Optical AberrationsOptical Aberrationsandand

AberrometryAberrometry

F. Karimian, MD 2002F. Karimian, MD 2002

AberrationsAberrationsPerfect EyePerfect Eye would image every infinitesimal would image every infinitesimal

point in a scene to a corresponding infinitesimal point in a scene to a corresponding infinitesimal small point on retinasmall point on retina

No blurring for each pointNo blurring for each point

Wavefronts are perfectly spherical Wavefronts are perfectly spherical emanate emanate outward, diverge from pointoutward, diverge from point

Perfect EyePerfect Eye:: converts diverging spherical waves converts diverging spherical waves

into converging wavesinto converging waves

converging waves must be converge to a converging waves must be converge to a perfectly spherical point on retinaperfectly spherical point on retina

Perfect imaging Never occurs at periphery

- diffraction - interaction with pupil margin

Aberration = Deviation of changing wave fronts from perfect sphere

Monochromatic AberrationsMonochromatic Aberrations-Aberrations for a specific wavelength ofAberrations for a specific wavelength of visible lightvisible light Classifications:- Spherical refractive error (defocus)- Cylindrical refractive error (astigmatism)- Spherical aberration- Coma- Higher-order aberrations

Chromatic AberrationsChromatic AberrationsDepends upon the color or light

wavelengthCauses:- light dispersion in the cornea,

aqueous, crystalline lens and vitreous -Variation index of refractionRefractive 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 Measurement of Optical QualityQuality

-By three common methods-By three common methodsMethod 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 IIMethod IIDescription of the loss of contrast in image of

a sinusoidal grating objectSinusoidal 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…Methods II… cont.. 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 IIIMethod 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 Definition and Interpretation of Aberration Mapsof 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 indexOptical 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 AberrationsCauses of AberrationsThickness 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

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

History of Measuring Aberration History of Measuring Aberration MapsMaps

Scheiner (1619) Scheiner’s disk with 2 pinholes single distant point of light optically imperfect eye

2 retinal imagePorterfield (1747) used Scheiner disk to measure

refractive errorSmirnov 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 Taxonomy of Optical AberrationsAberrations

• 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 RatioPSF 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 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 AberrationsOrdering 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. Corneal Topography Vs. Wavefront 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 Principles of WavefrontWavefront Measurement DevicesMeasurement 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 Outgoing Reflection Aberrometry (Shack – Hartmann)(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.

Outgoing Reflection aberrometry … Outgoing Reflection aberrometry … (cont.)(cont.)

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

Retinal Imaging Aberrometry Retinal Imaging Aberrometry (Tscherning and Ray Tracing)(Tscherning and Ray Tracing)

In 1997:Howland & Howland used Tscherning aberroscope design together with a cross cylinderSeilor: 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 Tscherning and Ray Tracing (cont.)(cont.)

Limitation: -This wave front sensing used an idealized eye model (Gullstrand)-The eye model is modified according to patient’s refractive errorTracey 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 Ingoing Adjustable Refractometry (Spatially Resolved Refractometer)(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 Ingoing adjustable Refractometry …(cont.) Refractometry …(cont.)

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

Commercial Wavefront Commercial Wavefront DevicesDevices

Outgoing Reflection Retinal lmaging Ingoing adjustableAbberrometry Abberrometry RefractometryShack-Hartmann principles Tscherring principle Scheiner principles

Alcon summit/ Autonomous wave light wavefront Emory vision SRR analyzer Nidek OPD scanCustom cornea meas.device Schwind wavefront (slit skioloscopy) analyzerVisX 20/10 perfect vision Tracey retinal ray wavescan tracingBausch & Lomb zyoptics Aesculap Medical WOSCA

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