School of Optometry
http://hdl.handle.net/2022/600
Tue, 23 May 2017 18:53:56 GMT2017-05-23T18:53:56ZMatlab Files for Fourier Analysis for Beginners
http://hdl.handle.net/2022/21366
Matlab Files for Fourier Analysis for Beginners
Thibos, Larry N.
Matlab files to accompany book developed to serve a graduate-level course called “Quantitative Methods for Vision Research” taught for many years at Indiana University School of Optometry, Bloomington, Indiana.
These matlab files were produced by a Macintosh computer running Matlab version 2015. Files with the extension *.m are unformatted text files that can be opened with any text editor. They are Matlab scripts and functions that can be opened and executed by Matlab. Files with the extension *.mat are binary data files that can be opened only by Matlab. These Matlab files are intended for readers of the monograph “Fourier Analysis for Beginners” who wish to review numerical examples and exercises mentioned in the text. See book at http://hdl.handle.net/2022/21365
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/2022/213662014-01-01T00:00:00ZFourier Analysis for Beginners
http://hdl.handle.net/2022/21365
Fourier Analysis for Beginners
Thibos, Larry N.
Fourier analysis is ubiquitous. In countless areas of science, engineering, and mathematics one finds Fourier analysis routinely used to solve real, important problems. Vision science is no exception: today's graduate student must understand Fourier analysis in order to pursue almost any research topic. This situation has not always been a source of concern. The roots of vision science are in "physiological optics", a term coined by Helmholtz which suggests a field populated more by physicists than by biologists. Indeed, vision science has traditionally attracted students from physics (especially optics) and engineering who were steeped in Fourier analysis as undergraduates. However, these days a vision scientist is just as likely to arrive from a more biological background with no more familiarity with Fourier analysis than with, say, French. Indeed, many of these advanced students are no more conversant with the language of
mathematics than they are with other foreign languages, which isn't surprising given the recent demise of foreign language and mathematics requirements at all but the most conservative universities. Consequently, a Fourier analysis course taught in a mathematics, physics, or engineering undergraduate department would be much too difficult for many vision science graduate students simply because of their lack of fluency in the languages of linear algebra, calculus, analytic geometry, and the algebra of complex numbers.
This introduction to the branch of mathematics called “Fourier analysis” was written for students who lack the mathematical background typically expected by authors of introductory textbooks of a similar title. The book was developed to serve a graduate-level course called “Quantitative Methods for Vision Research” taught for many years at Indiana University School of Optometry, Bloomington Indiana.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/2022/213652014-01-01T00:00:00ZTesting of Lagrange multiplier damped least-squares control algorithm for woofer-tweeter adaptive optics
http://hdl.handle.net/2022/19128
Testing of Lagrange multiplier damped least-squares control algorithm for woofer-tweeter adaptive optics
Zou, W.; Burns, S.A.
A Lagrange multiplier-based damped least-squares control algorithm for woofer-tweeter (W-T) dual deformable-mirror (DM) adaptive optics (AO) is tested with a breadboard system. We show that the algorithm can complementarily command the two DMs to correct wavefront aberrations within a single optimization process: the woofer DM correcting the high-stroke, low-order aberrations, and the tweeter DMcorrecting the low-stroke, high-order aberrations. The optimal damping factor for a DMis found to be the median of the eigenvalue spectrum of the influence matrix of that DM.Wavefront control accuracy is maximized with the optimized control parameters. For the breadboard system, the residual wavefront error can be controlled to the precision of 0.03 μm in root mean square. The W-T dual-DM AO has applications in both ophthalmology and astronomy
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/2022/191282012-01-01T00:00:00ZPhase-sensitive imaging of the outer retina using optical coherence tomography and adaptive optics
http://hdl.handle.net/2022/19127
Phase-sensitive imaging of the outer retina using optical coherence tomography and adaptive optics
Jonnal, R.S.; Kocaoglu, O.P.; Wang, Q.; Lee, S.; Miller, D.T.
The cone photoreceptor's outer segment (OS) experiences changes in optical path length, both in response to visible stimuli and as a matter of its daily course of renewal and shedding. These changes are of interest, to quantify function in healthy cells and assess dysfunction in diseased ones. While optical coherence tomography (OCT), combined with adaptive optics (AO), has permitted unprecedented three-dimensional resolution in the living retina, it has not generally been able to measure these OS dynamics, whose scale is smaller than OCT's axial resolution of a few microns. A possible solution is to take advantage of the phase information encoded in the OCT signal. Phase-sensitive implementationsof spectral-domain optical coherence tomography (SD-OCT) have been demonstrated, capable of resolving sample axial displacements much smaller than the imaging wavelength, but these have been limited to ex vivo samples. In this paper we present a novel technique for retrieving phase information from OCT volumes of the outer retina. The key component of our technique is quantification of phase differences within the retina. We provide a quantitative analysis of such phase information and show that- when combined with appropriate methods for filtering and unwrapping-it can improve the sensitivity to OS length change by more than an order of magnitude, down to 45 nm, slightly thicker than a single OS disc. We further show that phase sensitivity drops off with retinal eccentricity, and that the best location for phase imaging is close to the fovea. We apply the technique to the measurement of sub-resolution changes in the OS over matters of hours. Using custom software for registration and tracking, these microscopic changes are monitored in hundreds of cones over time. In two subjects, the OS was found to have average elongation rates of 150 nm/hr, values which agree with our previous findings.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/2022/191272012-01-01T00:00:00Z