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Tutorial on Computational Optical Imaging

University of Minnesota19-23 September

David J. BradyDuke University

www.disp.duke.edu

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Lectures

1. Computational Imaging2. Geometric Optics and Tomography3. Diffraction and optical elements4. Holography5. Lenses, Imaging and MTF6. Wavefront Coding and the impulse response7. Interferometry and the van Cittert Zernike Theorem8. Optical coherence tomography and modal analysis9. Spectra, coherence and polarization10. Computational spectroscopy and imaging

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Lecture 3. Diffractionand Optical Elements

• Harmonic analysis in optics

• Diffraction and the diffraction impulse response

• Fresnel diffraction

• Fraunhofer diffraction

• Optical Elements

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Wave Model of the Electromagnetic Field

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Harmonic Analysis of EM Fields

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Harmonic Analysis of EM Field

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Diffraction and the Impulse Response

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Shift Invariant Linear Transformation

H(u,v)=

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Fresnel Diffraction

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Uncertainty and the Fresnel Transform

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Fraunhoffer Diffraction

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Size Estimation from Fraunhofer Diffraction

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Optical Elements

prism

http://www.holonet.khm.de/jross/collection/reber.htmlgrating

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Transmittance Functions

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Prism Transmittance

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Grating Transmittance

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Absorption, density and surface gratings

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Lenses

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Lens transmittance

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The Lens as a Curved Prism

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3D optical elementshttp://www.canon.com/camera-museum/tech/l_plant/kumitate/ku_5/body5.html

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Photonic Crystals and Circuits

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Interesting Mathematical Issues

• How to simply model, understand and use 3D optical elements