August 2006
Volume 47, Issue 8
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Cornea  |   August 2006
Serial Measurements of Higher-Order Aberrations after Blinking in Normal Subjects
Author Affiliations
  • Shizuka Koh
    From the Departments of Ophthalmology and
  • Naoyuki Maeda
    From the Departments of Ophthalmology and
  • Yoko Hirohara
    Technical Research Institute, Topcon Corp., Tokyo, Japan.
  • Toshifumi Mihashi
    Technical Research Institute, Topcon Corp., Tokyo, Japan.
  • Sayuri Ninomiya
    Visual Science, Osaka University Medical School, Suita, Japan; and the
  • Kenichiro Bessho
    Visual Science, Osaka University Medical School, Suita, Japan; and the
  • Hitoshi Watanabe
    From the Departments of Ophthalmology and
  • Takashi Fujikado
    Visual Science, Osaka University Medical School, Suita, Japan; and the
  • Yasuo Tano
    From the Departments of Ophthalmology and
Investigative Ophthalmology & Visual Science August 2006, Vol.47, 3318-3324. doi:10.1167/iovs.06-0018
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      Shizuka Koh, Naoyuki Maeda, Yoko Hirohara, Toshifumi Mihashi, Sayuri Ninomiya, Kenichiro Bessho, Hitoshi Watanabe, Takashi Fujikado, Yasuo Tano; Serial Measurements of Higher-Order Aberrations after Blinking in Normal Subjects. Invest. Ophthalmol. Vis. Sci. 2006;47(8):3318-3324. doi: 10.1167/iovs.06-0018.

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      © 2015 Association for Research in Vision and Ophthalmology.

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purpose. To investigate sequential changes in the optical quality of normal eyes associated with blinking.

methods. Ocular higher-order aberrations (HOAs) were measured sequentially by using a wavefront sensor for 30 seconds in 20 eyes of 20 normal subjects. During the measurement, subjects were forced to blink every 10 seconds. The obtained aberration data were analyzed in the central 4-mm diameter for coma-like, spherical-like, and total HOAs up to the sixth-order Zernike polynomials.

results. The serial changes in the HOAs with blinking were classified into four groups by pattern: stable (25%), small-fluctuation (45%), sawtooth (20%), and others (10%). In the subjects with the sawtooth pattern, the total HOAs increased significantly (P < 0.001, one-way repeated-measures ANOVA) with time between blinks. Increased total HOAs and coma-like aberrations in the subjects with the sawtooth pattern suggested that the inferosuperior asymmetric change in tear film thickness is responsible.

conclusions. Dynamic changes in HOAs after blinking showed variations even in clinically normal subjects. Serial measurements of HOAs may be useful in evaluating the dynamic changes in tear film and the effects on the quality of vision after blinking.

Precorneal tear film maintained by blinking is important, not only to protect the ocular surface but also from an optical standpoint. Recently, much attention has been paid to the effect of tear film on the optical quality of the eye, and several studies have indicated that tear film breakup degrades optical quality. 1 2 3 4  
Results of studies in which corneal topographers were used revealed that fluctuations in the tear film cause increased irregular astigmatism. 5 6 7 Recently, continuous capture of corneal topographic data has been used to estimate the effect of tear film breakup on optical quality. 8 9 10 11 12 13 Montés-Micó et al. 14 measured the corneal higher-order aberrations (HOAs) at 1-second intervals for 15 seconds after a blink using corneal topography in normal and dry eyes. 14 15 Other studies used a wavefront sensor to assess tear film behavior. 16 17 18 19 20 21 For the first time, we quantified the effect of tear film breakup by measuring ocular HOAs before and after tear film breakup. 17 Because previous measurements of ocular HOAs have been performed only two or three times before and after blinking, 17 19 little is known about the continuous variations in postblink changes in ocular HOAs. 
Of interest is the sequential and dynamic effect of tear film on the aberrations in the entire eye after blinking. The purpose of the present study was to investigate the sequential postblink changes in the ocular HOAs with postblink tear dynamics determined by sequential wavefront measurements. 
Methods
Subjects
Twenty eyes of 20 normal volunteers (11 women, 9 men; average age, 30.0 ± 4.4 years) who had no ocular diseases except refractive errors were included. No subject wore contact lens or had undergone a previous ocular surgery, and none used eye drops or were taking a systemic medicine. Every eye had a best spectacle-corrected visual acuity of 20/20 or better. The average Schirmer I test result was 23.2 ± 8.5 mm, and slit-lamp examinations showed no fluorescein staining on the ocular surface. The mean tear film breakup time (BUT) was 7.0 ± 1.3 seconds. To avoid the effects of other tests on the wavefront measurement, tear function and slit-lamp examinations were conducted on a separate day before the wavefront measurements. 
This study adhered to the tenets of the Declaration of Helsinki; informed consent was obtained from all subjects after the nature and possible consequences of the study were explained fully. The measurements were conducted in a room at Osaka University in which the temperature was maintained at 22 ± 3°C and the humidity was 40% ± 4%. All measurements were conducted from 2 to 4 PM. 
Measurement of HOAs
Wavefront aberration data were obtained using the newly developed Hartmann-Shack wavefront aberrometer (Topcon, Corp., Tokyo, Japan) equipped with an automated function for measuring and recording sequential wavefront aberrations every second for 60 seconds. The diameter of each lenslet was 220 μm and the focal length was 500 μm, allowing approximately 250 to 260 sample points in the Hartmann image within a 4-mm diameter pupil (560∼570 sample points within a 6-mm diameter pupil). Wavefront measurements were obtained in a dark room through a natural pupil without use of dilating drugs. 
Subjects were forced to blink every 10 seconds with the metronome sound and subsequently to keep their eyes open and gaze at the built-in target with fogging of 1.0 D. The blinking interval in this study was similar to the blinking that occurs during work with a video display terminal (VDT). 22 23 Because variations in the blink interval during consecutive measurements may make statistical analysis difficult, a uniform blink interval was used. Subjects practiced this blinking pattern on the day before the measurements were taken. Thirty consecutive measurements consisting of three postblink intervals were obtained from the left eye. Each postblink segment consisted of 10 images. The images obtained during blinking were not analyzed because of background noise. 
The ocular HOAs were analyzed quantitatively in the central 4-mm diameter up to the sixth order by expanding the set of Zernike polynomials on computer (MatLab, ver. 7.01; The Mathworks, Inc., Natick, MA). From the Zernike coefficients, coma-like aberrations (the third-order component [S3], the fifth-order component [S5]; [S3+S5]), spherical-like aberrations (the fourth-order component [S4], the sixth-order component [S6]; [S4+S6]), and total HOAs (S3+S4+S5+S6) were calculated. 24  
Pattern of Sequential Change of the Total HOAs
The sequential changes in the ocular total HOAs were grouped into four patterns with visual inspection by three ophthalmologists: the stable pattern (defined as maintaining an almost constant value with little variation), the small-fluctuation pattern (defined as having fluctuations in sequential values compared with the stable pattern without a tendency to increase or decrease), the sawtooth pattern (defined as having total HOAs with an upward curve after blinking and decreasing at the blink), and other (defined as those patterns not classifiable as one of the three previously described patterns). 
For the classification, the data were plotted on a graph with the scale resolution of 0.01 μm, and the definition of fluctuation was the presence of zigzag configurations of 0.02 μm and greater in width at least twice in three postblink segments. 
Figure 1shows the scheme of the three classifiable patterns. Three independent observers were masked to the evaluation of the other observers. If the pattern assigned by one observer differed from that of the other two observers, the pattern assigned by the two observers was used. 
Fluctuation Index, Stability Index, and Time of Minimum Total HOAs
Three quantitative indices were designated to show the sequential changes in HOAs over time: the fluctuation index (FI) of the total HOAs, the stability index (SI) of the total HOAs, and the time of minimum total HOAs (T min) after blinking. FI was defined as the average of the SD of the ocular total HOAs obtained. This index was devised to indicate the fluctuations in the total HOAs measured between blinks. SI was defined as the slope of the linear regression line of the total ocular HOAs between blinks, to quantify the upward curve in the sawtooth pattern. T min was defined as the time at which the root mean square (RMS) of the ocular total HOAs reached the minimum in each postblink measurement. 9 14 The values measured between the blinks and the data from three postblinks were averaged for each subject. 
Data Analysis
Results of clinical tear function tests (BUT, Schirmer I test) and the three defined indices (FI, SI, and T min) were compared among the three patterns. The data were analyzed by using one-way analysis of variance (ANOVA) and a post hoc Tukey comparison procedure. In addition, the sequential changes in coma-like aberration, spherical-like aberration, and total HOAs also were investigated in each pattern. A one-way repeated-measures ANOVA was performed to analyze the sequential changes in the stable pattern and the small-fluctuation pattern. The Friedman repeated-measures ANOVA on ranks was used to analyze the sequential changes in the sawtooth pattern. P < 0.05 was considered significant. 
Results
The profiles of the subjects and the results of the BUT, the Schirmer I test, and serial measurements of ocular HOAs are shown in Table 1 . Five (25%), nine (45%), and four (20%) of the 20 eyes were classified as having stable, small-fluctuation, and sawtooth patterns, respectively. Two cases (subjects 19 and 20) were excluded from the analysis because reflex tearing occurred during the measurement or the repeatability in the three postblink sessions was poor. 
The results of the statistical analyses of the tear function tests among the patterns are shown in Table 2 . There was no difference in BUT among the groups (P = 0.429, by one-way ANOVA). There were no trends between the Schirmer I test and the classification of the pattern (P = 0.810, by one-way ANOVA). 
FI, SI, and Tmin
The mean FIs in the stable, small-fluctuation, and sawtooth groups were 0.008, 0.013, and 0.024, respectively. The saw-tooth pattern had a significantly higher value than did the stable pattern and the small-fluctuation pattern (P < 0.001, P < 0.001, by one-way ANOVA, Tukey test; Fig. 2 ). 
The mean SIs in each group were −0.0005, −0.0003, and 0.0080, respectively. The sawtooth group also had a significantly higher value than the stable and the small-fluctuation groups (P < 0.001, P < 0.001, by one-way ANOVA, Tukey test; Fig. 2 ). 
The mean T min values in each group were 5.6, 4.9, and 1.8 seconds, respectively. A comparison of T min among the three groups is shown in Figure 3 . In the sawtooth group, T min was significantly shorter than in the other two groups (P < 0.001, P < 0.001, by one-way ANOVA, Tukey test). 
There were no significant differences in FI, SI, and T min between the stable pattern and the small-fluctuation pattern. 
Serial Changes in HOAs in the Three Patterns
Shown in Figure 4are the averages of the sequential changes in HOAs during the measurements in the stable (Fig. 4A) , small-fluctuation (Fig. 4B) , and sawtooth (Fig. 4C)groups. The wavefront color-coded maps of ocular HOAs obtained between blinks in the representative cases of the stable and sawtooth patterns are shown with the changes in the simulated retinal images for a Landolt ring (optotype with log MAR value 0; Fig. 5 ). 
Stable Pattern.
The sequential total HOAs remained constant at each blink (Fig. 4A) . The sequential changes in coma-like, spherical-like, and total HOAs were stable, and there were no significant changes after blinking during nine measurements in each type of aberration (P = 0.640, P = 0.054, P = 0.852, respectively, by one-way repeated-measures ANOVA). 
Small-Fluctuation Pattern.
The sequential total HOAs tended to be stable with small fluctuations (Fig. 4B) . There were significant changes during nine measurements of the sequential postblink tear changes in the spherical-like aberrations over 10 seconds (P = 0.005, by one-way repeated measures ANOVA). Regarding coma-like aberrations and total HOAs, there were no significant changes among the nine measurements (P = 0.597 and P = 0.648, respectively, by one-way repeated-measures ANOVA). 
Sawtooth Pattern.
The total HOAs tended to show an upward curve between blinks and recovered with each blink. However, in the third postblink interval, the total HOAs did not recover to baseline despite the blink and continued to increase (Fig. 4C) . Regarding sequential postblink changes, there were significant changes in the coma-like and spherical-like aberrations and total HOAs (P < 0.001 for all; by Friedman repeated-measures ANOVA on ranks). 
Discussion
In this study, we measured the sequential ocular HOAs after blinking. To the best of our knowledge, this is the first study to measure the dynamic changes in the ocular HOAs associated with blinking in normal subjects. 
According to previous studies of normal subjects, total HOAs in the central 4-mm diameter increased significantly 15 seconds after blinking. 17 However, the total HOAs 10 seconds after blinking were comparable to those obtained immediately after blinking and did not increase significantly, 19 although continuous measurements after blinking were not performed in either study. 17 19  
A noteworthy finding in the present study is that a subgroup was identified with unstable variations in sequential postblink changes in total HOAs, even during the 10 seconds during which the postblink changes in ocular HOAs had been reported to be stable in normal subjects. 19 Although the eyes with a sawtooth pattern had not had dry eye diagnosed clinically, the tear film was not as stable in that group as in the other two groups. We speculated that forced eye opening for 10 seconds may cause instability of the tear film. In the eyes with a sawtooth pattern, significant changes were found in the sequential postblink changes in the coma-like and spherical-like aberrations and total HOAs (Fig. 4) . As previous reports have suggested that the postblink behavior of both the ocular and corneal HOAs correspond well with the pattern in coma-like aberrations rather than spherical aberrations, 14 15 19 25 the significant changes in the coma-like aberrations in the sawtooth pattern may suggest that the asymmetric changes in tear film thickness result from unstable tear film. Postblink changes in spherical-like aberrations have been reported to result from a higher rate of tear evaporation at the corneal center than in the periphery. 14 15 19 In the present study, significant changes in spherical-like aberration also were found in the subjects with the small-fluctuation pattern. A different tear film evaporation rate on the cornea may cause the fluctuation in HOAs. A comet-like ghost was seen in the sawtooth pattern (Fig. 5) . Consecutive postblink deterioration of the simulated retinal image may result from the coma-like aberrations, mainly because of the difference in tear film thickness between the superior and inferior cornea. 
In eyes with the sawtooth pattern, there was not only an upward curve of sequential HOAs at each postblink interval but also a rapidly increasing rate of HOAs between the blinks with time (Fig. 4C) . The HOAs in the third interblink period (21∼30 seconds) were higher than those in the first interblink period (1∼10 seconds). The increased HOAs did not recover to the baseline level. It seems that there may be less capacity for tear stability in eyes with the sawtooth pattern than in the other two patterns. An increased tear evaporation rate in dry eye has been reported, 26 27 28 and the tear evaporation rate in the eyes with the sawtooth pattern may be increased as in dry eye. We speculate that an enlarged exposed ocular surface area and increased evaporation during steady gaze may be responsible for the accelerated increasing HOAs. Moreover, because impaired functional visual acuity during staring in patients with dry eye has been reported, 3 4 the deterioration of the retinal image in eyes with the sawtooth pattern suggests the potential for the development of dry eye. It would be of interest to determine whether individuals with the sawtooth pattern complain of visual impairment while using a VDT with staring and blink suppression. 
Although the sawtooth pattern differs quantitatively from the other two patterns in FI, SI, and T min, there were no statistical differences in the FI and T min between the stable and small-fluctuation patterns. The value of the FI of the small-fluctuation pattern was relatively larger than that of the stable pattern, and the only significant difference was that the small-fluctuation pattern had significant postblink changes in spherical-like aberrations. The origin of the fluctuations in HOAs has not been identified specifically; however, potential factors that can be implicated include corneal (including tear film)/lenticular and retinal causes, accommodation, pupil fluctuation, and the subject’s fixation or attention. 29 30 31 Accommodation causes a negative shift in changes in spherical aberration. 32 33 34 In the present study, the C4 0 value (spherical aberration) among the Zernike coefficients did not show a significant negative shift during 10 seconds in any pattern, and there may be little effect of accommodation during the 10-second blink interval. 
Recently, the concept of tear build-up time (i.e., the time to reach the most regular tear film state and maximum optical quality), 9 14 15 has been proposed to evaluate the effect of tear film on optical quality. High-speed videokeratography in normal eyes has shown that the tear film reaches the most regular state at 7.1 ± 3.9 seconds. 9 Continuous measurement of the postblink corneal HOAs with a corneal topographer showed that the minimum value was reached at 6.1 ± 0.5 seconds after a blink in normal eyes and at 2.9 ± 0.4 seconds in dry eyes. 14 15 A recent report using the modulation transfer function (MTF) measured by a double-pass method showed that the optimal MTF was 6 seconds after a blink. 35 In the present study, it took 5.6 ± 2.8 and 4.9 ± 1.7 seconds, respectively, in the stable pattern and small-fluctuation pattern. When we compared our T min data with data reported in previous studies, 9 14 35 the minimal ocular HOAs occurred earlier than in previous reports (by approximately 1 to 2 seconds) in which the data were obtained using a corneal topographer 9 14 and earlier than in a study with MTF 35 by 0.5 to 1 second. In contrast, in the subjects with the unstable sawtooth pattern, the total HOAs reached the minimum 1.8 ± 0.4 seconds after a blink, which was significantly shorter than in the other two patterns, and increased gradually to a maximum at approximately 7 to 9 seconds. Of note, the temporal changes in ocular HOAs in the sawtooth pattern were similar to those of corneal HOAs in dry eyes. 15 This result may also suggest subclinical dry eye in the eyes with the sawtooth pattern. 
In the present study, the FI and SI were useful indices for evaluating the postblink changes in ocular HOAs for detecting the sawtooth pattern. Moreover, the behavior of the serial HOAs showed an upward curve with an early T min and differed significantly from the other two groups, while the tear film BUT in the eyes with the sawtooth pattern did not differ significantly compared with the other groups. 
Currently, revised worldwide criteria for dry eye are being considered 36 and are expected to reflect the quality of vision in dry eye. From an optical standpoint, it might be helpful to assess the effect of tear film stability on optical quality, using sequential wavefront measurements in a noninvasive and quantitative fashion. To evaluate the optical quality in dry eyes or eyes with a tear film disorder, it is important to measure sequential ocular HOAs after blinking in normal eyes and to compare the two. 
Blinking plays an important role in spreading tears smoothly on the ocular surface and maintaining a healthy ocular surface. At the same time, blinking is a physiologic function that may be affected by the environment and a subject’s state of mind. 37 38 Further studies in which serial wavefront measurements are obtained in patients with dry eye or in subjects who wear contact lenses would be helpful to understand the dynamic optical quality of the eye related to the tear film, because unstable and irregular tear film in these eyes may induce impaired optical quality during steady gaze. 
This study had some limitations. The ideal condition for the subjects as well as the sampling rate and the duration of the measurements should be determined in future studies. Forced blinking differs from spontaneous blinking, and incomplete blinking happens in real life. In this respect, the repeated forced blinking used in this study may have artificially distorted the tear film thickness and tear distribution over the cornea. Future studies with larger numbers of the subjects should clarify and confirm whether the T min of ocular HOAs agrees with that of topography measurements and MTF. 9 14 35 To evaluate the effect of tear film alone, corneal topography measurements might be sufficient; however, to determine the effect of the tear film after blinking on the optical quality of the entire eye, measurement, and analysis of ocular HOAs are required. In this regard, other factors such as eye movements, accommodation, errors in alignment, and wavefront aberrometer may also play important roles in the overall measurements. Simultaneous measurement of ocular and corneal HOAs would be helpful to that end. 
In conclusion, serial measurements of ocular HOAs may be useful as a noninvasive and objective method for evaluating tear film dynamics after blinking and the effect on the quality of vision. 
Figure 1.
 
Schematic drawings of the patterns of the sequentially measured total higher-order aberrations (HOAs). The stable pattern indicated an almost constant value. In the small-fluctuation pattern, fluctuations were seen in sequential total HOAs without tending to increase or decrease. In the sawtooth pattern, the postblink total HOAs showed an upward curve with time and decrease with blinking. Arrows: blinks.
Figure 1.
 
Schematic drawings of the patterns of the sequentially measured total higher-order aberrations (HOAs). The stable pattern indicated an almost constant value. In the small-fluctuation pattern, fluctuations were seen in sequential total HOAs without tending to increase or decrease. In the sawtooth pattern, the postblink total HOAs showed an upward curve with time and decrease with blinking. Arrows: blinks.
Table 1.
 
Total HOA Data with the Profile of Each Subject
Table 1.
 
Total HOA Data with the Profile of Each Subject
Subject Gender Age BUT (s) Schirmer I (mm) Pattern FI of Total HOAs (μm) SI of Total HOAs (μm) T min (s)
1 M 36 9 14 Stable 0.0063 0.0000 8.7
2 M 31 9 28 Stable 0.0063 0.0014 1.0
3 M 28 6 18 Stable 0.0076 −0.0011 5.3
4 F 29 6 31 Stable 0.0100 −0.0001 6.3
5 F 26 7 35 Stable 0.0094 −0.0026 6.7
6 F 30 9 10 Small-fluctuation 0.0086 −0.0009 5.3
7 F 34 9 18 Small-fluctuation 0.0083 −0.0001 3.3
8 F 35 7 20 Small-fluctuation 0.0094 −0.0012 7.7
9 F 28 7 28 Small-fluctuation 0.0106 −0.0012 7.0
10 F 23 6 35 Small-fluctuation 0.0109 0.0009 4.5
11 F 26 6 35 Small-fluctuation 0.0126 0.0008 5.3
12 M 31 7 18 Small-fluctuation 0.0163 −0.0033 4.5
13 M 25 9 20 Small-fluctuation 0.0171 −0.0019 4.3
14 M 35 6 20 Small-fluctuation 0.0172 0.0041 2.3
15 F 28 8 35 Sawtooth 0.0199 0.0064 1.7
16 F 39 6 35 Sawtooth 0.0221 0.0078 1.3
17 M 27 6 20 Sawtooth 0.0229 0.0080 1.7
18 M 34 6 13 Sawtooth 0.0309 0.0099 2.3
19 M 24 7 15 Other 0.0152 0.0033 NA
20 F 32 7 17 Other 0.0083 0.0007 NA
Table 2.
 
Tear Function Tests in the Three Patterns
Table 2.
 
Tear Function Tests in the Three Patterns
Pattern Stable Small-Fluctuation Sawtooth P *
Tear BUT (seconds) 7.4 ± 1.5 7.3 ± 1.3 6.5 ± 1.0 0.429
Schirmer I test (mm) 25.2 ± 8.8 22.7 ± 8.3 25.8 ± 11.1 0.810
Figure 2.
 
Comparison of the FI and the SI of the total higher-order aberrations. In the FI and SI, the sawtooth pattern has a significantly higher value than the stable pattern and the small-fluctuation pattern (P < 0.001 and P < 0.001, respectively, by one-way ANOVA, Tukey test).
Figure 2.
 
Comparison of the FI and the SI of the total higher-order aberrations. In the FI and SI, the sawtooth pattern has a significantly higher value than the stable pattern and the small-fluctuation pattern (P < 0.001 and P < 0.001, respectively, by one-way ANOVA, Tukey test).
Figure 3.
 
Comparison of the Tmin among the patterns. The Tmin of the sawtooth pattern is significantly shorter than in the other two groups (P < 0.001 and P < 0.001, respectively, by one-way ANOVA, Tukey test).
Figure 3.
 
Comparison of the Tmin among the patterns. The Tmin of the sawtooth pattern is significantly shorter than in the other two groups (P < 0.001 and P < 0.001, respectively, by one-way ANOVA, Tukey test).
Figure 4.
 
The sequential changes in higher-order aberrations during 30 consecutive measurements for 30 seconds consisting of three postblink intervals are shown for the three patterns. (A) Stable pattern, (B) small-fluctuation pattern, and (C) sawtooth pattern. Arrows: blinks.
Figure 4.
 
The sequential changes in higher-order aberrations during 30 consecutive measurements for 30 seconds consisting of three postblink intervals are shown for the three patterns. (A) Stable pattern, (B) small-fluctuation pattern, and (C) sawtooth pattern. Arrows: blinks.
Figure 5.
 
Representative sequential postblink changes in (A) eyes with the stable pattern (subject 2, Table 1 ) and the (B) sawtooth pattern (subject 16, Table 1 ). Changes in the color-coded map of ocular higher-order aberrations between blinks show stability throughout without marked changes in an eye with the stable pattern (A) and delayed wavefront inferiorly with time in the eye with the sawtooth pattern. (B) The simulated retinal images of a Landolt ring are almost normal throughout in the (A) eye with the stable pattern and (B) blur over time in the eye with the sawtooth pattern.
Figure 5.
 
Representative sequential postblink changes in (A) eyes with the stable pattern (subject 2, Table 1 ) and the (B) sawtooth pattern (subject 16, Table 1 ). Changes in the color-coded map of ocular higher-order aberrations between blinks show stability throughout without marked changes in an eye with the stable pattern (A) and delayed wavefront inferiorly with time in the eye with the sawtooth pattern. (B) The simulated retinal images of a Landolt ring are almost normal throughout in the (A) eye with the stable pattern and (B) blur over time in the eye with the sawtooth pattern.
 
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