Ординатура / Офтальмология / Английские материалы / Wavefront Customized Visual Correction The Quest for Super Vision II_Krueger, Applegate, MacRae_2003

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0.55µm. Laser ablation systems typically remove 0.25 µm of tissue per pulse. As this is stromal tissue with an index of refraction of 1.376, the OPL removed per pulse is 0.62 wave (dividing equation 1 by the wave length).

OPL = physical distance x index of refraction/wavelength

OPL = 0.25 x 1.376/0.55 = 0.62 waves

Since we are really interested in the change wavefront error caused by the ablation, what is important is the change in OPL from the case of light traveling through stromal tissue to that of light traveling through air, when the stromal tissue is removed. The change in OPL—d(OPL)—is the physical distance times the change in index of refraction. A single ablation pulse changes the OPL, in waves, by 0.17 waves:

d(OPL) = physical distance x (index of refraction in tissue - index of refraction in air)/wavelength

d(OPL) = 0.25 x (1.376 -1.000) /0.55 = 0.17 wave

There is little need to measure surface details to an accuracy greater than the minimum amount of tissue that can be removed.

To get an idea of the elevation resolution needed for custom ablation, let us first consider the variation in thickness for a tissue lens that represents a change in refractive power of 0.25 diopters (D). A change in refractive power of this magnitude can be expressed in terms of wavefront error if a pupil diameter is assumed. Using the simple approximation for sag of a sphere:

where D is the diameter of the aperture (in mm) and F is the power (in D), the sag is expressed in microns. The wavefront error, W, from the center to the edge of the aperture given in waves is the sag divided by the wavelength of light.

If a 3 mm pupil is chosen and the wavelength is 0.55 µm, W is 0.51 waves. It should be noted in passing that this is twice the Rayleigh criterion for the amount of wavefront error that is just enough to perceptibly change image quality. This fact provides a physical reason for the observation that 0.25 D blur is just noticeable under normal visual conditions. We should also note that often the wavefront error is not expressed as the difference from the aperture center to the edge but in terms of the root mean square (RMS) wavefront error. To convert W to RMS error for simple surface forms such as spheres, ellipsoids, and toric surfaces, a good approximation is found by multiplying W by the factor 0.30:

The RMS error corresponding to the Rayleigh quarter wave criterion is 0.075 wave:

0.075 = 0.3 X 0.25

To find out what a 0.25 D error means in terms of the variation in thickness of a corneal tissue lens, we may use the simple formula that is widely used to calculate ablation depths (equation 2 divided by n-1) :

where d is the variation in lens thickness (in µm), D is the diameter (in mm), F is the power (in D), and n is the index of refraction of the tissue. Choosing a pupil diameter of 3 mm, we find that the thickness variation from tissue lens center to edge is 0.75 µm. As this thickness is equivalent to the ablation effect of just three nominal pulses, it first shows us that customized ablation will require an ablation system to operate at the limit of its capability in any case. Interestingly, the change in measured RMS wavefront error for the higher-order aberrations found in recent LASIK studies show increases of about 0.15 wave. Removal of this error is certainly at the limit of a system that removes 0.17 waves per pulse.

It is clear that a corneal topography system needs to be able to measure surface elevation differences to better than 1 µm resolution to be useful in guiding customized ablation. This is not to say that corneal topography systems with less resolution are not useful in assessing larger corneal surface features. They are valuable in monitoring change both following corneal procedure and for other purposes. Wavefront errors beyond those of normal refractive errors are of a size that they will not be detected unless a measurement system has this resolution. Current Placido diskbased corneal topography systems using arc step reconstruction algorithms are able to resolve corneal surface elevation variations to about 0.7 µm. These systems give the best resolution available today.

This means that highest resolution corneal topography systems available are just able to detect the presence of surface variations that will contribute to higher-order wavefront errors as 0.7 µm of tissue removal converts to 0.48 wave of wavefront change.

For those more familiar with the performance of corneal topography system expressed in axial curvature values (keratometric diopters), the following example is given to illustrate the relationship between variation in surface elevation and variation in axial curvature in a local area of the corneal surface. Let us take a circular area of the corneal 1.5 mm in diameter and let it have an axial curvature value 1 D greater that the surrounding area. Then using equation 5 and the nominal index of refraction value taken to express keratometric diopter of 1.3375, we find the variation in elevation, d, to be 0.833 µm. As we know that the better corneal topography system can detect curvature changes of this size over this area, we see that they have resolution that is in the range that is useful for customized ablation. This simple test can be used to judge the suitability of any corneal topography system as a guide for customized ablation.

COMPARISON OF CORNEAL

TOPOGRAPHY TO WAVEFRONT SENSING

AS A GUIDE FOR CUSTOMIZED ABLATION

When corneal topography is used as a guide for customized ablation, the desired surface is not known and some reference surface is needed to find the wavefront error so that a correcting ablation profile can be generated. Wavefront error sensing devices, such an ophthalmic Shack-Hartmann wavefront sensor, are configured to directly measure the wavefront error of the

entire eye in the area of the pupil. For this area, they supply the information needed to create an ablation profile directly. In doing so, they also account for aberration induced by the lens in addition to that created by the cornea. They would therefore be superior to a corneal topographer as a guide to planning a customized ablation. However, certain characteristics of these devices must first be considered before completely accepting this view.

Wavefront sensing devices can only sample in the pupil area so it is important that the pupil be fully dilated so that areas of the pupil that are only used in low light conditions are sampled. It is also best if the accommodation is paralyzed during the measurement to remove the accommodation uncertainty in the crystalline lens. In essence, wavefront sensors are automatic refractors with a very high sample density so all the known precautions associated with obtaining good refractive information with automatic refractors applies directly to them. Corneal topographers, on the other hand, often sample over a larger area of the cornea and are unaffected by accommodation, pupil size, or other refractive effects.

Wavefront sensing devices measure the entire refractive state of the eye and cannot tell if measured aberrations are caused by the cornea or by a combination of effects of the cornea and crystalline lens. Unlike corneal topographers, they give no direct information on the state of the corneal surface.

Wavefront sensing devices sample in a different way from corneal topographers. The sample density is somewhat less, in general, and the sample pattern is different. Wavefront sensors divide the pupil in small areas, usually in a rectangular grid, and measure the average deflection of light exiting from each area. This deflection information is then processed to yield wavefront error. The most common corneal topographers sample the cornea with concentric rings and may be thought to measure the surface either only at boundaries between light and dark or averaged over the area illuminated by a ring. Because the ring images are often closer together than are the center spacing the lenslet array of the wavefront sensor and because very dense sampling is taken along a corneal topographer ring image, a higher sample density is usually obtained with a corneal topography system than can be obtained with a wavefront refractor, thereby allowing smaller irregularities to be detected. Counter balancing this view, it must also be recognized that the sample density of the polar measuring system employed by corneal topographers is nonuniform with the meridional sample density decreasing toward the periphery.

It seems that if wisely used, wavefront sensing devices serve better as guides for customized ablation than do corneal topographers. However, corneal topographers should not be neglected because they give direct information on the shape of the cornea, information that is unavailable from a wavefront sensor. They should therefore be routinely used as a “second opinion” when planning a customized ablation and to see if the desired ablation pattern was achieved. For corneal ablative procedures, subtracting postsurgical corneal elevations from presurgical elevations will reveal the nature of the obtained surgical lenticule. Comparisons of the desired lenticule to the obtained surgical lenticule contain valuable information that can be used to improve future surgeries.

Comparisons of the desired lenticule to the obtained surgical lenticule contain valuable information that can be used to improve future surgeries.

In addition, there are cases in which a wavefront sensor will not work well because wavefront sensing devices must be able to send and receive light from the retinal surface without significant interference from the ocular tissue. In cases of corneal trauma, the cornea may be compromised to the extent that it is not possible for the incoming beam of the wavefront sensing device to form a reasonably well-focused spot on the retina. When this happens, the detected spots of light may be so badly deformed that good measurements of higher-order aberrations are not possible. The corneal topographer has no such limitation. It can measure the corneal surface shape even in the presence of serious irregularity and this information is quite sufficient to plan an ablation pattern to correct this defect. Because the crystalline lens may be assumed to be a regular optical element even though its exact details are not known, its effect can safely be assumed in calculations and the major cause of the degradation of vision, the corneal irregularity, can be corrected using only corneal information. This suggests that the correlation between wavefront error measured with a wavefront sensor and wavefront error measured with a corneal topographer needs to be established so that when it is not possible to obtain wavefront error information from a wavefront sensing device, corneal topographical information can be reliably substituted.

As a first-order approximation, the crystalline lens can be assumed to be a regular optical element in calculations to assess the effects of corneal irregularities on vision.

USES OF CORNEAL TOPOGRAPHY TO ASSIST

WITH CORNEAL ABLATION PROCEDURES

There are other uses of corneal topographical information in the guidance of customized ablations of the cornea. Corneal topography displays can be used to simulate an ablation graphically illustrating what can be expected with different ablation patterns. As discussed above, historical displays showing the difference in corneal shape from that expected are useful to allow the surgeon to alter procedure to get desired results.

Similarly, one can simulate the anticipated effect of a given corneal ablation procedure. A simulated ablation feature first allows an ablation pattern to be specified. This specification includes such variables as the desired ablation zone size, the refractive error to be removed, the specification of transition zones between the corrected central optical zone and the unablated peripheral cornea, and the centration of the pattern with respect to the pupil center. Alternatively, the ablation pattern may be supplied by the laser ablation system, in which case it will be referred to as the treatment pattern. In either case, the ablation pattern is removed from the corneal shape as measured by the corneal topographer by the software program to produce a new corneal shape. This new shape is then displayed using one

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of the display modes of the topographer. The practitioner, familiar with corneal topography map presentations and their meaning, is now in a position to judge if the proposed ablation pattern will produce the desired effect.

A second effective way to use corneal topography information to assist with laser refractive surgery procedures is to use difference maps to graphically show the difference between two corneal surfaces. The first use of such a technique was to monitor changes in the corneal shape before and after surgery and then to monitor subsequent changes over time as corneal healing progressed. A more advanced use of difference information is to consider the difference found to represent a tissue lens that creates a wavefront error and then analyze this tissue lens wavefront error as one would any wavefront, expressing the aberrations in terms of Zernike polynomials coefficients, creating point spread patterns, convolving these point spreads with images, and calculating the modulation transfer function for the difference.

In all differencing techniques, the corneal topographical information needs preprocessing before comparison can be made. This is because the ring locations will invariably be slightly different when topographic changes occur in the corneal surface, so the data locations are not at the same horizontal and vertical positions on the cornea. The best plan is to chose a common grid to be used for comparison purposed and interpolate the elevation data sets onto this grid. There are several mathematical techniques available to do this. One interesting one is to use Zernike polynomials as fitting functions. This orthogonal polynomial set is quite capable of decomposing data on a randomly spaced grid into a set of coefficients. The coefficients, once so generated, may then be used to reconstruct the surface on the chosen grid.

Such interpolation has a second desirable feature when dealing with elevation data from a corneal topographer—that of imposing surface continuity across meridians and removing noise introduced in the reconstruction process. There is always noise introduced into the data as the ring locations are found from the video images of the reflected rings. Typically, a smoothing operation is done on each ring to remove discontinuities in radial position before reconstruction is done along meridians. This has the effect of imposing some meridian-to-meridian continuity in the reconstructed surface. However, when the better reconstruction methods—such as the arc step method—are used to reconstruct the surface one meridian at a time, there is continuity in the elevation data imposed only along meridians and that only through the first derivative. No cross meridian continuity is imposed. The interpolation discussed above imposes continuity to second degree and above if a method such a using Zernike polynomial functions is used.

Another use of the differencing method is to combine it with simulated ablation. A simulated postsurgical corneal shape is created by subtracting the treatment pattern from the presurgical corneal surface. A difference tissue lens is then created by taking the difference between the simulated postsurgical corneal surface and the actual postsurgical corneal surface as measured by the corneal topographer. In this way, actual results can be compared with expected results in a visual way and the above mentioned advanced techniques may be used to analyze the differences between the achieved and planned treatment. Because actual results are often slightly different from expected results, studies of this kind can serve as a guide to alter ablation patterns to get desired results.

While differencing techniques are also valuable when dealing with aberrometer data, there is one area in which the topographical analysis is clearly superior. This is in the monitoring of changes to the corneal shape in areas outside the treatment area. It has been found that the cornea not only changes its shape in the area of the ablation but also in areas peripheral to the treatment zone. These changes can never be seen by an aberrometer, limited as it is to measurement within the pupil area; yet these changes are important in understanding the response of the cornea to treatment.

Corneal topographers measure areas outside of the pupil, aberrometers cannot. Measurements outside the pupil are important in understanding the corneal response to surgery.

SPECIAL USES OF CURVATURE INFORMATION

Normally, curvature information obtained by corneal topographers and presented in the form of axial curvature or meridional curvature maps has been used clinically in a subjective way to assess the state of the corneal surface. Curvature information may be presented of other ways, as mentioned above, and these have special diagnostic advantages that are not as well known. Two types of these curvature displays will be mentioned here. They are both measures of local curvature and are true curvature measures in the sense of differential geometry as opposed to the common curvature measures, axial curvature and meridional curvature.

The first is mean local curvature. One may think of this measure as being similar to spherical equivalent power in that the mean local curvature is the mean of the maximum normal curvature and minimum local curvature at a surface location. This measure is particularly helpful in detecting power or curvature gradients on the corneal surface that may result from the type of refractive surgery performed either as an unplanned effect or as a planned treatment. Mean local power gradients are one of the indicators of a corneal surface that will in certain cases produce a variable power refractive effect (a type of presbyopic correction) or in others visual difficulties in enlarged pupil conditions.

The second special curvature display is of local Gaussian curvature. Whereas local mean curvature is the average of the maximum and minimum local curvatures, local Gaussian curvature is their product. As such, it has units of inverse area instead of units of inverse length as do other types of curvature. In effect, it measures the change in the area of a small local area of the surface from that of a plane surface that curved surface projects onto and in doing so gives a measure of how much a flat surface would have to be stretched or deformed to turn into the curved surface. This type of display can give information on corneal change following surgery if local Gaussian curvature difference maps are created. For areas of the corneal surface where ablation has not taken place but the Gaussian curvature has changed, we know that the corneal stroma has undergone stretching or compression. If precise corneal thickness measures are combined with precise anterior corneal surface measurements, posterior curvature information may be generated and so stretching and compression of the posterior stroma may be inferred from local Gaussian curvature maps.

CORNEAL TOPOGRAPHY AND WAVEFRONT

REFRACTION: COMPLEMENTARY TECHNOLOGIES

The above considerations show us that as we consider customized corneal ablation, we should consider corneal topography and wavefront refraction as complementary measurement technologies. Both should be included in any clinical practice that performs customized corneal ablation and both should be included in any program that enables laser systems for corneal reshaping to include customized ablations as an option. Whereas wavefront refraction should serve as the primary guide for planning customized ablations, corneal topography should serve as a

guide for monitoring the recovery process and as a means to learn how to subtly modify the planning process so as to obtain the best final visual results. Therefore, it is important to have both preoperative and postoperative corneal topography on all patients. It is also important to analytical means to most fully use the corneal information thus obtained.

Corneal topography and wavefront refraction are complementary measurement technologies.

INTRODUCTION

The wave aberration is a function that completely describes the image-forming properties of any optical system and, in particular, the eye. It is defined as the difference between the perfect (spherical) and the real wavefronts for every point over the eye’s pupil. It is typically represented as a two-dimensional gray or color image, where each gray or color level represents the amount of wave aberration expressed either in microns or number of wavelengths. An eye without aberrations forms a perfect retinal image of a point source (Airy disk). However, an eye with aberrations produces a larger and, in general, asymmetric retinal image.

The wave aberration is a function that completely describes the image-forming properties of any optical system and, in particular, the eye.

Since the eye is a relatively complex optical structure, every surface contributes differently to the overall quality of the retinal image.

cise evaluation of the contribution of the different ocular surfaces to the overall retinal image quality. The combined use of ocular and corneal aberrations has already been used to obtain more detailed information on the relative sources of aberrations in the human eye.5,6 If the aberrations produced by the cornea and the total aberrations are measured in the same eye, the aberrations of the internal ocular optics (ie, those produced by the posterior corneal surface and the lens) can be estimated. This approach is particularly powerful for most refractive surgery procedures where virtually any practical case would benefit from knowing the optical contribution of the ocular component that is being modified: the cornea in laser refractive surgery or the internal optics in cataract surgery.

The aberrations of the complete eye (ocular wave aberration), considered as one single imaging system, can be measured by using a large variety of wavefront sensors or aberrometers. On the other hand, the aberrations introduced only by the anterior corneal surface (corneal wave aberration) can be computed from data obtained by corneal topographers. The combined use of both corneal and ocular wave aberrations is a powerful tool to be applied in both basic and clinical studies.

Since the eye is a relatively complex optical structure, every surface contributes differently to the overall quality of the retinal image. The study of the relative contribution to the eye’s aberrations of the main ocular components—the crystalline lens and the cornea—has attracted the interest of researchers for centuries. In 1801, Young1 performed an experiment in his own eye to measure the contribution of the lens to ocular astigmatism. He neutralized the corneal contribution by immersing his eye in water. In clinical practice, it is commonly accepted that the lens compensates for moderate amounts of corneal astigmatism. Other, more recent studies continued the exploration in vivo of the sources of aberrations within the eye, although initially centered only in the spherical aberration,2,3 or used indirect estimates of image quality.4

The advent of new technology (ie, wavefront sensors and corneal topographers) opened new possibilities for a more pre-

The advent of new technology (ie, wavefront sensors and corneal topographers) opened new possibilities for a more precise evaluation of the contribution of the different ocular surfaces to the overall retinal image quality.

This chapter will review how to obtain and how to combine the corneal and ocular aberrations, with special emphasis on the problems and limitations of using data obtained with different instruments. In the final part, and to demonstrate the potential of this approach, examples of ocular, corneal, and internal aberrations in different eyes will be presented.

MEASURING CORNEAL WAVE ABERRATIONS

To determine the aberrations associated with the anterior surface of the cornea, it is necessary to determine the corneal shape with submicron precision. The need for an instrument capable of measuring with precision the corneal curvature at each point was already noted in the early 60s.7 Many techniques have been proposed to measure the corneal shape, from interferometry to profile photography or holography. However, most instruments in

clinical practice today (eg, videokeratoscopes) are based upon Placido’s disk principle. That is, a camera images series of concentric rings reflected off the corneal first surface and the corneal first surface geometry is obtained in each meridian from the ring spacing. Since this type of apparatus is widely used in the clinic, a number of studies have evaluated their precision in estimating the corneal surface, aiming to calculate corneal aberrations.8,9 Although it was accepted that Placido-based devices do not provide accurate topographic data in the periphery and when the surface severely differs from a sphere, a recent study9 showed that it is possible to determine corneal aberrations from this data with enough precision for small to medium pupil diameters.

Small to medium pupil diameters are between 4 and 6 millimeters (mm). Enough precision is defined to be between 0.05 and 0.20 microns (µm) of root mean square (RMS) error (spherical equivalent dioptric error of between 0.09 and 0.15 diopters [D]).

Even if we could measure perfectly the corneal topography, a second problem is the calculation procedure used to determinate the corneal aberrations. The direct and simplest approach is to obtain a “remainder lens” by subtracting the best conic surface fitted to the measured cornea and calculating the aberrations by multiplying by the refractive index difference. Another option is to perform a ray tracing to the corneal surface to compute the associated aberrations.9 Figure 37-1 show a schematic diagram of this type of procedure.

The corneal elevations, representing the distance (zi) from each point of the corneal surface to a reference plane tangential to the vertex of the cornea, are fitted to a Zernike expansion13

by using a Gram-Schmidt orthogonalization method. The wavefront aberration associated with the corneal surface (W) is obtained as the difference in optical path length between the principal ray that passes through the center of the pupil and a marginal ray (see Figure 37-1B):

where n and n’ are refractive indexes; z, d’, and s’ are the distances represented in Figure 37-1B. By using the Zernike representation for the corneal surface (equation 1), the corneal wave aberration is also obtained as another Zernike expansion:

where the coefficients cmn are linear combinations of the coefficients amn.9

The accuracy of this procedure to estimate the corneal wave aberration was evaluated using reference surfaces.9 For central regions of 4 and 6 mm diameter, the RMS error between the actual and the measured aberrations were found to be around 0.05 mm and 0.2 mm, respectively, which renders the method appropriate for aberration studies.

MEASURING OCULAR WAVE ABERRATIONS

Many different techniques have been proposed to estimate the wave aberration of the complete eye, both subjective and objective. Although they are described more extensively elsewhere in this book, some of them are the method of “vernier” alignment,14 the aberroscope,15 the Foucault-knife technique,16 calculations from double-pass retinal images,17,18 the pyramid sensor,19 and probably the most widely used method today, the ShackHartmann wavefront sensor.20-22 This system consists of a microlenslet array, conjugated with the eye’s pupil and a camera placed at its focal plane. If a plane wavefront reaches the

Figure 37-2. Schematic representation of the combination of corneal and ocular wave aberrations to estimate the wave aberration of the internal optics.

Figure 37-3B. RMS of the corneal aberrations as a function of the decentration of the pupil center in mm. The red horizontal lines indicate the average error expected in normal eyes when estimating corneal aberrations.

microlenslet array, the camera records a perfectly regular mosaic of spots. However, if a distorted (ie, aberrated) wavefront reaches the sensor, the pattern of spots is irregular. The displacement of each spot is proportional to the derivative of the wavefront over each microlens area. From the images of spots, the ocular wave aberration is computed, and in general it is also expressed as a Zernike polynomial expansion similar to that of equation 3.

COMBINING OCULAR AND

CORNEAL WAVE ABERRATIONS

If the wave aberrations of the complete eye and the cornea are available, the relative contributions of the different ocular surfaces to the retinal image quality can be evaluated. In particular, the wavefront aberration of the internal ocular optics (ie, principally the posterior surface of the cornea plus the crystalline lens) is estimated simply by direct subtraction of the ocular and corneal aberrations. Figure 37-2 shows a schematic representation of this procedure. In a simple model, having the two series of Zernike coefficients, both for the cornea (cnm) and the eye (c”nm), the aberrations of the internal optics are obtained by

(centered)

Figure 37-3A. Examples of corneal wave-aberrations calculated from the corneal elevations for different locations of the pupil center (0, 0.2, and 1 mm). The circles represent schematically the position of the pupil.

direct subtraction of each pair of coefficients (c’nm). It is assumed that the changes in the wave aberration are small for different axial planes (ie, from the corneal vertex to the pupil plane).

In general, when using this approach, ocular and corneal aberrations are obtained with two different instruments. Then a major problem is how to determine a correct reference centering for registration. If the corneal and ocular aberrations are obtained centered at different locations, subtraction will produce an incorrect estimate of the internal aberrations, and in consequence, an incorrect picture of the coupling of aberrations. Figures 37-3A and 37-3B show an example to clarify this point. From a given corneal elevation map (in a color representation in the figure), the corneal wave aberration was computed for different positions of the pupil center with respect to the corneal vertex. Figure 37-3A shows, as an example, three wave aberration maps, for 0, 0.2, and 1 mm, respectively, of relative decentering of the corneal vertex (where the topography is centered) to the center of the possible pupil. Figure 37-3B shows the RMS of the corneal aberrations calculated when changing the center of the pupil in a range of 2 mm along one diagonal. The two red horizontal lines indicate typical errors when estimating corneal wave aberrations from corneal topography measured with a videokeratographic instrument. These results indicate that, as anticipated, decentering can induce substantial changes in the aberrations (note the complete different map for the 1 mm decentration case in Figure 37-3A). However, in normally aberrated eyes, small misalignments (below 0.2 mm) would probably introduce errors in the calculated aberrations within the same magnitude that other errors also present in the measuring process (see Figure 37-3B). As a practical rule, an obvious choice for realignment of the ocular and corneal aberration maps is the geometrical center of the pupil. When doing this, it must be considered that the pupil center changes with dilatation.

Typically the pupil location varies less than 0.2 mm during normal physiologic pupil dilation and constriction.

Figure 37-4. Schematic procedure to estimate the aberrations of the cornea directly and from indirect measurements (complete eye and internal optics). The box shows the Zernike coefficients of the aberrations of the cornea in one subject, obtained from the shape (circles) and by subtraction of the aberrations of the whole eye and the internal surfaces (triangles).

Although decentering in a single plane of both wave aberrations is probably the most important source of error when combining ocular and corneal aberrations, it is not the only one.23 Most instruments measuring ocular aberrations use the line of sight as the alignment axis. However, this is not usually the case for videokeratoscopes providing the corneal elevations used to calculate the aberrations of the cornea. If this factor is not considered, the wave aberration for the cornea will be obtained for a plane forming a different angle as that of the wave aberration for the eye, introducing another potential registration problem. When this happens, it is also possible to correct computationally for the difference in axis, although this should implicate the assumption of approximate values for the angles involved in the instruments and the eyes.

Errors induced when estimating the internal aberrations by measuring the corneal aberrations in the plane tangent to the corneal apex and ocular aberrations in the plane of the entrance pupil can be minimized by referring the corneal aberrations back to the center of the entrance pupil.

An intuitive solution for these problems appearing when combining corneal and ocular aberrations is the use of one single instrument with a unique alignment axis to collect both corneal and ocular data under the same conditions. However, if the two sets of data are obtained with two apparatus, it is still possible to use different approaches to correct for the registration errors. One is to use a common pupil point, usually the geometrical center of the pupil, to calculate the aberrations of the cornea and the eye. The differences in the angle of axis may be also incorporated to the calculations. Another approach is the search of a registration position that minimizes the aberration differences between the cornea and the eye.24 This last approach may underestimate the real contribution of the internal optics.

HOW PRECISE ARE THE COMBINATION RESULTS?

With all the potential sources of error described in the previous section, plus those related to each instrument, the important question is how precise are the data obtained from the combination of ocular and corneal aberrations? A few experiments have been performed to address this question. Artal et al,5 in addition to measuring ocular and corneal aberrations, also directly measured the wave aberration for the internal optics, using a ShackHartmann wavefront sensor when the aberrations of the corneal surface were cancelled by immersing the eye in saline water using swimming goggles. This was a similar idea as that of Young1 and more recently Millodot and Sivak,25 but using current wavefront sensing technology. The comparison of the aberrations obtained from independent measurements is an indication of the validity of the combination approach. In particular, the aberrations of the cornea, measured both directly from its shape and by subtraction of the aberrations of the whole eye and the internal optics were compared in that study5 and found to be similar within the experimental variability. Figure 37-4 shows this comparison schematically, together with the Zernike coefficients obtained in one eye as an example. This result provides strong proof of the consistency of this type of procedure: the combination of ocular and corneal aberrations despite the experimental and methodological difficulties that are involved.

Another interesting type of experiment performed to test the validity of the combination approach was to compare the estimates of both ocular and corneal aberrations in highly aberrated eyes where the cornea were by far the main contributor to aberrations (eg, in an eye with keratoconus).24 In this situation, both aberrations for the eye and the cornea were quite similar, indicating again the reasonable accuracy of the combined use of corneal and aberration maps when most precautions were taken into account during data processing.

CORNEAL, INTERNAL, AND

OCULAR ABERRATIONS IN DIFFERENT EYES

By the combined use of corneal and ocular aberrations, the relative contribution to the aberrations of the cornea and the internal optics in different eyes has been evaluated in recent studies. As an example of the potential of the procedure, this section presents results for three types of eyes: normal young eyes, normal older eyes, and highly aberrated eyes due to an abnormal cornea.

Normal Young Eyes

Figure 37-5 shows an example of the wave aberrations and the associated point spread functions (PSFs) for the cornea, the internal optics, and the complete eye in a normal young eye. The magnitude of aberrations is larger in the cornea than in the complete eye. This indicates an active role of the lens for a partial reduction of the aberrations produced by the cornea. Figure 37-6 shows the Zernike terms for the aberrations of the cornea (solid symbols) and the internal optics (white symbols) for a number of young normal subjects.5 It is remarkable that the magnitude of several aberrations is similar for the two components, but they have an opposite sign. This indicates that the internal optics may

Figure 37-5. Example of wave aberrations (represented module-p) for the cornea, the internal optics and the complete eye in one normal young subject. The associated PSFs were calculated at the best image plane from the wave aberrations and subtends 20 minutes of arc of visual field. The aberrations of the internal optics compensate in part for the corneal aberrations.

Figure 37-7. Example of wave aberrations (represented module-p) for the cornea, the internal optics, and the complete eye in one normal older subject. The associated PSFs were calculated at the best image plane from the wave aberrations and subtend 20 minutes of arc of visual field.

play a significant role to compensate for the corneal aberrations in normal young eyes. This behavior may not be present in every young eye, depending on the amount of aberrations or the refractive error.23

Normal Older Eyes

It is now generally accepted that the amount of monochromatic aberrations in the eye increases approximately linearly with age (also see Chapter 11). 26-28 The combined study of the aberrations of the cornea and the whole eye provides useful information on the underlying cause of the increase of ocular aberration with age.6 While the optical aberration of the cornea increase moderately with age,29 the aberration of the internal surfaces show variability, but with a tendency to increase in middle age and older subjects. However, neither ocular component itself isolated appears to explain the change of aberrations in the entire eye. A different coupling between corneal and internal aberrations in young and older eyes explains the optical deterioration of the eye with age. Figure 37-7 shows an example of wave

Figure 37-6. Zernike terms for the cornea (solid symbols) and the internal optics (open symbols) for number of normal young subjects.

aberrations and their associated PSFs for the cornea, the internal optics, and the complete eye in a typical older eye. In this case, contrary to the coupling of the young eye, the internal optics do not compensate the corneal optics, but instead add aberrations to those of the cornea.

Highly Aberrated Eyes

An interesting case to apply the combined measurement of aberrations is in the highly aberrated eye, in particular those with the cornea as the major contributor to the ocular aberrations. For instance, the keratoconic eye, or an eye after penetrating keratoplasty, are excellent eyes for testing the whole procedure of calculating the aberration of the internal optics from corneal and whole eye measurements. In these eyes, both wave aberrations for the cornea and the eye are similar, indicating a minor role of the internal optics to modify the high corneal aberrations.

EXAMPLES OF THE CLINICAL

IMPACT OF THE COMBINED USE

OF CORNEAL AND OCULAR ABERRATIONS

The use of the combined information of the ocular and corneal aberrations helped to explain some facts that were not wellunderstood previously. One example was the optical performance of eyes after implantation of intraocular lenses (IOLs). These lenses usually have good image quality when measured in an optical bench, but the final optical performance in the implanted eye was typically lower than expected.30 One plausible reason is that the ideal substitute of the natural lens is not a lens with the best optical performance when isolated, but one designed to compensate for the aberrations of the cornea.31 Figure 37-8 schematically shows this situation. This has important implications for ophthalmic applications. IOLs and contact lenses should be designed with an aberration profile matching that of the cornea or the lens to maximize the quality of the retinal image. In addition, procedures in refractive surgery should ablate the cornea based on the overall ocular aberrations rather than use corneal aberrations to achieve the optimum retinal image.