Geometric optics on phase space:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
2004
|
| Series: | Texts and monographs in physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 355 - 363 |
| Physical Description: | XV, 373 S. graph. Darst. 24 cm |
| ISBN: | 3540220399 |
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MARC
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| 100 | 1 | |a Wolf, Kurt B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometric optics on phase space |c Kurt Bernardo Wolf |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 2004 | |
| 300 | |a XV, 373 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Texts and monographs in physics | |
| 500 | |a Literaturverz. S. 355 - 363 | ||
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| 650 | 4 | |a Phase space (Statistical physics) | |
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Record in the Search Index
| _version_ | 1804137927409664000 |
|---|---|
| adam_text | Contents
Part I Optical phase space, Hamiltonian systems and Lie algebras
Introduction
.................................................. 3
1
Two fundamental postulates
.............................. 5
1.1
Geometric postulate
.................................... 5
1.2
Dynamic postulate
..................................... 6
1.3
Conservation laws at discontinuities
....................... 7
1.4
Descartes sphere and the Ibn Sahl law of refraction
......... 8
1.5
Geometric optics and classical mechanics
.................. 11
2
Optical phase space
....................................... 15
2.1
Ray coordinates and their manifold
....................... 15
2.2
Hamilton equations on the screen
......................... 18
2.3
Guides and their index profile
............................ 21
2.4
Paraxial optics and mechanics
............................ 23
3
Canonical transformations
................................ 25
3.1
Beams and the conservation of light
...................... 25
3.2
Conservation of the Hamiltonian structure
................. 28
3.3
Hamiltonian evolution with
Poisson
brackets
............... 33
3.4
One-parameter Lie groups
............................... 34
3.5
Hamiltonian flow of phase space
.......................... 37
3.6
Some aberrations and their Fourier conjugates
............. 38
3.6.1
Spherical aberration and pocus
..................... 39
3.6.2
Distorsion
and coma
.............................. 40
3.7
Multiparameter Lie algebras and groups
................... 42
4
The roots of refraction and reflection
..................... 47
4.1
Refraction equations in screen coordinates
................. 48
4.2
Factorization of refraction
............................... 49
4.3
Canonicity of the root transformation
..................... 51
4.4
Aberration series expansion for the root transformation
..... 53
4.5
Refraction between inhomogeneous media
................. 54
4.6
Factorization of reflection
................................ 55
XII Contents
A Some historical comments
................................ 57
A.I Antiquity
.............................................. 57
A.2 Age of Reason
......................................... 58
A.3 Fermat s principle and the Lagrangian
.................... 59
A.4 Geometric optics in the nineteenth century
................ 60
A.5 Hamiltonian formulations
................................ 61
A.
6
The evolution of
Sophus
Lie
............................. 61
A.7 Symmetries and dynamics in the twentieth century
......... 63
Part II Symmetry and dynamics of optical systems
Introduction
.................................................. 67
5
Euclidean and Lorentzian maps
........................... 69
5.1
Presentations and realizations of symmetry
................ 69
5.2
Translations in 3-space
.................................. 72
5.3
Rotations of 3-space
.................................... 74
5.4
Rotations of the screen
.................................. 77
5.5
Euclidean and semidirect product groups
.................. 79
5.6
Lorentz
boost of light-like vectors
......................... 81
5.7
Relativistic aberration of images
.......................... 84
5.8
The
Lorentz
Lie algebra and group
....................... 87
5.9
Other global optical transformations
...................... 88
6
Conformai
optics
—
Maxwell fish-eyes
..................... 91
6.1
On the eyes of fish and point rotors
....................... 91
6.2
Phase space and rotations
............................... 94
6.3
Restriction to conies
.................................... 96
6.4 Stereographic map
of phase space
........................ 97
6.5
Hidden symmetry and the Hamiltonian
.................... 103
6.6
Dynamical Lie algebra of the fish-eye
..................... 106
6.7
Conformai Lie
algebra
.................................. 108
6.8
The Kepler system and its hidden rotor
................... 110
7
Axial symmetry reduction
................................113
7.1
Symmetry-adapted coordinates of phase space
..............113
7.2
Hamiltonian knife cuts hyperbolic onion
...................116
7.3
Stability of trajectories and critical rays
...................117
7.4
The reduced phase space of axis-symmetric systems
.........120
7.5
Hamiltonian structure on reduced phase space
.............122
7.6
Reconstruction of the ignored coordinate
..................123
Contents XIII
Anisotropie
optical media
................................. 127
8.1
Direction and momentum of rays
......................... 127
8.2
Hamilton equations for anisotropic media
.................. 128
8.3
Angular dependences of the refractive index
............... 129
8.4
Comparison with Maxwellian anisotropy
................... 131
Euclidean optical models
................................. 135
B.I Manifolds of rays, planes and frames
...................... 135
B.2 Coset spaces for geometric and wave models
............... 138
B.3 Conservation of volume and structure
..................... 141
B.4 Signal and Helmholtz models
............................ 144
B.5
Hubert
space of Helmholtz wavefields
..................... 145
B.6 Euclidean algebra in Helmholtz optics
..................... 148
B.7 The recipe for wavization
................................ 149
Part III The paraxial
régime
Introduction
..................................................155
9
Optical elements of the symplectic group
.................157
9.1
Free spaces, thin lenses, and action on phase space
..........157
9.2
Linear canonical maps and symplectic matrices
.............162
9.3
Orthogonal and unitary matrices
.........................165
9.4 Bargmann
parameters and group covers
...................168
9.5
The Iwasawa and other decompositions
....................173
10
Construction of optical systems
...........................179
10.1
Plane optical systems
...................................179
10.2
Astigmatic lenses and magnifiers
.........................184
10.2.1
Lenses
.......................................... 184
10.2.2
Magnifiers
....................................... 185
10.2.3
Reflectors and rotators
............................ 187
10.3
U(2) fractional Fourier transformers
....................... 188
10.3.1
Central Fourier transforms
........................189
10.3.2
Separable Fourier transforms
.......................189
10.3.3
SU(2)-Fourier transforms
..........................190
10.4
Systems cum reflection
..................................191
10.5
Minimal lens arrangements
..............................196
10.5.1
The abc-parameters
...............................196
10.5.2
One-lens DLD configurations
......................197
10.5.3
Two-lens configurations
...........................199
10.5.4
Three-lens configurations
..........................202
XIV Contents
11
Classical Lie algebras
.....................................205
11.1
Lie algebras of the linear groups
..........................205
11.2
The classical
Cartari
algebras
............................211
11.3
The Weyl trick for symplectic algebras
....................215
11.4
Phase space functions, operators and matrices
..............221
11.5
Roots and
multiplets
of the symplectic algebras
............224
11.6
Roots and
multiplets
of the unitary algebras
...............232
11.7
Roots of the orthogonal algebras
.........................237
12
Hamiltonian orbits
.......................................249
12.1
Orbits in sp(2, R) for plane systems
.......................249
12.2
Trajectories in Sp(2, R)
..................................252
12.3
sp(4, R) Hamiltonians and eigenvalues
.....................254
12.4
Hamiltonians in the so(3,
2)
basis
.........................258
12.5
Equivalence under Fourier transformers and magnifiers
......262
12.6
Separable, Lorentzian and Euclidean Hamiltonians
..........264
12.7
Evolution along sp(4, R)-guides
...........................267
12.8
Inhomogeneous Hamiltonians
............................270
С
Canonical Fourier optics
..................................273
C.I The Royal Road to Fourier optics
.........................273
C.2 Linear canonical transforms
..............................277
C.3 Hyperdifferential forms
..................................282
C.4 D-dim and radial canonical transforms
....................286
Part IV Hamilton-Lie aberrations
Introduction
..................................................291
13
Polynomials and aberrations in one dimension
............293
13.1
Monomials in
multiplets
.................................293
13.2
Rank-if aberration algebras
.............................296
13.3
Rank-if aberration groups
...............................298
13.4
Aberrations of phase space
..............................302
14
Axis-symmetric aberrations
...............................309
14.1
Axis-symmetric aberrations in the Cartesian basis
..........309
14.2
The harmonic basis of aberrations
........................315
14.3
Harmonic aberration family features
......................321
14.4
Concatenation of aberrating systems
......................329
14.5
Aberration coefficients for optical elements
.................333
Contents
XV
15
Parametric
correction
of fractional Fourier transformers
.. 341
15.1
The lens arrangement
...................................342
15.2
The warped-face guide arrangement
.......................347
15.3
The cat s eye arrangement
...............................349
15.4
Afterword
.............................................353
References
....................................................355
Index
.........................................................365
|
| adam_txt |
Contents
Part I Optical phase space, Hamiltonian systems and Lie algebras
Introduction
. 3
1
Two fundamental postulates
. 5
1.1
Geometric postulate
. 5
1.2
Dynamic postulate
. 6
1.3
Conservation laws at discontinuities
. 7
1.4
Descartes' sphere and the Ibn Sahl law of refraction
. 8
1.5
Geometric optics and classical mechanics
. 11
2
Optical phase space
. 15
2.1
Ray coordinates and their manifold
. 15
2.2
Hamilton equations on the screen
. 18
2.3
Guides and their index profile
. 21
2.4
Paraxial optics and mechanics
. 23
3
Canonical transformations
. 25
3.1
Beams and the conservation of light
. 25
3.2
Conservation of the Hamiltonian structure
. 28
3.3
Hamiltonian evolution with
Poisson
brackets
. 33
3.4
One-parameter Lie groups
. 34
3.5
Hamiltonian flow of phase space
. 37
3.6
Some aberrations and their Fourier conjugates
. 38
3.6.1
Spherical aberration and pocus
. 39
3.6.2
Distorsion
and coma
. 40
3.7
Multiparameter Lie algebras and groups
. 42
4
The roots of refraction and reflection
. 47
4.1
Refraction equations in screen coordinates
. 48
4.2
Factorization of refraction
. 49
4.3
Canonicity of the root transformation
. 51
4.4
Aberration series expansion for the root transformation
. 53
4.5
Refraction between inhomogeneous media
. 54
4.6
Factorization of reflection
. 55
XII Contents
A Some historical comments
. 57
A.I Antiquity
. 57
A.2 Age of Reason
. 58
A.3 Fermat's principle and the Lagrangian
. 59
A.4 Geometric optics in the nineteenth century
. 60
A.5 Hamiltonian formulations
. 61
A.
6
The evolution of
Sophus
Lie
. 61
A.7 Symmetries and dynamics in the twentieth century
. 63
Part II Symmetry and dynamics of optical systems
Introduction
. 67
5
Euclidean and Lorentzian maps
. 69
5.1
Presentations and realizations of symmetry
. 69
5.2
Translations in 3-space
. 72
5.3
Rotations of 3-space
. 74
5.4
Rotations of the screen
. 77
5.5
Euclidean and semidirect product groups
. 79
5.6
Lorentz
boost of light-like vectors
. 81
5.7
Relativistic aberration of images
. 84
5.8
The
Lorentz
Lie algebra and group
. 87
5.9
Other global optical transformations
. 88
6
Conformai
optics
—
Maxwell fish-eyes
. 91
6.1
On the eyes of fish and point rotors
. 91
6.2
Phase space and rotations
. 94
6.3
Restriction to conies
. 96
6.4 Stereographic map
of phase space
. 97
6.5
Hidden symmetry and the Hamiltonian
. 103
6.6
Dynamical Lie algebra of the fish-eye
. 106
6.7
Conformai Lie
algebra
. 108
6.8
The Kepler system and its hidden rotor
. 110
7
Axial symmetry reduction
.113
7.1
Symmetry-adapted coordinates of phase space
.113
7.2
Hamiltonian knife cuts hyperbolic onion
.116
7.3
Stability of trajectories and critical rays
.117
7.4
The reduced phase space of axis-symmetric systems
.120
7.5
Hamiltonian structure on reduced phase space
.122
7.6
Reconstruction of the ignored coordinate
.123
Contents XIII
Anisotropie
optical media
. 127
8.1
Direction and momentum of rays
. 127
8.2
Hamilton equations for anisotropic media
. 128
8.3
Angular dependences of the refractive index
. 129
8.4
Comparison with Maxwellian anisotropy
. 131
Euclidean optical models
. 135
B.I Manifolds of rays, planes and frames
. 135
B.2 Coset spaces for geometric and wave models
. 138
B.3 Conservation of volume and structure
. 141
B.4 Signal and Helmholtz models
. 144
B.5
Hubert
space of Helmholtz wavefields
. 145
B.6 Euclidean algebra in Helmholtz optics
. 148
B.7 The recipe for wavization
. 149
Part III The paraxial
régime
Introduction
.155
9
Optical elements of the symplectic group
.157
9.1
Free spaces, thin lenses, and action on phase space
.157
9.2
Linear canonical maps and symplectic matrices
.162
9.3
Orthogonal and unitary matrices
.165
9.4 Bargmann
parameters and group covers
.168
9.5
The Iwasawa and other decompositions
.173
10
Construction of optical systems
.179
10.1
Plane optical systems
.179
10.2
Astigmatic lenses and magnifiers
.184
10.2.1
Lenses
. 184
10.2.2
Magnifiers
. 185
10.2.3
Reflectors and rotators
. 187
10.3
U(2) fractional Fourier transformers
. 188
10.3.1
Central Fourier transforms
.189
10.3.2
Separable Fourier transforms
.189
10.3.3
SU(2)-Fourier transforms
.190
10.4
Systems cum reflection
.191
10.5
Minimal lens arrangements
.196
10.5.1
The abc-parameters
.196
10.5.2
One-lens DLD configurations
.197
10.5.3
Two-lens configurations
.199
10.5.4
Three-lens configurations
.202
XIV Contents
11
Classical Lie algebras
.205
11.1
Lie algebras of the linear groups
.205
11.2
The classical
Cartari
algebras
.211
11.3
The Weyl trick for symplectic algebras
.215
11.4
Phase space functions, operators and matrices
.221
11.5
Roots and
multiplets
of the symplectic algebras
.224
11.6
Roots and
multiplets
of the unitary algebras
.232
11.7
Roots of the orthogonal algebras
.237
12
Hamiltonian orbits
.249
12.1
Orbits in sp(2, R) for plane systems
.249
12.2
Trajectories in Sp(2, R)
.252
12.3
sp(4, R) Hamiltonians and eigenvalues
.254
12.4
Hamiltonians in the so(3,
2)
basis
.258
12.5
Equivalence under Fourier transformers and magnifiers
.262
12.6
Separable, Lorentzian and Euclidean Hamiltonians
.264
12.7
Evolution along sp(4, R)-guides
.267
12.8
Inhomogeneous Hamiltonians
.270
С
Canonical Fourier optics
.273
C.I The Royal Road to Fourier optics
.273
C.2 Linear canonical transforms
.277
C.3 Hyperdifferential forms
.282
C.4 D-dim and radial canonical transforms
.286
Part IV Hamilton-Lie aberrations
Introduction
.291
13
Polynomials and aberrations in one dimension
.293
13.1
Monomials in
multiplets
.293
13.2
Rank-if aberration algebras
.296
13.3
Rank-if aberration groups
.298
13.4
Aberrations of phase space
.302
14
Axis-symmetric aberrations
.309
14.1
Axis-symmetric aberrations in the Cartesian basis
.309
14.2
The harmonic basis of aberrations
.315
14.3
Harmonic aberration family features
.321
14.4
Concatenation of aberrating systems
.329
14.5
Aberration coefficients for optical elements
.333
Contents
XV
15
Parametric
correction
of fractional Fourier transformers
. 341
15.1
The lens arrangement
.342
15.2
The warped-face guide arrangement
.347
15.3
The cat's eye arrangement
.349
15.4
Afterword
.353
References
.355
Index
.365 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Wolf, Kurt B. |
| author_facet | Wolf, Kurt B. |
| author_role | aut |
| author_sort | Wolf, Kurt B. |
| author_variant | k b w kb kbw |
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| callnumber-subject | QC - Physics |
| classification_rvk | UH 5080 |
| ctrlnum | (OCoLC)56068481 (DE-599)BVBBV035007912 |
| dewey-full | 535/.32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 535 - Light and related radiation |
| dewey-raw | 535/.32 |
| dewey-search | 535/.32 |
| dewey-sort | 3535 232 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
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| id | DE-604.BV035007912 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:42:53Z |
| indexdate | 2024-07-09T21:20:04Z |
| institution | BVB |
| isbn | 3540220399 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016677204 |
| oclc_num | 56068481 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-634 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-634 DE-11 |
| physical | XV, 373 S. graph. Darst. 24 cm |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Texts and monographs in physics |
| spelling | Wolf, Kurt B. Verfasser aut Geometric optics on phase space Kurt Bernardo Wolf Berlin ; Heidelberg Springer 2004 XV, 373 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Texts and monographs in physics Literaturverz. S. 355 - 363 Geometrical optics Phase space (Statistical physics) Phasenraum (DE-588)4139912-2 gnd rswk-swf Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf Geometrische Optik (DE-588)4020241-0 gnd rswk-swf Geometrische Optik (DE-588)4020241-0 s Symplektische Geometrie (DE-588)4194232-2 s Phasenraum (DE-588)4139912-2 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016677204&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wolf, Kurt B. Geometric optics on phase space Geometrical optics Phase space (Statistical physics) Phasenraum (DE-588)4139912-2 gnd Symplektische Geometrie (DE-588)4194232-2 gnd Geometrische Optik (DE-588)4020241-0 gnd |
| subject_GND | (DE-588)4139912-2 (DE-588)4194232-2 (DE-588)4020241-0 |
| title | Geometric optics on phase space |
| title_auth | Geometric optics on phase space |
| title_exact_search | Geometric optics on phase space |
| title_exact_search_txtP | Geometric optics on phase space |
| title_full | Geometric optics on phase space Kurt Bernardo Wolf |
| title_fullStr | Geometric optics on phase space Kurt Bernardo Wolf |
| title_full_unstemmed | Geometric optics on phase space Kurt Bernardo Wolf |
| title_short | Geometric optics on phase space |
| title_sort | geometric optics on phase space |
| topic | Geometrical optics Phase space (Statistical physics) Phasenraum (DE-588)4139912-2 gnd Symplektische Geometrie (DE-588)4194232-2 gnd Geometrische Optik (DE-588)4020241-0 gnd |
| topic_facet | Geometrical optics Phase space (Statistical physics) Phasenraum Symplektische Geometrie Geometrische Optik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016677204&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wolfkurtb geometricopticsonphasespace |