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by: Trace Mante MD


Trace Mante MD

GPA 3.61


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Class Notes
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This 63 page Class Notes was uploaded by Trace Mante MD on Monday October 26, 2015. The Class Notes belongs to CSCE 763 at University of South Carolina - Columbia taught by Staff in Fall. Since its upload, it has received 33 views. For similar materials see /class/229588/csce-763-university-of-south-carolina-columbia in Computer Science and Engineering at University of South Carolina - Columbia.

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Date Created: 10/26/15
Aberration Theory Geunyoung Yoon PhD Assistant Professor Department of Ophthalmology Center for Visual Science University of Rochester Optics Quantum Optics Coherent Optics Diffractive Optics Fourier Optics Geometrical Optics Aberration theory Paraxial Optics First Order Optics Gaussian Optics Outline gt What I s Wavefront Huygens s principle Snell s law Fermat s principle ParaXial rst order approximation quot What Kind Of Mitrefont A bermtions Are Therequot I Why Are These A bt l l39tltiOtlS Important i110 w Can We M easure These Aberrations f T 110 Eye Outline gtWhat Kind Of Wavefront Aberrations Are There Monochromatic aberration Seidel and wave aberrations Chromatic aberration Longitudinal Transverse Outline gtWhy Are These Aberrations Important Relationship between aberrations and image quality Pupil function PSF MTF Image convolution Outline gtH0w Can We Measure These Aberrations Of The Eye Different types of wavefront sensors What IS Wavefront Huygens s principle Snell s law Fermat s principle ParaXial first order approximation Wavefront vs Ray A wavefront is a surface over which an optical disturbance has a constant Qhase Harmonic wave function 1 x t A sinkx wt V Phase Spherical wavefront Plane wavefront t0 t Wavefront vs Ray Rays are lines normal to the wavefronts at every point of intersection Plane wavefront Spherical wavefront Ray Huygens s Principle Every point on a primary wavefront serves as the source of spherical secondary wavelets such that the primary wavefront at some later time is the envelope of these wavelets Secondary spherical wavefront Primary spherical wavefront Snell s law normal Fast medium smaller refractive index ni Slow medium larger refractive index nt sin9t sin6i Re ection 91 9r nt Refraction Oi gt at When ni lt nt Fermat s Principle The path actually taken by light in going from some point S to a point P is the shortest optical path length 0PL 0PLniEnt 11th x2 nt lb2 a x2 n1 dOPL Ot OPL dx 0 mmlrmze ni x nt ax 0 th x2 Jbz a x2 1 sin6t nt sin6i Paraxial Optics First order optics a x p0 R p1 m 1 11 1 12 n1Rso R sine n2Rsl R sine P0 pl Approximation 3 65 67 n sm 6 z 6 3 5 7 Lens maker s formula S S R 0 l ParaXial Optics First order optics The emerging wavefront segment corresponding to these paraxial rays is essentially spherical and will form a perfect image at its center P Third Order Optics The paraxial approximation sin z is somewhat unsatisfactory if rays from the periphery of a lens are considered V Perpheral rays 7 Aberrations What Kinds Of Wavefront Aberrations Are There Monochromatic aberration Seidel and wave aberrations Chromatic aberration Longitudinal Transverse Monochromatic aberrations Seidel aberrations gtSpherical Aberration gtComa gtAstigmatism gtField Curvature gtDistortion Monochromatic aberrations Seidel aberrations gtSpherical Aberration Monochromatic aberrations Seidel aberrations gtComa Monochromatic aberrations Seidel aberrations gtAstigmatism JJHJBHIKKGI Monochromatic aberrations Seidel aberrations lens gtField Curvature Monochromatic aberrations Seidel aberrations E ii Pincushion distortion Image Object E Barrel distortion gtDistortion Monochromatic aberrations wave aberrations The optical deviations of the wavefront from a reference plane or spherical wavefront Reference spherical wavefront Reference plane wavefront l Aberrated wavefront Wave aberra ion Wave aberrations defocus Myopic near sighted eye Perfect eye Defocused wavefront Wave aberrations higher order Eye with higher order aberrations Perfect eye Aberrated wavefront Wave Aberration of a Surface Wavefront Aberration Wavetru nt Aberration microns mm superiorinferior O superiorinferior 395 395 mm rightlam mm rig htIeft Mathematical description of the aberration Zernike circle polynomials W0 2 c z0 I Wavefront zemike Zernike polynomials aberration COCffiCient wavefront mode if m angular frequency astigmatism 2 39 n radial order Zernike polynomials ZWPVGJ Second order aberrations Higher order abmaojons Wavefront mode for each Zernike polynomial N154321012345 def cus astignilatism astign mtism llld ll sphegzrical 2nd asti llld ll 2nd t refoil 2nd oma 2nd Emma refoil pentf0il 5 I I I I I afoil 2nd aqti 4 Wavefront aberration and Zernike coefficients Zernike Zernike polynomial coefficients mode I Wave gt Zernike aberration lt1 coefficients Wave aberration 03 05 Wavefront rms error 2 rms 2CZ39 gt Strehlzl ZTJI rms2 when rms is small Diffraction limited Strehl 2 08 0398 o g 06 E Rayleigh s 4 rule G 4 3 04 A m Wpv S I 02 1 0 002 004 006 008 01 012 014 016 rms Chromatic Aberration Lensmaker s formula i n 1 i L f R1 R2 11 n f f for polychromatic light 154 98 BK7 Schott glass R1 R2 50mm 1535 s 95 quotO 153 533 a H T a B 1525 03 o Dquot a A 3945 1 52 B m 5 1515 151 93 04 045 05 055 06 065 07 Wavelength mm Longitudinal axial chromatic aberration LCA Short wavelength White light Long wavelength LCA 0f the human eye Bennet and Rabbetts 1989 HIE 4m 5m 500 70 30 Wavelength nm 1 VD I Spectral sensitivity of the human eye Optical effect of eye s LCA on image quality z 02D defocus for monochromatic light 0D 1 l 08 02D gt r 06 3 03D U2 5 04 m 0 2 04D 08D 0 400 450 500 550 600 650 700 Wavelength nm Transverse lateral chromatic aberration TCA TCA Long wavelength Short wavelength Why Are These Aberrations Important Relationship between aberrations and image quality Pupil function Rms PSF SR OTF MTF PTF Image convolution Image quality Image plane Wave arratlons PSF SR MTF object image How well can an optical system form image We can improve image quality by correcting the aberrations Aberration vs Image quality Pupil function 211 aberration Pxa Axa yexplT Wxa Point Spread Function Strehl Ratio autocorrelation PSF Image convolution I Optical Transfer Function OTF Modulation Transfer Function Phase Transfer Function MTF PTF Point Spread Function PSF PSF FTPx y 2 The Point Spread Function or PSF is the image that an optical system forms of a point source The point source is the most fundamental object and forms the basis for any complex object Point Spread Function PSF Geomeuical optics Real World perfect optics The PSFfar a perfect optical system is the Airy disc which is the Fraunhafer diffraction pattern for a circular pupil Point Spread Function vs Pupil Size Perfect Eye 2mm 3mm Point Spread Function VS Pupil Size Typical Eye 2mm 3mm 0 or r Strehl Ratio diffractionlimited PSF with no aberrations 1L actual PSF with aberrations Image Convolution 7 7 7 FT391 FT PSFUJ FT 0xy 3607 lt29 I Modulation Transfer Function MTF MTF x fy ReF T PSF 96 The Modulation Transfer Function or M T F is a measure of the reduction in contrast from object to image The ratio of the image modulation to the object modulation at all spatial frequencies Modulation Transfer Function MTF Object 100 contrast Q Image diffraction only Image 7 diffraction 025D defocus 1 MTF Spatial Frequency Wave39mm Auenanun Mudmatmn nanva runcnun madmanan 35 quot ss st s3 an E 39O s Wave39mm Auenanun u 4 u w H 3 n2 0111 m I 7 in 2 9 5 Mudmatmn nanva runcnun madmanan 1532 ADD a 4m Waves Wave39mm Auenanun madmanan Mudmatmn nanva runcnun Optics Simulations Have fun Fundamental Optics B httpWebphysicsphmsstateedujavarnirrorjavalighthtm Wavefront Theory and Fourier Optics B httpWWWopticsarizonaedujcwyantmathhtm H 0w Can We Measure These Aberrations Of The Eye Different types of wavefront sensors to measure ocular aberrations Wavefront sensors for the eye Subjective method Objective method Ing0ing light Ingoing light Outcoming light Spatially Resolved Tcheming ShackHartmann Refractometer Laser Ray Tracing Measurement principle of wavefront sensors for the eye Measurement of wavefront slope lst derivative of wavefrow averaged over each subaperture on the pupil Original wavefront Wxy Spot displacement Ad d x y Averaged wavefront slope l subaperture 4 7 T WOW 8Wxy kAd 8x x kAdy 6y Spatially Resolved Refractometer Webb Penney and Thompson 1992 D I reference W Subject adjusts the incident angle of light until retinal 5mg intersects reference spot reference Muzzy Laser Ray Tracing Navarro amp Losada 1997 Molebny et al 1997 Adx dy m m V reference CCD Scanning different locations of the pupil Ad d x y CCD Tcherning Aberroscope Tscherning 1894 Dot pattern I mask ShackHartmann wavefront sensor Liang Grimm Goelz and Bille 1994 Liang and Williams 1997 Adx dy 4 Laser beacon CCD Perfect eye Real eye Comparison of wavefront measurements using different wavefront sensors ShackHartmann vs Spatially Resolved Refractometer Objective vs Subjective methods Salmon a 21 J Opt Soc Am A 15 1998 LT nannan mvelengm an lemnoral Ihermlon waymm pupll polmon mm ShackHartmann vs Laser Ray Tracing Outcoming vs Ingoing light MorenoBar uso and Navarro J Opt Soc Am A 17 2000 Arti cial Wave abandon um Wm bulnh an pm zemika Coe 39lclenl t ShackHartmann vs Laser Ray Tracing vs Spatially Resolved Refractometer MorenoBarriuso et al Optometry and Vision Science 78 2001 FUC URE 3 Conmur plans of the wave aberration Eur the right eye oi subject RN For HS l39eft1 LRT vicenter l and SRR Iright measurements Left represents tempmal side and right represents nasal side Pupil cmrdina nes rangg Emm 335 mm to 323 mm Step betweem adjacent cUnmur Pines is 05 yum Ti It terms ZI and Z2 and deiocus IIZ have been cance led Thank you


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