Download Document

Optical Aberrations
and
Aberrometry
F. Karimian, MD 2002
Aberrations
Perfect Eye  would image every infinitesimal
point in a scene to a corresponding infinitesimal
small point on retina

No blurring for each point
Wavefronts are perfectly spherical  emanate
outward, diverge from point
Perfect

Eye: converts diverging spherical waves
into converging waves
converging waves must be
perfectly spherical
converge to a
point on retina
Perfect imaging Never occurs 
at periphery
- diffraction
- interaction with pupil
margin
Aberration = Deviation of changing
wave fronts from perfect sphere
Monochromatic Aberrations
-Aberrations
for a specific wavelength of
visible light
Classifications:
- Spherical refractive error (defocus)
- Cylindrical refractive error (astigmatism)
- Spherical aberration
- Coma
- Higher-order aberrations
Chromatic Aberrations
 Depends
upon the color or light
wavelength
 Causes:- light dispersion in the cornea,
aqueous, crystalline lens and vitreous
-Variation index of refraction
 Refractive surgery techniques CANNOT
correct chromatic aberrations
 Spectral sensitivity of the eye helps to
reduce the effects of chromatic aberration
Yesterday! optical imperfection
and aberrations Only theory

No clinical practice
Today!  laser refractive surgery
 potential for correction

Needs knowledge
Measurement of Optical
Quality
-By three common methods
Method I : - Description of detailed shape of the image
for a simple geometrical object e.g. a point or line of
light
- PSF (point spread function): distribution of light in the
image plane for a point
- LSF (line spread function): distribution for a line
object
- Blurring effects: blur circle diameter (width of image)
- Strehl ratio (height)
Method II

Description of the loss of contrast in image
of a sinusoidal grating object
 Sinusoidal grating objects  aberrations of
the imaging system remains the same over
the full extent of the object i.e.
“preservation form”
 Ratio of image contrast to object contrast 
blurring effect of optical imperfections

 Variation of this ratio with spatial frequency
 Modulation transfer function (MTF)
Methods II… cont..
-Difference between spatial phase of image and phase
of the object + variation with spatial frequency and
orientation of the grating

Phase transfer function (PTF)
-MTF + PTF  Optical transfer function (OTF)
Fourier Transform:
-Mathematical linkage of PSF, LSF, MTF, PTF, OTF
-Computing the retinal image (naturally inaccessible)
for any visual object
Method III






Specifying optical quality in terms of optical
aberrations
Description: Ray aberrations (deviation of light
rays from perfect reference ray)
Wave front aberrations (deviation of optical wave
fronts from ideal wave front)
Aberrometry: description of optical imperfections
of the eye
All secondary measures of optical quality
(PSF,LSF,MTF,PTF, and OTF) may be derived
Useful approach for customized corneal ablation
Definition and Interpretation
of Aberration Maps
Optical Path Length (OPL):
number of times a light wave must oscillate in
traveling from one point to another
- product of physical path length with refractive index
Optical Path Difference (OPD):
- comparing the OPL for a ray passing in the plane of
exit pupil with the chief ray passing through pupil
center
- optical aberrations are differences in optical path
difference
Causes of Aberrations
 Thickness
anomalies of the tear film,
cornea, lens, anterior chamber, post
chamber
 Anomalies of refractive index in ocular
media due to aging, inflammation, etc.
 Decentering or tilting the various optical
components of the eye
retinal image  same optical
distance for all object point
 Wavefront aberration map  shows
extent of violated ideal condition
 Optimum
Reversing the direction of light
propagation
Map of OPD across the pupil plane 
shape of aberrated wave front
History of Measuring Aberration
Maps
Scheiner (1619)  Scheiner’s disk with 2 pinholes
single distant point of light  optically imperfect eye 
2 retinal image
Porterfield (1747)  used Scheiner disk to measure
refractive error
Smirnov  used Scheiner method  central fixed and
moveable light source for outer pinhole

Adjusting outer source horizontal or vertical

Redirect outer light  patient reports seeing single point
Hartmann method  numerous holes in opaque
screen  each hole aperture for a narrow ray bundle

Tracing errors in direction of propagation

Error in wavefront slope
Shack & Platt  an array of tiny lenses focusing into
an array of small spots

Measuring displacement for each spot from lenslet
axis

Shape of aberrated wavefront
(Shack-Hartmann)
Liang (1994): Used Shack-Hartmann
Wavefront sensor for Human Eye
2 relay lenses focusing lenslet array
onto the entrance pupil
Subdividing the reflected wavefront
immediately as it emerges from the eye
Spot images formed  capture by a
video sensor  computer analysis
Taxonomy of Optical
Aberrations
• Transverse ray aberration (slope):
Angle (t) between aberrated ray and the
non- aberrated reference ray
• Longitudinal ray aberration:
focusing error = 1/z (diopters) =
transverse aberration/ ray height at pupil
plane
If aberration is defocus  Longitudinal
aberration is constant = spherical refractive
error
- Coma or spherical aberration  longitudinal
aberration varies with pupil location
- Rate of slope of wavefront (i.e: local
curvature)
in horizontal and vertical directions

Laplacian map of the aberration ( in diopters)
-
PSF and Strehl’s Ratio
PSF = Squared magnitude of Fourier transform
- Strehl’s Ratio = actual intensity in the center of spot
maximum intensity of a diffraction – limited spot
Pupil diameter intensity of a diffraction – limited –
spot
PSF have multiple peaks  2 or more point images
for single point

Di- or polyplopia
Pupil diameter  excludes most of aberrations
Much improved image quality 
clearer more focused retinal image
-
Zernike Polynomials
-Wavefront
shape representation in
polar coordinates (r/q)
r = radial distance from pupil center
q = angle of the semi meridian for a
given point on the wavefront
Ordering of Aberrations
-Wavefront
(difference in shape between
the aberrated wave front from ideal
wave front ) for myopia, hyperopia and
astigmatism  second order
- Coma is third order aberration =
wavefront error is well fit with third
order polynomial
- Spherical aberration is fourth order
aberration.
Corneal Topography Vs.
Wavefront
Topography:
- Utilizes information from the corneal
surface
- Two – dimensional mapping profile of
keratometry
Wavefront measurement device:
- Two dimensional profile of refractive error
- Used to attempt to smooth corneal points
on the retinal fovea
Principles of Wavefront
Measurement Devices
-Three
Different principles by which,
wavefront aberration is collected and
measured:
1- Outgoing Reflection Aberrometry
(Shack – Hartmann)
2- Retinal lmaging aberrometry
(Tscherning and Ray Tracing)
3- Ingoing Adjustable Refractometry
(Spatially Resolved Refractometer)
Outgoing Reflection Aberrometry
(Shack – Hartmann)
-In
1994:Liang and Bill used Shack- Hartmann
principle
-In 1996: Adaptive optics as defined by ShackHartmann sensor use to view cone photoreceptors
- Shack- Hartmann wavefront sensor utilizes >100
spots, created by (> 100) lenslets
- The aberrated light exiting the eye  CCD
detection
-Distance of displaced (dx) focused spot from ideal
 shows aberration.
Outgoing Reflection aberrometry …
(cont.)
Limitation:
-Multiple scattering from choroidal
structures, interference echo
- insignificant in comparison to axial
length
Retinal Imaging Aberrometry
(Tscherning and Ray Tracing)
In 1997:Howland & Howland used Tscherning
aberroscope design together with a
cross cylinder
Seilor: used a spherical lens to project a 1mm
grid pattern onto the retina

Para- axial aperture system  visualization
and photography of aberrated pattern
Tscherning and Ray Tracing
(cont.)
Limitation:
-This wave front sensing used an idealized eye
model (Gullstrand)
-The eye model is modified according to patient’s
refractive error
Tracey Retinal ray tracing: slightly different
- Uses a sequential projection of spots onto the
retina
- Captured and traced to find wavefront pattern
- 64 sequential retinal spots can be traced in 12
ms
Ingoing Adjustable Refractometry
(Spatially Resolved Refractometer)
In 1961: - Smirnov used scheiner principle 
subjective adjustable refractometry
- Peripheral beams of incoming light are subjectively
redirected to a central target to cancel ocular
aberrations
- In 1998: Webb and Bums used spatially Resolved
refractometer (SRR)
- 37 testing spots are manually directed to overlap the
central target
- Limitation: - Lengthy time for subjective alignment
-
Ingoing adjustable
Refractometry …(cont.)
Objective variant:
- Slit retinoscopy  rapid scanning
along specific axis and orientation
- Capture of fundus reflection 
wavefront aberration
Commercial Wavefront
Devices
Outgoing Reflection
Abberrometry
Shack-Hartmann principles
Alcon summit/ Autonomous
Retinal lmaging
Abberrometry
Tscherring principle
wave light wavefront
analyzer
Custom cornea meas.device Schwind wavefront
analyzer
VisX 20/10 perfect vision
Tracey retinal ray
wavescan
tracing
Bausch & Lomb zyoptics
Aesculap Medical WOSCA
Ingoing adjustable
Refractometry
Scheiner principles
Emory vision SRR
Nidek OPD scan
(slit skioloscopy)
Careful comparison of various
wavefront measuring principles
and their specific devices has
not yet been performed
clinically