1. www.opticalimaging.org Tutorial on Computational Optical Imaging University of Minnesota 19-23 September David J. Brady Duke University www.disp.duke.edu

2. www.opticalimaging.org Lectures 1.Computational Imaging 2.Geometric Optics and Tomography 3.Fresnel Diffraction 4.Holography 5.Lenses, Imaging and MTF 6.Wavefront Coding and the impulse response 7.Interferometry and the van Cittert Zernike Theorem 8.Optical coherence tomography and modal analysis 9.Spectra, coherence and polarization 10.Computational spectroscopy and imaging

3. www.opticalimaging.org Lecture 6. Wavefront Coding Outline The Ambiguity Function Wavefront coding for extended depth of field Discrete sampling and MTF

4. www.opticalimaging.org The Ambiguity Function: See Cheney

5. www.opticalimaging.org Ambiguity Function: See Cathey and Dowski

6. www.opticalimaging.org Defocus Transfer Function

7. www.opticalimaging.org Defocus Transfer Function

8. www.opticalimaging.org Ambiguity and MTF Focal system

9. www.opticalimaging.org Structure of the Ambiguity Function

10. www.opticalimaging.org Cubic Phase Distortion

11. www.opticalimaging.org Cubic Phase Ambiguity Function

12. www.opticalimaging.org Focus and defocus PSF

13. www.opticalimaging.org MTF

14. www.opticalimaging.org Image Comparisons

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16. Is Wave front coding a good idea? SNR Why not stop the aperture? Why not multiple apertures?

17. www.opticalimaging.org Discrete Sampling and Optical Imaging http://www.astro.uni-bonn.de/~ccd/boccia/ccd_prinzip/

18. www.opticalimaging.org CCD vs. CMOS http://www.micron.com/products/imaging/technology/pixel.html http://www.dpreview.com/reviews/kodakdcs620x/

19. www.opticalimaging.org Discrete sampling on Focal planes

20. www.opticalimaging.org Discrete sampling on Focal planes

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22. Periods Fourier Space

23. www.opticalimaging.org Optical and pixel transfer functions

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25. Digital PSF characterization

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30. Characterization of sub-pixel optical PSF Approximately 4x undersampled Green: MTF from sampling grid Blue: FT of opt psf + grid Red: fit to MTF based on 3  m opt psf 1.8mm focal length lens, 3  m psf width, 5.6  m pixels Scan showing pixel-pixel progression of impulse Pixel number time

31. www.opticalimaging.org Demonstration of sub-pixel PSF in IR System Approximately 5x undersampled Green: MTF from sampling grid Blue: FT of ir psf + grid 25mm focal length lens, 13  m psf width, 30  m pixels

32. www.opticalimaging.org Interesting Mathematical Issues What are appropriate performance metrics for imaging system comparison? What are mathematical costs of multiple aperture vs. single aperture image synthesis? How could physical sampling be modified to improve image synthesis?