Ординатура / Офтальмология / Английские материалы / Wavefront Analysis Aberrometers and Corneal Topography_Boyd_2003

Conversion to the Ablation Profile

The next step in the process is converting the wavefront measurement into an actual ablation profile of tissue that needs to be removed from the cornea to correct the refractive error and high order aberrations. When implementing the step it is important to have a wavefront measurement which has been captured through at least a 7mm diameter pupil. To achieve a pupil diameter of this size, pharmacological dilation is necessary. However subtle variations in the wavefront pattern have been demonstrated with the use of pharmacologic agents and this needs to be considered when forming the wavefront composite to be used during surgery22.

The conversion of the measurement profile into an ablation profile is a complex mathematical inversion of the 3 dimensional profile. The ablation profile used by the Summit Autonomous LADARVision laser is defined by a 6.5mm optical zone together with a 1.25 mm transition zone for a total ablation diameter of 9mm. Also, the wavefront composite with a greater than 7mm pupil is converted into an ablation profile as demonstrated by the interference fringes and 2-dimensional profile of ablation depth.

In every instance of wavefront customized ablation, a blend zone is necessary to produce a smooth transition between the correction of high order aberrations at the edge of the optical zone and the residual unablated cornea. With the Tscherning Aberrometer link-up to the wavelight laser, a blend zone of at least .5mm is added to the calculated ablation zone. In cases where the residual stromal thickness after LASIK makes it unsafe to treat with a full 7mm optical zone, a slightly smaller optical zone diameter is implemented.

Before transferring the ablation profile to the laser, a final step is determining the excimer laser shot pattern. The ablation profile map which measures the depth or elevation of corneal tissue that

needs to be removed must be broken down into a calculation of the position of each excimer laser pulse to achieve the ablation profile. This step requires knowledge of the fluence and approximate ablation depth for each pulse as well as the proper gaussian overlap to achieve a smooth uniform ablation profile.

Transfer, Tracking and Alignment

The next step in linking up the wavefront with the laser is the actual transfer of the wavefront ablation information to the computer assisted input of the laser. At the present time the link-up is achieved by a computer disc which downloads the information from the wavefront device, and a computer which calculates the excimer laser spot pattern to the computer interface of the excimer laser. This information that is transferred by way of a floppy disc includes the orientation data gathered during the wavefront measurement.

The tracker of the excimer laser can than be engaged to align the laser pulse positioning with the movement of the eye, but more importantly, a step of XYZ alignment is necessary to assure that the wavefront determined pulsing sequence corresponds with the exact position of the aberrations as seen at the level of the cornea. The Summit Autonomous LADARVision laser has eye tracking which is maintained by locking onto the edge of the dilated pupil but aligned by the position and landmarks of the limbus.

The issue of proper ocular alignment is an important one. Further steps to assure proper centration beyond just the center of the pupil, as well as accurate alignment to include cyclotortion and tilt will be necessary as wavefront technology further advances. The steps required for centration and alignment used previously when treating only sphero-cylindrical error may not be adequate when considering the subtle deviations of higher order aberrations. Since the true visual axis, which connects the fovea with a fixation target, goes through

the nodal point of the eye, centering based on the center of the entrance pupil may introduce a slight error. Small decentrations in alignment would have allowed for incorrect registry of the wavefront ablation pattern onto the cornea.

Algorithm Development

Finally the last step of interfacing the wavefront ablation profile to the laser requires understanding the variables of the ablation process. Just as current excimer laser correction procedures utilize a carefully developed nomogram for the optimal visual outcome; so too, complex nomograms, considering the multiple variables associated with wavefront guided treatment, need to be developed and refined in order to successfully reduce the ocular aberrations. Attempts at wavefront guided LASIK with the Wavelight Laser and Tscherning aberrometer have so far shown only 40% reduction of the ocular aberrations in the best case scenario. Complex ablation considerations need to be considered in order to try to improve upon these results.

1. Corneal Topography (Shape) Even though the wavefront map fully characterizes the aberrations within the optical system of the eye, subtle shape changes in corneal topography may have a bearing into the proper placement of pulses onto the cornea.23 Corneas that are unduly flat or steep may impact the way in which the wavefront guided ablation pattern successfully remolds the cornea.

2. Flap Biomechanics (Surgery) The wavefront measurement profile, which is highly sensitive to the structure and orientation of the cornea, will likely change after making a corneal flap. The biomechanical changes of the cornea secondary to flap creation and positioning of the hinge are not thor-

oughly understood. Initial studies with the custom cornea measurement device have demonstrated induced coma along the axis of the hinge after making a corneal flap (personal communications with Christy Stevens OD, June 2000). Further analysis of wavefront profiles after making a flap alone will need to be analyzed and factored into the ablation nomogram.

3. Environmental Issues (humidity, temperature, etc). Another large variable that we currently face with laser vision correction is the hydration of the cornea which is in part dependent on the humidity, temperature, technique and length of treatment time. Uniform corneal hydration will be an important consideration in order to get a uniform pattern that fully corrects the wavefront error

As with all complex systems appropriate algorithms or nomograms will need to be developed to achieve the optimum optical result. Wavefront guided customized corneal ablation offers a unique new application to refractive surgery that will hold a great deal of research interest and attention in the years to come. Potential to correct not only the refractive error but the higher order aberrations has already been well demonstrated in physical applications such as the Hubble Telescope, and even of correcting the ocular aberration pattern when viewing cone photoreceptors in the retina. The promise of perfect optical quality after laser vision correction would be a well-received addition to our current techniques of laser vision correction. As we further explore this technology, its requirements as outlined in this chapter will likely be expanded upon. Nonetheless, the technology requirements outlined here serve as a foundational basis in our current attempts to provide wavefront guided customized corneal ablation.

REFERENCES

1.Seiler T, Kaemmerer M, Mierdel P, Krinke HE. Ocular optical aberrations after photorefractive keratectomy for myopia and myopic astigmatism. Arch ophthalmol 2000;118:17-21.

2.Marco S. Aberrations and visual performance following standard laser vision correction. J Refract Surg 2001; 17:596-601.

3.Mrochen, M., Krueger R., Bueeler M., Seiler T. Aberration sensing and wavefront-guided treatment: Management of decentered ablations. J Refract Surg 202; 18:418-29.

4.Campin JA, Pettit GH, Gray GP. Required laser beam resolution and PRK system configuration for custom high fidelity corneal shaping. Inves Oph Vis Sci 1999;38:S538.

5.Krueger RR, Saedy NF, McDonnell PJ. Clinical analysis of steep central islands after excimer laser photorefractive keratectomy. Arch Ophthalmol 1996;114:377-81.

6.Krueger RR. Steep central islands: Have we finally figured them out? J Refract Surg 1997;13:215-18.

7.Krueger RR, Seiler T, Gruchman T, Mrochen M, Berlin MS. Stress wave amplitudes during laser surgery of the cornea. Ophthalmology 2000 (in press).

8.Puliafito CA, Stern D, Krueger RR, Mandel ER. High speed photography of excimer laser ablation of the cornea. Arch Ophthalmol 1987;105:1255-59.

9.Arevalo JF, Ramirez E, Suarez E, Morales-Stopello J, et al. Incidence of vitreoretinal pathologic conditions with

24months after laser in-situ keratomileusis. Ophthalmology 2000;107:258-62.

10.Ozdomar A, Aras C, Sener B, et al. Bilateral retinal detachment associated with giant retinal tear after laserassisted keratomileusis. Retina 1998;18:176-7

11.Bollen E, Bax J, Van Dijk JG, Koning M, Bos JE, Kramer CGS, VanDer Welde EA. Variability of the main sequence. Inves Oph Vis Sci 1993;34:3700-04

12.Boghea D, Troost BT, Daroff RB, Dell’osso LF, Birkett JE. Characteristics of normal human saccades. Inves Oph Vis Sci 1974;13:619-23.

13.McDonald MR, Vanhorn LC. Autonomous T-PRK. In: Talamo JH, Krueger RR, eds. The Excimer Manual: A Clinicians Guide to Excimer Laser Surgery. Boston, MA: Little, Brown & Co;1997:355-68.

14.Krueger RR. In perspective: Eye tracking and Autonomous laser radar. J Refract Surg 1999;15:145-9.

15.Miller DT, Williams DR, Morris GM, Linag J. Images of cone photorecptors in the living human eye. Vision Research 1996;36(18);1067-79.

16.J. Liang, B. Grimms, S. Guelz, JF Bille. Objective measurement of wave aberrations of the human eye with the use of a Hartmann Shack wavefront sensor. J Opt Soc. Am A 1994;11(7):1949-57.

17.Tscherning M. Die monochromatischen aberrationen des menschlichen auges. Z Psychol Physiol Sinn 1894;6:456-71.

18.Howland HC, Howland B. A subjective method for the measurement of monochromatic aberrations of the eye. J Opt Soc Am 1977;67:1508-18.

19.Mierdel P, Wiegard W., Krinke HE, Kaemmerer M, Seiler T. Measuring device for determining monochromatic aberrations of the human eye. Ophthalmology, 1997;6:441-5.

20.Smirnov HS. Measurement of the wave aberration in the human eye. Biophys 1961;6:52-66.

Jorge L. Alió, MD, PhD

Robert Montés-Micó, OD, MPhil

INTRODUCTION TO WAVEFRONT ABERRATION.

Wavefront aberration is defined as the deviation between the reference wavefront that comes from a in ideal optic system and the wavefront that originates from a measured optical system. The unit used to measure it is microns of waves and it is shown as the root mean square (RMS). Wavefront analysis of the eye allows to determine the optical quality of the eye by evaluating the shape of its wavefront as wavefront aberrations.

There are several methods to evaluate the wavefront shape and are classified into the following three types:

1.- Outgoing wavefront aberrometry (Hartmann-Shack sensor1).

2.- Ingoing retinal imaging aberrometry (Cross cylinder aberroscope2, Tscherning aberroscope3 and the sequential retinal ray tracing method4).

3.- Ingoing feedback aberrometer (Spatially resolved refractometer5 and the optical path difference method6).

When the wavefront shape has been obtained, using any of the previous methods, it can be analyzed by expanding it into sets of Zernike polynomials to extract the characteristic components of the wavefront shape. As we have introduced in the

chapter of "Corneal Topography in Irregular Astigmatism", in the Zernike polynomial expansion, the different optical aberrations may be described by terms which are raised to different orders. First and second order terms describe tilt, astigmatism and spherical refractive error respectively; and third, fourth and higher-orders describe spherical aberration, coma and the rest of aberrations. Polynomials can be expanded up to any arbitrary order if sufficient numbers of measurements for calculations are made. Taking into account that previous chapters have reported a whole description of Zernike polynomials and its use in the evaluation of the optical aberrations and their impact on image quality, we are going to apply this methodology in patients with irregular astigmatism.

QUANTITATIVE ANALYSIS OF IRREGULAR ASTIGMATISM FROM ABERROMETRY

Several commercially available instruments of wavefront sensors are available actually in the market. In this case, we have used the Zywave aberrometer from Bausch&Lomb (Bausch&Lomb, Irvine, CA) which allows the measurement of the ocular aberrations. This device, based on the Hartmann-Shack aberrometer, is a fundus camera which takes multiple pictures of a single spot of light

produced by a HeNe laser beam that focus onto the retina by the eye’s optical system (figure 1a). The reflected light from the fundus is focused by a number of small lenses (lenslet array) and a CCD camera (figure 1b) captures the resulting picture. Ideally, each of the bright white spots focused by each of the small lenses should have the same intensity and pattern. This would equal a plane wavefront (reference wavefront), which means a perfect optical system

(figure 1c). When the white spots have different intensities and/or patterns (deviations of the wavefront from plano) this will indicate an imperfect optical system (aberrated eye). The displacement of each image relative to the grid of optical axes is determined by the local slope of the wavefront in x- and y-directions at the face of the corresponding lenslet (figure 1d). Integration of this slope reveals the shape of the aberrated wavefront.

Chapter 24: Aberrometry in Irregular Astigmatism

We are going to show step by step the procedure to analyze some cases of irregular astigmatism from an aberration pattern. Aberrometries were captured using the Zywave aberrometer in a darkened room to avoid the need to dilate the pupil pharmacologically and thus allowed measuring aberrations over the full extent of a physiologically natural pupil (up to 6.5-mm diameter). Figure 2 shows the image of the patient’s pupil before the measurement. Figure 3 shows the centroid view captured by the

CCD camera of the aberrometer. This centroid is compared with the referenced grid and the displacement of the spots positions from the grid generates the slope of the aberrated wavefront. From these calculation is created the Figure 4, which represents the total aberration pattern in a patient with irregular astigmatism. As usually, the subject evaluated was instructed to blink three of four times and fixate on a distant image created by the aberrometer. Then, several images were captured with the aberrometer.

Figure 2: Patient’s pupil view before the aberrometry measurement.

Figure 3: Captured centroid of the patient by means of the CCD camera of the aberrometer.

From the total aberration map is possible to separate in different orders, for example, Figure 5a represents the sphere and Figure 5b the astigmatism contribution to the aberrated wavefront. From these figures is easy to understand how a spherical or astigmatic error affects the wavefront. In Figure 5a, the deformation of the wave follows a circular shape around the center without deformities in the periphery, in contrast, from Figure 5b we can observe a but-

terfly pattern typically found in astigmatism that correspond with the regular astigmatism that the patient has. In both cases, we are able to study how each different error modifies the wavefront and the implications in the visual function that he has. It is interesting to note that the colour scale of the deformation (microns) is different for both figures, that is because the alteration of the spherical refractive error on the wavefront is greater than the astigmatic component

Chapter 24: Aberrometry in Irregular Astigmatism

does. This always will happen if the spherical error is larger than the astigmatic error.

However, when we are interested in to study the wavefront pattern in a patient with irregular astigmatism, in addition to know how spherical and astigmatism errors contribute to the wavefront, the main concern is to study the higher order aberrations, which include spherical aberration, coma and the rest of aberrations. In this way, figure 6 shows the high- er-order aberration contribution to the wavefront pattern deformation. In contrast to Figures 5a and 5b, as we can observe no defined pattern is found, this is because each aberration contributes in a different way to the deformation. If only spherical aberration

were evaluated a peripheral circular deformation would has been obtained. In the case of coma, as a function of horizontal or vertical coma, the deformation would be found in one or another meridian.

Then, in order to evaluate how each aberration affects to the wavefront pattern is necessary to study each one separately, but not only as a colourcoded map but quantifying each aberration by means of the Zernike coefficient and how these contribute to the visual function. A simple idea about how these aberrations affect to the visual function could be obtained comparing the theoretical Point Spread Function (PSF) with or without the correction of these higher-order aberrations. Figure 7 shows both

Figure 6: Wavefront aberration map of a patient with irregular astigmatism only including higher order aberrations (spherical aberration, coma, rest of aberrations).

Figure 7: Point Spread Function (PSF) for a standard correction (spherical and astigmatism error corrected) and a customized correction (spherical, astigmatism and higherorder aberrations corrected) in a patient with irregular astigmatism.

PSF, for a standard correction (spherical and astigmatism errors corrected) and a customized correction (spherical, astigmatism and higher-order aberrations corrected). It easy to elucidate the benefits of higherorder correction on the final PSF and this consequently manifest how these higher-order aberrations spoil the visual quality of this patient.

The aberroscopic wavefront data obtained were fitted with Zernike polynomials up to the sixth order to determine aberration coefficients, from which the wavefront aberration function was reconstructed7. From the Zernike coefficients the root- mean-square (RMS) wavefront errors for coma-like aberrations (third-order components Z3i and fifthorder components Z5i) and spherical-like aberrations (fourth-order component Z40 and sixth-order compo-

nent Z60) were calculated. Because of the linear independence of the Zernike terms, the total wavefront error was computed by summing all components (Z3i + Z4i + Z5i + Z6i)8. To derive aberration coefficients for different pupil diameters (4.5- and 6.5-mm), the raw data images were masked to include only the data inside the required pupil diameter before proceeding with Zernike analysis. Different pupil diameters were assessed to allow evaluation of the central-peripheral irregularity of the

cornea and its impact on optical aberrations.

Table 1 shows the numerical Zernike data coefficients for each optical aberration calculated both pupil diameters (4.5 and 6.5-mm) and the RMS wavefront error grouped by the same type of optical aberration (spherical aberration and coma). From this