In the modern era of aberrometry, optical astronomy contributed to the later development of an adaptive optical system to compensate for optical aberrations in the human eye. Initially, wavefront sensors were developed to simply analyze and quantify the higher order aberrations.12 Secondarily, the use of the wavefront sensing permitted the development of new excimer laser platforms designed to correct lower and higher order aberrations of the eye, initiating wavefront customized ablations.34 Several different technologies have been used to identify and correct optical aberrations in the eye. The majority of commercially available wavefront sensors are based on the Shack-Hartmann principle, but other available systems use different principles such as Tscherning aberrometry, Tracey retinal ray-tracing, scanning slit refractometry, or spatially resolved refractometry for wavefront analysis.5-12
Several recent publications have analyzed the results of customized laser treatments or wavefront abnormalities present in pathological corneas.5 7913"20 However, few studies have evaluated wavefront aberrations in normal eyes.21"26 The present study analyzed monochromatic aberrations and wavefront indices obtained in normal eyes using the WaveScan WavePrint system (VISX, Santa Clara, Calif). The accuracy of the wavefront-derived refractive data compared to manifest refraction performed with a phoropter was also evaluated.
PATIENTS AND METHODS
Between October 2002 and June 2003, 418 eyes of 226 consecutive patients had wavefront measurements obtained at the Refractive Surgical Center of the University of Washington, Seattle, Washington. This retrospective study was approved by the Investigational Review Board at the University of Washington.
Only patients with normal eyes who had not had previous surgery were included in the study. Patients were excluded if they had previous ocular diseases, trauma, or best spectacle-corrected visual acuity <20/20. All patients were aged ^18 years. Patients were excluded if they were taking medications that had known effects on accommodation. Soft contact lens wearers discontinued lens wear for a minimum of 3 days prior to examination. Gas permeable contact lenses were discontinued for at least 3 weeks prior to examination. Only patients without any abnormality on the corneal topography examination were enrolled in the study.
WAVEFRONT DEVICE AND MEASUREMENTS
The wavefront device used was the WaveScan WavePrint system (VISX, Santa Clara, Calif), which is based on the Shack-Hartmann principle.8 The system makes use of a laser beam approximately 1 mm in diameter and aimed at the fovea to create a point light source. The reflected light exits the eye to define the wavefront aberration pattern captured at the level of the entrance pupil by a charged-couple-device matrix camera. The wavefront pattern is defined by a micro lenslet array (217 small lenses arranged in a hexagonal array) that partitions the reflected wavefront of light emerging from the eye into a larger number of smaller wavefronts that are focused into a small spot.
Zernike polynomials were used to decompose the measured wavefront into its corresponding aberration components, using a double indexing scheme. The magnitude of each coefficient of the Zernike polynomial was represented using the micrometer unit. The Wavescan device also provides the "effective blur" index, which theoretically represents an objective measurement of the patient's expected refractive error, including the higher order aberration (in terms of spherical equivalent refraction).
The wavefront examination was performed by a VISX certified technician in accordance with the manufacturer's guidelines. Calibration was checked daily. All wavefront measurements were performed in a dark room before cycloplegic drops were dispensed and two different wavefront aperture diameters (3 and 6 mm) were used to capture the wavefront aberrations. We analyzed coma (Z1 and Z1), trefoil (Z"3 and Z3), and spherical aberrations (Z4, Z2, Z°, Z2, and Z4O.
Data were acquired from two acuity maps, a point spread function graphic, and the individual description of each aberration. These included the optical aberration index, total aberrations (root-mean-square [RMS] error from the acuity map), higher order aberrations (RMS error from the Wavefront higher order aberrations map), effective blur, and the level of each individual aberration: defocus, astigmatism, coma, trefoil, and spherical aberrations from the Normalized Polar Zernike Coefficient Table provided by the instrument. The higher order aberrations analyzed with the Wavescan device were up to 6th order. The wavefront autorefraction was determined using a vertex distance adjusted to 12.0 mm (from the corneal apex) and the examination was performed in a dark room. Auto focus provided by the instrument was used in all cases. The wavefront refractions were derived from a 6-mm pupil diameter when comparing the wavefront-determined refractions with manifest refractions.
The manifest refraction was acquired in a dark room using a Snellen chart and a ±0.25 D Jackson cross cylinder with fogging by the same technician before the cycloplegic drops were dispensed.
In this decomposition method, M represents the spherical equivalent refraction (S=spherical and C=cylinder); J0 represents the Jackson cross cylinder equivalent to a conventional cylinder with power at axis a = 0° = 180°; and J45 represents the Jackson cross cylinder with power at axis a = 45°.
Higher Order Aberrations Acquired Under 6-mm Pupil Diameter
Figure 1. Higher order aberrations obtained at 3- and 6-mm pupil diameter (HOA = higher order aberrations).
Data analysis was performed through a factorial analysis of variance. Differences were considered statistically significant when P<.05.
The mean age of patients undergoing wavefront evaluation was 42. 8± 10.5 years (range: 20 to 67 years). Male patients provided 53% of the eyes (223 eyes).
The mean spherical equivalent refraction acquired with the wavefront was -3.4 ±3.1 D (range: -10.7 to + 5.4 D). The mean sphere was 3.9±3.3 D (range: -11.7 to +5.2 D), and the mean cylinder was 1.1 ±1.0 D (range: 0.0 to 5.4 D).
The mean optical aberration index, which represents the percentage of higher order aberration in each eye, was 10.3% ±11.5% (range: 0.3% to 29%), acquired in a 6-mm wavefront aperture. The optical aberration index is defined as OAI = 1 - e(RMS), where 0 stands for a perfect optical system and 1 for infinite aberrations.
The higher order aberrations were determined in microns (pm) and its value represented by the RMS. The mean RMS value for the second through sixth order monochromatic aberrations was 4.0±2.4 µp? (range: 0.2 to 12.3 µm).
The mean value of higher order aberrations acquired at 6-mm pupil diameter was 0.2±0.1 µp? (range: 0.0 to 0.5 µp?). The mean values detected for defocus and astigmatism were 3.7±2.9 µm (range: -3.7 to 10.7 µm) and 0.7±0.7 µm (range: 0.0 to 3.6 µm), respectively.
The mean effective blur, acquired from the point spread function graphic, was 3.8±2.2 D (range: 0.3 to 12.3 D). (Despite the practical limitations to estimate visual quality from wavefront measurements, the effective blur provides the total amount of defocus necessary to theoretically produce the same level of visual blurriness as that resulting from the total aberrations of the eye.)
No statistically significant difference was noted in the mean higher order aberrations between males (0.2 µp?) and females (0.2 µm) or between right (0.3 µp?) and left (0.2 µm) eyes (P>.05).
The Table shows the higher order aberration values and each individual aberration acquired under 6-mm pupil diameter. In addition, Figure 1 shows the difference between values according to two different wavefront apertures (3- and 6-mm diameter). Figure 2 shows the distribution of higher order aberrations in different age groups, acquired under 6-mm pupil diameter.
Patients were also stratified into six different groups according to their refraction error, and their higher order aberrations, acquired under a 6-mm pupil diameter, were analyzed (Fig 3).
The wavefront-derived refractive error was compared to the manifest refraction obtained using a phoropter with a ±0.25 Jackson cross cylinder. The mean spherical equivalent refraction obtained with wavefront was -3.4±3.lD(range: -10.7 to +5.4 D) and the mean spherical equivalent refraction obtained from manifest refraction was - 3.0±3.0 D (range: -10.1 to + 5.2 D). The mean differences in sphere and cylinder components were - 0.4±0.4 D and -0.3 ±0.3 D, respectively. Figure 4 provides the vector power analysis of wavefront-derived refractive error, manifest refraction, and the differences between them.
Figure 5 illustrates the differences between the wavefront-derived refractive error and manifest refraction in patients divided according to refractive error. No statistically significant difference was noted between measurements in all groups; however, the standard deviation was higher in the high myopia group.
Twenty-eight (6.7%) eyes were excluded from this study because we were unable to obtain wavefront maps or because the analysis was unreliable (two or more red lights at the review screen).
Figure 2. Variations in higher order aberrations with age. The higher order aberrations were acquired under 6-mm pupil diameter (HOA = higher order aberrations, Sph Aber = spherical aberrations, n = number of patients).
Figure 3. Higher order aberrations in groups separated according to the spherical equivalent (HOA = higher order aberrations, Sph Aber = spherical aberrations, n = number of patients).
Wavefront analysis is a promising technology that has great potential for diagnosis of visual and corneal abnormalities and also provides data for using an excimer laser to correct higher order aberrations when they affect vision quality in an individual patient. Many studies have described the wavefront parameters obtained after refractive surgery.3'5"7'9,17"20 Other studies have compared the results obtained after conventional laser surgery with those obtained after customized laser surgery guided by wavefront analysis.28 We believe more reference data is needed in the refractive surgery population. A better knowledge of aberrations in the eye will lead to improved refractive error correction and provide a better understanding of patient complaints related to quality of vision after surgery.
It is difficult to compare data obtained with different wavefront equipment because of differences between the instruments provided by different manufacturers and the lack of a standard presentation format. However, accuracy and repeatability of higher order RMS measurements acquired with Shack-Hartmann aberrometers have been confirmed.29 This study provides reference values for the VISX WaveScan system, collected from normal candidates to laser vision correction. Despite the controversial lack of correlation between refractive level and amount of higher order aberration, it is important to stress that the population herein analyzed is myopically biased compared to the general population.23
In agreement with previous studies,2425 no statistically significant difference was noted in the higher order aberrations between right and left eyes when mirror symmetry was taken into account. Despite a random variation in the eye's aberrations from subject to subject, Porter et al25 reported a significant correlation between contralateral eyes for most of the higher order aberrations.
Vinciguerra et al30 analyzed the physiological aberrations in 1000 eyes, but only evaluated the aberrations present in the cornea. Mrochen et al31 analyzed corneal and total wavefront aberrations in myopic eyes and did not find a correlation between both for most high order aberrations. It seems that corneal and wavefront aberrations are optically balanced and because the cornea has been the main target for correcting refractive errors, the importance of its individual aberrations has also been investigated.32
In the present study, defocus and astigmatism were found to be the most significant aberrations in the eyes of patients being evaluated for refractive surgery. Porter et al25 identified defocus and astigmatism as responsible for 93% of the total ocular aberrations.
Figure 4. Scattergrams representing the power vector analysis of A) manifest refraction, B) wavefront-derived refractive error, and C) difference between the manifest refraction and wavefront-derived refractive error.
Similar to previous studies, we found significantly less higher order aberrations when wavefront examinations were acquired using a central 3-mm pupil in comparison to a larger pupil diameter (6 mm).5,6,2023 A significant increase was noted in the mean value of total and individual higher order aberrations obtained with 6-mm pupil size in comparison to the values obtained with 3-mm pupil size. The most frequent higher order aberrations acquired with the 3- and 6-mm pupil diameter were coma, trefoil, and spherical aberrations, respectively. These findings are in agreement with the data provided by Howland and Howland,26 which identified coma-like aberrations as the most prevalent group of higher order aberrations in the normal population. Even at 6-mm pupil size, coma remains the most prevalent aberration. In unmanipulated presurgical eyes, positive spherical aberrations of the cornea are at least partially compensated for by the negative spherical aberrations of the lens.20 However, a significant increase in spherical aberrations occurs when measurements are obtained with 6-mm pupil diameter.
Castejón-Mochón et al21 studied 108 eyes of a normal population and found that third to fifth order aberrations accounted for 9.2% of the total ocular aberrations, acquired under 5-mm pupil diameter. Wang and Koch24 also measured the ocular higher order aberrations using the Wavescan device and the mean RMS values of higher order aberrations, spherical-like aberrations, and coma-like aberrations were 0.305±0.095 pm, 0.128±0.074 µp?, and 0.170±0.089 µp?, respectively. These results are comparable to ours. The slightly higher values obtained by these authors are likely due to differences in patient inclusion criteria. In the present study, only patients with best spectacle-corrected visual acuity of 20/20 and completely normal corneal topography maps were included. Wang and Koch24 used criteria that were not as stringent.
We noted a progressive increase in higher order aberrations in older patients, which confirms the results of previous studies.24'313335 McLellan et al34 studied 38 normal eyes and observed a positive correlation between RMS wavefront error and age, analyzing high order aberration up to fourth order (P=. 042) and even more significant correlation analyzing higher order aberration up to seventh order (P=. 0002). Guirao et al35 also found a linear positive correlation (P<.003) between wavefront higher order aberration (RMS) and age for three ranges of pupil diameter (4,5, and 6 mm).
No statistically significant differences in wavefront measurements were noted between different groups of patients separated according to spherical equivalent refraction. However, the hyperopic groups had slightly higher values of higher order aberrations. This trend could be due to the relatively small number of patients in the hyperopic group, as well as a slightly higher age of patients in this group. Cheng et al23 analyzed 200 normal eyes distributed into five different refractive error groups and did not find any significant correlation between higher order aberrations and refractive error.
The refractive error determined from wavefront analysis provided reliable measurements compared to the fogged manifest refraction refined with a Jackson cross cylinder. Wang et al36 studied 28 normal eyes and reported a mean difference in spherical equivalent refraction, sphere, and cylinder of -0.35±0.40 D, -0.23±0.53 D, and - 0.25±0.38 D, respectively, between the WaveScandetermined refractive error and the manifest refraction. Our results are similar, although we did notice a larger difference between wavefront-determined refractive error and manifest refraction in eyes with high refractive errors. Patients with very high refractive errors, myopia or hyperopia, appear to have more variability with either method. Vector power analysis showed a satisfactory agreement between wavefront and manifest refraction in cylinder and cylinder axis. The main advantage of representing refractive errors by power vectors is that each of the three fundamental components of a power vector is mathematically independent of the others.
Figure 5. Difference between manifest refraction and wavefront-derived refractive error separated according to the level of refraction. (ΔM = difference between wavefront-derived and manifest refraction in terms of spherical equivalent; ΔJO = J -vector difference between the wavefront and manifest cylindrical, considering the power at axis α = 0° = 180°; ΔJ45 = J-vector difference between the wavefront and manifest cylindrical, considering the power at axis a = 45°) (P>.08; error bars = standard deviation)
It is the authors' opinion that the wavefront-determined refractive error should not be used as a substitute for the manifest refraction. Both measurements of refractive error are important and should be considered together in formulating a plan for surgery. The manifest refractions with subjective input by the patient takes into account the effects of central processing of visual information in the central nervous system, but measurements obtained with most available wavefront analysis systems do not.37 In some patients, these differences, attributable to central processing and compensation for optical aberrations, may be highly significant.
The main limitations of this study are the heterogeneous distribution of patients within specific subgroups, including refractive error and age groups. Another limitation is the inaccuracy of the Shack-Hartmann device to measure patients with high refractive errors or large amount of higher order aberrations. In this study, we were unable to accurately measure 6.7% of normal refractive surgery candidates. Wang et al36 could not measure 14% of normal eyes and presumed a partial limitation of Shack-Hartmann's technology, with large higher order aberrations causing crossover effects that preclude obtaining proper measurements.
This study analyzed the wavefront measurements acquired from patients undergoing preoperative analysis for refractive surgery using the WaveScan instrument. Thus, this study provides reference values for aberrations in normal refractive surgery candidates. The wavefront-derived refractive error was also evaluated and had a good correlation with the manifest refraction, although significant disparities are noted in a few patients.
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Higher Order Aberrations Acquired Under 6-mm Pupil Diameter
Figure 1. Higher order aberrations obtained at 3- and 6-mm pupil diameter (HOA = higher order aberrations).