wavefront error and visual performancevoi.opt.uh.edu/voi/wavefrontcongress/2003/presentations... ·...
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Wavefront Error and Visual Performance
Raymond A. Applegate, OD, Ph.D.Raymond A. Applegate, OD, Ph.D.Professor and Borish Chair of OptometryProfessor and Borish Chair of Optometry
University of HoustonUniversity of HoustonHouston, TX, USAHouston, TX, USA
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Once the wavefront error is determined,
image quality is defined.
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To understand wavefront error it is useful to change our thinking from rays of
light to waves of light.
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RaysRays
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WavefrontsWavefronts
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Focus
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RaysRays
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Wavefront afterrefraction
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Ideal Aberrated
Rays
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Ideal Aberrated
Waves and Rays
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Ideal Aberrated
Waves and Rays
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A particularly useful representation of wavefront
error is to fit the error between the actual wavefront and the
ideal wavefront with a Zernike expansion.
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Fitting the error data with a Zernike expansion parcels
the error into unique building blocks.
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CylinderSphere
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Each weighted Each weighted Zernike mode Zernike mode when added when added
together form a together form a representation of representation of the actual WFE.the actual WFE.
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LADARWave
Machines to measure wavefront error are available today from a variety of sources and generally look very much like corneal topography units.
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Wavefront error degrades the optical image it cannot
improve image quality above the diffraction limit.
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WFE =0.133 µm
WFE =0.041 µm
3mm pupil Typical non-surgical eyeBest spectacle correction
20/20
20/12
20/40
3mm pupil Post LASIK >1yrHappy patient 20/15 acuityBest spectacle correction
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Wavefront error defines the ideal compensating
optic.
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WFE specifies how much tissue or materialto remove at every location across the pupil.
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WFE specifies how much tissue or materialto remove at every location across the pupil.
Wavefront retarded:Remove more material
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WFE specifies how much tissue or materialto remove at every location across the pupil.
Wavefront advanced:Remove less material
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nnWFECremovetomaterialofAmount−
+=
'
Where: C = minimum amount of tissue to be removedWFE = wavefront errorn’ = optical index of the material light is enteringn = optical index of the material light is leaving
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But do higher order aberrations really matter?
• It depends on their magnitude.• It depends on the pupil size• It depends on our neural transfer function• It depends on the visual task• It depends on the object
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For many clinical eyes that we have thrown into the garbage bag of irregular astigmatism, it is very
important.
Magnitude
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For normal eyes the potential gains are significant for large pupil sizes and diminish as
the pupil size gets small.
Pupil Size
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To understand impact of aberrations on visual
performance it is very helpful to know which
aberrations are particularly bad and how they interact
with each other.
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Equally important to researchers and clinicians alike is the development of
single value metrics of optical quality capable of
predicting visual performance.
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An important feature of the normalized Zernike expansion is that the
magnitude of the coefficient for each mode
reflects its relative contribution to the total
wavefront error.UUHH RAARAA
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JH 09/28/00 6mm pupil Post LASIK >1yr
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JH 09/28/00 6mm pupil Post LASIK >1yr
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Just because the magnitude of the coefficient reflects its relative contribution to the total wavefront RMS error
does not mean that the largest Zernike coefficient will affect vision the most.
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Different modes of the Zernike expansion affect vision more than others.
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Further, modes can combine to lessen the
adverse visual effects or combine to further worsen
visual performance.
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Wavefront error fundamentally defines the
optical properties of the eye and can be used to calculate
other metrics of optical quality.
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FourierTransform
Error
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Wavefront error
PSF
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Astigmatism Defocus Astigmatism
Trefoil V. Coma H. Coma Trefoil
Quadrafoil 2nd Astigmatism Spherical 2nd Astigmatism Quadrafoil
Pentafoil 2nd Trefoil 2nd V. Coma 2nd H. Coma 2nd Trefoil Pentafoil
2
3
4
5
n-5 -4 -3 -2 -1 0 1 2 3 4 5m
PSF Z
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FourierTransform
Convolution
Error
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Such a transformation is a powerful tool for
visualizing and quantifying the impact of
aberrations on visual performance.
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Notice in the following simulations that as the
pupil size decreases WFE decreases despite the fact that the dioptric
defocus remains constant.
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Further, notice in the simulations that measuring wavefront error for a large pupil and comparing it to
visual performance measured through a smaller
pupil leads to erroneous conclusion.
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To determine how ocular wavefront error affects visual performance one
must measure both at the same pupil size.
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Pupil Diameter = 8.00 mm
Defocus = 0.25 D; RMS WFE = .58 µm
20/12
20/20
20/40
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Pupil Diameter = 6.00 mm
Defocus = 0.25 D; RMS WFE = 0.32 µm
20/12
20/20
20/40
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Pupil Diameter = 4.00 mm
Defocus = 0.25 D; RMS WFE = 0.14 µm
20/12
20/20
20/40
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Pupil Diameter = 2.00 mm
Defocus = 0.25 D; RMS WFE = 0.036 µm
20/12
20/20
20/40
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Wavefront error tells us that the image is getting
better. dioptric error does not.
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While we have demonstrated that visual
acuity decreases with increasing wavefront error for any single
mode…
OVS in press.UUHH RAARAA
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we have also reported that all aberrrations are not equal…
JRS: 18:S556-S562, 2002.
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and that aberrations interact to increase or decrease visual
performance.
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-12
-10
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0
2
2 3 4 5 6 7 8 9 10 1112 1314 1516 17
Pred
icte
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Gai
ned
or L
ost
Zernike Coefficient
2nd Order
3rd Order
4thOrder
Sphere &Cylinder
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-12
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-2
0
2
2 3 4 5 6 7 8 9 10 1112 1314 1516 17
HC
Let
ters
Gai
ned
or L
ost
Zernike Coefficient
2nd Order
3rd Order
4thOrder
Sphere &Cylinder
© RAAUUHH
JRS: 18:S556-S562, 2002.
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Equivalent Diopters = 0.19 DUUHH RAARAA
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Equivalent Diopters = 0.19 DUUHH RAARAA
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Zernike terms interact to affect visual performance.
© RAAUUHH
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RAARAA© RAA
m
m
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© RAAUUHH
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+ =
0.25+ =RMS in µ © RAA
22 15.02.0 +UUHH
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-12
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0
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4Le
tters
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.03 .05 .08 .1 .13 .15 .17 .2 .23 .25 .28RMS
The SSCP Matrix is singular.
Regression PlotInclusion criteria: Total RMS is .25 from Metrics Data.svd
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So if wavefront error and equivalent diopters do
not serve well to explain the variations in visual performance, is there
something better?
© RAAUUHH
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-12
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4Le
tters
Los
t
.2 .3 .4 .5 .6 .7 .8 .9 1 1.1Rayleigh
Y = -12.764 + 12.029 * X; R^2 = .263
Regression PlotInclusion criteria: Total RMS is .25 from Metrics Data.svd
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0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 1.1Marachel
Y = -9.887 + 6.031 * X; R^2 = .494
Regression PlotInclusion criteria: Total RMS is .25 from Metrics Data.svd
Marechel
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In addressing this question, it is important to remember that retinal image quality is the first
step in the visual process.
© RAAUUHH
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Camera opticsCamera optics
FilmFilm
DevelopingDeveloping
Enlarging OpticsEnlarging Opticsand Printingand Printing
Eye’s opticsEye’s optics
PhotoreceptorsPhotoreceptors
Neural ProcessingNeural Processing
Visual PerceptVisual PerceptThe Mind’s EyeThe Mind’s Eye
© RAAUUHH
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Camera opticsCamera optics
FilmFilm
DevelopingDeveloping
Enlarging OpticsEnlarging Opticsand Printingand Printing
Eye’s opticsEye’s optics
PhotoreceptorsPhotoreceptors
Neural ProcessingNeural Processing
Visual PerceptVisual PerceptThe Mind’s EyeThe Mind’s Eye
© RAAUUHH
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Camera opticsCamera optics
FilmFilm
DevelopingDeveloping
Enlarging OpticsEnlarging Opticsand Printingand Printing
Eye’s opticsEye’s optics
PhotoreceptorsPhotoreceptors
Neural ProcessingNeural Processing
Visual PerceptVisual PerceptThe Mind’s EyeThe Mind’s Eye
© RAAUUHH
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Camera opticsCamera optics
FilmFilm
DevelopingDeveloping
Enlarging OpticsEnlarging Opticsand Printingand Printing
Eye’s opticsEye’s optics
PhotoreceptorsPhotoreceptors
Neural ProcessingNeural Processing
Visual PerceptVisual PerceptThe Mind’s EyeThe Mind’s Eye
© RAAUUHH
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Camera opticsCamera optics
FilmFilm
DevelopingDeveloping
Enlarging OpticsEnlarging Opticsand Printingand Printing
Eye’s opticsEye’s optics
PhotoreceptorsPhotoreceptors
Neural ProcessingNeural Processing
Visual PerceptVisual PerceptThe Mind’s EyeThe Mind’s Eye
© RAAUUHH
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Camera opticsCamera optics
FilmFilm
DevelopingDeveloping
Enlarging OpticsEnlarging Opticsand Printingand Printing
Eye’s opticsEye’s optics
PhotoreceptorsPhotoreceptors
Neural ProcessingNeural Processing
Visual PerceptVisual PerceptThe Mind’s EyeThe Mind’s Eye
© RAAUUHH
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Camera opticsCamera optics
FilmFilm
DevelopingDeveloping
Enlarging OpticsEnlarging Opticsand Printingand Printing
Eye’s opticsEye’s optics
PhotoreceptorsPhotoreceptors
Neural ProcessingNeural Processing
Visual PerceptVisual PerceptThe Mind’s EyeThe Mind’s Eye
© RAAUUHH
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The measurement of the wavefront error of the eye
provides the best possible assessment of the retinal image quality.
© RAAUUHH
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It does not tell us how the brain transfers the image
into a visual percept.
© RAAUUHH
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None-the-less, we do have good estimates of
the neural transfer function in the typical
normal eye.
© RAAUUHH
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Figure 7-9 from MacRae, Krueger and Applegate, Customized Corneal Ablation: The Quest for Super Vision, Slack, Inc. 2001.UUHH RAARAA
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r = 0.85
Dioptric equivalent of 0.19 D
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tters
Los
t
.1 .15 .2 .25 .3 .35 .4 .45 .5 .55CS w eighted OTF/CS w eighted dif OTF
Y = -12.107 + 19.827 * X; R^2 = .719
Regression PlotInclusion criteria: Total RMS is .25 from Metrics Data.svd
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-12-10-8-6-4-202468
10Le
tters
Los
t
0 .2 .4 .6 .8 1
CS w eighted OTF/CS w eighted dif OTFY = -12.107 + 19.827 * X; R^2 = .719
Regression PlotInclusion criteria: Total RMS is .25 from Metrics Data.svd
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Finally, it is wise to remember that even if we
know the optical and neural transfer functions of the
eye we do not always know how the mind’s eye will
interpret the information.
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All Is Vanity, By GilbertAll Is Vanity, By GilbertUUHH RAARAA
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All is Vanity, By GilbertAll is Vanity, By GilbertUUHH RAARAA
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In Summary• New clinically viable aberrometers are
changing the way we correct the refractive errors of the normal and clinical eye.
• Zernike modes interact to increase or decrease visual perception.
• Pupil size plays an important role in visual perception.
• To compare the affects of aberrations on visual performance both have to be measured at the same pupil size.
© RAAUUHH
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In Summary
• The best visual image and best visual perception occurs when aberrations are minimized.
• New single parameter metrics calculated from wavefront error can be used to predict visual performance measures like acuity.
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The animation, simulations, and graphics of WFE in this presentation were generated using a program call
CTView.
www.sarverassociates.com
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The eye graphics in this presentation were generated using a program call
EyeView.
www.sarverassociates.com
RAARAAUUHH
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www.slackbooks.com
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Thank you
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