Tutorial on Computational Optical Imaging

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Presentation transcript:

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

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 www.opticalimaging.org

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

Hologram Formation www.opticalimaging.org

Hologram Reconstruction www.opticalimaging.org

Signal Bandwidth and off-axis Holography www.opticalimaging.org

Display Holograms http://www.holographer.com/panorama.htm www.opticalimaging.org

Volume vs. Thin Holograms www.opticalimaging.org

Digital Holograms vs. Digital Holography www.opticalimaging.org

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

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

Mathematical Analysis of Coherent Fields Fourier Methods are popular because -Fourier techniques are computationally efficient www.opticalimaging.org

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

Bases for Diffraction Hermite-Gaussian Functions www.opticalimaging.org

Fresnel Uncertainty www.opticalimaging.org

Space-Bandwidth Product Conservation www.opticalimaging.org

“Field-like” vs. “Image-like” Bases www.opticalimaging.org

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. 2424-2430, December 2004. www.opticalimaging.org

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

www.opticalimaging.org

www.opticalimaging.org

Tomography vs. Holographic Field Propagation www.opticalimaging.org

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