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1 From the Instituto de Óptica "Daza de Valdés," Consejo Superior de Investigaciones Científicas, Spain; and 2 Instituto de Oftalmobiología Aplicada (IOBA), Universidad de Valladolid, Spain.
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Abstract |
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METHODS. The ocular aberrations of 22 normal myopic eyes (preoperative refraction ranged from -13 to -2 D) were measured before (2.9 ± 4.3 weeks) and after (7.7 ± 3.2 weeks) LASIK refractive surgery using a laser ray tracing technique. A set of laser pencils is sequentially delivered onto the eye through different pupil locations. For each ray, the corresponding retinal image is collected on a CCD camera. The displacement of the image centroid with respect to a reference provides direct information of the ocular aberrations. Root-mean-square (RMS) wavefront error was taken as image quality metric.
RESULTS. RMS wavefront error increased significantly in all eyes but two after surgery. On average, LASIK induced a significant (P = 0.0003) 1.9-fold increase in the RMS error for a 6.5-mm pupil. The main contribution was due to the increase (fourfold, P < 0.0001) of spherical aberration. The increase in the RMS for a 3-mm pupil (1.7-fold) was also significant (P = 0.02). The modulation transfer (computed for 6.5-mm pupil) decreased on average by a factor of 2 for middle-high spatial frequencies.
CONCLUSIONS. (1) Laser ray tracing is a well-suited, robust, and reliable technique for the evaluation of the change of ocular aberrations with refractive surgery. (2) Refractive surgery induces important amounts of 3rd and higher order aberrations. The largest increase occurs for spherical aberration. Decentration of the ablation pattern seems to generate 3rd order aberrations. (3) This result is important for the design of customized ablation algorithms, which should cancel existing preoperative aberrations while avoiding the generation of new aberrations.
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Introduction |
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In contrast to the fast evolution of refractive surgery, there has not been such an update of the clinical methods used to evaluate objectively the impact of refractive surgery on the overall optical quality. Routine postoperative evaluation consists mainly of measuring, under photopic conditions (small pupil sizes), subjective refraction, visual acuity, and, in some cases, contrast sensitivity (CSF). Some visual acuity loss, particularly for low contrast charts and dilated pupils has been reported after surgery.3 4
Most of the analysis reported in the literature is based on corneal topography data.5 6 7 8 Corneal aberrations are computed from corneal height maps, which provide information on the imaging-forming capability of the cornea alone. Results from different authors indicate that corneal aberrations increase substantially after refractive surgery, which suggests a degradation of the overall image quality.5 9
Although the optical changes induced in refractive surgery occur on the cornea and the anterior corneal surface provides the main contribution to refraction, corneal aberrations are not sufficient to describe the overall optical quality of the eye, because other parameters (position, thickness, and refractive index of the lens, axial length, or pupil centration) also play an important role in image formation. Predictions of the overall optical quality have been made using virtual ray-tracing in model eyes provided with measured10 or theoretical11 surgical corneal shapes. Nevertheless, the experimental measurement of the overall ocular aberrations is the most direct and accurate way to evaluate the effects of refractive surgery on global image quality, and it can be directly related to visual performance. Several objective techniques are available for the measurement of ocular aberrations,12 13 14 15 some of which have already been used to measure the effect of refractive surgery on image quality. Campbell et al.16 collected data in PRK patients and in a control group, using a Hartmann-Shack wavefront sensor, and found a degradation of image quality after PRK. The image analysis was limited to the computation of the aberration at the edge of the pupil, probably because of indexing problems of the particular implementation of the Hartmann-Shack technique used in that study or to the degraded quality of the postsurgical data. Thibos and Hong17 presented data on one eye measured with a Hartmann-Shack aberrometer both before and on the day after LASIK refractive surgery to demonstrate the applicability of the technique and reported the limits to the technique for highly aberrated eyes. To our knowledge, there is only one published quantitative study by Seiler et al.18 studying in detail the change in the overall ocular aberrations induced by conventional refractive surgery (PRK), for which they used a video-aberroscope of the Tscherning type.14 This study shows that the overall aberrations increase significantly after surgery especially for large pupils, the spherical aberration becoming the dominant aberration.
In the present article, we show the change of the individual ocular aberrations induced by standard myopic LASIK corneal refractive surgery, by measuring the aberration pattern before and after surgery with a laser ray tracing (LRT) technique.15 The sequential nature of the LRT (as opposed to the parallel nature of other techniques) permits one to measure large amounts of aberrations and seems especially suitable for pathologic eyes. As concluded by previous studies, we found that with the current standard corneal refractive surgery procedures, the compensation of low-order refractive errors (such as myopia) is associated with the generation of high-order aberrations.
The next generation of refractive surgery procedures is heading toward a customized ablation, aiming at the cancellation of not only low-order aberrations, but also of the individual high-order aberrations.19 20 21 Algorithms to produce an aberration-free eye should also avoid the generation of high-order aberrations (as we show in this article) inherent to standard ablation patterns.9
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Methods |
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We analyzed left and right eyes independently for two reasons: (1) recent work indicates that the pattern of aberration is not necessarily symmetric between left and right eyes of the same subject,22 and (2) surgery is conducted independently for left and right eyes. Postoperative measurements were conducted between 24 and 103 days (average, 54 ± 23 days), because recent studies report healing process duration of less than 1 month.3 Surgery and follow-up study of the patients was performed at the Instituto de Oftalmobiología Aplicada, University of Valladolid (Spain). The equipment used for LASIK was a narrow-beam (flying spot) excimer laser (Chiron Technolas 217-C-LASIK; Bausch & Lomb Surgical), with an emission wavelength of 193 nm, a fixed pulse repetition rate of 50 Hz, and a radiant exposure of 400 mJ. The hinged flap, set to 180-µm depth and 8.5-mm diameter, was cut with a Hansatome microkeratome and was always superior. All patients underwent photoablation of a 6-mm optical zone, with a 9-mm transition zone. The surgery was assisted by the eye tracker in 20 of the 22 eyes.
LRT Measurements
Ocular aberrations were measured using LRT, which is an
objective technique developed at the Institute of Optics in Madrid
(Spain).15
23
24
Subjects’ pupils were dilated by
instillation of 1 drop of tropicamide 1%, and typically both eyes were
measured in a single session. Stabilization was achieved by means of a
dental impression. Each individual run, consisting of 37 rays, lasted
between 4 and 14 seconds (depending on the CCD camera used). An entire
session (including consent form explanation, dental impression
fabrication, pupil dilation, and the recording of five successive runs
in similar conditions for each eye) lasted around 45 minutes. Defocus
was corrected by means of a trial lens placed in the front of the eye
in the manner of spectacles. For patients for whom the trial lens could
not be placed closer than 40 mm because of the face anatomy or for
spherical errors <5 D, the subject was left uncorrected, because the
system allows to perform measurements in eyes with ±10 D of spherical
error without compensation. The eye’s pupil is centered to the optical
axis of the system by means of a XYZ positioner on which the dental
impression is mounted. The eye’s pupil is viewed on a TV monitor to
ensure a correct centration throughout the experiment.
The basic setup of the LRT technique is depicted in Figure 1 . A set of parallel laser pencils is delivered sequentially onto the eye’s pupil. The pupil was sampled at steps of 1-mm and by following a hexagonal pattern (37 rays for a 6.5-mm effective pupil). The laser source was a green (543 nm) HeNe laser. Irradiance was at least one order of magnitude below safety standards.25 Each retinal image (associated to a given pupil location) is projected onto a CCD camera and recorded. We compute subsequently the displacement (A'O') of the image’s centroid with respect to a reference position, taken as the centroid for the image associated to the center of the pupil (chief ray). This geometrical distance (A'O') is equal (in angular units) to the displacement between the corresponding retinal images (AO).26 AO is proportional to the slope (or derivative) of the wavefront at the pupil position sampled.27 The combined plot of all the image centroids is called "spot diagram," which is a good approximation to the shape of the retinal PSF.28 In the spot diagram associated to an aberration-free eye, all the spots would overlap. As an example, Figure 2A shows the series of 37 images recorded for eye 17 after surgery. Images are arranged according to the associated entry pupil position. Figure 2B shows the corresponding retinal spot diagram. Five runs (each consisting of 37 images) were collected per eye both in the pre- and in the post-LASIK session.
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Results |
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Change in Overall Image Quality (RMS Wavefront Error)
Figure 5
shows the RMS (for 3rd and higher order aberrations), for all 22 eyes,
before (white bars) and after (black bars) LASIK surgery, for a 6.5-mm
pupil. Eyes are sorted by preoperative spherical error. Eyes 1 to 12
had preoperative myopic spherical errors below 6.5 D, whereas eyes 13
to 22 had errors between 6.5 and 13 D.
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Table 1 (first row) shows the average (±SD) preoperative and postoperative RMS wavefront error and average increase in RMS ratio (post-RMS/pre-RMS) with LASIK surgery for this group of patients, for a 6.5-mm pupil (columns 1–3) and for a 3-mm pupil (columns 6–8). The increase in aberrations induced by surgery is smaller for 3 than for 6.5 mm. If we exclude 2nd order aberrations (defocus and astigmatism), the average increase of the wavefront error is approximately 67%. The increase of RMS for a 6.5-mm pupil is highly statistically significant (P < 0.0003) and marginally statistically significant for a 3-mm pupil (P = 0.0212), as shown in columns 4 and 9, respectively.
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We did not find any significant increase in high order terms (5th and higher), either for a 6.5- or a 3-mm pupil. The corresponding pre- and postoperative values, SDs, average increase and P values are shown in Table 1 , line 4.
Modulation Transfer Function
Modulation Transfer Functions (MTF; contrast loss as a function of
spatial frequency) before and after surgery was computed for each eye
from the corresponding wave aberration, assuming a 6.5-mm pupil and
ignoring apodization imposed by the Stiles-Crawford effect.
Contribution of tilts, defocus, and astigmatism (all
Z1i and
Z2j)29
was cancelled.
Figure 8 shows the average MTF (logarithmic scale, radial profile) for the pre- and the post-LASIK eyes, together with the corresponding diffraction-limited MTF (6.5-mm pupil diameter and 543-nm wavelength) for comparison purposes. Error bars represent ± SE across eyes. There is a significant contrast loss for all spatial frequencies. As an example, the MTF for 30c/deg decreases by a factor of 2, on average.
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Discussion |
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Comparison with Previous Studies
Although a direct comparison across studies is limited by the
particular surgical procedures and the group of patients under test, we
can get some insight on (i) the average differences in the optical
quality and visual performance outcomes provided by the different
surgical techniques and (ii) the complementary information provided by
the different methods of evaluation (corneal topography, visual
performance, and overall aberration measurements).
Differences in the surgical procedures include the following: (1) type of surgery (RK, PRK, or LASIK); (2) ablation zone and transition zones diameters; (3) type of laser (wide beam with a variable-size diaphragm or narrow-beam flying spot laser); (4) presence or not of an eye tracker to compensate for eye movements; (5) surgeon’s choice of reference axis; and (6) type of microkeratome and flap cutting procedures. Differences in the population under test include the following: (1) different age groups; (2) different preoperative spherical error range; and (3) different preoperative astigmatism and higher order aberration pattern.
Studies Based on Corneal Aberrations.
Our results agree well with previous studies based on corneal
topography data, which also report that corneal aberrations
increase substantially after refractive surgery, suggesting a
degradation of overall image quality. Applegate et al.8
reported an increase of corneal aberrations of RK
patients at large pupil sizes, which was highly correlated with the
decrease of visual performance (CSF). Verdon et al.4
found
similar results for PRK patients. Oshika et al.5
found an
increase of 3rd and higher order corneal aberrations (2.7-fold for
LASIK and 2.3-fold for PRK), with respect to preoperative values in the
same eyes, comparable with the 1.91-fold increase found in the present
study for overall aberrations after LASIK surgery. We found a greater
relative contribution of spherical aberration, which increases with the
level of attempted correction. The correlation between preoperative
refraction and induced spherical aberration agrees with results by
Schwiegerling,9
by Martinez et al.,6
and by
Applegate et al.8
for corneal aberrations alone or by
Hersh et al.31
based on postoperative corneal asphericity.
Studies Based on Wave Aberration Measurements.
To our knowledge, there is only one published quantitative
study18
on the changes in individual optical aberrations
induced by standard refractive surgery (PRK). In this study the total
wavefront error (RMS), excluding first- and second-order aberrations,
increases by a factor of 4.2 on average (P < 0.001).
However, such increase was found to be statistically significant
(P < 0.05) only for large pupils (6–7 mm), whereas we
find it significant for both large (6.5-mm) and small (3-mm) pupils.
Although in preoperative eyes third-order aberrations are dominant,
Seiler et al. found that 4th-order aberrations (spherical-type)
dominated on postoperative eyes. We found that 3rd order aberrations
are still dominant after surgery, despite the fact that the patients in
our study presented higher preoperative myopia (-6.5 D on average, as
opposed to -4.8 D in Seiler’s), which tends to induce larger amounts
of spherical aberration. This difference might be due to higher
induction rates of spherical aberration for a given attempted
correction in the surgical procedure used on the patients from
Seiler’s study. Table 1
displays the increase ratios obtained in this
study and by Seiler et al. Note that they fitted 27 Zernike
coefficients (up to 6th order), whereas we fitted 35 (up to 7th order).
Although both studies show a significant degradation of best-corrected
optical quality after refractive surgery, we found an average RMS
increase half of that found by Seiler et al. Intersubject variability
is smaller in our group of patients (lower P values).
Differences between the surgical techniques (PRK in Seiler et al.
study, LASIK in our study) may be the main reason for the discrepancy.
Although some authors have reported better outcome for PRK in terms of
optical quality from corneal topography data,5
we believe
that part of the difference is due to the improved system used in the
surgery reported here (i.e., incorporation of an eye tracker device and
flying spot laser).
Studies Based on Visual Performance.
The change in visual performance after LASIK surgery has been
frequently assessed in terms of visual acuity (usually number of lines
lost), which, in general, does not suffer a significant decrease.
Recent data indicate that most changes occur in contrast sensitivity
(CSF), low contrast visual acuity, and visual acuity measured under low
illumination (i.e., with large pupils). A decrease in the MTF for large
pupils, as that shown in Figure 8
must be directly correlated to a
decrease in CSF at low light levels. This is in agreement with findings
by Applegate et al.8
on RK patients, who observed a good
correlation between the increase in the variance of the corneal wave
aberration and the decrease of the area under the CSF.
Causes for the Increase of Ocular Aberrations after Surgery
Corneal Asphericity.
Our results show that spherical aberration is the aberration that has
the largest increase after refractive surgery. Also, as found in
previous studies, induced spherical aberration is highly correlated
with preoperative refraction.7
9
This indicates that the
change in the asphericity of the cornea31
induced by
current ablation algorithms is the main cause of retinal image quality
degradation after conventional LASIK surgery.
Decentration.
There seems to be a direct relation between the amount of coma induced
and the decentration of the ablation pattern. In many cases the
ablation pattern appears slightly decentered. The laser system used in
this study was provided with an eye tracker, which maintains centration
by compensating for involuntary eye movements. Two eyes (14 and 17) for
which the eye tracker was off during surgery had an increase in
coma-like aberrations (4.2 and 2.3, respectively) above the average
(2.1-fold). The use of an eye tracker might explain the fact that the
average increase in coma-like aberrations in our study is less than
half the increase found by Seiler et al.18
(4.7- versus
2.1-fold). Nevertheless, despite the improvement in centration achieved
in eye-tracker–assisted surgeries, it seems to be a factor that can be
still further improved and that could reduce considerably the impact of
surgery on image quality. In agreement with Tsai et al.,32
our results suggest that an eye tracker helps to avoid severe
decentration but does not ensure a perfect centration.
Corneal Irregularities.
We have found a slight increase of 5th and higher order aberrations,
not statistically significant (P = 0.17), which is in
agreement with Seiler et al.18
In their study, 5th and
higher order aberrations had an average 3.9 increase, but the increase
was significant only for 2 of the 13 coefficients. It seems that the
impact of surgery occurs on 3rd and 4th order aberrations, whereas 5th
and higher remain almost unaffected. This might suggest that PRK
and LASIK do not induce microirregularities in the cornea (at
least of sizes larger than the measurement beam size, which is
0.5 mm in our study).
Haze.
Corneal haze is due to the presence of stromal opacities induced by
refractive surgery (probably caused by an increased reflectivity of
anterior stromal wound healing keratocytes),33
which
produces a loss of corneal transparency, and to increased scattering.
The LRT technique is unable to quantify effects operating at scale
below the beam size, and therefore an objective evaluation of the
contribution of corneal haze should be addressed by other methods.
Wound Healing.
Histologic experiments have shown that wound healing is a major cause
of refractive instability and intersubject variability outcomes.
Although stromal reaction seems to be less extensive in LASIK than PRK,
it is still one of the main concerns on the operation
outcomes.34
35
Wound healing is expected to be similar in
left and right eyes of the same patient, and therefore its impact on
the aberration pattern should not change between eyes of the same
subject. The correlation between the left and right RMS wavefront does
not decrease significantly after surgery (coefficient of correlation:
preoperative, r = 0.65; postoperative,
r = 0.58). The major difference comes from coma-like
terms (r = 0.45 and r = 0.41,
respectively), which depends on centration during surgery (and
therefore is independent between eyes), whereas the correlation between
left and right eyes for spherical aberration remains unchanged
(r = 0.84 and r = 0.84, respectively).
The fact that the two eyes not following the trend in Figure 7
(those
who experienced little increase in spherical aberration despite having
>6 D of preoperative myopia) correspond to the same subject may
suggest a potential role of wound healing on the surprisingly good
outcome for this patient.
Time after Surgery.
Wave aberration measurements were conducted from 24 to 103 days after
surgery. Although refractive stability after LASIK seems to be achieved
in a short period, one may argue that differences in the recovery time
across eyes may be influencing the results. For a group of eyes with
close preoperative spherical errors (-5.25 through -7.5 D), we did
not find any correlation between time after surgery and RMS wavefront
error (r = 0.11).
Implications of Our Results
Our results confirm that standard refractive surgery procedures
induce considerable amounts of 3rd and higher order overall
aberrations. Their impact increases notably for large pupil sizes,
which explains reported experience of night vision problems, such as
halos.36
The decrease in contrast modulation predicted by
our measurements explains a decrease of the CSF under low light levels
or of the low contrast visual acuity.3
The presence of
asymmetrical aberrations affects not only the modulus of the optical
transfer function (MTF), but also its phase. A phase change can cause
ghost or double images, contrast reversals, and halos, which are not
necessarily detected during clinical routine measurements. Thus, the
objective measure of overall aberrations results on a fast and valuable
method to evaluate the outcomes of refractive surgery, in many ways
more complete than standard clinical subjective procedures.
Our results show the lowest reported degree of image quality degradation after conventional (non–wavefront-guided) myopic LASIK surgery, which suggests that procedures, laser systems, and algorithms have improved over the years. However, the amount of spherical aberration induced, inherent to the ablation profile, suggests that further improvements are needed. Schwiegerling9 computed the ideal ablation pattern for a particular eye that would minimize the impact of spherical aberration while correcting the spherical error. He found that this ideal pattern would require a deeper ablation of the central cornea and a more abrupt transition at the edge of the optical zone, which is a drawback, particularly for higher attempted corrections.
The knowledge of the individual aberration pattern before surgery has attracted surgeons to the idea of surgically canceling not only conventional refractive errors, but also the higher order aberrations naturally occurring in each eye (customized ablation). The first wavefront-guided refractive surgeries have already been carried out,19 20 with variable results. From ours as well as from previous data in the literature, it becomes clear that, before the cancellation of existing high-order aberrations, design of optimal ablation algorithms and procedures avoiding new aberrations while attaining the desired refractive error correction is essential. The impact of wound healing on a fine corneal photograph-sculpture still remains unclear, and other alternatives (such as customized intraocular lenses) are being suggested.37
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Acknowledgements |
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Footnotes |
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Submitted for publication October 18, 2000; revised January 16, 2001; accepted January 24, 2001.
Commercial relationships policy: N.
The publication costs of this article were defrayed in part by page
charge payment. This article must therefore be marked
"advertisement" in accordance with 18 U.S.C. 
1734
solely to indicate this fact.
Corresponding author: Susana Marcos, Instituto de Óptica "Daza de Valdés," Consejo Superior de Investigaciones Científicas (CSIC), Serrano 121, 28006 Madrid, Spain. susana{at}io.cfmac.csic.es
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, entry pupils within 6.5-mm
pupil). The extent of the retinal field represented is 1.5°.
) and after (
) LASIK refractive
surgery. Data are sorted by ascending preoperative defocus.
