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Clinical
Wavefront Technology
Dr.Yeswant Rajagopal, Medical Consultant, Aravind Eye Hospital, Madurai
Wavefront analysis
The wave theory of light has one of its major
applications in wavefront analysis. An optically
perfect imaging system brings all rays from a single
object point to a point focus. Fermat’s principle
states that it is possible only when the amount of
time required for light to travel from the object
point to the image point is identical for all possible
paths the light might take. If the rays do not reach
the image point simultaneously, the image is
astigmatic. The shape of the ideal optical system
precisely balances each path so that no matter what
path the light travels, it reaches the image at the
same time. Otherwise the focus is astigmatic.2 The
wavefront of the light that is transmitted through
an optical system is an imaginary surface that
remains normal to the direction of propagation
at all cross-sectional points within the optical
pathway. Any deviations from a perfect plane
wave are the result of optical errors in the optic
system (the eye) and are called the wavefront error
of the system.
Aberrations
The term aberration derives from the latin
word ab-erratio, which means going off track
or deviating. A ray of light which is misdirected
from its desired image point is an aberrated
ray of light. There are two concepts possible to
describe aberrations, namely ray and wave optics.
If we compare the real output wavefront to the
ideal one, we call the difference as wavefront
aberration. The more the wavefront aberration
differs from zero, the more the real image differs
from the ideal image. Wavefront aberrations as a
physical quantity should be identified by means of
decomposition in a conventional system called a
basis. The commonly used bases are orthogonality
(locality) basis, Taylor basis and Zernike basis.
Aberrations can be described quantitatively by
Zernike polynomials (mathematical formulae
used to describe surfaces). These mathematical
models are adequate for describing the wavefront
measurements of the eye, because they are defined
based on a circular form. The shape of the
wavefront is described in the x and y coordinates
while the third dimension, height is described in
the z axis. The final figure is obtained from the
sum of the Zernike polynomials describing all
types of deformation.1 Aberrations can be divided
into chromatic and monochromatic.
1. Chromatic aberrations : caused by the difference
in distribution of incident polychromatic
radiation throughout a medium and depends
on the wavelength of light penetrating the eye.
It is influenced by the composition of ocular
structures and not their shape. This type of
aberration cannot be corrected.
2. Monochromatic aberrations : related to a
specific wavefront and include spherical,
cylindrical refractive errors and high – order
aberration (HOA). HOA cannot be corrected
by sphere and cylinder.
Based on Zernike’s polynomials, aberrations
are described numerically and ranked accordingly.
Low – Order Aberrations
Non-visually significant lower order
aberrations
• Order-Zero (no order): (Piston) these
aberrations are characterized by axial symmetry
and flat wavefront.
• First-order : These linear aberrations describe
the tilt or prismatic error of the eye.
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• Third - order aberrations: correspond to
horizontal and vertical coma and triangular
astigmatism with the base along the x-or y-axis
(trefoil).
• Fourth - order aberration include spherical
aberration, tetrafoil and secondary astigmatism.
• Fifth - tenth order aberration are important
only when the pupil is greatly dilated.1
Most significant higher order aberration.
Likely to decrease contrast sensitivity.
Before the advent of wavefront sensing,
second order aberrations (defocus and regular
astigmatism) could easily be measured with
refractometry and corrected with spectacles and
contact lenses, but higher-order aberrations, such
as coma, trefoil, and spherical aberration, were
designated as irregular astigmatism. Patients with
cornea-derived higher-order aberrations were
best corrected with suboptimal visual results
with spectacles, contact lenses, intraocular lenses
(IOLs), and conventional refractive surgery.
With the introduction of wavefront sensing,
characterization, accurate measurement, and
customized correction of higher-order aberrations
became possible. Custom ablation is an ablation
profile designed to meet optical correction
requirements for a specific individual eye.2
Clinically relevant aberrations
• Astigmatism demonstrates that different
meridian focus at different planes and generate
a toric wavefront.
• Secondary astigmatism : When the luminous
light source is not co-axial with the optic axis,
the luminous rays generated from it follow a
different pathway to the axis of the system.
• Defocus (spherical refractive error) : Observed
in presence of myopic and hyperopic ametropia
where the light rays focus at a different point
than emmetropia.
• Coma : Rays at one edge of the pupil cross the
finish line first, where as rays at the opposite
edge of the pupil cross the finish line last.
The effect is that the image of each object
point resembles a comet, having vertical and
horizontal components. Common in patients
with decentered laser ablation.
• Spherical aberrations : When peripheral light
rays focus in front of more central rays the
effect is called spherical aberration. Commonly
increased after myopic LASIK. Results in halos
around point images.
Aberrometry and wavefront analysis
The principle of operation of wavefront sensors
used in ocular aberrometers is to measure the
deviation of individual rays of light passing
through various locations in the pupil of the eye.
This is done by measuring reflected light from the
retinal spot created by the central reference beam.
This spot serves as a point source that radiates
light back out of the eye where the direction of
propagating' rays can be easily measured at various
pupil locations with a single parallel measurement
of all the pupil locations simultaneously with a
brief flash of light.
Modal and zonal methods are commonly
used for integrating wavefront measurements to
reconstruct the wavefront. The zonal method
uses numerical integration. The modal method
fits the wavefront data with analytical functions
that are integrated to reconstruct the wavefront.
The Zernike polynomials are one popular set of
analytical functions used for this purpose.3
Wavefront refraction can be conceptualized
as spatial refraction (knowing the refraction of
the eye at every given point on the cornea). It is
analogous to measuring topography of the whole
Visually significant lower order aberrations
Second order: Spherical defocus and astigmatism
describe the spherical error and astigmatic
component and its orientation or axis. Myopia,
hyperopia and regular astigmatism can be
expressed as wavefront aberrations. Myopia as
positive defocus and hyperopia as negative defocus.
Regular astigmatism produces wavefront that has
orthogonal and oblique components.
High – order aberrations
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eye as an optical system, in contradistinction to
corneal topography that measures aberrations of
the corneal surface. There are several methods of
measuring the aberrations of the eye:
1. Shack-Hartman Aberrometer (outgoing
optics) - a thin laser beam enters the eye and
is focused on the retina. As the emerging rays
reflect off the macula and refracts out of the eye
through each part of the optical media, they are
captured by a grid and focused onto an array of
lenslets which quantifies their deviation, and
creates the wavefront pattern from the recorded
deviations.
2. Tscherning Device (ingoing optics) - A grid
of laser beams is projected into the eye. The
deviation of this grid from an ideal pattern
is used to quantify and compute a wavefront
map.
AECS Illumination
3. Adaptive optics (ingoing optics) - involves
recording the ingoing rays of light which are
manually steered by the patient to define the
wavefront needed to cancel ocular aberrations.
4. Slit Skiascopy also called Double Pass
Aberrometry (ingoing and outgoing optics)a slit of light is scanned into the eye along a
given meridian. The timing and scan rate of
the reflected light can be determined by photo
detectors to determine the wave aberrations
along that meridian. Multiple meridians are
scanned to analyze the full area of the entrance
pupil.
Following analysis all of the systems produce
a graphical image, the aberrometric maps.
Wavefront analysis data is transformed using
accurate algorithms into a customized pattern that
accounts for the biomechanical effects of excimer
laser ablation on the cornea.1
References
1. Kerry D.Soloman, Luis E. Fernandez de Castro, Helga P. Sandoval, David T. Vroman. Comparison of
wavefront sensing devices. Ophthalmol Clin N Am.2004; 17:119 -127.
2. Refractive surgery. BCSC American Academy of Ophthalmology. Section 13:2006-06; 13-17.
3. Larry N. Thibos. The optics of wavefront sensing. Ophthalmol Clin N Am.2004; 17: 111 – 117.