis stigmatic aspheric lens -- 4.1. Introduction -- 4.2. Finite object finite image -- 4.3. Evolution tables of the shape of on-axis stigmatic lens -- 4.4. Stigmatic aspheric collector -- 4.5. Stigmatic aspheric collimator -- 4.6. The single-lens telescope -- 4.7. Conclusions , 5. Geometry of on-axis stigmatic lenses -- 5.1. Introduction -- 5.2. Lens free of spherical aberration finite-finite case -- 5.3. Lens free of spherical aberration infinite-finite case -- 5.4. Lens free of spherical aberration finite-infinite case -- 5.5. Lens free of spherical aberration infinite-infinite case -- 5.6. Conclusions , 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 , 7. The gaxicon -- 7.1. Introduction -- 7.2. Geometrical model -- 7.3. Gallery of axicons -- 7.4. Conclusions , 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 , part III. Stigmatic and astigmatic freeform singlets. 9. On-axis stigmatic freeform lens -- 9.1. Introduction -- 9.2. Finite image-object -- 9.3. The freeform collector lens -- 9.4. The freeform collimator lens -- 9.5. The beam-shaper -- 9.6. Conclusions , 10. On-axis astigmatic freeform lens -- 10.1. Introduction -- 10.2. Mathematical model -- 10.3. Galley of examples -- 10.4. Conclusions , part IV. Stigmatic optical systems. 11. On-axis sequential optical systems -- 11.1. Introduction -- 11.2. Mathematical model -- 11.3. Illustrative examples -- 11.4. Conclusions , 12. On-axis sequential refractive-reflective telescope -- 12.1. Introduction -- 12.2. Examples -- 12.3. Conclusions , part V. Aplanatic singlets. 13. Off-axis stigmatic lens -- 13.1. Introduction -- 13.2. Mathematical model -- 13.3. Illustrative examples -- 13.4. Mathematical implications of a non-symmetric solution -- 13.5. Conclusions , 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 , 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. , Also available in print. , Mode of access: World Wide Web. , System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

Additional Edition: Print version: ISBN 9780750331654

Additional Edition: ISBN 9780750331685

Language: English

DOI: 10.1088/978-0-7503-3167-8

URL: https://iopscience.iop.org/book/978-0-7503-3167-8