{"id":913,"date":"2019-08-02T11:50:40","date_gmt":"2019-08-02T18:50:40","guid":{"rendered":"https:\/\/live-optics-wp.pantheonsite.io\/visualopticslab\/?page_id=913"},"modified":"2021-01-11T12:13:51","modified_gmt":"2021-01-11T19:13:51","slug":"opti-512r-linear-systems-fourier-transforms","status":"publish","type":"page","link":"https:\/\/wp.optics.arizona.edu\/visualopticslab\/opti-512r-linear-systems-fourier-transforms\/","title":{"rendered":"OPTI 512R: Linear Systems, Fourier Transforms"},"content":{"rendered":"<ul>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/08\/Opti-512-Overview.pdf\">Overview<\/a> (PDF)<\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/08\/OPTI-512R-Syllabus-2020.pdf\">Syllabus<\/a> (PDF)<\/li>\n<li><a href=\"#homework\">Homework<\/a><\/li>\n<li><a href=\"#solutions\">Homework Solutions<\/a><\/li>\n<li><a href=\"#midterms\">Midterms<\/a><\/li>\n<li><a href=\"#finals\">Finals<\/a><\/li>\n<li><a href=\"#recitations\">Recitations<\/a><\/li>\n<li><a href=\"#demos\">Demos<\/a><\/li>\n<li><a href=\"#videos\">Videos<\/a><\/li>\n<\/ul>\n<hr \/>\n<h2 id=\"texts\">Recommended Texts<\/h2>\n<ul>\n<li>Jack Gaskill&#8217;s LINEAR SYSTEMS, FOURIER TRANSFORMS, AND OPTICS<\/li>\n<li>Joseph W. Goodman&#8217;s INTRODUCTION TO FOURIER OPTICS<\/li>\n<li>Tyo, JS, Alenin A.\u00a0 Field Guide to Linear Systems in Optics. SPIE Press. 2015.<\/li>\n<\/ul>\n<p><a href=\"#top\">Back to Top<\/a><\/p>\n<hr \/>\n<h2 id=\"outline\">Course Outline<\/h2>\n<h3>Mathematical Background<\/h3>\n<ul>\n<li>Complex numbers\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/08\/OPTI512-1_12.pdf\">Notes 1_12<\/a><\/li>\n<li>Special functions, the impulse function and functions based on the impulse\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/08\/OPTI512-13_27.pdf\">Notes 13_27<\/a><\/li>\n<li>Harmonic Analysis and the Fourier Series, truncated Fourier series\u00a0 <a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/09\/OPTI512-28_45-1.pdf\">Notes 28_45<\/a><\/li>\n<li>Operators and Linear Shift-Invariant Systems. Convolution and its properties\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/08\/OPTI512-46_58-1.pdf\">Notes 46_58<\/a><\/li>\n<li>Fourier Transform and its properties\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/08\/OPTI512-59_69.pdf\">Notes 59_69<\/a><\/li>\n<li>Convolution Theorem and other special theorems for the Fourier transform (Rayleigh energy, Wiener-Khinchine)\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/09\/OPTI512-70_71.pdf\">Notes 70_71<\/a><\/li>\n<li>Two-dimensional functions, Fourier transforms, and convolution. The Hankel transform and the Radon transform.\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/10\/OPTI512-72_82.pdf\">Notes 72_82<\/a><\/li>\n<\/ul>\n<h3>Signal Processing and Sampling<\/h3>\n<ul>\n<li>Filters: Low Pass, High Pass, Band Pass; Amplitude and Phase Filters\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/10\/OPTI512-83_89.pdf\">Notes 83_89<\/a><\/li>\n<li>Signal processing, noise reduction, equalization\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/10\/OPTI512-90_93.pdf\">Notes 90_93<\/a><\/li>\n<li>Sampling and Reconstruction; Aliasing\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/10\/OPTI512-94_104.pdf\">Notes 94_104<\/a><\/li>\n<li>Discrete Fourier Transform and Discrete Convolution\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/11\/OPTI512-105_111.pdf\">Notes 105_111<\/a><\/li>\n<\/ul>\n<h3>Electromagnetic Wave Propagation and Diffraction<\/h3>\n<ul>\n<li>Plane waves, the plane wave spectrum\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/11\/OPTI512-112_123.pdf\">Notes 112_123<\/a><\/li>\n<li>Gaussian beam propagation\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/11\/OPTI512-124_131.pdf\">Notes 124_131<\/a><\/li>\n<li>Spherical waves, Fresnel and Fraunhofer diffraction\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/11\/OPTI512-132_137.pdf\">Notes 132_137<\/a><\/li>\n<li>Examples of Fraunhofer and Fresnel diffraction, Fresnel zone plates\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/11\/OPTI512-138_151.pdf\">Notes 138_151<\/a><\/li>\n<\/ul>\n<h3>Imaging Systems and Fourier Optics<\/h3>\n<ul>\n<li>Fresnel diffraction from Lenses and Fourier transforming properties of lenses\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/12\/OPTI512-152_159.pdf\">Notes 152_159<\/a><\/li>\n<li>Diffraction limited imaging systems\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/12\/OPTI512-160_167.pdf\">Notes 160_167<\/a><\/li>\n<li>Performance of optical imaging systems with coherent and incoherent illumination, OTF, MTF, PSF, Aberrations\u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/12\/OPTI512-168_178.pdf\">Notes 168_178<\/a><\/li>\n<\/ul>\n<p><a href=\"#top\">Back to Top<\/a><\/p>\n<hr \/>\n<h2 id=\"homework\">Homework<\/h2>\n<ul>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/08\/512HW1_2020.pdf\">Homework 1<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/09\/512HW2_2020.pdf\">Homework 2<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/09\/512HW3_2020.pdf\">Homework 3<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/09\/512HW4_2020.pdf\">Homework 4<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/10\/512HW5_2020.pdf\">Homework 5<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/10\/512HW6_2020.pdf\">Homework 6<\/a>\u00a0 \u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/10\/LunarOrbiterAug23_1966-Quad.jpg\">Lunar Image<\/a> <a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/10\/OPTI512RHW6Template.zip\">Matlab 2D FFT Template<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/11\/512HW7_2020.pdf\">Homework 7<\/a> \u00a0 <a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/11\/HW7-Files.zip\">HW7 Files<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/11\/512HW8_2020.pdf\">Homework 8<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/11\/512HW9_2020.pdf\">Homework 9<\/a> \u00a0 <a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/11\/phase2.zip\">HW9 File<\/a><\/li>\n<\/ul>\n<p><a href=\"#top\">Back to Top<\/a><\/p>\n<hr \/>\n<h2 id=\"solutions\">Homework Solutions<\/h2>\n<ul>\n<li><\/li>\n<\/ul>\n<p><a href=\"#top\">Back to Top<\/a><\/p>\n<hr \/>\n<h2 id=\"midterms\">Midterms<\/h2>\n<ul>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/11\/512Midterm_2019-full.pdf\">Midterm 2019<\/a> \u00a0\u00a0<a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2019\/11\/512Midterm_2019-Solutions.pdf\">Midterm Solutions<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/10\/512Midterm_2020.pdf\">Midterm 2020<\/a> \u00a0 <a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/11\/512Midterm_2020-Solutions.pdf\">Midterm Solutions<\/a><\/li>\n<\/ul>\n<p><a href=\"#top\">Back to Top<\/a><\/p>\n<hr \/>\n<h2 id=\"finals\">Finals<\/h2>\n<ul>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/08\/512Final_2019-with-Eqs.pdf\">Final 2019<\/a> \u00a0 <a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/08\/512Final_2019-Solutions.pdf\">Final 2019 Solutions<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/12\/512Final_2020.pdf\">Final 2020<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/12\/OPTI512ReviewProblems.zip\">Review Problems<\/a><\/li>\n<\/ul>\n<p><a href=\"#top\">Back to Top<\/a><\/p>\n<hr \/>\n<h2 id=\"recitations\">Recitations<\/h2>\n<ul>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/09\/Special-Functions-Examples.pdf\">Special Functions Examples<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/09\/Harmonic-Analysis-Examples.pdf\">Harmonic Analysis Examples<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/09\/Recitation-September-14-2020.pdf\">Delta Function Examples<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/09\/Linear-Shift-Invariant-LSI-Systems.pdf\">Example LSI Systems<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/10\/Convolution2020.pdf\">Convolution Example<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/10\/Matlab-Examples.zip\">Matlab Examples<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/10\/Mathematica-Examples.zip\">Mathematica Examples<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/10\/DFT-Examples.pdf\">DFT Examples<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/11\/Radon-Transform-Examples.pdf\">Radon Transform Examples<\/a><\/li>\n<li><a href=\"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-content\/uploads\/sites\/52\/2020\/12\/DFT-Examples2.zip\">DFT Examples2<\/a><\/li>\n<\/ul>\n<p><a href=\"#top\">Back to Top<\/a><\/p>\n<hr \/>\n<h2 id=\"demos\">Demos<\/h2>\n<p><a href=\"#top\">Back to Top<\/a><\/p>\n<hr \/>\n<h2 id=\"videos\">Videos<\/h2>\n<p><a href=\"#top\">Back to Top<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Overview (PDF) Syllabus (PDF) Homework Homework Solutions Midterms Finals Recitations Demos Videos Recommended Texts Jack Gaskill&#8217;s LINEAR SYSTEMS, FOURIER TRANSFORMS, AND OPTICS Joseph W. Goodman&#8217;s INTRODUCTION TO FOURIER OPTICS Tyo, JS, Alenin A.\u00a0 Field Guide to Linear Systems in Optics. SPIE Press. 2015. Back to Top Course Outline Mathematical Background Complex numbers\u00a0\u00a0Notes 1_12 Special functions, the impulse function and functions<\/p>\n","protected":false},"author":57,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-913","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-json\/wp\/v2\/pages\/913","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-json\/wp\/v2\/users\/57"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-json\/wp\/v2\/comments?post=913"}],"version-history":[{"count":96,"href":"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-json\/wp\/v2\/pages\/913\/revisions"}],"predecessor-version":[{"id":1244,"href":"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-json\/wp\/v2\/pages\/913\/revisions\/1244"}],"wp:attachment":[{"href":"https:\/\/wp.optics.arizona.edu\/visualopticslab\/wp-json\/wp\/v2\/media?parent=913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}