1. Tutorial on Computational Optical Imaging
University of Minnesota
19-23 September
David J. Brady
Duke University

2. Lectures Computational Imaging Geometric Optics and Tomography
Diffraction and Optical Elements
Holography
Lenses, Imaging and MTF
Wavefront Coding
Interferometry and the van Cittert Zernike Theorem
Optical coherence tomography and modal analysis
Spectra, coherence and polarization
Computational spectroscopy and imaging

3. Lecture 4. Holography Outline
Hologram formation and reconstruction
Holography, spatial bandwidth and sampling
Digital holography
Fresnelets

4. Hologram Formation

5. Hologram Reconstruction

6. Signal Bandwidth and off-axis Holography

7. Display Holograms http://www.holographer.com/panorama.htm

8. Volume vs. Thin Holograms

9. Digital Holograms vs. Digital Holography

10. Mathematical Analysis of Coherent Fields
Fourier Methods are popular because
- The Maxwell equations are linear

11. Mathematical Analysis of Coherent Fields
Fourier Methods are popular because
- Optical fields tend to be spectrally narrow band

12. Mathematical Analysis of Coherent Fields
Fourier Methods are popular because
-Fourier techniques are computationally efficient

13. Challenges for Fourier Methods
Sampling and sampling functions
Global vs. local information/sparsity
Tomography and field analysis
Complex and 3D geometries

14. Bases for Diffraction Hermite-Gaussian Functions

15. Fresnel Uncertainty

16. Space-Bandwidth Product Conservation

17. “Field-like” vs. “Image-like” Bases

18. Fresnelets
M. Liebling, M. Unser, " Autofocus for Digital Fresnel Holograms by Use of a Fresnelet-Sparsity Criterion ," Journal of the Optical Society of America A, vol. 21, no. 12, pp , December 2004.

19. Properties of Fresnelets
Fresnel transform of a Riesz basis produces a Riesz basis
Analytically calculable for B-splines
New generating function for each scale

22. Tomography vs. Holographic Field Propagation

23. Interesting Mathematical Issues
How to efficiently represent image fields?
How to efficiently and effectively analyze propagation?
How to implement holographic tomography?