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Aberrations of the Human Eye: Structure

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Aberrations of the Human Eye: Structure Aberrations of the human eye: Structure Jason Porter Advisor: David R. Williams March 20, 2003 The Institute of Optics and Center for Visual Science University of Rochester Classical Eye Models Gullstrand #1 Schematic Eye (1911) Radii of Curvature (Relaxed Eye) Radii of Curvature (Accommodated Eye) Anterior cornea = 7.7 mm Anterior cornea = 7.7 mm Posterior cornea = 6.8 mm Posterior cornea = 6.8 mm Anterior lens = 10.0 mm Anterior lens = 5.33 mm Anterior lens core = 7.911 mm Anterior lens core = 2.655 mm Posterior lens core = -5.76 mm Posterior lens core = -2.655 mm Posterior lens = -6.0 mm Posterior lens = -5.33 mm Goss and West. Introduction to the Optics of the Eye. 2002. Atchison and Smith. Optics of the Human Eye. 2000. Classical Eye Models Schematic eye Simplified schematic eye Reduced eye (4 refracting surfaces) Gullstrand-Emsley (1 refracting surface) Simplified Gullstrand #2 (1911) (3 refracting surfaces) Emsley (1953) Le Grand and El Hage (1980) Emsley (1953) Radii of Curvature* Radii of Curvature Radii of Curvature Anterior cornea = 7.8 mm Anterior cornea = 7.8 mm Anterior cornea = 5.55 mm Posterior cornea = 6.5 mm Anterior lens = 10.0 mm Anterior lens = 10.2 mm Posterior lens = -6.0 mm Posterior lens = -6.0 mm * from Le Grand and El Hage Modified Eye Models • The refractive surfaces are aspherical. • The crystalline lens is slightly decentered with respect to the axis of the cornea. • The crystalline lens has different refractive index increasing toward its center. Cornea Crystalline lens Classical eye model Modified eye model Visual axis Lens axis Classical eye model Modified eye model Not widely used - poor predictors of retinal image quality, don’t account for aberrations of real eyes Spherical wavefront Aberrated wavefront Planar wavefront Perfect Eye Aberrated Eye Every eye has a different pattern of higher order aberrations Perfect eye MRB GY AG MAK (diffraction limit) Wave Aberration 5.7 mm pupil Pointspread Function Retinal Image 0.5 deg Williams, Yoon, Guirao, Hofer, Porter, Cus. Corneal Ablation, 2001 Aberrations increase with pupil diameter 7 mm 7 mm 5.8 mm 4.6 mm 3 mm Artal & Navarro, JOSA A, 1994 Aberration structure tends to be mirror symmetric between eyes in most normal observers Perfect Correlation Liang and Williams, JOSA A, 1997 Aberration structure tends to be mirror symmetric between eyes in most normal observers Left Eye Right Eye Left Eye Right Eye High degree of mirror 5.7 mm MDG SUB 5 symmetry JP SUB 4 Low degree of mirror symmetry MAK SUB 2 Porter et al., JOSA A, 2001 Radial Zernike Modes Order 2nd Lower Order Aberrations -2 0 2 Z 2 Z2 Z2 astigmatismdefocus astigmatism Higher Order 3rd Aberrations Z-3 -1 1 Z3 3 Z 3 Z3 3 trefoil coma coma trefoil 4th 0 2 4 -4 Z-2 Z Z Z Z 4 4 4 4 4 secondary secondary quadrafoilastigmatism spherical astigmatism quadrafoil 5th -5 Z-3 -1 1 Z3 Z5 Z 5 5 Z 5 Z5 5 5 secondary secondary secondary secondary pentafoiltrefoil coma coma trefoil pentafoil Population Statistics of the Eye’s Wave Aberration 4 0.5 3.5 80% Mean of 109 subjects 0.4 5.7 mm pupil 3 0.3 2.5 0.2 2 0.1 1.5 0 1 Z-2 Z2 Z-1 Z1 Z-3 Z3 Z0 Z2 Z-2 Z4 Z-4 Z1 Z-1 Z3 -3 Z5 -5 2 2 3 3 3 3 4 4 4 4 4 5 5 5 Z 5 5 Z 5 0.5 10% RMS wavefront error (µm) 2.7% 1.8% 0.9% 1.6% 0.9% 0.7% 0 Z0 Z-2 Z2 Z-1 Z1 Z-3 Z3 Z0 Z2 Z-2 Z4 Z-4 Z1 Z-1 Z3 -3 Z5 -5 2 2 2 3 3 3 3 4 4 4 4 4 5 5 5 Z 5 5 Z 5 Defocus Coma Spherical Astigmatism Aberration Porter et al., JOSA A, 2001 The means of almost all Zernike modes are approximately zero and have a large intersubject variability 8 0.3 Mean of 109 subjects 0.2 5.7 mm pupil 6 Spherical 0.1 aberration 0 4 -0.1 -0.2 2 -0.3 -1 1 -3 3 0 2 -2 4 -4 1 -1 3 -3 5 -5 Z 3 Z3 Z 3 Z3 Z4 Z4 Z 4 Z4 Z 4 Z5 Z 5 Z5 Z 5 Z5 Z 5 Microns of Aberration 0 -2 0 -2 2 -1 1 -3 3 0 2 -2 4 -4 1 -1 3 -3 5 -5 Z2 Z 2 Z2 Z 3 Z3 Z 3 Z3 Z4 Z4 Z 4 Z4 Z 4 Z5 Z 5 Z5 Z 5 Z5 Z 5 Zernike Mode Porter et al., JOSA A, 2001 Repeatability of measuring Zernike aberrations 0.08 astigmatism 0.07 3rd order aberrations 4th order aberrations 0.06 5th order aberrations 0.05 6th order aberrations 0.04 0.03 0.02 0.01 0 Rms measurement variability (microns) Subject 1 within a day Subject 2 within a day Subject 3 within a day Subject11 within a year Williams, Yoon, Guirao, Hofer, Porter, Cus. Corneal Ablation, 2001 The eye’s higher order aberrations severely degrade retinal image quality 1 diffraction no mono best refraction 0.8 uncorrected 5.7 mm pupil 0.6 Chromatic aberration 0.4 MTF (white light) 0.2 MTF (white light) 0 0 102030405060 spatialSpatial frequency frequency (c/deg) (c/deg) Guirao, Porter, Williams, Cox, JOSA A, 2002 The loss in contrast due to higher order aberrations is equivalent to 0.3 Diopters of defocus 1 Monochromatic aberrations corrected Defocus and astigmatism corrected 0.8 -0.3 D Average eye 0.6 5.7 mm pupil 0.4 MTF (white light) 0.2 0 0 102030405060 Spatial frequency (c/deg) Guirao, Porter, Williams, Cox, JOSA A, 2002 Visual Benefit of correcting higher order aberrations Mean of 109 subjects 5.7 mm pupil 1 3.5 all monochromatic 5.7 mm pupil 0.8 aberrations corrected 3 4 mm pupil 0.6 only defocus and 2.5 3 mm pupil astigmatism corrected 0.4 2 0.2 Visual benefit 1.5 Modulation transfer 0 1 0 102030405060 0 4 8 121620242832 Spatial frequency (c/deg) Spatial frequency (c/deg) Guirao, Porter, Williams, Cox, JOSA A, 2002 Distribution of visual benefit for 113 subjects 40 16 c/deg 35 5.7 mm pupil Keratoconics 30 25 20 15 10 Number of Subjects 5 0 0246810 12 14 16 18 20 22 24 Visual Benefit Guirao, Porter, Williams, Cox, JOSA A, 2002 Distribution of visual benefit for 113 subjects 40 32 c/deg 35 5.7 mm pupil Keratoconics 30 25 20 15 10 Number of Subjects 5 0 02468 12 14 16 18 20 22 24 Visual Benefit Guirao, Porter, Williams, Cox, JOSA A, 2002 Average Visual Benefit of correcting higher order aberrations in 4 keratoconic eyes 15 5.7 mm 13 4.4 mm 3 mm 11 9 7 Visual benefit 5 3 1 048121620242832 Spatial frequency (c/deg) Guirao, Porter, Williams, Cox, JOSA A, 2002 Benefits of higher order correction can be obtained mostly for large pupils 100 100 3.0 mm Pupil 7.3 mm Pupil 10 10 Ratio Ratio Visual Visual Benefit Benefit 1.0 1 10 20 30 40 50 60 70 80 90 1.0 1 20 40 60 80 100 120 140 160 180 200 0.8 Aberration-free 0.8 Aberration-free 0.6 Correction for 0.6 Correction for defocus defocus 0.4 0.4 MTF and astigmatism and astigmatism 0.2 0.2 0.0 0.0 Modulation transfer 0 10 20 30 40 50 60 70 80 90 0 20 40 60 80 100 120 140 160 180 200 Spatial frequency (c/deg) Liang and Williams, JOSA A, 1997 Temporal Properties of the Eye’s Wave Aberration Short Term Instability Wave Aberration Point Spread Function HH viewing distant target, 5.8 mm pupil, 550 nm monochromatic light Videos represent wave aberration measurements taken at 25.6 Hz during a 5 second interval. Average defocus and astigmatism have been removed. Temporal fluctuations with natural accommodation across a 4.7 mm pupil Accommodating at 2 D 1.5 artificial eye total rms wavefront error total rms wavefront error 1 defocus astigmatism 0.5 coma Microns of aberration 0 spherical aberration -0.5 012345 Time (Seconds) Hofer et al., JOSA A, 2001 Power spectra of fluctuations in the total rms wavefront error for 4.7 mm pupil 10 Real eye, 1 paralyzed accommodation 0.1 0.01 Artificial eye Power per Hertz 0.001 0.0001 0.1 1 10 Frequency in Hertz Hofer et al., JOSA A, 2001 Spectra of Zernike modes with and without paralyzed accommodation for 4.7 mm pupil Paralyzed accommodation Natural accommodation 100 100 10 10 1 1 defocus 0.1 0.1 astigmatism Power per Hertz 0.01 0.01 3rd orders 0.001 0.001 4th orders 5th orders 0.0001 0.0001 0.1 1 10 0.1 110 Frequency in Hertz Frequency in Hertz Hofer et al., JOSA A, 2001 Visual benefit of a static correction of the eye’s optics when incorporating the temporal fluctuations in the eye’s aberrations 20 Without temporal variability 18 16 5.8 mm pupil 14 12 10 8 6 With temporal variability 4 Monochromatic Visual Benefit 2 0 0 102030405060 Spatial Frequency (c/deg) Aberrations change with accommodation 2.5 SC 2.5 HH 2.5 PA 2 2 2 Coma Astigmatism 1.5 1.5 1.5 Spherical aberration 1 1 1 0.5 0.5 0.5 0 0 0 -0.5 -0.5 -0.5 -1 -1 -1 -1.5 -1.5 -1.5 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Seidel aberration coefficient (microns) Accommodation (diopters) Williams, Yoon, Guirao, Hofer, Porter, Cus.
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