Spherical abberation Chromatic abberation

1. WAVEFRONT ABLATION
The eye is a complex, imperfect optical system.As lightrays from distantobjects pass through the
optical components of the eye, they refract at the tear film,as well as at corneal and crystallinelens
interfaces.Any deviation from a perfectly focused optical systemis referred to as ‘aberration.’
‘lower-order aberrations -
myopia, hyperopia,and regular astigmatism,known as ‘lower-order aberrations (LOA),’ which can be
corrected with spherocylindrical spectacles.Other lower-order aberrations arenon- visually significant
aberrations known as firstorder aberrations,such as prisms and zero-order aberrations (piston).Low
order aberrations accountfor approximately 90%of the overall wave aberration in the eye
higher order aberrations (HOA)- There are numerous higher-order aberrations, of
which only spherical aberration, coma, irregular astigmatism and trefoil are of clinical
interest .HOA may decrease the quality of vision and cause symptoms in up to 15% of
the general population.
THE WAVEFRONT APPROACH TO ABERRATIONS
Aberration theory falls within thedisciplineof geometrical optics, so diffraction and other wave
phenomena are completely ignored . In aberration theory, lightpropagation obeys the basic laws of
reflection, refraction, and rectilinear propagation. All three laws areencompassed by Fermat’s
principle, which states that between any two points light travels the fastest path. Ideally, a pencil of
rays filling the entrance pupil of an optical system emergesfrom the exit pupil as a pencil
converging to a perfect image point- stigmatic focus.
Accordingto Fermat’s principle,to achievea stigmatic focus,all lightradiatingfromthe object point
at a particular instantmustarrivesimultaneously atthe image point, or equivalently,must cross the
reference sphere simultaneously.In mostcases, however, image rays do not emerge from the exit
pupil as a pencil convergingto a singlepointbut rather converge to a small irregularly shaped
region-the focus is not stigmatic.Itis always possibleto drawa surfacethrough the center of the exit
pupil that all rayscrosssimultaneously,and when the focus is not stigmatic that surface,called the
actual wavefront, is not spherical.Thedifference between the reference sphere and actual wavefront
is the wave aberration . The wavefront and reference sphere are both surfaces and the difference

2. between these two surfaces,the wave aberration,is likewisea surface.
The word wavefront is misnomer- aberration theory is based on geometrical optics that, by
definition, ignore the wave properties of light.It is a common misconception that there is only one
wave aberration for each optical system. In fact, there is a different wave aberration for everyobject
point. Each object point produces its own pencil and each object pencil has its own unique wavefront
aberration.Individual aberrationsareeither field dependent or field independent.
1.The aberration is field independent if the amount of the aberration is the same for both an axial
object point and an off-axis pointin the same transverseplaneand field dependent otherwise. The
majority of aberrations arefield dependent, but several importantaberrations arefield independent.

3. 2. Aberrations may also bepupil dependent or pupil independent. If the aberration is pupil
independent itdoes not change as pupil sizechanges.Most aberrations arepupil dependent and do
change with pupil size.However, myopia, hyperopia,and regular astigmatismarepupil independent
which is why it is unnecessary to check pupil sizeto prescribeglasses.
3.Stigmatic focus means image rays converge to a perfect point either at the ideal imagepointor
elsewhere. When the focus is nonstigmatic,rays do not converge to a perfect pointeven at the best
possiblefocus.Aberrations can existeven when the focus is stigmatic.In such cas es rays still converge
to a perfect point, but the pointis in the wrong place(i.e., not at the paraxial imagepoint).

4. DEFOCUS
In aberration theory, defocus encompasses both myopia and hyperopia. If the only defect of an
optical systemis myopia,then the image rays still focus stigmatically butto a point closer to the exit
pupil than the ideal imagepoint . Since the focus remains stigmatic,all rayssimultaneously cross a
sphere centered on the actual imagepoint but no longer cross the reference sphere simultaneously.
The actual wavefront has a smaller radius than the reference sphere. In hyperopia the actual
wavefront has a larger radius than the reference sphere.The difference between the reference
sphere and the actual wavefront, i.e., the wave aberration, has a paraboloidal or bowl shape.In
myopia the bowl is upright(i.e., holds water) and in hyperopia the bowl is upsidedown (i.e., spills
water). Whilemyopia is corrected by minus lenses,the correspondingwave aberration is called
positive defocus because of well-established algebraic sign conventions used by lens designers.
Conversely, hyperopia is negative defocus. Defocus is both pupil and field independent.
REGULAR ASTIGMATISM
the wave aberration associated with regular astigmatism(RA) has a cylindrical shape. Like defocus,
RA is both pupil and field independent, but unlikedefocus,RA is nonstigmatic. RA should not be
confused with astigmatismof obliqueincidence,which is an entirely different aberration although it
does have some similar features.
SPHERICAL ABERRATION
In spherical aberration raysnear the center of the lens focus atthe ideal image pointbut more
peripheral rays focus in a different location .In positiveSA, peripheral rays focus in front of the ideal
image point and the more peripheral the ray the more anterior the focus.In negative SA, peripheral

5. rays focus behind the ideal imagepoint and, again,the more peripheral the rays the more posterior
their focus.The wave aberration representing SA also has a bowl shape.In SA the center of
the bowl is flatter and the edges steeper than the paraboloid representingdefocus.SA is one of the
most important aberrations thatis not partof the classic clinical triad of hyperopia,myopia,and
regular astigmatism. SA is a pupil dependent, nonstigmatic, field independent aberration.
PositiveSA shifts the best focus towards myopia,whereas negative SA shifts the focus towards
hyperopia.However, even at the best position the focus is nonstigmatic.
Most lenses have spherical surfaces becausethey are the easiestto manufacture accurately.
However, a sphere is too steep peripherally so peripheral rays do notfocus in the same location as
central rays.The problem can be eliminated by usinglenses with aspheric surfaces thatflatten
peripherally.
The anterior cornea (with the overlying tear film) is the eye’s strongest refracting surface and,
therefore, potentially contributes the most spherical aberration. However, the cornea flattens
peripherally to a degree that largely eliminates corneal spherical aberration.
The Stiles– Crawford effect also mitigates the influenceof SA on vision becausephotoreceptors are
less sensitiveto peripheral rays.
SA is pupil dependent and changes the position of best focus.There is an uncommon condition called
night myopia seen in patients who do have an unusually high amountof positiveSA. When their pupil
dilates the increasein SA makes them more myopic, blurringtheir vision.
Corneal SA varies fromperson to person so an implantthat corrects a fixed amount of SA is unlikely to
benefit all patients.To properly compensate corneal SA with an implantthe patient’s corneal SA
should be measured preoperatively and an implantselected not only by its power but also by the
amount of SA corrected, which is notcurrent clinical practice.Raytracingdata on model eyes show
that the amount of SA corrected by an implantvaries substantially if theanterior chamber depth
changes by tenths of millimeters,or if the implantis tilted or decentered.
DISTORTION ,
Distortion occurs when the transversemagnification isnotconstantbut changes as distancefromthe
axis increases within a transverseplane.

6. In pincushion distortion,magnification increasesas distancefromthe axis i ncreases (in thesame
transverseplane),whereas in barrel distortion,magnification decreases as distancefromthe axis
increases .Distortion is field dependent, pupil independent, and stigmatic. Pincushion distortion
occurs in practically all spectacle corrected aphakes and is occasionally seen in high myopes after
clear lens extraction. Originally,oneof the principal reasonsfor the use of intraocularlens implants
was the visual improvement achieved by eliminatingdistortion. distortion has practica lly
disappeared sincethe introduction of intraocular lenses.
COMA
When coma is present image rays ‘flareout’ from the image pointin a fashion reminiscentof a
comet’s tail . Coma is nonstigmatic,field dependent, and pupil independent. Coma is increased
when multipleoptical elements do not sharethe same optical axis.After defocus and regular
astigmatism,coma accounts for most of the residual aberration in otherwisenormal eyes, sincenone
of the ocular media sharea common axis.Clinically,coma is rarely detected. However, coma can
produce symptoms if there is a large amount present, which can occur (along with other
higher-order aberrations) in off-axis keratorefractive surgery or when the corneal vertex of a
full-thickness graft is displaced by an unusual amount.
ASTIGMATISM OF OBLIQUE INCIDENCE

7. It is easy to confuse this aberration with regular astigmatism(RA), but the two are quite different.
Both RA and AOI are nonstigmatic,pupilindependentaberrations.However, RA is field independent
and second order, whereas AOI is field dependent and fourth order. Cli nically AOI is much less
important than RA. AOI is mentioned here mainly to clarify the distinction between RA and AOI.
PISTON ERROR Piston error is clinically irrelevant.
HIGHER-ORDER ABERRATIONS There are infinitely many aberrations although as a practical matter
there is rarely any need to consider more than 20,if that many (many authors discuss36 Zernike
polynomials butseveral Zernikepolynomials existin pairsthatarebasically thesame aberration).The
basic aberrationsdiscussed here are the most important and have specific names.Many ‘higher-order
aberrations’do not have specific names and aredenoted only by the mathematical formulas that
describetheir shape.
MATHEMATICAL CONSIDERATIONS : Each individual aberration is represented by a surfacewith a
unique characteristic shape.The surfaceis multiplied by a constantthat represents the amount of
that particular aberration presentin an eye or optical system.Multiplication by a constantdoes not
change the basic shapeof the surface,just its height (or depth). Zernike polynomials arean
alternativeway of classifyingaberrations.Theprincipal advantageof Zernike polynomials isthe
mathematical property of orthogonality on a continuous unit circle.However, mathematical
orthogonality has no clinical significance.Moreover orthogonality does not apply to clinical data,
which are always discrete,not continuous.Although attempts have been made to standardizethe
notation for Zernike polynomials,there is no universally accepted method of s pecification.
Most Zernike polynomials arenotpure aberrations butactually a mixtureof several aberrations.For
instance,the eighth Zernike polynomial thatmany believe represents SA is actually a combination of
SA, defocus, and piston error.There are different ways to define the order of a Zernike polynomial.It
is importantto note that the wave aberration coefficients areexpressed in units of length, typically
micrometers, whereas clinically refractiveerrors areexpressed in terms of inverse length (diopters).
Technically,there is no way to convert between the different units.However, for an eye with average
dimensions,−1.00 D of myopia corresponds to about 2 µm of defocus, which is fairly largecompared
to most higher-order aberrations.
CHROMATIC ABERRATION
All of the aberrations discussed so far aremonochromatic – measured at a singlewavelength.
Chromatic aberration is oneof the most prominent aberrations in theeye. A complete description of
the eye’s aberrations would requirethe measurement of the monochromatic aberrations atseveral
wavelengths.
CLINICAL MEASUREMENT OF ABERRATIONS
1. In 1896 Tscherningwas the firstto observe higher order aberrations in his own eyes.28 Consider
an eye that is emmetropic in the sense that there is no hyperopia,myopia, or regular astigmatism,but
still has other aberrations.Asmall,distantsourceis viewed through a +5.00 D lens with a grid of small
apertures placed behind it. The grid divides the lightinto parallel pencilsthatfocus in front of the
retina, then diverge forming a grid pattern on the retina. The grid will notbe regularly spaced if
aberrations arepresent. By drawingthe appearanceof the grid,ocular aberrationscan beestimated. .
As a clinical method for measuringaberrations the Tscherning aberrometer suffers from the obvious
limitation thatitis subjective,relyingon the patient’s ability to observe and accurately locatethe
displaced pencils.Nonetheless,itis a useful conceptual tool.

8. 2. The subjectivelimitations of Tcherning’s approach can beovercome by photographing the grid on
the retina. However, photography introduces another problem – doublepass.To be photographed,
each grid spoton the retina acts as a lightsource,which passes through the eye sufferingits
aberrations a second time. The second pass complicates the analysis of aberrations, although the
Allegretto™ Wave Analyzer is based on this approach.
3. There are several ways to overcome the double pass problem.One approach is to focus a laser (at
low power of course) on the retina. Sincethe laser traverses only a small amountof the pupil,itis
essentially unaffected by ocular aberrations;practically speaking,this isa singlepass technique.The
small area of laser-illuminated retina becomes a sourcefrom which lightemerges from the eye. If the
eye is aberration-free,the emerging lightwill haveplanar wavefronts.Aberrations distortthe
wavefront shape.Using an approach suggested by Roland Shack,the wavefront is measured usinga
lensletarray that focuses small areasof the wavefront on a charge-coupled device. Each lenslet
produces a small doton the detector that is displaced depending on the wavefront’s shape. Shack’s
approach is probably themost reliableway of measuringsmall amounts of higher-order aberration in
an otherwise wellcorrected eye or optical system. The technique is not as well -suited to the
measurement of largeamounts of low-order aberrations.The majority of aberrometers utilizesome
variation of the Hartmann– Shack approach.
4. Automated retinoscopy is another means of measuringaberrations and is incorporated into the
ARK 10000™(Nidek™). The Tracey™ uses the Tscherningapproach but performs itsequentially by
scanninga singlelaser beamover the pupil and observingthe beam’s deviation on the pupil.
It is very difficultto verify the accuracy of an aberrometer. Ocular aberrations,especially higher
order aberrations,changewith the slightestchangein tear filmthickness,or changes in choroidal
thickness that occur duringthe cardiac cycle,accommodation,hippus,ocular movement, head
movement, or fixation change.
Regardless of the method used, all clinical measurements produce a set of discrete data points.The
wavefront’s shape between data points is not known but can be interpolated (i.e., estimated) with
excellent accuracy by a least-squares curve-fittingprocedure.If the measured data points are
accurate,only a few hundred are needed to calculatethe coefficients of a Zernike or alternate wave
aberration expansion.The data-fittingprocedure is a critical step becauseitconverts a samplingof
data points to a continuous surfacedescribed by a set of coefficients.
Notes for wavefront refractive surgery

9. advanced treatments involvethe use of a wavefront-guided laser refractivetechnique to create a
completely customized reshapingof the surfaceof the cornea that leads to a more optically desired
outcome.
A customized corneal shapingrequires wavefrontanalysisof the eye (aberrometry).
For reproducibility the waveform can be decomposed into components, usingeither Zernike
polynomials or Fourier analysis.
The wavefront map is digitally interfaced with an excimer laser,to control the delivery of laser beam
across thecornea in a customized fashion.
WAVEFRONT OPTICS
The wavefront is the locus of points in an optical pathway having the same phase. If all incoming
rays areparallel,and the eye is free from any aberrations,the resultantemerging wavefront is
perfectly flat. In other words, all lightrays comingfrom a pointsource of lightlocated at infinity focus
at a singlepointon the retina. In reality,though, the focusingproperties of a real eye arenot
completely uniform: some areas bend lightmore strongly than others.
The wavefront aberration is thedeviation of a particular eye’s wavefront from the ideal wavefront in
the pupillary plane.Its magnitude is entirely dependent on the diameter of the pupil;a larger
diameter leads to a larger wavefront error
HIGHER-ORDER ABERRATIONS
HOA aremonochromatic refractivedisorders thatlimitthe vision of healthy eyes to less than the
retinal detection threshold. HOA cannotbe corrected with spherocylindrical lenses or with standard
refractivesurgery. They have been categorized usingZernike polynomialsby radial order and by
angular frequency, with third order and higher constitutingHOA. The higher the order, the less
visually significanttheaberration.
The two most frequently discussed aberrationsarespherical aberration (which causes halos and night
vision disturbances) and coma (which is associated with monocular diplopia).
The wavefront in spherical aberration isspherical in thecenter of the pupil butchanges its curvature
toward the edge of the pupil,givingconcentric rings of focus that resultin point images with halos.
In coma, the wavefront is asymmetric,producinga comet-shaped pattern
Trefoil,quadrifoil,pentafoil,and secondary astigmatismareother HOA
IDEAL CORNEAL SHAPE
The shapeof the cornea is prolate(more curved in the center) to allowfor a lower total HOA. The
Q-factor of the cornea in a normal population mean is −0.25, meaning that the central cornea has a
stronger curvaturethan the periphery. This aspheric shapeallows for focusingof rays comingfrom
the periphery and those comingfrom the center on one point, correctingfor inherent spherical
aberration of spherical lenses.Any change in the average prolate corneal shapetowards a more
oblate profile(less curved in its center) leads to induction of spherical aberrations,and consequently
a decrease in night vision and contrastsensitivity.
MEASUREMENTS OF WAVEFRONT ABERRATIONS

11. Zernike polynomials and Fourier transforms areused to analyzethe ocular wavefront. Zernike
polynomials area sequenceof polynomialsorthogonal on the unit disk,whileFourier transforms
represent mathematical functions of frequency. Most aberrometers used for customized laser surgery
rely on Zernike polynomialsto decompose the wavefront aberrations.They can,in principle,measure
an infinitenumber of aberration orders.Clinically,data up to the Zernike fifth order capturenearly all
the aberration variancetypically found in normal human eyes. The Fourier analysiscan decomposean
image into spatial frequency components . The measured wavefront errors are represented as root
mean squaredeviations (RMS)
.WAVEFRONT-MEASURING DEVICES

13. Several methods for assessingthe wavefront aberrations in human eyes are currently available.Each
method has its own way of measuringthedisplacement of a ray of lightfrom its ideal position.They
can be generally classified as:outgoing or ingoing aberrometers.
Outgoing Devices based on the Hartmann–Shack principlearecurrently the most widely used. These
devices analyzean outgoing lightthat emerges or is returned from the retina and passes through the
optical systemof the eye.A narrowbeam of lightis projected onto the retina,and its image passes
through the lens and the cornea and exits the eye. The Hartmann–Shack sensor has a lensletarray
that consists of a matrix of small lenses.14,15 Thelightthat emerges from the eye is focused on a
charge-coupled device (CCD) camera through each lensletto form a spot-pattern. The spot-pattern of
an ideal subjectwith a perfect wavefront will be exactly the same pattern as the reference grid,and a
distorted wavefront will create an irregular spot-pattern.Displacementof lensletimages from their
reference position is used to calculatethe shapeof the wavefront. The advantages of this system
includethe factthat itmeasures wavefront in one shot; hence it is faster,leadingto a higher
resolution and a higher repeatability
Ingoing
. Tscherning aberrometry analyzes the ingoing light, which forms an image on the retina.A grid
pattern formed by multiplespots is projected through the optical systemof the eye and forms an
image on the retina. This image is observed, evaluated, and captured on a CCD similar to a fundus
camera. The distortion of the grid pattern enables calculation of the aberrations of the optical system
of the eye.
Ray tracing aberrometry measures ingoinglightthat passes through the optical systemof the eye and
forms an image on the retina. It measures rays sequentially makingitmuch slower (the total time of
scanningis 10–40 milliseconds) and decreasingits precision.The iTraceaberrometer (Tracey
Technologies,Houston, TX) is the only one based on the retinal ray tracingtechnology.
The scanning slit refractometer is a double-pass aberrometer (slitskioloscopy) thatis based on
retinoscopic principles.This principleisused in theARK 10000 Optical Path Difference Scanning
System (OPD-Scan) distributed by Nidek.
WAVEFRONT-BASED SURGERY

14. The aim of wavefront custom ablation, in addition to spherocylindrical correction, is
to adjust for the pre-existing aberrations, as well as those that may be induced by
conventional laser vision correction. Spherical aberration is the cause of night
myopia and is commonly increased after myopic LASIK and surface ablation. It
results in halos around point images
challenges to wavefront measurements.
1.Tear filmabnormalities can significantly affectthe quality of wavefront analysis.
2. Eyes with small-diameter pupils may be difficultto measure and provideinformation beyond the 3
mm optical zone and, therefore, require pharmacological dilatation.However, some variationsin the
wavefront maps have been seen with some pharmaceutical agents:ithas been reported that
cyclopentolateeye drops lead to a significantdifferencein the preoperative refractive error
wavefront as compared to the subjectiverefraction
3. An eye with marked aberrations such as scarsor keratoconus may be difficultto measure.
4. The algorithmfor converting measurements into an ablation profileshould also befaithful to the
original maps.Itshould beoptimized to providethe best optical quality over the optical zone and
tapering of the ablation in thesurroundingzone. Another important issuefor successful custom
ablation surgery is eye registration and eye trackingduringcorneal laser ablation.Thewavefront data
must be transferred to the laser machineand applied to the same location on the eye from which
they were captured. A small misalignmentin the axis can havesignificantimpacton the results of the
procedure. It may actually causenew HOA due to misalignmentof the pattern of treatment to the
actual wavefront error on the eye. It is common to have 5–7 degrees of cyclotorsion when changing
from sittingposition to supineposition.It has been reported that 50% of the vi sual benefitcorrection
of HOA is lostwith a 250 µm decentration or a 10 degree eye rotation.
Two main methods of usingwavefront information in refractivesurgery are: wavefront-optimized
ablation and wavefront-customized ablation.
Wavefront-optimized ablation aims atpreservingthe eye’s pre-existingoptical aberrationsusing
adjustments based on population averages,and at optimizingthe asphericity of the cornea. The
ablation profileis based on an ideal model, without evaluatingthe patient’s own a berrometry.
Wavefront-customized ablation leads to havingan individual treatment ablation profilebased on the
patient’s own aberrometry, therefore it would be ableto correctfor pre-existingHOA.
CLINICAL implication OF ABERRATION THEORY
With the emergence of keratorefractive surgery came the possibility of correctingaberrations
uncorrectableby spectacles.Initially someoverly optimistic claims weremade, includingthe
possibility of achieving20/6 acuity.These claims werebased on an incomplete understandingof
aberration theory as well as other optical and non-optical factors thatinfluenceacuity.Alteringthe
shapeof justthe anterior corneal surfacecannotcorrect all ocular aberrations. Even if itwere
possibleto eliminate(or reduce to insignificance) all aberrations,other factors such as diffraction and
intraocularlightscatteringwould limitvision.After the correction of defocus and RA, for pupils

15. smaller than about 2.5 mm acuity is limited by diffraction nothigher-order aberrations.Consequently,
the correction of higher-order aberrations would not lead to further visual improvement in patients
with smaller pupils.Intraocularlightscatteringalso decreases acuity.Whileincompletely understood,
neural mechanisms doubtless play an importantrole. Visual processingcan decreasethe influence
of some aberrations.The largeamount of chromatic aberration present in most eyes is largely
neutralized by visual processingand likewisemodest amounts of SA are also compensated by visual
processing.Cliniciansshould beawarethat irregular astigmatismis notuncommon but rather
ubiquitous.All eyes have a largeamount of uncorrected chromatic aberration.
WAVEFRONT PLATFORMS