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

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) RMS wavefront 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

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

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

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

Visual benefit 5

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 Modulation 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. Corneal Ablation, 2001 Visual benefit changes with viewing distance

Corrected for infinity, accommodating at infinity Corrected for infinity, accommodating at two diopters

7 SC 7 HH 7 PA 6 6 6 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 0 1020304050600 1020304050600 102030405060

Monochromatic Visual Benefit Monochromatic Spatial Frequency in Cycles per Degree

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 t (Artal, Guirao, Berrio, Williams) - Directly measure: Total WA, Corneal Topography (Shape) - Calculate: Corneal WA, Internal WA

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 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 Back Surface Surface Methods to determine Corneal Aberrations

1. Direct Calculation - Corneal Topography t (Artal, Guirao, Berrio, Williams) - Directly measure: Total WA, Corneal Topography (Shape) - Calculate: Corneal WA, Internal WA

2. Indirect Calculation cornea + internal = total eye - Goggles Experiment (Artal, Guirao, Berrio, Williams) - Directly measure: Total WA, Internal WA internal optics (directly) - Calculate: Corneal WA

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 RMS Partial compensationofthecorneal aberrations Cornea by aberrationsfrom theinternaloptics Internal Artal, Guirao, Berrio,and Williams,Journal ofVision,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 Back Surface Surface Corneal Topography: Keratoconus

Front Back Surface Surface Keratoconics suffer from abnormally high amounts of aberration. Pointspread Wave Aberration Retinal Image Function

Typical Subject

Keratoconus

5.7 mm pupil 1 deg PK - Corneal Transplant

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

A cloudy cornea resulting from Fuch's corneal dystrophy PK - Corneal Transplant

The donor cornea Round shaped A donor button White arrow shows is sutured into portion of cornea of clear cornea damaged cornea place removed is replaced Corneal Topography: Penetrating Keratoplasty 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

µm Normal 1 (HORMS = 0.36) Normal 2 (HORMS = 0.47) Normal 3 (HORMS = 0.34) 1

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

5.7 mm pupil The images formed on the eye’s retina:

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

5.7 mm pupil 3

4 mm pupil 2.5 3 mm pupil

2 Visual benefit 1.5

1 0 4 8 121620242832

Spatial frequency (c/deg) Radial PSFs from Zernike Modes Order 2nd

astigmatismdefocus astigmatism

3rd

trefoil coma coma trefoil

4th

secondary secondary quadrafoil astigmatism sphericalastigmatism quadrafoil

5th

secondary secondary secondary secondary pentafoiltrefoil coma coma trefoil pentafoil Radial Convolved Objects from Zernike Modes Order 2nd

astigmatismdefocus astigmatism Diffraction- limited object 3rd

trefoil coma coma trefoil

4th

secondary secondary quadrafoil astigmatism sphericalastigmatism quadrafoil

5th

secondary secondary secondary secondary pentafoiltrefoil coma coma trefoil pentafoil Nyquist Foveal Cone Limit Sampling Frequency

1 632.8 nm

0.1 Modulation Transfer

2 3 4 5 0.01 6 7.3 mm 0 50 100 150 200 250 Spatial Frequency (c/deg) Fig.9 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

Spatial frequency (c/deg) Castejón-Mochón et al., Vision Res., 2002