University Sétif 1 FERHAT ABBAS Faculty of Sciences
Détail de l'indexation
Ouvrages de la bibliothèque en indexation 530
Ajouter le résultat dans votre panier Affiner la recherche
The Essential Physics of Medical Imaging, Third Edition / Jerrold T. Bushberg
Titre : The Essential Physics of Medical Imaging, Third Edition Type de document : texte imprimé Auteurs : Jerrold T. Bushberg Editeur : Lippincott Williams & Année de publication : 2011 Importance : 1 vol. (1030 p.) Format : 24 cm ISBN/ISSN/EAN : 978-0-7817-8057-5 Note générale : 978-0-7817-8057-5 Langues : Anglais (eng) Catégories : Physique Mots-clés : physique
Imagerie médicale
Imagerie diagnostique :méthodesIndex. décimale : 530 Physique Résumé :
This renowned work is derived from the authors' acclaimed national review course ("Physics of Medical Imaging") at the University of California-Davis for radiology residents. The text is a guide to the fundamental principles of medical imaging physics, radiation protection and radiation biology, with complex topics presented in the clear and concise manner and style for which these authors are known. Coverage includes the production, characteristics and interactions of ionizing radiation used in medical imaging and the imaging modalities in which they are used, including radiography, mammography, fluoroscopy, computed tomography and nuclear medicine. Special attention is paid to optimizing patient dose in each of these modalities. Sections of the book address topics common to all forms of diagnostic imaging, including image quality and medical informatics as well as the non-ionizing medical imaging modalities of MRI and ultrasound.
The basic science important to nuclear imaging, including the nature and production of radioactivity, internal dosimetry and radiation detection and measurement, are presented clearly and concisely. Current concepts in the fields of radiation biology and radiation protection relevant to medical imaging, and a number of helpful appendices complete this comprehensive textbook. The text is enhanced by numerous full color charts, tables, images and superb illustrations that reinforce central concepts. The book is ideal for medical imaging professionals, and teachers and students in medical physics and biomedical engineering. Radiology residents will find this text especially useful in bolstering their understanding of imaging physics and related topics prior to board exams.
-- NEW Four-color throughout
-- NEW Companion website with fully searchable text and images
--Basic line drawings help to explain concepts
--Comprehensive coverage of diagnostic imaging modalities
--Superb writing style of the author team helps make a difficult subject approachable and engagingNote de contenu :
Sommaire
Section I. Basic concepts
1. Introduction to medical imaging
2. Radiation and the atom
3. Interaction of radiation with matter
4. Image quality
5. Imaging informatics
Section II. Diagnostic radiology
6. X-ray production, X-ray tubes, and generators
7. Radiography
8. Mammography
9. Fluoroscopy
10. Computed tomography
11. X-ray dosimetry in projection imaging and computed tomography
12. Magnetic resonance basics: magnetic fields, nuclear magnetic characteristics, tissue contrast, image acquisition
13. Magnetic resonance imaging: advanced image acquisition methods, artifacts, spectroscopy, quality control, siting, bioeffects, and safety
14. Ultrasound
Section III. Nuclear medicine
15. Radioactivity and nuclear transformation
16. Radionuclide production, radiopharmaceuticals, and internal dosimetry
17. Radiation detection and measurement
18. Nuclear imaging: scintillation camera
19. Nuclear imaging: emission tomography
Section IV. Radiation biology and protection
20. Radiation biology
21. Radiation protection
Section V. Appendices
A. Fundamental principles of physics
B. Digital computers
C. Physical constants, prefixes, geometry, conversion factors, and radiologic data
D. Mass attenuation coefficients
E. Effective doses, organ doses, and fetal doses from medical imaging procedures
F. Radiopharmaceutical characteristics and dosimetry
G. Convolution and Fourier transforms
H. Radiation dose: perspectives and comparisons
I. Radionuclide therapy home care guidelines
Côte titre : Fs/14257-14258 The Essential Physics of Medical Imaging, Third Edition [texte imprimé] / Jerrold T. Bushberg . - [S.l.] : Lippincott Williams &, 2011 . - 1 vol. (1030 p.) ; 24 cm.
ISBN : 978-0-7817-8057-5
978-0-7817-8057-5
Langues : Anglais (eng)
Catégories : Physique Mots-clés : physique
Imagerie médicale
Imagerie diagnostique :méthodesIndex. décimale : 530 Physique Résumé :
This renowned work is derived from the authors' acclaimed national review course ("Physics of Medical Imaging") at the University of California-Davis for radiology residents. The text is a guide to the fundamental principles of medical imaging physics, radiation protection and radiation biology, with complex topics presented in the clear and concise manner and style for which these authors are known. Coverage includes the production, characteristics and interactions of ionizing radiation used in medical imaging and the imaging modalities in which they are used, including radiography, mammography, fluoroscopy, computed tomography and nuclear medicine. Special attention is paid to optimizing patient dose in each of these modalities. Sections of the book address topics common to all forms of diagnostic imaging, including image quality and medical informatics as well as the non-ionizing medical imaging modalities of MRI and ultrasound.
The basic science important to nuclear imaging, including the nature and production of radioactivity, internal dosimetry and radiation detection and measurement, are presented clearly and concisely. Current concepts in the fields of radiation biology and radiation protection relevant to medical imaging, and a number of helpful appendices complete this comprehensive textbook. The text is enhanced by numerous full color charts, tables, images and superb illustrations that reinforce central concepts. The book is ideal for medical imaging professionals, and teachers and students in medical physics and biomedical engineering. Radiology residents will find this text especially useful in bolstering their understanding of imaging physics and related topics prior to board exams.
-- NEW Four-color throughout
-- NEW Companion website with fully searchable text and images
--Basic line drawings help to explain concepts
--Comprehensive coverage of diagnostic imaging modalities
--Superb writing style of the author team helps make a difficult subject approachable and engagingNote de contenu :
Sommaire
Section I. Basic concepts
1. Introduction to medical imaging
2. Radiation and the atom
3. Interaction of radiation with matter
4. Image quality
5. Imaging informatics
Section II. Diagnostic radiology
6. X-ray production, X-ray tubes, and generators
7. Radiography
8. Mammography
9. Fluoroscopy
10. Computed tomography
11. X-ray dosimetry in projection imaging and computed tomography
12. Magnetic resonance basics: magnetic fields, nuclear magnetic characteristics, tissue contrast, image acquisition
13. Magnetic resonance imaging: advanced image acquisition methods, artifacts, spectroscopy, quality control, siting, bioeffects, and safety
14. Ultrasound
Section III. Nuclear medicine
15. Radioactivity and nuclear transformation
16. Radionuclide production, radiopharmaceuticals, and internal dosimetry
17. Radiation detection and measurement
18. Nuclear imaging: scintillation camera
19. Nuclear imaging: emission tomography
Section IV. Radiation biology and protection
20. Radiation biology
21. Radiation protection
Section V. Appendices
A. Fundamental principles of physics
B. Digital computers
C. Physical constants, prefixes, geometry, conversion factors, and radiologic data
D. Mass attenuation coefficients
E. Effective doses, organ doses, and fetal doses from medical imaging procedures
F. Radiopharmaceutical characteristics and dosimetry
G. Convolution and Fourier transforms
H. Radiation dose: perspectives and comparisons
I. Radionuclide therapy home care guidelines
Côte titre : Fs/14257-14258 Exemplaires (2)
Code-barres Cote Support Localisation Section Disponibilité Fs/14257 Fs/14257-14258 livre Bibliothéque des sciences Anglais Disponible
DisponibleFs/14258 Fs/14257-14258 livre Bibliothéque des sciences Anglais Disponible
DisponibleThe experimental foundations of particle physics / Cahn, Robert N.
Titre : The experimental foundations of particle physics Type de document : texte imprimé Auteurs : Cahn, Robert N. Mention d'édition : 2e éd. Editeur : Cambridge : Cambridge university press Année de publication : 2009 Importance : 1 vol (553 p.) Format : 24 cm ISBN/ISSN/EAN : 978-0-521-52147-5 Note générale : 978-0-521-52147-5 Catégories : Physique Mots-clés : physique
Particles (Nuclear physics)
Particules (physique nucléaire)
Elementary particlesIndex. décimale : 530 Physique Résumé :
Our current understanding of elementary particles and their interactions emerged from break-through experiments. This book presents these experiments, beginning with the discoveries of the neutron and positron, and following them through mesons, strange particles, antiparticles, and quarks and gluons. This second edition contains new chapters on the W and Z bosons, the top quark, B-meson mixing and CP violation, and neutrino oscillations. This book provides an insight into particle physics for researchers, advanced undergraduate and graduate students. Throughout the book, the fundamental equations required to understand the experiments are derived clearly and simply. Each chapter is accompanied by reprinted articles and a collection of problems with a broad range of difficultyNote de contenu :
Sommaire
Chapter 1-The atom completed and a new particle
Chapter 2-The muon and the pion
Chapter 3-Strangeness
Chapter 4-Antibaryons
Chapter 5-The resonances
Chapter 6-Weak interactions
Chapter 7-The neutral kaon system
Chapter 8-The structure of the nucleon
Chapter 9-The J/psi, the tau, and charm
Chapter 10-Quarks, gluons, and jets
Chapter 11-The fifth quark
Chapter 12-From neutral currents to weak vector bosons
Chapter 13-Testing the Standard Model
Chapter 14-Top Quark
Chapter 15-B-Bbar Mixing and CP Violation
Chapter 16-Neutrino Masses and OscillationsCôte titre : Fs/14259-14260 The experimental foundations of particle physics [texte imprimé] / Cahn, Robert N. . - 2e éd. . - Cambridge : Cambridge university press, 2009 . - 1 vol (553 p.) ; 24 cm.
ISBN : 978-0-521-52147-5
978-0-521-52147-5
Catégories : Physique Mots-clés : physique
Particles (Nuclear physics)
Particules (physique nucléaire)
Elementary particlesIndex. décimale : 530 Physique Résumé :
Our current understanding of elementary particles and their interactions emerged from break-through experiments. This book presents these experiments, beginning with the discoveries of the neutron and positron, and following them through mesons, strange particles, antiparticles, and quarks and gluons. This second edition contains new chapters on the W and Z bosons, the top quark, B-meson mixing and CP violation, and neutrino oscillations. This book provides an insight into particle physics for researchers, advanced undergraduate and graduate students. Throughout the book, the fundamental equations required to understand the experiments are derived clearly and simply. Each chapter is accompanied by reprinted articles and a collection of problems with a broad range of difficultyNote de contenu :
Sommaire
Chapter 1-The atom completed and a new particle
Chapter 2-The muon and the pion
Chapter 3-Strangeness
Chapter 4-Antibaryons
Chapter 5-The resonances
Chapter 6-Weak interactions
Chapter 7-The neutral kaon system
Chapter 8-The structure of the nucleon
Chapter 9-The J/psi, the tau, and charm
Chapter 10-Quarks, gluons, and jets
Chapter 11-The fifth quark
Chapter 12-From neutral currents to weak vector bosons
Chapter 13-Testing the Standard Model
Chapter 14-Top Quark
Chapter 15-B-Bbar Mixing and CP Violation
Chapter 16-Neutrino Masses and OscillationsCôte titre : Fs/14259-14260 Exemplaires (2)
Code-barres Cote Support Localisation Section Disponibilité Fs/14259 Fs/14259-14260 livre Bibliothéque des sciences Anglais Disponible
DisponibleFs/14260 Fs/14259-14260 livre Bibliothéque des sciences Anglais Disponible
DisponibleThe Foundations of Magnetic Recording / John C Mallinson
Titre : The Foundations of Magnetic Recording Type de document : texte imprimé Auteurs : John C Mallinson, Auteur Editeur : Academic press Année de publication : 1987 Importance : 1 vol (175 p.) Format : 24 cm ISBN/ISSN/EAN : 978-0-12-466625-6 Langues : Anglais (eng) Catégories : Physique Mots-clés : Physique Index. décimale : 530 Physique Résumé :
This expanded and updated new edition provides a comprehensive overview of the science and technology of magnetic recording. In the six years since the publication of the first edition, the magnetic recording and storage industry has burgeoned with the introduction of a host of new ideas and technologies. His book contains a discussion of almost every technologically important aspect of recording.Côte titre : Fs/24406 The Foundations of Magnetic Recording [texte imprimé] / John C Mallinson, Auteur . - Florida : Academic press, 1987 . - 1 vol (175 p.) ; 24 cm.
ISSN : 978-0-12-466625-6
Langues : Anglais (eng)
Catégories : Physique Mots-clés : Physique Index. décimale : 530 Physique Résumé :
This expanded and updated new edition provides a comprehensive overview of the science and technology of magnetic recording. In the six years since the publication of the first edition, the magnetic recording and storage industry has burgeoned with the introduction of a host of new ideas and technologies. His book contains a discussion of almost every technologically important aspect of recording.Côte titre : Fs/24406 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité Fs/24406 Fs/24406 livre Bibliothéque des sciences Anglais Disponible
Disponible
Titre : The geometric phase of the 2d harmonic oscillator in the presence of the ab effect Type de document : texte imprimé Auteurs : Rania Bayane ; Nadir Chaabi, Directeur de thèse Editeur : Setif:UFA Année de publication : 2021 Importance : 1 vol. (38 f.) Format : 29 cm Langues : Français (fre) Catégories : Thèses & Mémoires:Physique Mots-clés : Théorème adiabatique
Oscillateur harmonique
Phase géométrique
Phase de Berry
Effet Aharonov-BohmIndex. décimale : 530 Physique Résumé :
Dans ce travail, nous considérons le théorème adiabatique pour l'oscillateur harmonique à 2D en présence de l'effet Aharonov-Bohm avec paramètres dépendants du temps. Nous déterminons la solution de l’équation de Schrödinger correspondante dans le cadre de l’approximation adiabatique, dont nous calculons la phase géométrique correspondante (phase de Berry).Côte titre : MAPH/0490 En ligne : https://drive.google.com/file/d/1zZ7CndioPNx0E7Z-RJgVaUe7d3LRRmQj/view?usp=shari [...] Format de la ressource électronique : The geometric phase of the 2d harmonic oscillator in the presence of the ab effect [texte imprimé] / Rania Bayane ; Nadir Chaabi, Directeur de thèse . - [S.l.] : Setif:UFA, 2021 . - 1 vol. (38 f.) ; 29 cm.
Langues : Français (fre)
Catégories : Thèses & Mémoires:Physique Mots-clés : Théorème adiabatique
Oscillateur harmonique
Phase géométrique
Phase de Berry
Effet Aharonov-BohmIndex. décimale : 530 Physique Résumé :
Dans ce travail, nous considérons le théorème adiabatique pour l'oscillateur harmonique à 2D en présence de l'effet Aharonov-Bohm avec paramètres dépendants du temps. Nous déterminons la solution de l’équation de Schrödinger correspondante dans le cadre de l’approximation adiabatique, dont nous calculons la phase géométrique correspondante (phase de Berry).Côte titre : MAPH/0490 En ligne : https://drive.google.com/file/d/1zZ7CndioPNx0E7Z-RJgVaUe7d3LRRmQj/view?usp=shari [...] Format de la ressource électronique : Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité MAPH/0490 MAPH/0490 Mémoire Bibliothéque des sciences Anglais Disponible
DisponibleThe mathematics of geometrical and physical optics / Orestes N. Stavroudis
Titre : The mathematics of geometrical and physical optics : The k-function and its Ramifications Type de document : texte imprimé Auteurs : Orestes N. Stavroudis Editeur : Wiley-VCH Année de publication : 2006 Importance : 1 vol (226 p.) Format : 24 cm ISBN/ISSN/EAN : 978-3-527-30338-3 Note générale : 978-3527303383 Langues : Anglais (eng) Catégories : Physique Mots-clés : physique Index. décimale : 530 Physique Résumé :
In this sequel to his book, "The Optics of Rays, Wavefronts, and Caustics," Stavroudis not only covers his own research results, but also includes more recent developments. The book is divided into three parts, starting with basic mathematical concepts that are further applied in the book. Surface geometry is treated with classical mathematics, while the second part covers the k–function, discussing and solving the eikonal equation as well as Maxwell equations in this context. A final part on applications consists of conclusions drawn or developed in the first two parts of the book, discussing such topics as the Cartesian oval, the modern Schiefspiegler, Huygen′s principle, and Maxwell′s model of Gauss′ perfect lensNote de contenu :
Sommaire
I Preliminaries 1
1 Fermat’s Principle and the Variational Calculus 3
1.1 Rays in Inhomogeneous Media ........................ 4
1.2 The Calculus of Variations .......................... 5
1.3 The Parametric Representation ........................ 7
1.4 The Vector Notation .............................. 9
1.5 The Inhomogeneous Optical Medium . . . . . . . . . . . . . . . . . . . . 10
1.6 The Maxwell Fish Eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.7 The Homogeneous Medium . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.8 Anisotropic Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Space Curves and Ray Paths 15
2.1 Space Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 The Vector Trihedron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 The Frenet-Serret Equations . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 When the Parameter is Arbitrary . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 The Directional Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 The Cylindrical Helix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7 The Conic Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.8 The Ray Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.9 More on the Fish Eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 The Hilbert Integral and the Hamilton-Jacobi Theory 29
3.1 A Digression on the Gradient . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 The Hilbert Integral. Parametric Case . . . . . . . . . . . . . . . . . . . . 33
3.3 Application to Geometrical Optics . . . . . . . . . . . . . . . . . . . . . . 34
3.4 The Condition for Transversality . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 The Total Differential Equation . . . . . . . . . . . . . . . . . . . . . . . . 35
3.6 More on the Helix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.7 Snell’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.8 The Hamilton-Jacobi Partial Differential Equations . . . . . . . . . . . . . 41
3.9 The Eikonal Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 The Differential Geometry of Surfaces 45
4.1 Parametric Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Surface Normals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3 The Theorem of Meusnier . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 The Theorem of Gauss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.5 Geodesics on a Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.6 The Weingarten Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.7 Transformation of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.8 When the Parametric Curves are Conjugates . . . . . . . . . . . . . . . . . 57
4.9 When F = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.10 The Structure of the Prolate Spheroid . . . . . . . . . . . . . . . . . . . . 61
4.11 Other Ways of Representing Surfaces . . . . . . . . . . . . . . . . . . . . 64
5 Partial Differential Equations of the First Order 67
5.1 The Linear Equation. The Method of Characteristics . . . . . . . . . . . . 68
5.2 The Homogeneous Function . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3 The Bilinear Concomitant . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.4 Non-Linear Equation: The Method of Lagrange and Charpit . . . . . . . . 72
5.5 The General Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.6 The Extension to Three Independent Variables . . . . . . . . . . . . . . . . 76
5.7 The Eikonal Equation. The Complete Integral . . . . . . . . . . . . . . . . 77
5.8 The Eikonal Equation. The General Solution . . . . . . . . . . . . . . . . 79
5.9 The Eikonal Equation. Proof of the Pudding . . . . . . . . . . . . . . . . . 81
II The k-function 83
6 The Geometry of Wave Fronts 85
6.1 Preliminary Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2 The Caustic Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.3 Special Surfaces I: Plane and Spherical Wavefronts . . . . . . . . . . . . . 90
6.4 Parameter Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.5 Asymptotic Curves and Isotropic Directions . . . . . . . . . . . . . . . . . 94
7 Ray Tracing: Generalized and Otherwise 97
7.1 The Transfer Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.2 The Ancillary Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.3 The Refraction Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.4 Rotational Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.5 The Paraxial Approximation . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.6 Generalized Ray Tracing – Transfer . . . . . . . . . . . . . . . . . . . . . 104
7.7 Generalized Ray Tracing – Preliminary Calculations . . . . . . . . . . . . 105
7.8 Generalized Ray Tracing – Refraction . . . . . . . . . . . . . . . . . . . . 109
7.9 The Caustic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.10 The Prolate Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.11 Rays in the Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8 Aberrations in Finite Terms 121
8.1 Herzberger’s Diapoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8.2 Herzberger’s Fundamental Optical Invariant . . . . . . . . . . . . . . . . . 122
8.3 The Lens Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
8.4 Aberrations in Finite Terms . . . . . . . . . . . . . . . . . . . . . . . . . . 126
8.5 Half-Symmetric, Symmetric and Sharp Images . . . . . . . . . . . . . . . 127
Refracting the k-Function 131
9.1 Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
9.2 The Refracting Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
9.3 The Partial Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
9.4 The Finite Object Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
9.5 The Quest for C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
9.6 Developing the Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
9.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
10 Maxwell Equations and the k-Function 147
10.1 The Wavefront . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10.2 The Maxwell Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10.3 Generalized Coordinates and the Nabla Operator . . . . . . . . . . . . . . 149
10.4 Application to the Maxwell Equations . . . . . . . . . . . . . . . . . . . . 150
10.5 Conditions on V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
10.6 Conditions on the Vector V . . . . . . . . . . . . . . . . . . . . . . . . . . 158
10.7 Spherical Wavefronts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
III Ramifications 163
11 The Modern Schiefspiegler 165
11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
11.2 The Single Prolate Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . 167
11.3 Coupled Spheroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
11.4 The Condition for the Pseudo Axis . . . . . . . . . . . . . . . . . . . . . . 172
11.5 Magnification and Distortion . . . . . . . . . . . . . . . . . . . . . . . . . 175
11.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
12 The Cartesian Oval and its Kin 179
12.1 The Algebraic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
12.2 The Object at Infinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
12.3 The Prolate Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
12.4 The Hyperboloid of Two Sheets . . . . . . . . . . . . . . . . . . . . . . . 183
12.5 Other Surfaces that Make Perfect Images . . . . . . . . . . . . . . . . . . . 184
13 The Pseudo Maxwell Equations 187
13.1 Maxwell Equations for Inhomogeneous Media . . . . . . . . . . . . . . . . 187
13.2 The Frenet-Serret Equations . . . . . . . . . . . . . . . . . . . . . . . . . 188
13.3 Initial Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
13.4 Divergence and Curl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
13.5 Establishing the Relationship . . . . . . . . . . . . . . . . . . . . . . . . . 192
14 The Perfect Lenses of Gauss and Maxwell 197
14.1 Gauss’ Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
14.2 Maxwell’s Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
A Appendix. Vector Identities 205
A.1 Algebraic Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
A.2 Identities Involving First Derivatives . . . . . . . . . . . . . . . . . . . . . 207
A.3 Identities Involving Second Derivatives . . . . . . . . . . . . . . . . . . . 207
A.4 Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
A.5 Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
A.6 Curl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
A.7 Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
A.8 Directional Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
A.9 Operations on W and its Derivatives . . . . . . . . . . . . . . . . . . . . . 213
A.10 An Additional Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
B Bibliography 217
Index 223Côte titre : Fs/14263-14265 The mathematics of geometrical and physical optics : The k-function and its Ramifications [texte imprimé] / Orestes N. Stavroudis . - [S.l.] : Wiley-VCH, 2006 . - 1 vol (226 p.) ; 24 cm.
ISSN : 978-3-527-30338-3
978-3527303383
Langues : Anglais (eng)
Catégories : Physique Mots-clés : physique Index. décimale : 530 Physique Résumé :
In this sequel to his book, "The Optics of Rays, Wavefronts, and Caustics," Stavroudis not only covers his own research results, but also includes more recent developments. The book is divided into three parts, starting with basic mathematical concepts that are further applied in the book. Surface geometry is treated with classical mathematics, while the second part covers the k–function, discussing and solving the eikonal equation as well as Maxwell equations in this context. A final part on applications consists of conclusions drawn or developed in the first two parts of the book, discussing such topics as the Cartesian oval, the modern Schiefspiegler, Huygen′s principle, and Maxwell′s model of Gauss′ perfect lensNote de contenu :
Sommaire
I Preliminaries 1
1 Fermat’s Principle and the Variational Calculus 3
1.1 Rays in Inhomogeneous Media ........................ 4
1.2 The Calculus of Variations .......................... 5
1.3 The Parametric Representation ........................ 7
1.4 The Vector Notation .............................. 9
1.5 The Inhomogeneous Optical Medium . . . . . . . . . . . . . . . . . . . . 10
1.6 The Maxwell Fish Eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.7 The Homogeneous Medium . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.8 Anisotropic Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Space Curves and Ray Paths 15
2.1 Space Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 The Vector Trihedron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 The Frenet-Serret Equations . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 When the Parameter is Arbitrary . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 The Directional Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 The Cylindrical Helix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7 The Conic Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.8 The Ray Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.9 More on the Fish Eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 The Hilbert Integral and the Hamilton-Jacobi Theory 29
3.1 A Digression on the Gradient . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 The Hilbert Integral. Parametric Case . . . . . . . . . . . . . . . . . . . . 33
3.3 Application to Geometrical Optics . . . . . . . . . . . . . . . . . . . . . . 34
3.4 The Condition for Transversality . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 The Total Differential Equation . . . . . . . . . . . . . . . . . . . . . . . . 35
3.6 More on the Helix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.7 Snell’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.8 The Hamilton-Jacobi Partial Differential Equations . . . . . . . . . . . . . 41
3.9 The Eikonal Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 The Differential Geometry of Surfaces 45
4.1 Parametric Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Surface Normals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3 The Theorem of Meusnier . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 The Theorem of Gauss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.5 Geodesics on a Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.6 The Weingarten Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.7 Transformation of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.8 When the Parametric Curves are Conjugates . . . . . . . . . . . . . . . . . 57
4.9 When F = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.10 The Structure of the Prolate Spheroid . . . . . . . . . . . . . . . . . . . . 61
4.11 Other Ways of Representing Surfaces . . . . . . . . . . . . . . . . . . . . 64
5 Partial Differential Equations of the First Order 67
5.1 The Linear Equation. The Method of Characteristics . . . . . . . . . . . . 68
5.2 The Homogeneous Function . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3 The Bilinear Concomitant . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.4 Non-Linear Equation: The Method of Lagrange and Charpit . . . . . . . . 72
5.5 The General Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.6 The Extension to Three Independent Variables . . . . . . . . . . . . . . . . 76
5.7 The Eikonal Equation. The Complete Integral . . . . . . . . . . . . . . . . 77
5.8 The Eikonal Equation. The General Solution . . . . . . . . . . . . . . . . 79
5.9 The Eikonal Equation. Proof of the Pudding . . . . . . . . . . . . . . . . . 81
II The k-function 83
6 The Geometry of Wave Fronts 85
6.1 Preliminary Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2 The Caustic Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.3 Special Surfaces I: Plane and Spherical Wavefronts . . . . . . . . . . . . . 90
6.4 Parameter Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.5 Asymptotic Curves and Isotropic Directions . . . . . . . . . . . . . . . . . 94
7 Ray Tracing: Generalized and Otherwise 97
7.1 The Transfer Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.2 The Ancillary Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.3 The Refraction Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.4 Rotational Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.5 The Paraxial Approximation . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.6 Generalized Ray Tracing – Transfer . . . . . . . . . . . . . . . . . . . . . 104
7.7 Generalized Ray Tracing – Preliminary Calculations . . . . . . . . . . . . 105
7.8 Generalized Ray Tracing – Refraction . . . . . . . . . . . . . . . . . . . . 109
7.9 The Caustic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.10 The Prolate Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.11 Rays in the Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8 Aberrations in Finite Terms 121
8.1 Herzberger’s Diapoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8.2 Herzberger’s Fundamental Optical Invariant . . . . . . . . . . . . . . . . . 122
8.3 The Lens Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
8.4 Aberrations in Finite Terms . . . . . . . . . . . . . . . . . . . . . . . . . . 126
8.5 Half-Symmetric, Symmetric and Sharp Images . . . . . . . . . . . . . . . 127
Refracting the k-Function 131
9.1 Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
9.2 The Refracting Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
9.3 The Partial Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
9.4 The Finite Object Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
9.5 The Quest for C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
9.6 Developing the Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
9.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
10 Maxwell Equations and the k-Function 147
10.1 The Wavefront . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10.2 The Maxwell Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10.3 Generalized Coordinates and the Nabla Operator . . . . . . . . . . . . . . 149
10.4 Application to the Maxwell Equations . . . . . . . . . . . . . . . . . . . . 150
10.5 Conditions on V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
10.6 Conditions on the Vector V . . . . . . . . . . . . . . . . . . . . . . . . . . 158
10.7 Spherical Wavefronts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
III Ramifications 163
11 The Modern Schiefspiegler 165
11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
11.2 The Single Prolate Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . 167
11.3 Coupled Spheroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
11.4 The Condition for the Pseudo Axis . . . . . . . . . . . . . . . . . . . . . . 172
11.5 Magnification and Distortion . . . . . . . . . . . . . . . . . . . . . . . . . 175
11.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
12 The Cartesian Oval and its Kin 179
12.1 The Algebraic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
12.2 The Object at Infinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
12.3 The Prolate Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
12.4 The Hyperboloid of Two Sheets . . . . . . . . . . . . . . . . . . . . . . . 183
12.5 Other Surfaces that Make Perfect Images . . . . . . . . . . . . . . . . . . . 184
13 The Pseudo Maxwell Equations 187
13.1 Maxwell Equations for Inhomogeneous Media . . . . . . . . . . . . . . . . 187
13.2 The Frenet-Serret Equations . . . . . . . . . . . . . . . . . . . . . . . . . 188
13.3 Initial Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
13.4 Divergence and Curl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
13.5 Establishing the Relationship . . . . . . . . . . . . . . . . . . . . . . . . . 192
14 The Perfect Lenses of Gauss and Maxwell 197
14.1 Gauss’ Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
14.2 Maxwell’s Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
A Appendix. Vector Identities 205
A.1 Algebraic Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
A.2 Identities Involving First Derivatives . . . . . . . . . . . . . . . . . . . . . 207
A.3 Identities Involving Second Derivatives . . . . . . . . . . . . . . . . . . . 207
A.4 Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
A.5 Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
A.6 Curl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
A.7 Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
A.8 Directional Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
A.9 Operations on W and its Derivatives . . . . . . . . . . . . . . . . . . . . . 213
A.10 An Additional Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
B Bibliography 217
Index 223Côte titre : Fs/14263-14265 Exemplaires (3)
Code-barres Cote Support Localisation Section Disponibilité Fs/14263 Fs/14263-14265 livre Bibliothéque des sciences Anglais Disponible
DisponibleFs/14264 Fs/14263-14265 livre Bibliothéque des sciences Anglais Disponible
DisponibleFs/14265 Fs/14263-14265 livre Bibliothéque des sciences Anglais Disponible
DisponibleThe quantum theory of radiation / Heitler,W
PermalinkThe Standard model / Mark Burgess
PermalinkThe theory of Photons and Electrons / Jauch,Josef M
PermalinkThe theory of Relativity / Moller,C
PermalinkThe three dimensional time dependent generalized Dirac oscillator (Adiabatic solution) / Aitou ,Madjda
PermalinkPermalinkLes théorèmes de Noether / Kosmann-Schwarzbach, Yvette
PermalinkPermalinkThéorie ergodique et systèmes dynamiques / Coudène, Yves
PermalinkPermalink