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) Anterior cornea = 7.7 mm Posterior cornea = 6.8 mm Anterior lens = 10.0 mm Anterior lens core = 7.911 mm Posterior lens core = -5.76 mm Posterior lens = -6.0 mm Radii of Curvature (Accommodated Eye) Anterior cornea = 7.7 mm Posterior cornea = 6.8 mm Anterior lens = 5.33 mm Anterior lens core = 2.655 mm Posterior lens core = -2.655 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.

Schematic eye (4 refracting surfaces) Simplified Gullstrand #2 (1911) Le Grand and El Hage (1980) Classical Eye Models Simplified schematic eye Gullstrand-Emsley (3 refracting surfaces) Emsley (1953) Reduced eye (1 refracting surface) Emsley (1953) Radii of Curvature* Anterior cornea = 7.8 mm Posterior cornea = 6.5 mm Anterior lens = 10.2 mm Posterior lens = -6.0 mm * from Le Grand and El Hage Radii of Curvature Anterior cornea = 7.8 mm Anterior lens = 10.0 mm Posterior lens = -6.0 mm Radii of Curvature Anterior cornea = 5.55 mm

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 Planar wavefront Aberrated wavefront Perfect Eye Aberrated Eye

Every eye has a different pattern of higher order aberrations Perfect eye (diffraction limit) MRB GY AG MAK 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 5.8 mm 7 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 symmetry 5.7 mm MDG SUB 5 JP SUB 4 Low degree of mirror symmetry Porter et al., JOSA A, 2001 MAK SUB 2

Radial Order 2nd 3rd astigmatism Zernike Modes 0 Z -2 2 2 Z 2 Z 2 defocus astigmatism Lower Order Aberrations Higher Order Aberrations -3 Z 3 Z -1 1 3 Z 3 trefoil coma coma trefoil Z 3 3 4th Z -4 4 0 Z 2 Z -2 4 4 Z 4 Z 4 4 quadrafoil secondary astigmatism spherical secondary astigmatism quadrafoil 5th pentafoil Z -5 5 secondary trefoil Z -3 1 5 Z -1 5 Z 5 Z 3 5 5 Z 5 secondary coma secondary coma secondary trefoil pentafoil

Population Statistics of the Eye s Wave Aberration RMS wavefront error (µm) 4 3.5 3 2.5 2 1.5 1 0.5 0 80% 0.5 0.4 0.3 0.2 0.1 0 10% 2.7% 1.8% 0.9% 1.6% 0.9% 0.7% Mean of 109 subjects 5.7 mm pupil Z -2 2 2 Z 2 Z -1 1-3 3 0 3 Z 3 Z 2 3 Z3 Z4 Z4 Z -2 4 4 Z 4 Z -4 1 4 Z 5 Z -1 3 5 Z 5 Z -3 5 5 Z 5 Z -5 5 0 Z 2 Z -2 2 2 Z 2 Z -1 1-3 3 3 Z 3 Z 0 2 3 Z3 Z4 Z4 Z -2 4 4 Z 4 Z -4 1 4 Z 5 Z -1 3 5 Z 5 Z -3 5 5 Z 5 Z -5 5 Defocus Coma Astigmatism Spherical Aberration Porter et al., JOSA A, 2001

The means of almost all Zernike modes are approximately zero and have a large intersubject variability Microns of Aberration 8 6 4 2 0.3 0.2 0.1 0-0.1-0.2-0.3 Mean of 109 subjects 5.7 mm pupil Z -1 1-3 3 3 Z 3 Z 0 2 3 Z3 Z4 Z4 Z -2 4 4 Z 4 Z -4 1 4 Z 5 Z -1 3 5 Z 5 Z -3 5 5 Z 5 Z -5 5 Spherical aberration 0-2 0 Z 2 Z -2 2 2 Z 2 Z -1 1 3 Z 3 Z -3 3 0 2 3 Z 3 Z4 Z4 Z -2 4 4 Z 4 Z -4 1 4 Z 5 Z -1 3 5 Z 5 Z -3 5 5 Z 5 Z -5 5 Zernike Mode Porter et al., JOSA A, 2001

Repeatability of measuring Zernike aberrations Rms measurement variability (microns) 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 Subject 1 within a day Subject 2 within a day Subject 3 within a day Subject11 within a year astigmatism 3rd order aberrations 4th order aberrations 5th order aberrations 6th order aberrations Williams, Yoon, Guirao, Hofer, Porter, Cus. Corneal Ablation, 2001

The eye s higher order aberrations severely degrade retinal image quality MTF (white light) MTF (white light) 1 0.8 0.6 0.4 0.2 Chromatic aberration diffraction no mono best refraction uncorrected 5.7 mm pupil 0 0 10 20 30 40 50 60 spatial frequency (c/deg) Spatial frequency (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 MTF (white light) 1 0.8 0.6 0.4 0.2 Average eye 5.7 mm pupil Monochromatic aberrations corrected Defocus and astigmatism corrected -0.3 D 0 0 10 20 30 40 50 60 Spatial frequency (c/deg) Guirao, Porter, Williams, Cox, JOSA A, 2002

Visual Benefit of correcting higher order aberrations Mean of 109 subjects Modulation transfer 1 0.8 0.6 0.4 0.2 5.7 mm pupil all monochromatic aberrations corrected only defocus and astigmatism corrected Visual benefit 3.5 3 2.5 2 1.5 4 mm pupil 3 mm pupil 5.7 mm pupil 0 0 10 20 30 40 50 60 Spatial frequency (c/deg) 1 0 4 8 12 16 20 24 28 32 Spatial frequency (c/deg) Guirao, Porter, Williams, Cox, JOSA A, 2002

Distribution of visual benefit for 113 subjects Number of Subjects 40 35 30 25 20 15 10 5 Keratoconics 16 c/deg 5.7 mm pupil 0 0 2 4 6 8 10 12 14 16 18 20 22 24 Visual Benefit Guirao, Porter, Williams, Cox, JOSA A, 2002

Distribution of visual benefit for 113 subjects Number of Subjects 40 35 30 25 20 15 10 5 Keratoconics 32 c/deg 5.7 mm pupil 0 0 2 4 6 8 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 Visual benefit 15 13 11 9 7 5 5.7 mm 4.4 mm 3 mm 3 1 0 4 8 12 16 20 24 28 32 Spatial frequency (c/deg) Guirao, Porter, Williams, Cox, JOSA A, 2002

Benefits of higher order correction can be obtained mostly for large pupils 100 3.0 mm Pupil 7.3 mm Pupil 100 10 10 Visual Ratio Benefit Visual Ratio Benefit Modulation MTF transfer 1.0 0.8 0.6 0.4 0.2 0.0 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 Aberration-free 80 1 90 Correction for defocus and astigmatism 90 1.0 0.8 0.6 0.4 0.2 0.0 0 20 20 40 40 60 60 80 Aberration-free 80 1 100 120 140 160 180 200 Correction for defocus and astigmatism 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 Microns of aberration 1.5 1 0.5 0 Accommodating at 2 D artificial eye total rms wavefront error total rms wavefront error defocus astigmatism coma spherical aberration -0.5 0 1 2 3 4 5 Time (Seconds) Hofer et al., JOSA A, 2001

Power spectra of fluctuations in the total rms wavefront error for 4.7 mm pupil 10 Power per Hertz 1 0.1 0.01 0.001 Real eye, paralyzed accommodation Artificial eye 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 100 Paralyzed accommodation 100 Natural accommodation Power per Hertz 10 1 0.1 0.01 10 1 0.1 0.01 defocus astigmatism 3rd orders 0.001 0.001 4th orders 0.0001 0.0001 5th orders 0.1 1 10 Frequency in Hertz 0.1 1 10 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 Monochromatic Visual Benefit 18 16 14 12 10 8 6 4 2 0 With temporal variability 0 10 20 30 40 50 60 Spatial Frequency (c/deg) 5.8 mm pupil

Aberrations change with accommodation Seidel aberration coefficient (microns) 2.5 2 1.5 1 0.5 0-0.5-1 -1.5 0 0.5 1 1.5 2 SC 2.5 HH 2.5 PA 2 1.5 1 0.5 0-0.5-1 -1.5 0 0.5 1 1.5 2 Accommodation (diopters) 2 1.5 1 0.5 0-0.5-1 Coma Astigmatism Spherical aberration -1.5 0 0.5 1 1.5 2 Williams, Yoon, Guirao, Hofer, Porter, Cus. Corneal Ablation, 2001

Visual benefit changes with viewing distance Monochromatic Visual Benefit 7 6 5 4 3 2 1 0 Corrected for infinity, accommodating at infinity Corrected for infinity, accommodating at two diopters 5 4 3 2 1 0 0 10 20 30 40 50 60 0 10 20 30 40 50 60 7 SC HH PA 6 Spatial Frequency in Cycles per Degree 7 6 5 4 3 2 1 0 0 10 20 30 40 50 60 Williams, Yoon, Guirao, Hofer, Porter, Cus. Corneal Ablation, 2001

Relative Contributions of the Cornea and Internal Optics to the Total Wave Aberration of the Eye

Methods to determine Corneal Aberrations 1. Direct Calculation - Corneal Topography (Artal, Guirao, Berrio, Williams) - Directly measure: Total WA, Corneal Topography (Shape) - Calculate: Corneal WA, Internal WA t Artal, et al., Journal of Vision,1, 2001

Looking at the Cornea: Corneal Topography Measures power, shape and thickness of the cornea and it s constituent surfaces

Methods to calculate the corneal wave aberration - Corneal topography Placido s rings Image of Placido s rings Perfect cornea Astigmatic cornea

Corneal Topography: Normal Cornea Front Surface Back Surface

Methods to determine Corneal Aberrations 1. Direct Calculation - Corneal Topography (Artal, Guirao, Berrio, Williams) - Directly measure: Total WA, Corneal Topography (Shape) - Calculate: Corneal WA, Internal WA t 2. Indirect Calculation - Goggles Experiment (Artal, Guirao, Berrio, Williams) - Directly measure: Total WA, Internal WA - Calculate: Corneal WA cornea + internal = total eye internal optics (directly) Artal, et al., Journal of Vision,1, 2001

The Whole Eye is Better than the Sum of Its Parts Artal, Guirao, Berrio, and Williams, Journal of Vision,1, 2001 Cornea Internal Optics Whole Eye

Partial compensation of the corneal aberrations by aberrations from the internal optics Cornea Internal RMS Artal, Guirao, Berrio, and Williams, Journal of Vision,1, 2001

Aberrations increase with age 1.2 1.0 0.8 0.6 0.4 0.2 0.0 25 30 35 40 45 50 55 60 65 70 Age (years) Artal et al., JOSA A, 2002

YOUNG EYE OLDER EYE cornea internal surfaces entire eye Artal et al., J. Opt. Soc. Am. A, 19, 137-143 (2002)

Compensation of corneal aberrations by internal optics breaks down as the eye ages 5.9 mm pupil Artal et al., J. Opt. Soc. Am. A, 19, 137-143 (2002)

Aberrations of Irregular Corneas Keratoconus Penetrating keratoplasty, PK (Corneal Transplant)

Keratoconus Normal Eye Early Keratoconus Moderate Keratoconus http://www.kcenter.org/news/what_is_keratoconus.html

Corneal Topography: Normal Cornea Front Surface Back Surface

Corneal Topography: Keratoconus Front Surface Back Surface

Keratoconics suffer from abnormally high amounts of aberration. Wave Aberration Pointspread Function Retinal Image Typical Subject Keratoconus 5.7 mm pupil 1 deg

PK - Corneal Transplant White arrow shows damaged cornea Round shaped portion of cornea removed A donor button of clear cornea is replaced The donor cornea is sutured into place A cloudy cornea resulting from Fuch's corneal dystrophy

PK - Corneal Transplant White arrow shows damaged cornea Round shaped portion of cornea removed A donor button of clear cornea is replaced The donor cornea is sutured into place

Corneal Topography: Penetrating Keratoplasty

Abnormal vs. Normal Higher Order Wavefront Aberrations 6.0 mm Pupil µm 15 Keratoconus (HORMS = 4.00) PK (HORMS = 3.80) PK (HORMS = 2.46) 0-10 Normal 1 (HORMS = 0.36) Normal 2 (HORMS = 0.47) Normal 3 (HORMS = 0.34) µm 1 0 Normal 1 Normal 2 Normal 3-2

Every eye has a different pattern of higher order aberrations Perfect eye (diffraction limited) MRB GYY MAK Wave Aberration 5.7 mm pupil Pointspread Function Retinal Image 0.5 deg

Every eye has a different pattern of aberrations Aberration maps of the eye s pupil: Perfect eye (diffraction limited) MRB GYY MAK Keratoconic patient The images formed on the eye s retina: 5.7 mm pupil 0.5 deg Just as no two people have identical fingerprints, no two people have identical patterns of aberrations. Because everyone has different aberrations, the images everyone sees are also slightly different.

In theory, some visual benefit could be obtained from a customized correction for small pupils 3.5 Mean of 109 subjects 3 5.7 mm pupil Visual benefit 2.5 2 1.5 3 mm pupil 4 mm pupil 1 0 4 8 12 16 20 24 28 32 Spatial frequency (c/deg)

Radial Order 2nd PSFs from Zernike Modes astigmatism defocus astigmatism 3rd trefoil coma coma trefoil 4th quadrafoil secondary astigmatism spherical secondary astigmatism quadrafoil 5th pentafoil secondary trefoil secondary coma secondary coma secondary trefoil pentafoil

Radial Order 2nd Convolved Objects from Zernike Modes astigmatism defocus astigmatism Diffractionlimited object 3rd trefoil coma coma trefoil 4th quadrafoil secondary astigmatism spherical secondary astigmatism quadrafoil 5th pentafoil secondary trefoil secondary coma secondary coma secondary trefoil pentafoil

Nyquist Limit Foveal Cone Sampling Frequency 1 632.8 nm Modulation Transfer 0.1 0.01 2 3 4 5 6 7.3 mm 0 50 100 150 200 250 Spatial Frequency (c/deg)

Partial compensation of the corneal aberrations by aberrations from the internal optics Younger Subjects (25-45 years) 5.9 mm pupil Spatial frequency (c/deg) Older Subjects (45-70 years) Artal et al., J. Opt. Soc. Am. A, 19, 137-143 (2002)

Keratoconus Normal Eye Early Keratoconus Moderate Keratoconus http://www.kcenter.org/news/what_is_keratoconus.html

There is inter-subject variability in the eye s MTF MTF Castejón-Mochón et al., Vision Res., 2002 Spatial frequency (c/deg)