Optical Aberrations and Aberrometry F. Karimian, MD 2002

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Optical AberrationsandAberrometryF.
Karimian, MD 2002
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AberrationsPerfect Eye ? would image every
infinitesimal point in a scene to a corresponding
infinitesimal small point on retina?No blurring
for each pointWavefronts are perfectly spherical
? emanate outward, diverge from point?Perfect
Eye converts diverging spherical waves into
converging wavesconverging waves must be
converge to a perfectly spherical
point on retina
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• Perfect imaging Never occurs ?
• at periphery
• - diffraction - interaction with pupil
• margin
  
• Aberration Deviation of changing wave fronts
  from perfect sphere

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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

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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

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• Yesterday! ?optical imperfection and aberrations
  ?Only theory
• ?
• No clinical practice
• Today! ? laser refractive surgery ? potential for
  correction
• ?
• Needs knowledge

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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)

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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)

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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

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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

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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

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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

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• 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

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History of Measuring Aberration Maps

• Scheiner (1619) ? Scheiners 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

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• 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)

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• 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

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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

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• 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)
  

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PSF and Strehls Ratio

• PSF Squared magnitude of Fourier transform
• Strehls 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

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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

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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.

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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

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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)

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Outgoing Reflection Aberrometry (Shack Hartmann)

• In 1994Liang 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 gt100
• spots, created by (gt 100) lenslets
• The aberrated light exiting the eye ? CCD
• detection
• Distance of displaced (dx) focused spot from
  ideal ? shows aberration.

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Outgoing Reflection aberrometry (cont.)

• Limitation
• Multiple scattering from choroidal
• structures, interference echo
• insignificant in comparison to axial
• length

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Retinal Imaging Aberrometry (Tscherning and Ray
Tracing)

• In 1997Howland 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

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Tscherning and Ray Tracing (cont.)

• Limitation
• -This wave front sensing used an idealized eye
• model (Gullstrand)
• -The eye model is modified according to patients
• 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

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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

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Ingoing adjustable Refractometry (cont.)

• Objective variant
• Slit retinoscopy ? rapid scanning
• along specific axis and orientation
• Capture of fundus reflection ?
• wavefront aberration

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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

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