Optical Aberrations
Resident Lecture
The Perfect Image
There is no such thing as a perfect image
All light rays passing through optical systems are subject to distortions
Outline
 Chromatic Aberration
 Spherical Aberration
 Oblique Astigmatism
 Coma
 Curvature of Field
 Distortion
 Point Spread
Function
 Modulation Transfer
 Wavefront Analysis
 Custom Lasik and
Zernicke Polynomials
Chromatic Aberration
Lens
Eye
 A lens will not focus
different colors in exactly
the same place.
 the focal length depends
on refraction and the
index of refraction
 Short wavelength has
higher n and is refracted
more than long
wavelength
 The amount of chromatic
aberration depends on
the dispersion of the
glass.
http://micro.magnet.fsu.edu/primer/java/aberrations/spherical/index.html
Chromatic Aberration
 Dispersive power (abbe
value) is based on
change in index for
different wavelengths
 If the index is the same
for all wavelengths, there
is NO DISPERSION
 The n increases as
wavelength decreases
Chromatic Aberration
 Some patients can detect this
 Dispersion usually increases in high index
 May be noticeable with IOL’s
Chromatic Aberration
Duochrome Test
 Duochrome test helps
you determine
position of focal point
with respect to the
fovea
 Useful to avoid
overminusing pt.
Duochrome Test
Too much minus green
is clearer
Too much plus red
is clearer
Chromatic AberrationDuochrome Test
Red clarity= green clarity
then image is positioned
correctly.
534
560
564
Correction of Chromatic Aberration
 An achromat doublet does not
completely eliminate chromatic
aberration, but can eliminate it
for two colors, say red and
blue.
 The idea is to use a lens pair –
a strong lens of low dispersion
coupled with a weaker one of
high dispersion calculated to
match the focal lengths for two
chosen wavelengths.
 Cemented doublets of this type
are a mainstay of lens design.
Achromatic Doublets
Correction of Chromatic Aberration
APOCHROMATIC LENS
The addition of a third lens corrects for three colors
(red, blue and green), greatly reducing the fuzziness
caused by the colors uncorrected in the achromatic
doublet.
Correction of Chromatic Aberration
In the human eye, chromatic aberration is
reduced by the lens, which changes index
from the nucleus outward.
Spherical Aberration
For lenses made with spherical surfaces, rays which are parallel to
the optic axis but at different distances from the optic axis fail to
converge to the same point.
http://www.olympusmicro.com/primer/java/aberrations/spherical
Spherical Aberrationcorrection
Spherical aberration in the human
eye is reduced by the aspheric
shape of the lens and the cornea
Spherical Aberration- Correction
Meniscus Lenses
The amount of spherical aberration in a
lens made from spherical surfaces
depends upon its shape. Best form,
depends on base curve
Oblique Astigmatism
This aberration primarily influences the image quality of
spherical lenses. When the wearer looks at an angle through
the lens, there is a deviation which he perceives as blur. The
higher the dioptric power of the lens, the more pronounced this
error becomes.
Oblique Astigmatism
A dot is no longer imaged as a dot, but as two image lines.
Oblique astigmatism- correction
Mitigated by deviating from the
spherical shape
Aspheric Surfaces to the Rescue
Coma
.
Coma is an aberration which causes rays from
an off-axis point of light in the object plane to
create a trailing "comet-like" blur directed away
from the optic axis.
Coma
 A lens with
considerable coma
may produce a sharp
image in the center of
the field, but become
increasingly blurred
toward the edges.
Coma
The resulting image is called a comatic circle.
The coma flare, which owes its name to its cometlike tail, is
often considered the worst of all aberrations, primarily
because of its asymmetric configuration.
Coma- correction
For a single lens, coma can be partially
corrected by bending the lens. More
complete correction can be achieved by
using a combination of lenses symmetric
about a central stop.
Coma is not well compensated for in the
human eye.
Curvature of Field
Causes an planar object to
project a curved
(nonplanar) image. It can
be thought of as arising
from a "power error" for
rays at a large angle.
Those rays treat the lens
as having an effectively
smaller diameter and an
effectively higher power,
forming the image of the
off axis points closer to the
lens.
Curvature of Field
A lens aberration that causes a flat object
surface to be imaged onto a curved
surface rather than a plane.
=n*f2
http://www.microscopyu.com/tutorials/java/aberrations/curvatureoffield/
Curvature of Field- Correction
The surface of the image formed by the
eye is also curved, fortunately, the retina is
also curved!
For lens systems, using best form lenses
with non-spherical shapes can help.
Image Distortion
 Not about sharpness, but faithful reproduction of
the shape of the object.
 It occurs when magnification varies with the
distance of the object from the optic axis.
 Problem only for high powers
 Tends to falsify the positions of objects and
cause vertical lines to wave
 Aphakes!
 Minimized by very steep back base curves
Image Distortion
Plus lens
Minus lens
Outline
 Chromatic Aberration
 Spherical Aberration
 Oblique Astigmatism
 Coma
 Curvature of Field
 Distortion
 Point Spread
Function
 Modulation Transfer
 Wavefront Analysis
 Custom Lasik and
Zernicke Polynomials
Beyond sphere and cylinder…
Higher order aberrations have been
traditionally ignored clinically
Now are routinely considered
Post lasik increase in higher order aberrations
Can be easily measured
Wavefront guided correction available
Patient expectations
History of wavefront sensing
 DOD in the 1980’s to support “star wars”
 Measure the constantly fluctuating refractive power of the
atmosphere to improve accuracy of satellite photos and
accuracy of weapons
 Led to adaptive optics – real time measurements of refractions
using “deformable mirrors” that rapidly
 Astronomers were interested to improve telescope images
www.opt.pacificu.edu
Shack-Hartmann wavefront sensor
Hartmann first looked at this a century ago
Shack elaborated on this in the 1980’s
working for the air force
Liang was the first to use the wavefront
sensor to measure the human eye in
1994.
By the late 1990’s commercial
development was occuring.
Airy Disc
An Airy disc shows how a point image is degraded by aberration
When wave encounters and obstruction, the direction of the wave changes.
This is called DIFFRACTION
Point Spread Function
Consider an object consisting of a perfect point. The image of
this object will be at least one point wide. Normally it’s image will
consist instead of a spot of several points, brightest in the centre
and progressively darker away from the centre. This image
function is the point-spread function.
Point Spread Function
 used to assess the spatial resolution of an
imaging system.
 The PSF need not be symmetrical, so there may
be different spatial resolutions in different
directions.
 Note that the PSF is, in most cases, a function
with significant variation over the field of view.
Modulation Transfer Function
 Used to assess the overall spatial resolution of an
imaging system. It is formally defined as the magnitude
of the Fourier transformed point spread function
The concept of the MTF is to portray how much of the
contrast at a specific resolution is maintained by the
imaging process.
Modulation Transfer Function
How can the degradation of an optical
system be evaluated?
Max luminance
SQUARE WAVE
Modulation= Lmax-Lmin/Lmax+Lmin
Min luminance
Modulation Transfer Function
Square wave grating of specific frequency
and contrast is passed through an optical
system. The MODULATION can then be
measured
MTF= Mi/Mo
Luminance of image
Luminance of stimulus
Modulation Transfer Function
In the optimal case, the MTF value is
1 meaning that object and image
contrast are identical.
MTF usually starts with a value 1 at 0
spatial frequency which represents a
homogeneous background. It then
drops in a system-specific manner
down to zero. By using the MTF, two
systems can readily be compared: At
each spatial frequency (or
1/resolution) that system with the
higher MTF maintains better contrast.
Wavefront analysis (wavescan)
Light is has both particle and wave
characteristics
Wavefront analysis describes the wave
behavior of light in the eye
Actual image displacement of the point
source from foveola as it passes through
the optical system of the eye compared to
the ideal image.
Custom Lasik-Wavescan
Wavescan uses the principles of MTF
Custom can correct for
Myopia or hyperopia
Astigmatism
Spherical Aberration
Coma
Custom does not correct for
Chromatic aberration
Diffraction
Hartmann-Shack Aberrommetry
How does it work….
Analyze light that emerges or is reflected
from the retina and passes through the
optical system of the eye.
Produces a “fingerprint” of the aberrations
for an individual eye.
Measuring Aberrations
Emmetropia/ no aberrations
Myopia/distorted wavefront
Aberrometers measure the shape of the wavefront
Wavefront analysis
The distance between the wavefront surface and a reference plane
Wavefront exiting
The eye. Distance
From the reference
Plane is measured
At many points.
Hartmann Shack aberrometer
Each lenslet is a fraction of a mm. It divides the broad beam of light
Into many sub-beams for measurement. Each lenslet focuses onto the
Video sensor. We analyze the position of each spot.
Wavefront Analysis
Wavefront Analysis
In an aberration free eye dot is centered and focused with respect
To a grid/array.
Wavefront Analysis
Wavefront Analysis
Sometimes it is easier to visualize the wavefront in a 3D surface plot
Wavefront Analysis
Spherical Aberration
Astigmatism
Trefoil
Quadrafoil
Wavefront Analysis –
Root Mean Square
Measure of the deviation of an actual
image from an ideal image of the source
point object
RMS of ideal system is 0
RMS of human eye increases from 0.1 to
0.25 at 60yo.
Standard LASIK increases RMS especially
for large pupils.
What are Zernicke polynomials?
 Monochromatic aberrations can be decomposed
into Zernicke polynomials
 Each ZP corresponds to a specific geometric
pattern of aberration and are grouped into
orders
 These are mathematical expressions that
describe how much of what type of geometric
pattern is contributing to the total wavefront
aberration.
 Basically it is a system for categorizing higher
order aberrations
Wavefront Errors described
By Zernicke analysis
Custom Lasik- Zernicke Polynomials
 Each mode will have a number that is + or -.
This coefficient tells you how much of that
aberration is present
 The units are not diopters, but microns
 Pupil size is included
 Will give you RMS
 Zernicke modes are grouped into orders
2nd order non wavefront
3rd order and above are “higher order”. They are labelled
using a double index scheme Znm, where n refers to the
order and m to the mode within the order.
 Some of the modes have names
Higher order aberrations and relative risk of symptoms
after LASIK. Sharma M, Wachler BS, Chan CC.
RESULTS: Blurring of vision was the most common symptom
(41.6%) followed by double image (19.4%), halo (16.7%), and
fluctuation in vision (13.9%) in symptomatic patients. A
statistically significant difference was noted in UCVA (P =
.001), BSCVA (P = .001), contrast sensitivity (P < .001), and
manifest cylinder (P = .001) in the two groups. The
percentage difference between the symptomatic and control
group mean root-mean-square (RMS) values ranged from
157% to 206% or 1.57 to 2.06 times greater. CONCLUSIONS:
Patients with visual symptoms after LASIK have significantly
lower visual acuity and contrast sensitivity and higher mean
RMS values for higher order aberrations than patients without
symptoms. Root-mean-square values of greater than two
times the normal after-LASIK J refractive surgery March 2007
Ocular higher-order aberrations and contrast
sensitivity after conventional laser in situ
keratomileusis Yamane N, Miyata K, Samejima T,
IOVS 2004
Summary
Understand that ametropia is not the only
thing that causes blurry vision
Understand that aberrations also plague
lens systems in glasses, microscopes, etc.
Introduction to how refractive surgery (and
IOL’s, spectacls and CLS) is attempting to
compensate for aberrations inherent in the
optics of the eye.
Presbyopic IOLs
Multifocal IOLs
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http://www.eyeclinic.com.br/acrysoft/foto_04.jpg
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