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www.opticalimaging.org Tutorial on Computational Optical Imaging University of Minnesota 19-23 September David J. Brady Duke University www.disp.duke.edu
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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
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www.opticalimaging.org Lecture 1. Computational Imaging Outline Three revolutions and the history of optical imaging Multiple aperture/multiple channel imaging Computation and imaging, pinhole and coded aperture imaging Noise and imaging metrics
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www.opticalimaging.org Revolution 1: The invention of optical instruments
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www.opticalimaging.org Imaging without optics
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www.opticalimaging.org Imaging with optics
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www.opticalimaging.org Revolution 2: Photochemistry Taken in 1839, this picture of a boulevard gives the impression of empty streets, because with long exposures moving objects would not register. http://www.rleggat.com/photohistory/ DAGUERRE, Louis Jacques Mande b. 18 November 1787; d. 10 July 1851
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www.opticalimaging.org Revolution 3: Electronic Recording
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www.opticalimaging.org Electronic recording enables Electronic transmission (television) Multidimensional imaging (tomography) Feature extraction/enhancement Computational improvement of image metrics –Enhanced resolution –Extended depth of field –Imaging of spectra, coherence and polarization features –….
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www.opticalimaging.org Example of an Emerging Computational System TOMBO Architecture R. Shogenji, Y. Kitamura, K. Yamada, S. Miyatake, and J. Tanida, "Multispectral imaging using compact compound optics," Opt. Express 12, 1643-1655 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1643
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www.opticalimaging.org Spectroscopic TOMBO
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www.opticalimaging.org Geometric Pixel Projection in TOMBO
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www.opticalimaging.org TOMBO Image Reconstruction
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www.opticalimaging.org Reconstructed Image
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www.opticalimaging.org Comments What is the data model for TOMBO? What is multiplex imaging? How do spectral spaces map onto each other?
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www.opticalimaging.org Data Models, Imaging and the Whittaker Shannon Sampling Theorem
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www.opticalimaging.org The Sampling Theorem
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www.opticalimaging.org Discrete and Continuous Signals in Imaging
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www.opticalimaging.org Generalized Sampling and Filter Banks
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www.opticalimaging.org Example 2: Coding Elements and Coded Aperture Imaging
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www.opticalimaging.org Visibility and Fields g(B)=s h(A,B)f(A)dA
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www.opticalimaging.org Visibility Detection Models
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www.opticalimaging.org Pinhole Visibility Model
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www.opticalimaging.org Challenges of Pinhole Imaging Throughput/resolution trade-off
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www.opticalimaging.org Coded Aperture Imaging
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www.opticalimaging.org Afternoon Lessons
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www.opticalimaging.org 2D Coded Aperture Imaging
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www.opticalimaging.org Deconvolution Ideally
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www.opticalimaging.org Uniformly Redundant Arrays Quadratic residues
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www.opticalimaging.org Inversion Code
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SNR for Coded Aperture Systems Coded Aperture SNR Isomorphic SNR
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www.opticalimaging.org SNR in TOMBO systems and data models Single aperture mapping g i =f i +n Multiple aperture mapping
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Linear estimation For The least mean square linear estimator is
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www.opticalimaging.org Estimation Covariance
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www.opticalimaging.org Mean Square Error Single aperture case Multiple aperture case
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www.opticalimaging.org Compressive Coding SNR reduction factor
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www.opticalimaging.org Optimization Minimization of Is a classic problem, with minima derived from the use of Hadamard-related matrices for H
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www.opticalimaging.org Interesting Mathematical Issues Optical elements filter, redirect and block light. Pre-filtering is fundamental in optics but similar mechanisms are not used in radio or acoustic systems, where “the signal” is directly detected. Why are light signals different? Physical coding is inherent in optical system design. How would codes for nonlinear estimation processes be developed/optimized? Is there a fundamental cost for multiplexing in optical systems? What is the meaning of multiplexing in application specific sensing?
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