Optical Aberrations and Aberrometry F. Karimian, MD 2002

1. Optical AberrationsandAberrometryF. Karimian, MD 2002

2. 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

4. 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. 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. 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 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

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 ReflectionRetinal lmagingIngoing 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