Paraxial Optics(Gaussian Optics)(Aberration theory)Diffractive Optics( - PDF document

Optics Paraxial Optics(Gaussian Optics)(Aberration theory)Diffractive Optics(Fourier Optics) Paraxial (first order) approximationMonochromatic aberration (Seidel and wave aberrations)Chromatic aberration (Longitudinal, Transverse) s law, FermatParaxial (first order) approximationMonochromatic aberration (Seidel and wave aberrations)Chromatic aberration (Longitudinal, Transverse) s law, FermatParaxial (first order) approximationMonochromatic aberration (Seidel and wave aberrations)Chromatic aberration (Longitudinal, Transverse) s law, FermatParaxial (first order) approximationMonochromatic aberration (Seidel and wave aberrations)Chromatic aberration (Longitudinal, Transverse)
    Wavefront vs Ray .”Harmonic wave function),(ttx
  Plane wavefrontSpherical wavefrontxxxx Wavefront vs Ray Plane wavefrontSpherical wavefront Ray Huygens’s Principle Primaryspherical wavefront Secondaryspherical wavefront Snell’s law Fast medium(smaller refractive index, ni)Slow medium(larger refractive index, nt) i
t
r ttinn


r

t when ni nt Fermat’s Principle OPSOnOPLti
+
= 2222)(

+
++
= OPnSOnOPLti
+
=“The path actually taken by light in going from some point S to a point Pis the shortest optical path length (OPL).” ni i
tnt OS r xa-x = 0 to minimize OPLx 0)()(2222=+
++




 )ttinn









n1
n2S osipopiR Rnnsnsnio1221=+ iioopRsRnpRsRn((21

Paraxial Optics (First order optics)Lens maker’s formula Paraxial Optics (First order optics) 1n2S essentially spherical and will form a ”perfect” image at its center P.” Third Order Optics 3sin3


n1n2S “The paraxial approximation, sin_
_, is somewhat unsatisfactoryif rays from the periphery of a lens are considered.” Paraxial rays
    222121221112112iiooiosRsnRssnhRnnsnsn (Seidel and wave aberrations) Monochromatic aberrations (Seidel aberrations)Field Curvature Field Curvature Lens Monochromatic aberrations (Seidel aberrations) Spot diagram Field Curvature Monochromatic aberrations (Seidel aberrations) Monochromatic aberrations (Seidel aberrations)Field Curvature Monochromatic aberrations (Seidel aberrations)Field Curvature Field Curvature Monochromatic aberrations (Seidel aberrations)      “The optical deviations of the wavefront from a reference plane or spherical wavefront.”   Aberrated Wave aberrations (defocus) Myopic (near sighted) eye
 Wave aberrations (higher order) Eye with higher order aberrations -3 -2 -1 1 2 3 -2 -1 1 2 3 Wavefront Aberration Wave Aberration of a Surface Zernike circle polynomials Z2) = _2 cos2
: angular frequency n: radial order Zernike polynomials Second orderaberrations Higher orderaberrations Wavefront mode for each Zernike polynomial -5-4-3-2-1012345 astigmatismdefocusastigmatismcomacomatrefoilspherical2nd astigmatismquadrafoilquadrafoilpentafoilpentafoil2nd trefoil2nd trefoil Wavefront aberration and Zernike coefficients = 0.3°ø- 0.2°ø+ 0.4°ø- 0.5°ø- 0.2°ø+ ……………++ Wave aberration 00.020.040.060.080.10.120.140.16 2mnC Diffraction-limited Rayleigh’s _/4 rulerms (_) 14
 Chromatic Aberration Lensmaker’s formula: 0.40.450.50.550.60.650.7 =
 = (_) for polychromatic light Longitudinal (axial) chromatic aberration(LCA) Long wavelengthShort wavelengthWhite light LCA Bennet and Rabbetts (1989) ~2.2DLCA of the human eyeWavelength (nm) 400450500550600650700 Optical effect of eye’s LCA on image quality
0.2D defocus for monochromatic light Transverse (lateral) chromatic aberration(TCA) Long wavelengthShort wavelengthWhite light TCA (Pupil function, Rms, PSF, SR, OTF, Wave aberrationsImage planePSF, SR, MTF… How well can an optical system form image? Aberration vs Image qualityPoint Spread Function(PSF)Optical Transfer Function(OTF)Strehl Ratio (MTF)Phase Transfer Function(PTF) Image convolution autocorrelationPupil function(aberration)
 yxWiyxAyxP,2),(  Point Spread Function (PSF)() ,yxPFTPSF=The Point Spread Function, or PSF, is the image that anoptical system forms of a point source.The point source is the most fundamental object, and formsthe basis for any complex object. Point Spread Function (PSF) The PSF for a perfect optical system is the Airy disc, which is Geometrical optics Real world Diffraction 1 mm2 mm3 mm4 mm5 mm6 mm7 mm Point Spread Function vs. Pupil Size pupil imagesfollowed by psfs for changing pupil size 1 mm2 mm3 mm4 mm5 mm6 mm7 mm Point Spread Function vs. Pupil SizeTypical Eye Strehl Ratio diffraction-limited PSF(with no aberrations) actual PSF (with aberrations) Strehl Ratio (,)  Image ConvolutionFT [ FTx,y) ) °ø(x,y) ) ] = I(x,y) Modulation Transfer Function (MTF) () () ] The Modulation Transfer Function, or MTF, is a measure of Modulation Transfer Function (MTF) Spatial Frequency 01 Optics Simulations- Have fun!!! -http://webphysics.ph.msstate.edu/javamirror/java/light.htmFundamental OpticsWavefront Theory and Fourier Optics Different types of wavefront sensors Ingoing lightIngoing light Measurement principle of wavefront Measurement of wavefront slope (1st derivative of wavefront averaged over each subaperture on the pupil ydkyyxW
),( Original wavefrontW(x,y)wavefront slope subaperture Spot displacement
dx, _dy Webb, Penney and Thompson (1992) reference dx, _dy Subject adjusts the incidentangle of light until retinal spotintersects reference spot. Navarro & Losada (1997), Molebny et al. (1997) reference dx, _dy dx, _dy Scanning differentlocations of the pupil CCD CCD Tcherning Aberroscope Tscherning (1894)
dx, _dy Dot patternmask Liang, Grimm, Goelz, and Bille (1994), Liang and Williams (1997) Laser beacon
dx, _dy Perfect eye Real eye Comparison of wavefront measurements (Objective vs Subjective methods) S-H (Outcoming vs Ingoing light) Moreno-Barriuso and Navarro, J. Opt. Soc. Am. A, 17 (2000) Shack-Hartmann vs Laser Ray TracingMoreno-Barriuso et al., Optometry and Vision Science, 78 (2001) Thank you! Aberration TheoryGeunyoung Yoon, Ph.D.Assistant ProfessorDepartment of OphthalmologyCenter for Visual ScienceUniversity of Rochester