1. Optical Aberrations and Aberrometry F. Karimian, MD 2002

2. 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 converge to a perfectly spherical point on retina

4. Aberration = Deviation of changing wave fronts from perfect sphere
Perfect imaging Never occurs 
at periphery
- diffraction interaction with pupil
margin
Aberration = Deviation of changing wave fronts from perfect sphere

5. 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

7. 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

8.  Yesterday! optical imperfection and aberrations Only theory
No clinical practice
Today!  laser refractive surgery  potential for correction
Needs knowledge

9. 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)

10. 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)

11. 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

12. 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

13. 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

14. 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

15. Optimum retinal image  same optical distance for all object point
Wavefront aberration map  shows extent of violated ideal condition
Reversing the direction of light propagation
Map of OPD across the pupil plane  shape of aberrated wave front

16. 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

19. Tracing errors in direction of propagation Error in wavefront slope
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)

20. 2 relay lenses focusing lenslet array onto the entrance pupil
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

24. 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

26. 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)

28. 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

30. 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

33. 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.

34. Corneal Topography Vs. Wavefront
- 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

35. 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)

36. Outgoing Reflection Aberrometry (Shack – Hartmann)
In 1994:Liang and Bill used Shack- Hartmann
principle
In 1996: Adaptive optics as defined by Shack-
Hartmann 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.

39. Outgoing Reflection aberrometry … (cont.)
Limitation:
Multiple scattering from choroidal
structures, interference echo
insignificant in comparison to axial
length

40. 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

41. 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

43. 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

44. Ingoing adjustable Refractometry …(cont.)
Objective variant:
Slit retinoscopy  rapid scanning
along specific axis and orientation
Capture of fundus reflection 
wavefront aberration

45. Commercial Wavefront Devices
Outgoing Reflection Retinal lmaging Ingoing adjustable
Abberrometry Abberrometry Refractometry
Shack-Hartmann principles Tscherring principle Scheiner principles
Alcon summit/ Autonomous wave light wavefront Emory vision SRR
analyzer Nidek OPD scan
Custom cornea meas.device Schwind wavefront (slit skioloscopy)
analyzer
VisX 20/10 perfect vision Tracey retinal ray
wavescan tracing
Bausch & Lomb zyoptics
Aesculap Medical WOSCA

46. Careful comparison of various wavefront measuring principles and their specific devices has not yet been performed clinically