WAVEFRONT ABLATION

The eye is a complex, imperfect optical system. As light rays from distant objects pass through the optical components of the eye, they refract at the tear film, as well as at corneal and crystalline lens interfaces. Any deviation from a perfectly focused optical system is 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 are non- visually significant aberrations known as first order aberrations, such as prisms and zero-order aberrations (piston). Low order aberrations account for 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 the discipline of geometrical optics, so diffraction and other wave phenomena are completely ignored . In aberration theory, light propagation obeys the basic laws of reflection, refraction, and rectilinear propagation. All three laws are encompassed 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 emerges from the exit pupil as a pencil converging to a perfect image point- stigmatic focus. According to Fermat’s principle, to achieve a stigmatic focus, all light radiating from the object point at a particular instant must arrive simultaneously at the image point, or equivalently, must cross the reference sphere simultaneously. In most cases, however, image rays do not emerge from the exit pupil as a pencil converging to a single point but rather converge to a small irregularly shaped region-the focus is not stigmatic. It is always possible to draw a surface through the center of the exit pupil that all rays cross simultaneously, and when the focus is not stigmatic that surface, called the actual wavefront, is not spherical. The difference between the reference sphere and actual wavefront is the wave aberration . The wavefront and reference sphere are both surfaces and the difference between these two surfaces, the wave aberration, is likewise a surface.

The word wavefront is misnomer- aberration theory is based on geometrical optics that, bydefinition, 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 every object point. Each object point produces its own pencil and each object pencil has its own unique wavefront aberration. Individual aberrations are either 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 point in the same transverse plane and field dependent otherwise. The majority of aberrations are field dependent, but several important aberrations are field independent.

2. Aberrations may also be pupil dependent or pupil independent. If the aberration is pupil independent it does not change as pupil size changes. Most aberrations are pupil dependent and do change with pupil size. However, myopia, hyperopia, and regular astigmatism are pupil independent which is why it is unnecessary to check pupil size to prescribe glasses. 3.Stigmatic focus means image rays converge to a perfect point either at the ideal image point or elsewhere. When the focus is nonstigmatic, rays do not converge to a perfect point even at the best possible focus. Aberrations can exist even when the focus is stigmatic. In such cases rays still converge to a perfect point, but the point is in the wrong place (i.e., not at the paraxial image point).

DEFOCUS In aberration theory, defocus encompasses both myopia and hyperopia. If the only defect of an optical system is myopia, then the image rays still focus stigmatically but to a point closer to the exit pupil than the ideal image point . Since the focus remains stigmatic, all rays simultaneously cross a sphere centered on the actual image point 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 upside down (i.e., spills water). While myopia is corrected by minus lenses, the corresponding wave 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 unlike defocus, RA is nonstigmatic. RA should not be confused with astigmatism of oblique incidence, which is an entirely different aberration although it does have some similar features. SPHERICAL ABERRATION In spherical aberration rays near the center of the lens focus at the ideal image point but more peripheral rays focus in a different location . In positive SA, 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 rays focus behind the ideal image point 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 representing defocus. SA is one of the most important aberrations that is not part of the classic clinical triad of hyperopia, myopia, and

regular astigmatism. SA is a pupil dependent, nonstigmatic, field independent aberration. Positive SA 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 because they are the easiest to manufacture accurately. However, a sphere is too steep peripherally so peripheral rays do not focus in the same location as central rays. The problem can be eliminated by using lenses with aspheric surfaces that flatten 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 influence of SA on vision because photoreceptors are less sensitive to 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 amount of positive SA. When their pupil dilates the increase in SA makes them more myopic, blurring their vision.Corneal SA varies from person to person so an implant that corrects a fixed amount of SA is unlikely to benefit all patients. To properly compensate corneal SA with an implant the patient’s corneal SA should be measured preoperatively and an implant selected not only by its power but also by the amount of SA corrected, which is not current clinical practice.Raytracing data on model eyes show that the amount of SA corrected by an implant varies substantially if the anterior chamber depth changes by tenths of millimeters, or if the implant is tilted or decentered. DISTORTION , Distortion occurs when the transverse magnification is not constant but changes as distance from the axis increases within a transverse plane. In pincushion distortion, magnification increases as distance from the axis increases (in the same transverse plane), whereas in barrel distortion, magnification decreases as distance from the 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, one of the principal reasons for the use of intraocular lens implants was the visual improvement achieved by eliminating distortion. distortion has practically disappeared since the introduction of intraocular lenses. COMA When coma is present image rays ‘flare out’ from the image point in a fashion reminiscent of a comet’s tail . Coma is nonstigmatic, field dependent, and pupil independent. Coma is increased when multiple optical elements do not share the same optical axis. After defocus and regular astigmatism, coma accounts for most of the residual aberration in otherwise normal eyes, since none of the ocular media share a 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 It is easy to confuse this aberration with regular astigmatism (RA), but the two are quite different. Both RA and AOI are nonstigmatic, pupilindependent aberrations. However, RA is field independent and second order, whereas AOI is field dependent and fourth order. Clinically 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 discuss 36 Zernike polynomials but several Zernike polynomials exist in pairs that are basically the same aberration). The basic aberrations discussed here are the most important and have specific names. Many ‘higher-order aberrations’ do not have specific names and are denoted only by the mathematical formulas that describe their shape. MATHEMATICAL CONSIDERATIONS : Each individual aberration is represented by a surface with a unique characteristic shape. The surface is multiplied by a constant that represents the amount of that particular aberration present in an eye or optical system. Multiplication by a constant does not change the basic shape of the surface, just its height (or depth). Zernike polynomials are an alternative way of classifying aberrations.The principal advantage of Zernike polynomials is the 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 standardize the notation for Zernike polynomials, there is no universally accepted method of specification. Most Zernike polynomials are not pure aberrations but actually a mixture of several aberrations. For

instance, the eighth Zernike polynomial that many 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 important to note that the wave aberration coefficients are expressed in units of length, typically micrometers, whereas clinically refractive errors are expressed 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 large compared to most higher-order aberrations. CHROMATIC ABERRATION All of the aberrations discussed so far are monochromatic – measured at a single wavelength. Chromatic aberration is one of the most prominent aberrations in the eye. A complete description of the eye’s aberrations would require the measurement of the monochromatic aberrations at several wavelengths.

CLINICAL MEASUREMENT OF ABERRATIONS1. In 1896 Tscherning was the first to 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. A small, distant source is viewed through a +5.00 D lens with a grid of small apertures placed behind it. The grid divides the light into parallel pencils that focus in front of the retina, then diverge forming a grid pattern on the retina. The grid will not be regularly spaced if aberrations are present. By drawing the appearance of the grid, ocular aberrations can be estimated. . As a clinical method for measuring aberrations the Tscherning aberrometer suffers from the obvious limitation that it is subjective, relying on the patient’s ability to observe and accurately locate the displaced pencils. Nonetheless, it is a useful conceptual tool. 2. The subjective limitations of Tcherning’s approach can be overcome by photographing the grid on the retina. However, photography introduces another problem – double pass. To be photographed, each grid spot on the retina acts as a light source, which passes through the eye suffering its 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. Since the laser traverses only a small amount of the pupil, it is essentially unaffected by ocular aberrations; practically speaking, this is a single pass technique. The small area of laser-illuminated retina becomes a source from which light emerges from the eye. If the eye is aberration-free, the emerging light will have planar wavefronts. Aberrations distort the wavefront shape. Using an approach suggested by Roland Shack, the wavefront is measured using a lenslet array that focuses small areas of the wavefront on a charge-coupled device. Each lenslet produces a small dot on the detector that is displaced depending on the wavefront’s shape. Shack’s approach is probably the most reliable way of measuring small amounts of higher-order aberration in an otherwise wellcorrected eye or optical system. The technique is not as well-suited to the measurement of large amounts of low-order aberrations. The majority of aberrometers utilize some variation of the Hartmann– Shack approach. 4. Automated retinoscopy is another means of measuring aberrations and is incorporated into the ARK 10000™ (Nidek™). The Tracey™ uses the Tscherning approach but performs it sequentially by scanning a single laser beam over the pupil and observing the beam’s deviation on the pupil.

It is very difficult to verify the accuracy of an aberrometer. Ocular aberrations, especially higher order aberrations, change with the slightest change in tear film thickness, or changes in choroidal thickness that occur during the 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-fitting procedure. If the measured data points are accurate, only a few hundred are needed to calculate the coefficients of a Zernike or alternate wave aberration expansion. The data-fitting procedure is a critical step because it converts a sampling of data points to a continuous surface described by a set of coefficients.

Notes for wavefront refractive surgery

advanced treatments involve the use of a wavefront-guided laser refractive technique to create a completely customized reshaping of the surface of the cornea that leads to a more optically desired outcome.A customized corneal shaping requires wavefront analysis of the eye (aberrometry). For reproducibility the waveform can be decomposed into components, using either Zernike polynomials or Fourier analysis. The wavefront map is digitally interfaced with an excimer laser, to control the delivery of laser beam across the cornea 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 are parallel, and the eye is free from any aberrations, the resultant emerging wavefront is perfectly flat. In other words, all light rays coming from a point source of light located at infinity focus at a single point on the retina. In reality, though, the focusing properties of a real eye are not completely uniform: some areas bend light more strongly than others. The wavefront aberration is the deviation 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 are monochromatic refractive disorders that limit the vision of healthy eyes to less than the retinal detection threshold. HOA cannot be corrected with spherocylindrical lenses or with standard refractive surgery. They have been categorized using Zernike polynomials by radial order and by angular frequency, with third order and higher constituting HOA. The higher the order, the less visually significant the aberration. The two most frequently discussed aberrations are spherical aberration (which causes halos and night vision disturbances) and coma (which is associated with monocular diplopia). The wavefront in spherical aberration is spherical in the center of the pupil but changes its curvature toward the edge of the pupil, giving concentric rings of focus that result in point images with halos. In coma, the wavefront is asymmetric, producing a comet-shaped pattern Trefoil, quadrifoil, pentafoil, and secondary astigmatism are other HOA IDEAL CORNEAL SHAPE The shape of the cornea is prolate (more curved in the center) to allow for 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 curvature than the periphery. This aspheric shape allows for focusing of rays coming from the periphery and those coming from the center on one point, correcting for inherent spherical aberration of spherical lenses. Any change in the average prolate corneal shape towards a more oblate profile (less curved in its center) leads to induction of spherical aberrations, and consequently a decrease in night vision and contrast sensitivity. MEASUREMENTS OF WAVEFRONT ABERRATIONS

Zernike polynomials and Fourier transforms are used to analyze the ocular wavefront. Zernike polynomials are a sequence of polynomials orthogonal on the unit disk, while Fourier transforms represent mathematical functions of frequency. Most aberrometers used for customized laser surgery rely on Zernike polynomials to decompose the wavefront aberrations. They can, in principle, measure an infinite number of aberration orders. Clinically, data up to the Zernike fifth order capture nearly all the aberration variance typically found in normal human eyes. The Fourier analysis can decompose an image into spatial frequency components . The measured wavefront errors are represented as root mean square deviations (RMS).WAVEFRONT-MEASURING DEVICES

Several methods for assessing the wavefront aberrations in human eyes are currently available. Each method has its own way of measuring thedisplacement of a ray of light from its ideal position. They can be generally classified as: outgoing or ingoing aberrometers.Outgoing Devices based on the Hartmann–Shack principle are currently the most widely used. These devices analyze an outgoing light that emerges or is returned from the retina and passes through the optical system of the eye.A narrow beam of light is projected onto the retina, and its image passes through the lens and the cornea and exits the eye. The Hartmann–Shack sensor has a lenslet array that consists of a matrix of small lenses.14,15 The light that emerges from the eye is focused on a charge-coupled device (CCD) camera through each lenslet to form a spot-pattern. The spot-pattern of an ideal subject with a perfect wavefront will be exactly the same pattern as the reference grid, and a distorted wavefront will create an irregular spot-pattern. Displacement of lenslet images from their reference position is used to calculate the shape of the wavefront. The advantages of this system include the fact that it measures wavefront in one shot; hence it is faster, leading to 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 multiple spots is projected through the optical system of 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 ingoing light that passes through the optical system of the eye and forms an image on the retina. It measures rays sequentially making it much slower (the total time of scanning is 10–40 milliseconds) and decreasing its precision. The iTrace aberrometer (Tracey Technologies, Houston, TX) is the only one based on the retinal ray tracing technology. The scanning slit refractometer is a double-pass aberrometer (slit skioloscopy) that is based on retinoscopic principles. This principle is used in theARK 10000 Optical Path Difference Scanning System (OPD-Scan) distributed by Nidek. WAVEFRONT-BASED SURGERY

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 film abnormalities can significantly affect the quality of wavefront analysis.2. Eyes with small-diameter pupils may be difficult to measure and provide information beyond the 3 mm optical zone and, therefore, require pharmacological dilatation. However, some variations in the wavefront maps have been seen with some pharmaceutical agents: it has been reported that cyclopentolate eye drops lead to a significant difference in the preoperative refractive error wavefront as compared to the subjective refraction3. An eye with marked aberrations such as scars or keratoconus may be difficult to measure.

4. The algorithm for converting measurements into an ablation profile should also be faithful to the original maps. It should be optimized to provide the best optical quality over the optical zone and tapering of the ablation in the surrounding zone. Another important issue for successful custom ablation surgery is eye registration and eye tracking during corneal laser ablation. The wavefront data must be transferred to the laser machine and applied to the same location on the eye from which they were captured. A small misalignment in the axis can have significant impact on the results of the procedure. It may actually cause new HOA due to misalignment of 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 sitting position to supine position. It has been reported that 50% of the visual benefit correction of HOA is lost with a 250 µm decentration or a 10 degree eye rotation.

Two main methods of using wavefront information in refractive surgery are: wavefront-optimized ablation and wavefront-customized ablation. Wavefront-optimized ablation aims at preserving the eye’s pre-existing optical aberrations using adjustments based on population averages, and at optimizing the asphericity of the cornea. The ablation profile is based on an ideal model, without evaluating the patient’s own aberrometry.

Wavefront-customized ablation leads to having an individual treatment ablation profile based on the patient’s own aberrometry, therefore it would be able to correct for pre-existing HOA. CLINICAL implication OF ABERRATION THEORY With the emergence of keratorefractive surgery came the possibility of correcting aberrations uncorrectable by spectacles. Initially some overly optimistic claims were made, including the possibility of achieving 20/6 acuity. These claims were based on an incomplete understanding of aberration theory as well as other optical and non-optical factors that influence acuity. Altering the shape of just the anterior corneal surface cannot correct all ocular aberrations. Even if it were possible to eliminate (or reduce to insignificance) all aberrations, other factors such as diffraction and intraocular light scattering would limit vision. After the correction of defocus and RA, for pupils smaller than about 2.5 mm acuity is limited by diffraction not higher-order aberrations.Consequently, the correction of higher-order aberrations would not lead to further visual improvement in patients with smaller pupils. Intraocular light scattering also decreases acuity. While incompletely understood, neural mechanisms doubtless play an important role. Visual processing can decrease the influence of some aberrations. The large amount of chromatic aberration present in most eyes is largely neutralized by visual processing and likewise modest amounts of SA are also compensated by visual processing. Clinicians should be aware that irregular astigmatism is not uncommon but rather ubiquitous. All eyes have a large amount of uncorrected chromatic aberration.

WAVEFRONT PLATFORMS