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OPTICAL SCIENCES 627: Computer-Generated Holograms -- Spring 2005
Monday |
Wednesday |
Friday |
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January 10 No Class |
January 12 Lecture 01 Fourier Transforms |
January 14
Lecture 02
Linear Systems Lecture 02a Matlab - Prototype.m (DOWNLOAD) |
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January 17 Holiday |
January 19
Lecture 03
Holography |
January 21
Lecture 04 Optical
FT |
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January 24
Lecture 05 |
January 26
Lecture 06 - Phase ramp - Blazed grating - Discussions about Project #1 |
January 28
Lecture 07 - DUE: Project #1 - Grating Simulations a. Fourier Diffraction of a Prism b. Fourier Diffraction of a Cosine Grating c. Fourier Diffraction of a Ronchi Ruling |
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January 31
Lecture 08 - Discussions about Project #2, 3, 4 |
February 2
Lecture 09 |
February 4
Lecture 10 |
| February 7 Lecture 11 |
February 9
Lecture 12 |
February 11
Lecture 13 - DUE: Project #2 - Matlab-Only Simulations a. Perfect CGH b. Cosine CGH - Scan c. Squarewave CGH - Scan |
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February 14
Lecture 14 |
February 16 No Class |
February 18
Lecture 15 - DUE: Project #3 Scan &Film CGH's a. Phase-Only Cosine CGH b. Phase-Only Squarewave CGH c. Crossed-Squarewave CGH |
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February 21
Lecture 16 |
February 23
Lecture 17 |
February 25
Lecture 18 - DUE: Project #4 - Matlab-Only Simulations a. Phase Squarewave CGH b. Blazed CGH c. Kinoform - Use GS diffuser |
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February 28
Lecture 19 |
March
2
Lecture 20 |
March
4
Lecture 21 - DUE: Project #5 - Simulations a. Cosine FZP - Scan b. Amplitude Squarewave FZP -Scan c. Phase Squarewave FZP d. Blazed FZP |
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March
7
Lecture 22 |
March
9 Lecture 23 |
March 11 Lecture 24 |
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March 16 Spring Break |
March 18 Spring Break |
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March 21
Lecture
25 - MLT Guidelines - Link to MLT WEB page |
March 23
Lecture 26 |
March 25
Lecture 27 - DUE: Project #6 - Disperser |
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March 28
Lecture
28 |
March
30
Lecture
29
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April 1
Lecture 30 - DUE: Project #7a - MTL Format Practice |
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April
4
Lecture 32 |
April 6
Lecture 33 |
April 8
Lecture 34 (No Lecture) - MLT Laboratory - Group 1: 11am-12pm - Group 2: 12pm-1pm - Group 3: 1pm-2pm - Reconstruction Lab 2pm |
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April 11
Lecture 35 |
April 13
Lecture 36 - Guest Lecturer - Jim Burge - CGH's for Optical Testing |
April
15 Lecture
37 |
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April 18
Lecture
38
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April 20
Lecture
39 |
April 22
Lecture 40 |
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April 25
Lecture
41 |
April 27
Lecture 42 |
April 29
Lecture 43 |
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May 2 Lecture 44 |
May 4
Lecture 45 |
May 6
No Class |
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Who, what, when and,
where |
|
Lectures |
Instructor: Professor William J. Dallas |
| The course grade will be based on 10 projects. |
PART I: MATHEMATICAL PRELIMINARIES
| Introduction |
| 1-D Fourier transform |
| 2-D Fourier transform |
| Fourier series and two related definitions |
| Discrete Fourier transform (DFT) |
| Appendix A: Three- and Four-dimensional Fourier transform |
| Appendix B: Three- and Four-dimensional Fourier transform |
| Appendix C: The N-dimensional vector Fourier transform |
| Appendix D: The Fourier transform in polar coordinates |
| Appendix E: The Fourier transform in spherical coordinates |
| Appendix F: The Fourier transform in hyperspherical coordinates |
| Appendix G: Relation of the FFT to the DFT |
| Appendix H: The Fresnel transform |
| Appendix I: The uncertainty relation |
| Appendix J: The uncertainty relation and the Gaussian |
| Appendix K: The uncertainty relation and CGH's |
| Appendix L: Fourier transform tables |
2. Comb Math
| Introduction |
| The Dirac delta function |
| Fourier transform of the Dirac delta function |
| The comb function |
| Fourier relations of comb functions |
| Relation of the Fourier series to the Fourier transform |
| Relation of the discrete Fourier transform (DFT) to the Fourier transform |
| Encoding phase in fringe shifts |
| Appendix A: The Gaussian convergence factor and the delta function |
| Appendix B: Fourierr transforms and the Gaussian convergence factor |
| The Delta function of a function |
3. Sampling
| Introduction |
| The Whittaker-Shannon sampling theorem |
| Sampling real functions: the Nyquist sampling rate |
| Over-sampling |
| Under-sampling and aliasing |
| The sampling theorem in two dimensions |
| Appendix A: Uniformly shifted sample points |
| Appendix B: Non-rectangular apertures |
| Appendix C: Sampling on non-rectangular lattices |
| Appendix D: A sampling theorem for a function and its derivative |
| Appendix E: A sampling theorem for the Fresnel transform |
| Appendix F: Cross artifacts and symmetry |
| Appendix G: The Lagrange sampling theorem |
| Introduction |
| Cosine-carrier modulation |
| Squarewave-carrier modulation |
| The modulation image superpostion |
5. MATLAB
| Introduction |
| Variables |
| Operators |
| Flow-control structures |
| Input/output commands |
| Disk commands |
| Other functions |
| Appendix A: Matrix filling examples |
| Appendix B: flow-control structure sxamples |
| Appendix C: Example M-file: DFT of a uniformly filled array |
| Appendix D: CGH program |
| Copyable M-file CGH script |
| System diagrams |
| Operational calculus |
| Hilbert-space representation of a system |
| Power-series operators |
| Expansion to first-order: linear systems |
| Shift-invariant systems |
| Linear shift-invariant (LSI) systems |
PART II: THE CGH
| What is a hologram? |
| Selected events in the history of holography |
| Waves |
| The parabolic approximation |
| Optical elements |
| The optical Fourier transform |
| Recording media characteristics |
| The hologram as a distorted diffraction grating |
| Fringe distortions in interferometric holograms |
| Binary holograms |
| Detour phase |
| Diffusers |
| Phase-only holograms |
| Depth effects |
| Appendix A: The parabolic approximation |
2. Simulating the Optical Fourier Transform
| Introduction |
| Application of comb math |
| Object space |
| Fourier space |
| Reduced coordinates |
| A remark on normalization |
| Diffraction efficiency |
| Bleached binary CGH's |
3. Point-Oriented Versus Cell-Oriented CGH's
| Introduction |
| Contrasting the two CGH families |
| Point-oriented example |
| Simulating a point-oritented CGH |
| Fabricating a point-oriented CGH |
| Cell-oriented example |
| Simulating a cell-oriented CGH |
| Fabricating a cell-oriented CGH |
| Introduction |
| The perfect CGH |
| The referenceless on-axis computer hologram (ROACH) |
| The greytone CGH |
| The squarewave CGH |
| The crossed-squarewave CGH |
| Appendix A: The sandwich hologram |
| Appendix B: The referenceless on-axis complex hologram (ROACH) |
| Appendix C: CGH's that reconstruct in higher diffraction orders |
| Appendix D: Multiplex CGH's |
| Introduction |
| The Lohmann Type-III binary hologram |
| The gap and overlap problem: circular overflow solution |
| Appendix A: A useful identity |
| Appendix B: Fabricating a CGH |
| Introduction |
| Illumination |
| Transmission |
| Reflection |
| Propagation |
| Additional considerations for propagation |
| CGH's grouped by propagation region |
| CGH's with circular carriers |
| Appendix A: The wave equation |
| Appendix B: Characteristic bodies |
| Appendix C: Depth effects for Fresnel CGH's |
| Appendix D: Depth effects for near-Fourier CGH's |
| Appendix E: Depth effects for image-plane CGH's |
| Appendix F: Depth effects for near-field CGH' |
| Appendix G: Imaging in the parabolic approximation |
| Appendix H: Transforming the spherical wave |
7. Computer Simulation of Non-Fourier Holograms
| Introduction |
| The two-pPlane self-luminous object |
| Adjusting the viewing perspective |
| Depth effects in modulation images |
PART III: ADVANCED TOPICS
1. Diffusers
| Introduction |
| Desirable properties of the Fourier spectrum |
| Diffusers for interferometric holograms |
| Random vs deterministic diffuser functions |
| General purpose (object independent) vs specific (object dependent) diffuser functions |
| RADAR codes |
| Schroeder codes |
| Frank-Heimiller codes |
| Calabro-Wolf (hyperbolic) codes |
| Modern methods |
| Simulated annealing |
| Gerchberg-Saxton (Lesem-Hirsch-Jordan) procedure |
| Speckle suppression |
| Complex amplitude distortions |
| Sampling and point-oriented CGH's |
| Fourier domain phase quantization |
| Shift effect of Fourier domain phase quantization |
| Depth effects of Fourier domain phase quantization |
| Effects on irradiance |
| Introduction |
| Thresholding |
| Wandering threshold |
| Halftoning |
| Dot density |
| Dithering or tesselating |
| Error diffusion |
| Dynamic programming (Bellman optimization) |
PART IV: APPLICATIONS
1. Replication, Fanouts and Interconnects
| Introduction |
| Replication |
| Fanouts and interconnects |
| Introduction |
| Information reduction |
| Shading models |
| Multiplexing and color display |
| Real-time display |
| Introduction |
| Complex amplitude linear filters |
| Image enhancement |
| Image recognition |
| Encryption |
| Irradiance linear filters |
| Introduction |
| Interferometry |
| Blanks ( rough surfaces) |
| Polarization |
| White Light |
5. Diffractive Optical Elements
| Introduction |
| Prisms |
| Lenses |
| Near-field optics |
6. Beam Shaping
7. Mode Selection (Outline)
| References |
| Introduction |
| Wave modes |
| Computer-generated holograms as modans |
| Mode selection |
| Analysis of modan imperfections |
| Modan applications |
PART V: REFERENCES