Tutorial on Computational Optical Imaging University of Minnesota September David J. Brady Duke University

Lectures 1.Computational Imaging 2.Geometric Optics and Tomography 3.Diffraction and optical elements 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

Lecture 3. Diffraction and Optical Elements Harmonic analysis in optics Diffraction and the diffraction impulse response Fresnel diffraction Fraunhofer diffraction Optical Elements

Wave Model of the Electromagnetic Field

Harmonic Analysis of EM Fields

Harmonic Analysis of EM Field

Diffraction and the Impulse Response

Shift Invariant Linear Transformation H(u,v)=

Fresnel Diffraction

Uncertainty and the Fresnel Transform

Fraunhoffer Diffraction

Size Estimation from Fraunhofer Diffraction

Optical Elements prism grating

Transmittance Functions

Prism Transmittance

Grating Transmittance

Absorption, density and surface gratings

Lenses

Lens transmittance

The Lens as a Curved Prism

3D optical elements

Photonic Crystals and Circuits

Interesting Mathematical Issues How to simply model, understand and use 3D optical elements