Corneal laser surgery for refractive corrections

Abstract

Corneal laser surgery with the modern excimer laser is known to be the most frequently applied laser procedure in medicine. World-wide, more than 2.5 million procedures were performed in 2001. Surgical techniques such as photorefractive keratectomy (PRK) and laser-assisted in-situ keratomileusis (LASIK) are used to correct optical imperfections of the eye, such as short (myopia) and long (hyperopia) sightedness, as well as astigmatism. However, the use of corneal laser surgery is also associated with disadvantages and complications. In particular, the increase of higher-order optical imaging errors (wavefront errors) after laser treatment leads to visual discomfort in poor illumination conditions, e.g., driving a car at night. This chapter provides an overview of the basic principles of corneal laser surgery, side-effects, complications, and future developments.

Introduction

More than 15 years after the discovery that corneal tissue can be micromachined in a nonthermal fashion with remarkable precision, the application of the ArF-excimer laser on the cornea for myopic, hyperopic, and astigmatic corrections has gradually been accepted by the ophthalmic community.1 During the past years, the safety of photorefractive keratectomy (PRK) and laser-assisted in-situ keratomileusis (LASIK) has improved significantly, mainly due to the increasing experience of surgeons and the development of new and more reliable technologies. However, the use of modern ArF-excimer lasers enables surgeons not only to correct sphero-cylin- drical errors, but also to correct optical imaging errors (wavefront aberrations) in order to improve the natural optical quality of the human eye.

Optical aberrations of the human eye

The term ‘monochromatic optical aberrations’ was coined in the early 19th century and, at that time, included all optical errors of the eye, except for spherical myopic or hyperopic refractive errors.2 During that time, Hermann von Helmholtz described the optics of the eye to be imperfect, and questioned the quality of the retinal image projected by cornea and lens.3 At the end of the 19th century, Tscherning investigated the non-refractive errors of the eye in more detail.4 However, Von Helmholtz described these higher-order errors as being of minor importance,3 in contrast to Tscherning4 and Gullstrand.5 Donders6 defined and specified the measurement and correction of ocular astigmatism, introducing the sphero-cylindrical error and, thus, reducing the ‘monochromatic optical aberrations’ to higher-order optical errors, such as spherical aberrations and coma (Fig. 1).

During the second half of the last century, several techniques for measuring monochromatic aberrations of the human eye were developed. One of the first was the crossed cylinder aberroscope introduced by Howland and Howland for subjective measurements,7 and the improved version for objective measurements introduced by Walsh et al.8 and Atchison et al.9 Artal, Santamaria, and Bescos10,11 developed a device to measure the point-spread function of the human eye, and introduced methods to calculate the wavefront aberrations from such data. He et al.12 used a psychophysical procedure to measure wavefront aberrations.

In 1994, Liang et al.13,14 presented the first measurement of ocular aberrations using a HartmannShack sensor. The operation principle of a HartmannShack wavefront sensor is demonstrated in Figure

2; the processing of an aberrated wave is depicted on the left-hand side. The incident wave results in a distorted grid of spots in the focal plane of the microlens array. On the right-hand side of Figure 2, a camera image of a distorted wave is shown. This distorted wavefront causes lateral displacement of the spots on the CCD camera. This displacement is equal to the first derivation of the wavefront. Thus,

the shape of the incident wavefront can be reconstructed on the basis of appropriate curve-fitting algorithms from the spot pattern.

Mierdel et al.15 demonstrated the clinical use of an automated aberrometer based on the principles of Tscherning’s aberrometry,4 as depicted in Figure 3. Basically, this ray-tracing method uses the mathematical analysis of a retinal spot pattern that

is grabbed by a video camera. From the deviation of the spot positions to their ideal positions, the first derivative of the wavefront can be calculated and the measured wavefront easily reconstructed.

Wavefront sensing provides detailed information on the image quality at the retina of an individual eye. In contrast, corneal topography provides shape information on the anterior front surface. Consequently, only wavefront sensing serves to obtain relevant data in order to rate the imaging quality of an individual eye. However, corneal topography is used even more frequently in ophthalmology in order to determine the optical imaging quality of the anterior surface, which is known to account for approximately 70% of the total refraction of the eye’s optic. Most of the commercial topography systems are based on the placido disc technique (Fig. 4). Here, a set of concentric rings are imaged onto the corneal front surface, and the resulting image of the ring distortions is captured by video camera, analyzed, and the corneal surface mathematically reconstructed. As usual, the data provided by topography measurements are represented in diopters maps.

In technical optics, the quality of an optical system is defined by the aberrations of the wavefront from its ideal plane or spherical shape.16 Anwar Gullstrand5 established a complicated mathematical formula to describe such wavefront aberrations, which never found acceptance in technical optics or

clinical ophthalmology. Zernike17, Thibos et al.18 introduced a more practical mathematical formula which is still used in technical optics, using special polynomials to describe the wavefront aberrations that are associated with special optical errors such as tilt, defocus, astigmatism of different orders, spherical aberrations, coma, and n-fold of the wavefront (Fig. 5). A quantitative measure of the optical imaging quality is the rms-wavefront error (root-mean-square) of the wavefront deviation. An optical system is considered good if all Zernike coefficients are close to zero and, as a consequence, the rms-wavefront error is smaller than 1/14 of the wavelength (Marechal criterion).19,20

However, the ‘average human eye’ only has minimal wavefront errors, indicating that, in principle, the construction of the human eye provides excellent optics, exceeding the Marechal-criterion only by a factor of two.21 However, such minimal aberrations were only measured in a small percentage (5-10%) of the normal population. This discrepancy is mainly due to the high variability of the wavefront aberrations in each individual eye. Consequently, the ‘average human eye’ consists of a good optical quality, while the optical quality of an individual eye is known to be of poor imaging quality. It should be mentioned that various research groups presented data leaning towards an aberration balancing between corneal aberrations and the optical elements within

the eye that reduce the aberration from the cornea by a certain degree.22,23 In particular, the spherical aberration of the cornea is nearly fully compensated by the intraocular structures of the eye.

Wavefront analysis was never a clinical issue however, mainly because there was no therapeutic approach to correct wavefront errors by optical means such as spectacles or contact lenses. This has changed since the introduction of excimer laser treatment of the cornea24 and, more specifically, customized ablations such as wavefront-guided treatments.25,26

Photoablation of the cornea

In 1983, Trokel, Srinivasan and Braren27 realized that intense excimer laser light can be used not only for etching plastics, but also for corneal tissue. Such excimer lasers are gas lasers in which the lasing medium inside the resonator consists of a gas mixture that is excited by special pretreatment. Depending on the gas composition used, an excimer laser is able to emit laser light at various wavelengths, although only the 193-nm wavelength has gained clinical attention in ophthalmology. This far ultraviolet light is obtained by means of a mixture of argon (Ar) and fluorine (F) gas inside the laser tube. The pulse duration of such excimer lasers used for refractive surgery is in the order of 20 nsec.

Numerous publications have reported the physics of the laser-tissue interaction for 193-nm tissue removal. However, there is still confusion in the literature as to whether this ‘photoablative decomposition’ or simply ‘photoablation’ (laser-tissue interaction process) is photochemical or photothermal in nature, although the best model probably uses a combination of these processes. Basically, the intense 193-nm radiation is mainly absorbed by the collagen macromolecules of the cornea at the start of the laser pulse. Here, the high photon energy of the 193-nm wavelength is capable of disrupting the chemical bonds of the molecules such as C-C (photochemical process). However, the later part of the laser pulse is more strongly absorbed by the tissue than the early part. The major part of the incoming energy is then converted into heat by inter-systemic energy transfer. The increase in temperature results in a breaking of the hydrogen bonds of the tissue water and, as a consequence, the water of the cornea becomes a strong absorber at a wavelength of 193 nm (photothermal process). The material undergoes a phase transition into gas, which is heated to several hundred degrees Celsius during the photoablation process. This hot gas, including the protein fragments, bursts out due to increased pressure. Gas chromatography and mass spectroscopy of the expelled products have revealed molecules typical of thermal changes in the protein fraction. In contrast, the remainder only shows minimal signs of thermal processing, since the photoablation process occurs within a few nanoseconds. Therefore, the photo-

Fig. 6. Ablation depth per ArF-excimer laser pulse for corneal tissue as a function of the radiant exposure. The intersection of the logarithmic fit (R² = 0.94; p < 0,001) yields an ablation threshold of 50 mJ/cm². The radiant exposure of commercially available medical excimer lasers ranges from 120-250 mJ/ cm².

ablation process was termed ‘cold laser ablation’. The major advantage of ArF-excimer lasers for photorefractive surgery is the high precision obtained from corneal photoablation. A common method of studying photoablation is to irradiate a sample with series of laser pulses, and then to measure the resulting etch crater depth. A collection of reported corneal etch data for 193-nm laser radiation is shown in Figure 6. The ablation threshold, the minimum radiant exposure for tissue removal, has been measured at approximately 50 mJ/cm². Above this threshold, the etch depth per pulse, known as ablation rate, increases in a logarithmic fashion with the radiant exposure. Since currently-used clinical excimer lasers work with a radiant exposure of between 120 and 250 mJ/cm², the resulting ablation rate ranges

from 0.2-0.5 µm per pulse (Fig. 6).

The use of intensive ultraviolet laser light in photorefractive surgery is accompanied by minimal thermal, mechanical, and actinic damage to the remaining corneal tissue. As mentioned earlier, the ablation products that are expelled with ultrasonic speed are in the physical state of a hot gas, and may have temperatures of more than 500° K.28 This hot gas condenses and creates heat, as well as a thin layer at the ‘cold’ edges of the remaining tissue. However, this ‘pseudo membrane’ disappears within a few days after surgery, due to wound healing. Under standard surgical conditions, the maximum averaged temperature increase at the edge of the irradiated tissue ranges from 5-10° K, which is not considered to be significant.29 In summary, thermal side-effects during excimer laser surgery are minimal and should not induce any kind of inflammation of the cornea.

During laser refractive surgery, mechanical damage to the deeper layers of the cornea may originate from acoustic stress waves produced during the ablation process. Kermani and Lubatschowski found pressure waves with an amplitude of 80 bar at a distance of 3 mm behind the cornea when an excimer laser beam, with a diameter of 4 mm and a radiant expo-

sure of 200 mJ/cm², was applied to the corneal surface.30 These waves travel with sonic velocity through the eye and, in contrast to the shock waves generated by Nd:YAG laser photodisruption, the amplitude falls slowly with distance. However, stress waves of less than 100 bar probably do not induce damage in the cellular ocular structures, except for the corneal endothelium, but might contribute to the development of postoperative subretinal hemhorrages, which have occasionally been reported after laser refractive surgery.

Ultraviolet light is known to have the potential to generate actinic damage. Light with wavelengths of 300 nm or less is considered to be cytotoxic and mutagenic because, in this wavelength range, DNA shows strong absorption. However, ArF-excimer laser light penetrates the tissue by less than 1 µm, and so this radiation is unlikely to reach the nucleus of human cells (cytoplasmatic shielding). Cytobiological experiments showed that the initial 193-nm light carries little risk of causing mutagenic changes in mammalian cells.31 However, during photoablation of the cornea, a faint bluish light is observed, the so-called secondary radiation or fluorescence, which includes wavelengths longer than 193 nm and has components in the dangerous 250-300 nm range. It is this secondary radiation that accounts for the mutagenic cellular damage that has been detected by very sensitive assays. The radiant exposure, however, has been determined to be less than 5 µJ/cm², well below the estimated mutagenic threshold of 10 µJ/cm².32,33 Therefore, the mutagenic potential of 193nm laser light is not considered to be significant, in accordance with the clinical absence of neoplasms after photorefractive surgery in millions of cases.

Tissue can be removed from a large area in two ways. Either the cornea can be irradiated with a number of laser pulses, each of which with a varied energy distribution, or the eye can be irradiated with a series of laser pulses of uniform irradiance but varying geometry. In case of a Gaussian beam profile, the center of the laser beam contains the highest concentration of energy, which decreases towards the beam periphery. This beam will remove more tissue centrally than peripherally with each pulse, which flattens the cornea for myopic correction. If the irradiance in the periphery was made larger, more tissue would be removed from the edges than from the center, which would steepen the corneal hyperopic correction. In principle, any contour can be transferred to the cornea by controlling the energy distribution with the laser beam. The same effect can be achieved by exposing the corneal surface to a series of circular laser beams of uniform energy density but increasing diameter up to 7 mm. The result of this is that, for example, the center of the cornea receives more laser pulses, and has more tissue removed.

Use of a small diameter spot or narrow slit beam scanned across the ablation area allows wide area ablations by means of a laser not generating the high energies required by lasers that use a stationary large

beam. Therefore, the clinical device can be smaller and less expensive. Recently, small ArF-excimer lasers have been used to perform such ‘scanningspot’ photorefractive surgery. To complete the treatment within a reasonably short period of time, the small diameter spot must be rapidly scanned across the cornea, and the repetition rate must be higher than with large diameter spot excimer lasers. However, small inevitable eye movements that have almost no impact on large diameter refractive surgery must be considered during scanning-spot corneal laser surgery for the precise positioning of each single laser spot, in order to omit increased surface roughness, which may result in a greater stromal wound healing response and haze. Reasonably fast optical eye-tracking systems have been instituted to overcome this problem.

Currently, excimer laser systems with large beam diameters of more than 6 mm and which scan with a circle beam diameter of 0.5-2 mm, as well as with a narrow slit beam, are in clinical use. Some systems combine scanning elements with large area beams in an attempt to develop maximum flexibility in the computer-controlled scanning algorithms.

Photorefractive keratectomy

PRK and photorefractive astigmatic keratectomy have become clinical standard techniques for correcting myopia and astigmatism. During PRK for the correction of myopia, direct flattening is achieved by the removal of a convex-concave lenticule of tissue from the outer surface of the central cornea. The central depth (a0) of the keratectomy is determined by the intended change of refraction, but is even more dependent upon the diameter of the ablation zone.34 The following approximation for a0 (in microns) enables the rapid estimation of this central ablation depth:

where ∆D represents the refractive change in diopters, and d the diameter of the ablation zone in millimeters. For example, a myopic correction of –6 D, with a typical diameter of 6.0 mm of the ablation zone, results in a central ablation depth of 72 µm.

On the whole, data on the efficacy of refractive correction after PRK generally report two overall measures: the percentage of eyes that achieve a postoperative refraction within 1 D of emmetropia, and the percentage of eyes that achieve 20/40 or better uncorrected visual acuity. Clinical studies determined refractive success rates of between 80 and 95% for corrections of up to –6 D of myopia, and the range of patients achieving 20/40 or better distance acuity without correction ranges between 80 and 100%.1 The overall incidence of vision-threatening compli-

cations such as a loss of best-corrected visual acuity and decreased contrast sensitivity was established to be in the order of 1-2% for corrections of moderate myopia with < –6 diopters. Higher myopic correction leads to a significantly higher regression and to a high risk of scarring during wound healing. Thus, PRK is considered an effective and safe surgical technique for myopic corrections up to –6 D.

It is important to relate these success rates to a defined time after surgery, because of the wound healing. Epithelial as well as stromal wound healing has been documented to occur over a period of months after PRK and, therefore, we choose a fol- low-up time of 12 months. Also, the success rates are helpful for assessing the efficacy and predictability of a procedure, but are not absolute measures of ‘refractive success’. Patients with preoperative refractive errors close to emmetropia may continue to complain of the need for spectacle or contact-lens correction, at least for part of the day. In contrast, patients with a residual myopia of, for example, –1.5 D, may consider the procedure successful if the eye was highly myopic prior to surgery. In addition, glare and halos around sources of light, or loss of contrast sensitivity, may not be detected under conditions typically used for measuring postoperative acuity. Because pupil diameter and variation in pupil diameter affect acuity, measuring visual acuities with a single ambient light will, therefore, not necessarily reflect the acuity experienced by the patient.

Laser in-situ keratomileusis

The older literature on excimer laser PRK for myopia describes ablation starting at the corneal surface and extending into the deeper structures of the cornea, such as Bowman’s layer and the stroma. A modification of this technique involves the initial creation of a lamellar flap (average thickness, 120160 µm) of anterior corneal stroma, followed by refractive ablation of the exposed stromal bed. This flap is then repositioned on to the exposed stroma, and good adhesion is usually obtained without the need for sutures (Fig. 7). Known as LASIK, this procedure was particularly investigated in eyes needing high myopic corrections of more than –6 D, for which the precision and stability of the refractive outcome after PRK have been somewhat disappointing. However, today the percentage of eyes achieving a postoperative refraction within 1 D of emmetropia is in the range of 90-98%, and the percentage of eyes achieving 20/40 or better uncorrected visual acuity is in the order of 90-100% in cases of moderate myopia. Other advantages of this application include rapid visual recovery, because no central epithelial defect is created, and a relative decrease in corneal haze compared to surface ablations of similar magnitude.

A potential disadvantage of this technique is the large amount of tissue removed during surgery and

Cutting the flap

Laser

treatment

Repositioning of the flap

Fig. 7. Scheme of the LASIK procedure.

Fig. 8. Currently approved refractive corrections using PRK or LASIK.

laser treatment, commonly leading to an effective central thickness of a ‘normal’ cornea (520 µm) of 260 µm. When applying biomechanical data, the maximum myopic corrections (6-mm ablation zone; 160-µm flap thickness) would be limited to –3 D in

a thin (500 µm) and –10 D in a thick (600 µm) cornea. Thus, the maximum myopic correction with LASIK is somewhere in the order of –10 D. Besides the risk of creating a residual corneal thickness of less than 250-270 µm, the reported intraand postoperative complications with LASIK are in the order of 1-2%, comparable with the complication rate that occurs after PRK.35 The acceptable ranges for correcting refractive errors of the eye by means of corneal laser surgery are shown in Figure 8.

Optical aberrations after corneal laser surgery

Both corneal (topographic irregularities) and total wavefront aberrations are found to be significantly increased after corneal laser surgery. In general, the higher the preoperative refraction, the higher the increase in optical aberrations. Such an increase of optical aberrations impairs the visual performance of the eyes treated. To put this in more detail, scotopic visual measures such as low-contrast visual acuity and glare visual acuity suffer most from refractive corrections. This loss of visual performance is more dominant in dim light (larger pupil) because of the strong dependence of the optical aberrations on pupil size.

Seiler et al.36 reported an increased factor of 17.65 (pupil diameter 7 mm) measurable in 15 eyes three months after conventional PRK. Martinez et al.37 have shown that PRK changes the relative contribution of coma-like and spherical-like corneal aberrations by analyzing videokeratographs obtained preand 24 months postoperatively, and for a 7-mm virtual pupil, the total wavefront aberration increased 11-fold from the preoperative situation. Furthermore, while pupillary dilation from 3-7 mm in the preoperative eye only caused a nine-fold increase in total wavefront aberrations, the same dilatation caused a 100-fold increase one month after surgery, and an approximately 70-fold increase thereafter. Similar results were reported earlier by Oliver et al.38 Marcos et al.23 studied the optical response to LASIK surgery for myopia from total and corneal aberration measurements. Because LASIK surgery induces changes in the anterior corneal surface, most changes in the total aberration pattern can be attributed to changes in anterior corneal aberrations. However, because of individual interactions of the aberrations in the ocular components, a combination of corneal and total aberration measurements is critical to understanding individual outcomes. Unfortunately, little is known about optical aberrations when comparing PRK and LASIK, and, therefore, there may be different increased factors for PRK and LASIK due to corneal wound healing.39

The increase in higher-order optical aberrations could have a variety of reasons: pupil centration, preoperative internal optics, biomechanical response, and changes in the anterior corneal surface due to epithelial and stromal wound healing. In particular,

misalignment of the ablation on the cornea, whether this is caused by an initial placement error or by the intraoperative eye movements of the patient, was shown to play an important role in this context.40-43 Alignment of the procedure relative to the eye is a task with six degrees of freedom. Apart from lateral shifts (with a horizontal and a vertical component) and axial movements, rotations with potential components in three axes have to be taken into account.

One of the major difficulties in centering any ophthalmic procedure is the fact that the alignment cannot be completely controlled by the operator himself. He relies on the collaboration of the patient, who is asked to fixate on a target during the measurement and the surgical procedure. Alignment errors can occur systematically or randomly. In the first case, an initial displacement of the treatment relative to the reference coordinate system is maintained as a constant offset error and causes a drastic increase, especially in coma-like aberrations. Precise alignment techniques are required in order to avoid this type of centration error. Random decentrations are due to eye movements such as drifts and tremors, and might be practically avoided by active intraoperative eye tracking. Such eye-tracking systems detect the eye’s motion and move the scanning mirrors that are used for positioning of the laser beam, with respect to the detected eye movement.

Wavefront-guided corneal laser surgery

The aim of customized ablations such as wavefrontguided treatments is, first of all, to avoid an unpleasant increase in higher-order aberrations that might cause the visual performance to deteriorate. Nevertheless, the possibility of improving the optical performance by means of a surgical procedure might further improve the visual outcome to its neuronal limits.

A key concept in wavefront-guided refractive procedures is the transfer of the wavefront aberration measurements into an ablation profile to correct the aberrations.15,44 In more detail, the wavefront measured by means of a wavefront sensor is translated into a set of laser spot positions and directly transferred to the laser without taking the subjectively determined refraction data into consideration. Briefly, the plane wavefront of parallel (laser) light entering the eye is distorted after propagating through the optics of the eye at the retinal image plane, according to geometrical irregularities and inhomogeneities in the refractive index. Since the wavefront aberration W(x,y) is defined by optical paths, its dimension is length in meters or in units of the wavelength (Fig. 9). To first order, the wavefront aberrations introduced by the eye are considered to be independent of the wavelength of the light within the visible spectrum.

As main refractive surface and site of ablation, we accept the anterior corneal surface with a refrac-

tive index of n = 1.337 (tear film) and, in principle, the ablation profile is determined by:

max(W(x,y)) – W(x,y)

This ablation profile a(x,y) has to be approximated by a series of spot ablations, including appropriate overlaps (Fig. 10). The ablation pattern calculated from the wavefront deviation map typically has an optical zone with a diameter of between 6.0 and 7.0 mm, surrounded by a transition zone of up to 2.0 mm.

Wavefront-guided treatments are currently under investigation by various groups. However, the first clinical data presented already demonstrate that wave- front-guided treatments are a promising technique

with the potential for correcting refractive errors, improving visual acuity, and increasing the quality of vision, especially under mesopic conditions. Mrochen et al.45 have reported a prospective study in which 35 eyes of 28 patients were enrolled, with an average preoperative spherical refraction of –4.8

±2.3 D and a cylinder of –1.1 ± 0.9 D. Preand postoperative wavefront analysis was performed with a Tscherning-type aberrometer. A scanning spot laser with a spot size of 1 mm and a laser repetition rate of 200 Hz was used. The eye tracking system had a response time of less than 6 msec. The treatment area diameter ranged from 6-7 mm, surrounded by a transition zone of 1 mm. At three months, 68% of the eyes were within ± 0.5 D and 93.5% within

±1.0 D of emmetropia. Unaided visual acuity (UVA) was 20/20 or better in 93.5% of the cases. None of

the eyes lost more than one line of low contrast, glare, and best-spectacle corrected visual acuity (BCVA). Supernormal vision (20/10 or better in BCVA) was achieved in 16%. The correction of higher-order aberrations (spherical aberration, coma) was insufficient, with an increased factor of the overall rmswavefront error of 1.44 ± 0.74 at three months after surgery. Coma could be better corrected than spherical aberration. Based on these data, wavefront-guided LASIK offers the potential for correcting refractive errors, improving visual acuity, and increasing the quality of vision, especially under mesopic conditions. In order to achieve better correction of the aberrations, further studies are necessary and should include selective overcorrrections of different Zernike components. In addition, further prospectively-con- trolled clinical studies are needed to clarify the major benefits of wavefront-guided LASIK.

Conclusions

There has been rapid evolution in the technology for treating patients with corneal laser surgery. Newly refined diagnostic technology, such as topography and wavefront sensing, and more sophisticated spot laser delivery systems with eye tracking, provide the refractive surgeon with much greater flexibility for tackling the often-challenging optical abnormalities of the human eye. The next decade in corneal laser surgery promises to provide huge gains in visual function by increasing retinal image quality.

References

1.Seiler T, McDonnell PJ: Excimer laser photorefractive keratectomy. Surv Ophthalmol 40:89-118, 1995

2.Volkmann AW: Sehen. In: Wagner R (ed) Handwörterbuch der Physiologie III, pp 289-293. Braunschweig: Vieweg und Sohn 1846

3.Helmholtz H: Handbuch der physiologischen Optik, pp 137147. Leipzig: Leopold Voss 1867

4.Tscherning M: Die monochromatischen Aberrationen des menschlichen Auges. Z Psychol Physiol Sinne 6:456-471, 1894

5.Gullstrand A: Die Dioptrik des Auges, V. Die monochromatischen Aberrationen des Auges. In: Von Helmholtz H (ed) Handbuch der physiologischen Optik, 3rd edn, pp 353-367. Leipzig: Leopold Voss 1909

6.Donders FC: Astigmatismus und cylindrische Glaeser. Verlag von Hermann Peters 1862

7.Howland HC, Howland B: A subjective method for the measurement of monochromatic aberrations of the human eye. J Opt Soc Am 67:1508-1518, 1977

8.Walsh G, Charman WN, Howland HC: Objective technique for determination of monochromatic aberrations of the human eye. J Opt Soc Am 1(9):987-992, 1984

9.Atchison DA, Collins MJ, Wildsoet CF, Christensen J, Waterworth MD: Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique. Vision Res 35(3): 313-323, 1995

10.Artal P, Santamaria J, Bescos J: Retrieval of wave aberra-

tion of human eyes from actual point-spread-function data. J Opt Soc Am 5(8):1201-1206, 1988

11.Santamaria J, Artal P, Bescos J: Determination of the pointspread function of human eyes using a hybrid optical-digi- tal method. J Opt Soc Am 4(6):1109-1114, 1987

12.He JC, Marcos S, Webb RH, Burns SA: Measurement of the wave-front aberration of the eye using a fast psychophysical procedure. J Opt Soc Am 15(9):2449-2456, 1998

13.Liang J, Williams DR, Miller DT: Supernormal vision and high-resolution retinal imaging through adaptive optics. J Opt Soc Am 14:2884-2892, 1997

14.Liang J, Williams DR: Aberrations and retinal image quality of the normal human eye. J Opt Soc Am 14(11):28732883, 1997

15.Mierdel P, Wiegand W, Krinke HE, Kaemmerer M, Seiler

T:Measuring device for determining monochromatic aberration of the human eye. Ophthalmologe 6:441-445, 1997

16.Born M, Wolf E: Principles of Optics. Oxford: Pergamon Press 1987

17.Zernike F: Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form der Phasenkontrastmethode. Physica I 2:689-704, 1934

18.Thibos LN, Applegate RA, Schwiegerling JT, Webb R: Standards for reporting the optical aberrations of eyes. In: McRae S, Applegate RA, Krueger R (eds) Customized Corneal Ablation: The Quest for Super Vision, pp 348-361. Thorofare, NJ: Slack Inc 2001

19.Marechal A: Etude des effets combines de la diffraction et des aberrations geometriques sur l’image d’un point lumineux. Rev Opt: 257-277, 1947

20.Mahajan VN: Aberration theory made simple, Part 2. SPIE Optical Engineering Press 1991

21.Mrochen M, Kaemmerer M, Mierdel P, Krinke HE, Seiler

T:Is the human eye a perfect optic? SPIE Proc Ophthalmic Technol 11(4245):30-36, 2001

22.Artal P, Berrio E, Guirao A, Piers P: Contribution of the corneal and internal surfaces to the changes of ocular aberrations with age. J Opt Soc Am 19:137-143, 2002

23.Marcos S, Babero S, Llorente L, Merayo-Lloves J: Optical response to LASIK surgery for myopia from total and corneal aberration measurements. Invest Ophthalmol Vis Sci 42: 3349-3356, 2001

24.Seiler T, Genth U, Holschbach A, Derse MSO: Aspheric photorefractive keratectomy with excimer laser. Refract Corneal Surg 9:166-172, 1993

25.Gibralter R, Trokel SL: Correction of irregular astigmatism with the excimer laser. Ophthalmology 101(7):1310-1314, 1994

26.Mrochen M, Kaemmerer M, Seiler T: Wavefront-guided laser in situ keratomileusis: early results in three eyes. J Refract Surg 16:116-121, 2000

27.Trokel SL, Srinivasan R, Braren B: Excimer laser surgery of the cornea. Am J Ophthalmol 96:710-715, 1983

28.Valderame GL, Fredin LG, Berry MJ: Temperature distribution in laser-irradiated tissue. SPIE Proc 1427:200-213, 1991

29.Bende T, Seiler T, Wollensak J: Side effects in excimer corneal surgery: corneal thermal gradients. Graefe’s Arch Clin Exp Ophthalmol 226:277-280, 1988

30.Kermani O, Lubatschowski H: Struktur und Dynamic photoakustischer Schockwellen bei der 193 nm Excimerlaserphotoablation. Fortschr Ophthalmol 88:748-753, 1991

31.Kochevar IE: Cytotoxicity and mutagenicity of excimer laser radiation. Laser Surg Med 9:440-445, 1989

32.Lubatschowski H, Kermani O: 193 nm Excimerlaserphotoablation der Hornhaut: Spektrum und Transmissionsverhalten von Sekundärstrahlung. Ophthalmologe 89:134-138, 1992

33.Machette LS, Waynant RW, Royston DD et al: Induction

of lambda prophage near the site of focused UV laser radiation. Photochem Photobiol 49:161-167, 1989

34.Munnerlyn CR, Koons SJ, Marshall J: Photorefractive keratectomy: a technique for laser refractive surgery. J Cataract Refract Surg 14:46-52, 1988

35.Knorz MC, Jendritza B, Hugger P, Liermann A: Komplikationen der Laser-in-situ Keratomileusis (LASIK). Ophthalmologe 96:503-508, 1999

36.Seiler T, Kaemmerer M, Mierdel P, Krinke HE: Ocular optical aberrations after photorefractive keratectomy for myopia and myopic astigmatism. Arch Ophthalmol 118:1721, 2000

37.Martinez CE, Applegate RA, Klyce SD, McDonald MB, Median JP, Howland HC: Effect of pupillary dilation on corneal optical aberrations after photorefractive keratectomy. Arch Ophthalmol 116:1053-1062, 1998

38.Oliver KM, Hemenger RP, Corbett MC et al: Corneal optical aberrations induced by photorefractive keratectomy. J Refract Surg 13:246-254, 1997

39.Oshika T, Klyce SD, Applegate RA, Howland HC, Danasoury MAE: Comparison of corneal wavefront aberrations after photorefractive keratectomy and laser in situ kerato-

mileusis. Am J Ophthalmol 127(1):1-7, 1999

40.Verdon W, Bullimore M, Maloney RK: Visual performance after photorefractive keratectomy. Arch Ophthalmol 144: 1465-1472, 1996

41.Mrochen M, Kaemmerer M, Mierdel P, Seiler T: Increased higher-order optical aberrations after laser refractive surgery; a problem of subclinical decentration. J Cataract Refract Surg 27:362-369, 2001

42.Guirao A, Williams DR, Cox IG: Effect of rotation and translation on the expected benefit of an ideal method to correct the eye’s higher-order aberrations. J Opt Soc Am 18(5):1003-1015, 2001

43.Bueeler M, Mrochen M, Seiler T: Required accuracy of lateral centration in aberration sensing and wavefront guided treatments. J Cataract Refract Surg 2002 (in press)

44.Klein SA: Optimal corneal ablation for eyes with arbitrary Hartmann-Shack aberrations. J Opt Soc Am A 15(9):25802588, 1998

45.Mrochen M, Kaemmerer M, Seiler T: Clinical results of wavefront-guided LASIK at 3 months after surgery. J Cataract Refract Surg 27:201-207, 2001