MIT 2.717Jwk1-b p-12.717J/MAS.857JOptical EngineeringWelcome to ...MIT 2.717Jwk1-b p-2This class is about• Statistical Optics– models of random optical fields, their propagation and statistical properties (i.e. coherence)– imaging methods based on statistical properties of light: coherence imaging, coherence tomography• Inverse Problems– to what degree can a light source be determined by measurements of the light fields that the source generates?– how much information is “transmitted” through an imaging system? (related issues: what does _resolution_ really mean? what is the space-bandwidth product?)MIT 2.717Jwk1-b p-3The van Cittert-Zernike theoremGalaxy, ~100 millionlight-years awayradiowavesVery Large Array (VLA)Cross-Correlation+Fouriertransformimage( )optical imageImage credits:hubble.nasa.govwww.nrao.eduMIT 2.717Jwk1-b p-4Optical coherence tomographyCoronary arteryIntestinal polypsEsophagusImage credits:www.lightlabimaging.comMIT 2.717Jwk1-b p-5Inverse Radon transform(aka Filtered Backprojection)Magnetic Resonance Imaging (MRI)The principleThe hardwareThe imageImage credits:www.cis.rit.edu/htbooks/mri/www.ge.comMIT 2.717Jwk1-b p-6You can take this class if• You took one of the following classes at MIT– 2.996/2.997 during the academic years 97-98 and 99-00– 2.717 during fall ’00– 2.710 at anytimeOR• You have taken a class elsewhere that covered Geometrical Optics, Diffraction, and Fourier Optics• Some background in probability & statistics is helpful but not necessaryMIT 2.717Jwk1-b p-7Syllabus (summary)• Review of Fourier Optics, probability & statistics 4 weeks• Light statistics and theory of coherence 2 weeks• The van Cittert-Zernicke theorem and applications of statistical optics to imaging 3 weeks• Basic concepts of inverse problems (ill-posedness, regularization) and examples (Radon transform and its inversion) 2 weeks• Likelihood and information methods for imaging channel inversion 2 weeksTextbooks:• J. W. Goodman, Statistical Optics, Wiley.• M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging, IoP publishing.•Richard E. Blahut, Theory of Remote Image Formation, CambridgeMIT 2.717Jwk1-b p-8What you have to do• 4 homeworks (1/week for the first 4 weeks)•3 Projects:– Project 1: a simple calculation of intensity statistics from a model in Goodman (~2 weeks, 1-page report)– Project 2: study one out of several topics in the application ofcoherence theory and the van Cittert-Zernicke theorem from Goodman (~4 weeks, lecture-style presentation)– Project 3: a more elaborate calculation of information capacity of imaging channels based on prior work by Barbastathis & Neifeld (~4 weeks, conference-style presentation)• Alternative projects ok (please propose early)• No quizzes or final examMIT 2.717Jwk1-b p-9Administrative• Website http://web.mit.edu/2.717/www• Broadcast list will be setup soon• Instructor’s coordinatesGeorge Barbastathis 3-461c [email protected]• Please do not phone-call• Office hours TBA• Admin. Assistant Nikki Hanafin 3-461 [email protected] 4-0449 & 3-5592• Class meets in 1-242– Mondays 1-3pm (main coverage of the material)– Wednesdays 2-3pm (examples and discussion)– presentations only: Wednesdays 7pm-??, pizza servedMIT 2.717Jwk1-b p-10The 4F system1f1f2f2f()yxg ,1⎟⎟⎠⎞⎜⎜⎝⎛′′′′111,fyfxGλλ⎟⎟⎠⎞⎜⎜⎝⎛′−′− yffxffg21211,object planeFourier planeImage planeMIT 2.717Jwk1-b p-11The 4F system1f1f2f2f()yxg ,1⎟⎟⎠⎞⎜⎜⎝⎛′′′′111,fyfxGλλ⎟⎟⎠⎞⎜⎜⎝⎛′−′− yffxffg21211,object planeFourier planeImage plane()vuG ,1θxλθλθyxvusinsin==MIT 2.717Jwk1-b p-12Low-pass filtering with the 4F system()yxg ,in⎟⎟⎠⎞⎜⎜⎝⎛′′+′′×⎟⎟⎠⎞⎜⎜⎝⎛′′′′RyxfyfxG2211incirc,λλ()⎟⎟⎠⎞⎜⎜⎝⎛′−′−∗ yffxffg2121in, jincobject planetransparencyFourier planecirc-apertureImage planeobserved field1f1f2f2f⎟⎟⎠⎞⎜⎜⎝⎛′′′′11in,fyfxGλλ()⎟⎟⎠⎞⎜⎜⎝⎛′′+′′=′′′′RyxyxH22circ,field arrivingat Fourier planemonochromaticcoherent on-axisilluminationfield departingfrom Fourier planeℑℑFouriertransformFouriertransformx′′x′xMIT 2.717Jwk1-b p-13Spatial filtering with the 4F system()yxg ,in()yxHfyfxG′′′′×⎟⎟⎠⎞⎜⎜⎝⎛′′′′,,11inλλ()⎟⎟⎠⎞⎜⎜⎝⎛′−′−∗ yffxffhg2121in, object planetransparencyFourier planetransparencyImage planeobserved field1f1f2f2f⎟⎟⎠⎞⎜⎜⎝⎛′′′′11in,fyfxGλλ()yxH′′′′,field arrivingat Fourier planemonochromaticcoherent on-axisilluminationfield departingfrom Fourier planeℑℑFouriertransformFouriertransformx′′x′xMIT 2.717Jwk1-b p-14Coherent imaging as a linear, shift-invariant systemThin transparency()yxt ,()yxg ,1()),( ,),( 12yxtyxgyxg==(≡plane wave spectrum)()vuG ,2impulse responsetransfer function()),(),(, 23yxhyxgyxg∗==′′Fourier transform),(),(),( 23vuHvuGvuG==output amplitudeconvolutionmultiplicationFourier transformilluminationtransfer function H(u ,v): aka pupil functionMIT 2.717Jwk1-b p-15Coherent imaging as a linear, shift-invariant systemThin transparency()yxt ,()yxg ,1(≡plane wave spectrum)impulse responsetransfer function⎟⎟⎠⎞⎜⎜⎝⎛′⎟⎟⎠⎞⎜⎜⎝⎛′=22sincsinc),(fbyfaxyxhλλ()),(),(, 23yxhyxgyxg∗==′′()⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛=bfvafuvuHλλrectrect,Fourier transformoutput amplitudeconvolutionmultiplicationFourier transformillumination()),( ,),( 12yxtyxgyxg==Example: 4F system with rectangularrectangular aperture @ Fourier plane()vuG ,2),(),(),( 23vuHvuGvuG==MIT 2.717Jwk1-b p-16Coherent imaging as a linear, shift-invariant systemThin transparency()yxt ,()yxg ,1(≡plane wave spectrum)impulse responsetransfer function⎟⎟⎠⎞⎜⎜⎝⎛′=2jinc),(fRryxhλ()),(),(, 23yxhyxgyxg∗==′′()⎟⎟⎠⎞⎜⎜⎝⎛+=RvufvuH22circ,λFourier transformoutput amplitudeconvolutionmultiplicationFourier transformillumination()),( ,),( 12yxtyxgyxg==()vuG ,2),(),(),( 23vuHvuGvuG==Example: 4F system with circularcircular aperture @ Fourier planeMIT 2.717Jwk1-b p-17Examples: the amplitude MIT patternMIT 2.717Jwk1-b p-18Weak low–pass filteringFourier filterIntensity @ image planef1=20cmλ=0.5µmMIT 2.717Jwk1-b p-19Strong low–pass filteringFourier filterIntensity @ image planef1=20cmλ=0.5µmMIT 2.717Jwk1-b p-20Phase objectsglass
View Full Document