| １． |
Outline |
|
Students will learn the followings in this course,
(1) The canonical form of geometric optics
(2) Hamilton and Jacobi's theory of the wavefronts and light rays
(3) Linear optics and the theory of image formation from the modern view point
(4) Simplectic maps.
|
| ２． |
Objectives |
|
Technologies for dealing with image information are in a new developing era today due to the recent astounding evolution of computing power.
However, at the very core of these advancements lie the seemingly hackneyed theories of geometric optics and image formation.
These theories have been often taken as phenomenological, but they can actually be firmly founded on the physical theory of light rays in 4D phase space (Canonical transformation theory) and are also in deep connection with up-to-date imaging modalities as 4D light field imaging.
In this course we shall learn, by reading the textbook and some part of the reference book in turn, the geometric optics and the theory of image formation from the modern view point of the canonical transformation theory and the simplectic maps in order to comprehend them enough to be prepared for the advancement of the 21st century image science research.
|
| ３． |
Grading Policy |
|
You will be graded by the presentation at your turn (70%) and report marks (30%).
Comments are appropriately provided for feedback.
|
| ４． |
Textbook and Reference |
|
Textbook
Students may choose either of textbooks below:
[1] Yoshitaka Yamamoto, "Canonical theory of geometric optics", Suugaku Shobou, in Japanese (2014),
[2] Kurt Bernardo Wolf, "Geometric Optics on Phase Space", Springer (2004).
|
| ５． |
Requirements (Assignments) |
|
Read the assigned part of the textbook carefully and prepare the necessary materials in order to be able to answer colleagues' questions (3 hours~).
The schedule is in accordance with [1], but you can basically find the same contents in [2].
|
| ６． |
Note |
|
None.
|
| ７． |
Schedule |
|
| １. Ray optics 1 (The idea of light rays and their uncertainties) |
| ２. Ray optics 2 (The light ray equations and the ray paths) |
| ３. Ray optics 3 (Noether's theorem) |
| ４. Ray optics 4 (Maxwell fish eye and the perfect imaging) |
| ５. Canonical form of geometric optics 1 (Configuration space and state space, canonical variables and Hamilton equations) |
| ６. Canonical form of geometric optics 2 (Optical canonical transformation theory) |
| ７. Canonical form of geometric optics 3 (Canonical equations and Poisson brackets, Lie operators and Lie transforms) |
| ８. Canonical form of geometric optics 4 (Simplectic conditions, Liouville theorem) |
| ９. The theory of wavefronts and light rays 1 (Malus-Dupin theorem, wavefronts and eikonal equations) |
| 10. The theory of wavefronts and light rays 2 (Geodesic field and Hamilton-Jacobi equations, Jacobi theorem) |
| 11. The theory of wavefronts and light rays 3 (Hamilton-Jacobi equations and eikonale) |
| 12. The theory of wavefronts and light rays 4 (Huygens theorem) |
| 13. Linear optics and the theory of image formation 1 (Optical elements and linear transforms, image formation and aberrations) |
| 14. Linear optics and the theory of image formation 2 (Gaussian optics and ABCD matrices, image formation and its conditions) |
| 15. Linear optics and the theory of image formation 3 (Simplectic maps). |
|
| １． |
Outline |
|
Students will learn the followings in this course,
(1) The canonical form of geometric optics
(2) Hamilton and Jacobi's theory of the wavefronts and light rays
(3) Linear optics and the theory of image formation from the modern view point
(4) Simplectic maps.
|
| ２． |
Objectives |
|
Technologies for dealing with image information are in a new developing era today due to the recent astounding evolution of computing power.
However, at the very core of these advancements lie the seemingly hackneyed theories of geometric optics and image formation.
These theories have been often taken as phenomenological, but they can actually be firmly founded on the physical theory of light rays in 4D phase space (Canonical transformation theory) and are also in deep connection with up-to-date imaging modalities as 4D light field imaging.
In this course we shall learn, by reading the textbook and some part of the reference book in turn, the geometric optics and the theory of image formation from the modern view point of the canonical transformation theory and the simplectic maps in order to comprehend them enough to be prepared for the advancement of the 21st century image science research.
|
| ３． |
Grading Policy |
|
You will be graded by the presentation at your turn (70%) and report marks (30%).
Comments are appropriately provided for feedback.
|
| ４． |
Textbook and Reference |
|
Textbook
Students may choose either of textbooks below:
[1] Yoshitaka Yamamoto, "Canonical theory of geometric optics", Suugaku Shobou, in Japanese (2014),
[2] Kurt Bernardo Wolf, "Geometric Optics on Phase Space", Springer (2004).
|
| ５． |
Requirements (Assignments) |
|
Read the assigned part of the textbook carefully and prepare the necessary materials in order to be able to answer colleagues' questions (3 hours~).
The schedule is in accordance with [1], but you can basically find the same contents in [2].
|
| ６． |
Note |
|
None.
|
| ７． |
Schedule |
|
| １. Ray optics 1 (The idea of light rays and their uncertainties) |
| ２. Ray optics 2 (The light ray equations and the ray paths) |
| ３. Ray optics 3 (Noether's theorem) |
| ４. Ray optics 4 (Maxwell fish eye and the perfect imaging) |
| ５. Canonical form of geometric optics 1 (Configuration space and state space, canonical variables and Hamilton equations) |
| ６. Canonical form of geometric optics 2 (Optical canonical transformation theory) |
| ７. Canonical form of geometric optics 3 (Canonical equations and Poisson brackets, Lie operators and Lie transforms) |
| ８. Canonical form of geometric optics 4 (Simplectic conditions, Liouville theorem) |
| ９. The theory of wavefronts and light rays 1 (Malus-Dupin theorem, wavefronts and eikonal equations) |
| 10. The theory of wavefronts and light rays 2 (Geodesic field and Hamilton-Jacobi equations, Jacobi theorem) |
| 11. The theory of wavefronts and light rays 3 (Hamilton-Jacobi equations and eikonale) |
| 12. The theory of wavefronts and light rays 4 (Huygens theorem) |
| 13. Linear optics and the theory of image formation 1 (Optical elements and linear transforms, image formation and aberrations) |
| 14. Linear optics and the theory of image formation 2 (Gaussian optics and ABCD matrices, image formation and its conditions) |
| 15. Linear optics and the theory of image formation 3 (Simplectic maps). |
|
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