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Tutorial on Computational

Optical ImagingUniversity of Minnesota

19-23 September 

David J. BradyDuke University

www.disp.duke.edu

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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

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Lecture 6. Wavefront Coding

Outline

• The Ambiguity Function

• Wavefront coding for extended depth of 

field• Discrete sampling and MTF

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The Ambiguity Function:

See Cheney

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 Ambiguity Function:

See Cathey and Dowski

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Defocus Transfer Function

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Defocus Transfer Function

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 Ambiguity and MTF Focal system

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Structure of the Ambiguity Function

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

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Cubic Phase Distortion

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Cubic Phase Ambiguity Function

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Focus and defocus PSF

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MTF

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Image Comparisons

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Is Wave front coding a good idea?

• SNR

• Why not stop the aperture?

• Why not multiple apertures?

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Discrete Sampling and Optical

Imaging

http://www.astro.uni-bonn.de/~ccd/boccia/ccd_prinzip/

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CCD vs. CMOS

http://www.micron.com/products/imaging/technology/pixel.html

http://www.dpreview.com/reviews/kodakdcs620x/

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Discrete sampling on Focal planes

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Discrete sampling on Focal planes

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Periods Fourier Space

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Optical and pixel transfer functions

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Digital PSF characterization

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Characterization of sub pixel optical

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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 3µm opt

psf  

1.8mm focal length lens,

3µm psf width, 5.6µm pixels

Scan showing pixel-pixel progression of impulse

   P   i  x

  e   l   n  u  m   b  e  r

time

Demonstration of sub pixel PSF in IR

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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,

13µm psf width, 30µm pixels

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Interesting Mathematical Issues

• What are appropriate performance metrics

for imaging system comparison?

•What are mathematical costs of multipleaperture vs. single aperture image

synthesis?

• How could physical sampling be modified

to improve image synthesis?