# Reliability of Ocular Aberration Measurements in Children with Moderate and Low Myopia under Scotopic Conditions

Authors: Zhouyue Li; Dongmei Cui; Sichun Ao; Weizhong Lan; Xiao Yang
Journal: Journal of Ophthalmology
 (2018)

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## Abstract

Purpose. To investigate the reliability of ocular aberration measurement in myopic children under scotopic conditions and to validate the mathematical Zernike pupil scaling-down technique. Methods. Ocular aberrations of 45 myopic children were examined under scotopic conditions via iTrace aberrometer. The intra- and intersession repeatability was evaluated for both the measured values with the true pupil sizes and the estimated ones that were determined by scaling down the pupil sizes to the largest integer value across all measurements. Results. The intra- and intersession difference of clinically measured aberration was generally insignificant, and the ICCs for each aberration component exhibited good to excellent reliability (ICCs > 0.4). Similar results were found for the estimated aberration using the scaling-down technique. Although the majority of the estimated Zernike components were comparable with the corresponding measured one, the estimated values of defocus, coma, and the corresponding total aberrations were found significantly smaller than the measured values (all P<0.01). Conclusions. The ocular aberration measurements in myopic children under the circumstances described are reliable. The scaling-down technique is a useful option for comparing the results obtained from different pupil sizes, but the estimated Zernike coefficients were not always comparable with the corresponding measured values.


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## Body

## 1. Introduction

Myopia, which is a common cause of distance vision impairment, is reaching epidemic proportions in some Asian countries [1, 2]. Even in the United States and Europe, a dramatic increase of myopic population has been observed over the last half a century ago [3]. Myopia was estimated to affect approximately 20% of the world’s population in the year 2000, and this number was predicted to increase significantly to approximately 50% in 2050 [4]. Despite the urgent situation, the exact mechanism of myopia is still not very clear. Recently, a growing body of literature has suggested that ocular aberration might play a role in myopia pathogenesis [5–7] and impact the outcome of interventions [8, 9]. It is well known that ocular aberration is very dynamic and tends to be influenced by a series of factors, such as pupil size [10, 11] and accommodation status [12–14]. These influencing factors impose more challenges for aberration measurements in children than in adults because children usually have greater pupil sizes and a more sensitive accommodation tonus. In addition, the changing course of myopia extends throughout the adolescent period, which requires multiple follow-up visits. The reliability of related measurement, including ocular aberration, is therefore very critical for correctly evaluating the disorder as well as the performance of any interventions.Although the application of cycloplegic agents could stabilize the pupil size and accommodation status, this manner is not welcomed in clinical practice due to the side effects of the cycloplegic agents (e.g., transient photophobia and blurred near vision). An alternative method might be applied to measure the ocular aberration in a scotopic condition. However, the repeatability of the results under such circumstances in children is not well documented. Therefore, the purpose of the study was to assess the reliability of this method in children with myopia. In addition, many instruments offer an estimation of aberration that uses the pupil scaling-down technique [15] to facilitate the comparison of results obtained from different pupil sizes. The second purpose of the study was to evaluate the validity of this “simulation” technique in this population.


## 2. Subjects and Methods

### 2.1. Subjects

A total of 45 myopic children were recruited into the study, with ages ranging from 8 to 15 years (11.2 ± 1.7 years). Prior to the study, written consent was obtained from all children and their parents after a thorough explanation of the purposes and risks of all procedures throughout the study was provided. The study was conducted in accordance with the tenets of the Declaration of Helsinki and was approved by the ethical committee of Zhongshan Ophthalmic Center, Sun Yat-sen University. Before the study, each participant underwent an ophthalmic examination to ensure ocular health. All subjects had a best spectacle-corrected visual acuity of logMAR 0.00 or better. The mean spherical equivalent refractive error (SER) was −2.72 ± 0.87 DS (range: −4.00~−0.50 DS). The mean axial length was 24.82 ± 0.76 mm (range: 23.16~26.16 mm). No subject had systemic diseases that might induce ocular disorders such as diabetes. No subject had previous ocular surgery or wore contact lenses. Additionally, the pupils of each subject were bigger than 3.0 mm under low mesopic conditions.


### 2.2. Procedures

Ocular aberration was measured by iTRACE (Tracey Technologies Corp., Houston, TX, USA). The experiment consisted of two sessions. In the first session, each subject underwent dark adaption in a quiet and dim room (illumination of approximately 30 lux) for at least 10 minutes. The subject was required to place his or her chin on the chin rest and use the right eye to fixate on a distant target located 4 meters away through a peekhole that was centered on the placido disk of the device and thus served as an accommodative control. The distant target was a red star sign with approximately 30 cm × 30 cm of size provided by the manufacturer, which was easy to be seen in such circumstance.Ocular aberration of the right eye was then measured twice (measures 1-1 and 1-2). Subsequently, the subject had a rest outside the dim room with illumination of approximately 250 lux for at least 10 minutes. Then, ocular aberration was remeasured (measures 2-1 and 2-2) using the same protocol as in the first session. To avoid the potential influence of different examiners, only one examiner performed the measurements throughout the study.


### 2.3. Data Analysis

Zernike polynomials from the 2nd to 4th order were used to describe the ocular aberration. Low- and high-order total aberrations (LOA and HOA, resp.) were also summarized using the root mean square (RMS). In addition, a modulation transfer function (MTF) was employed to compare the visual quality. It is known that pupil size tends to vary between measurements and is one of the major factors that influence ocular aberration. Estimated aberration was therefore obtained by using the scaling-down technique of the instrument, with the identical pupil size determined based on the largest integer pupil size of the total four measurements.All statistical analyses were performed using SPSS version 16.0 (SPSS 16.0 Inc., Chicago, IL, USA). The average level of ocular aberration for each session was expressed as the mean ± 1 standard deviation (1 SD), unless otherwise stated. The difference between measurements was calculated and compared within each session (intrasession) and between sessions (intersession) by using a pairedt-test. A p value of less than 0.05 at two tails was considered statistically significant. To evaluate the impact of the variation between measurements, the relative difference was calculated (i.e., the difference between measurements was divided by the average of the measurements). Additionally, an intraclass correlation coefficient (ICC) was adopted to assess the intra- and intersession repeatability, as suggested by Bland and Altman [16]. An ICC > 0.75 was considered as excellent measurement reliability, ICC ≥ 0.4 was good reliability, and ICC < 0.4 was poor reliability [17].


## 2.1. Subjects

A total of 45 myopic children were recruited into the study, with ages ranging from 8 to 15 years (11.2 ± 1.7 years). Prior to the study, written consent was obtained from all children and their parents after a thorough explanation of the purposes and risks of all procedures throughout the study was provided. The study was conducted in accordance with the tenets of the Declaration of Helsinki and was approved by the ethical committee of Zhongshan Ophthalmic Center, Sun Yat-sen University. Before the study, each participant underwent an ophthalmic examination to ensure ocular health. All subjects had a best spectacle-corrected visual acuity of logMAR 0.00 or better. The mean spherical equivalent refractive error (SER) was −2.72 ± 0.87 DS (range: −4.00~−0.50 DS). The mean axial length was 24.82 ± 0.76 mm (range: 23.16~26.16 mm). No subject had systemic diseases that might induce ocular disorders such as diabetes. No subject had previous ocular surgery or wore contact lenses. Additionally, the pupils of each subject were bigger than 3.0 mm under low mesopic conditions.


## 2.2. Procedures

Ocular aberration was measured by iTRACE (Tracey Technologies Corp., Houston, TX, USA). The experiment consisted of two sessions. In the first session, each subject underwent dark adaption in a quiet and dim room (illumination of approximately 30 lux) for at least 10 minutes. The subject was required to place his or her chin on the chin rest and use the right eye to fixate on a distant target located 4 meters away through a peekhole that was centered on the placido disk of the device and thus served as an accommodative control. The distant target was a red star sign with approximately 30 cm × 30 cm of size provided by the manufacturer, which was easy to be seen in such circumstance.Ocular aberration of the right eye was then measured twice (measures 1-1 and 1-2). Subsequently, the subject had a rest outside the dim room with illumination of approximately 250 lux for at least 10 minutes. Then, ocular aberration was remeasured (measures 2-1 and 2-2) using the same protocol as in the first session. To avoid the potential influence of different examiners, only one examiner performed the measurements throughout the study.


## 2.3. Data Analysis

Zernike polynomials from the 2nd to 4th order were used to describe the ocular aberration. Low- and high-order total aberrations (LOA and HOA, resp.) were also summarized using the root mean square (RMS). In addition, a modulation transfer function (MTF) was employed to compare the visual quality. It is known that pupil size tends to vary between measurements and is one of the major factors that influence ocular aberration. Estimated aberration was therefore obtained by using the scaling-down technique of the instrument, with the identical pupil size determined based on the largest integer pupil size of the total four measurements.All statistical analyses were performed using SPSS version 16.0 (SPSS 16.0 Inc., Chicago, IL, USA). The average level of ocular aberration for each session was expressed as the mean ± 1 standard deviation (1 SD), unless otherwise stated. The difference between measurements was calculated and compared within each session (intrasession) and between sessions (intersession) by using a pairedt-test. A p value of less than 0.05 at two tails was considered statistically significant. To evaluate the impact of the variation between measurements, the relative difference was calculated (i.e., the difference between measurements was divided by the average of the measurements). Additionally, an intraclass correlation coefficient (ICC) was adopted to assess the intra- and intersession repeatability, as suggested by Bland and Altman [16]. An ICC > 0.75 was considered as excellent measurement reliability, ICC ≥ 0.4 was good reliability, and ICC < 0.4 was poor reliability [17].


## 3. Results

### 3.1. Variation in Pupil Size

The values of pupil sizes obtained by iTrace under natural scotopic circumstance are illustrated in Table1. There was no statistically significant difference between the results either within sessions or between the sessions. The ICC values of the three comparisons were basically greater than 0.75, suggesting excellent intra- and intersession reliability under such circumstances.Table 1
The intrasession and intersession repeatability of the pupil sizes measured in natural scotopic circumstances.
Parameters
Process
Average
Intrasession difference
P
Difference/average (%)
95% LOA
ICC
Pupil size
Section 1
5.20 ± 0.53
−0.02
0.719
0.38
[−0.84, 0.80]
0.744
Section 2
5.13 ± 0.62
−0.09
0.106
1.75
[−0.83, 0.65]
0.841
Intersession
5.15 ± 0.55
−0.07
0.256
1.36
[−0.90, 0.76]
0.767
Note:P: P values of the intrasession difference; 95% LOA: 95% limits of agreement for the intrasession difference; ICC: intraclass correlation coefficient.


### 3.2. Reproducibility of Ocular Aberration Measurements in Natural Scotopic Circumstances

The Zernike components measured in natural scotopic circumstances are summarized in Table2. The intra- and intersession differences in aberration expressed by RMS, individual Zernike components, or MTF at varied spatial frequencies were generally insignificant, except for the intrasession difference of total RMS, defocus, and MTF@5cpd. However, the relative difference for the three parameters that had statistical significance was rather small (ranging from 4.31% to 7.41%), which suggested mild clinical significance. Similarly, the ICCs for all of the comparisons were generally greater than 0.4, indicating the good to excellent reproducibility of the aberration measured. It is noted, however, that the ICC for MTF@15cpd was only 0.339 in session 1 but was 0.561 in session 2 and 0.617 for both sessions.Table 2
The intrasession and intersession repeatability of ocular aberration measured in natural scotopic circumstances.
Average
Intrasession difference
P
Difference/average (%)
95% LOA
ICC
Total RMS
Session 1
3.78 ± 1.24
−0.07
0.464
1.85
[−1.31, 1.17]
0.883
Session 2
3.71 ± 1.20
−0.16
0.031∗
4.31
[−1.12, 0.80]
0.922
Intersession
3.74 ± 1.18
−0.08
0.390
2.14
[−1.28, 1.12]
0.877
LOA total RMS
Session 1
3.73 ± 1.27
0.00
0.998
0.00
[−1.46, 1.46]
0.847
Session 2
3.65 ± 1.23
−0.09
0.388
2.47
[−1.49, 1.31]
0.852
Intersession
3.69 ± 1.21
−0.08
0.425
2.17
[−1.38, 1.22]
0.863
HOA total RMS
Session 1
0.33 ± 0.16
−0.01
0.654
3.03
[−0.31, 0.29]
0.668
Session 2
0.35 ± 0.15
0.00
0.951
0.00
[−0.38, 0.38]
0.426
Intersession
0.34 ± 0.14
0.01
0.503
2.94
[−0.23, 0.25]
0.712
Defocus
Session 1
3.64 ± 1.20
−0.07
0.644
1.92
[−2.01, 1.87]
0.719
Session 2
3.63 ± 1.18
−0.15
0.038∗
4.13
[−1.09, 0.79]
0.923
Intersession
3.64 ± 1.14
−0.01
0.941
0.27
[−1.43, 1.41]
0.824
Astigmatism
Session 1
0.59 ± 0.40
0.00
0.987
0.00
[−0.38, 0.38]
0.900
Session 2
0.57 ± 0.35
−0.03
0.137
5.26
[−0.33, 0.27]
0.914
Intersession
0.58 ± 0.37
−0.02
0.246
3.45
[−0.28, 0.24]
0.943
Coma
Session 1
0.24 ± 0.14
−0.02
0.403
8.33
[−0.28, 0.24]
0.682
Session 2
0.25 ± 0.13
−0.03
0.128
12.00
[−0.31, 0.25]
0.540
Intersession
0.24 ± 0.13
0.01
0.566
4.17
[−0.19, 0.21]
0.738
Trefoil
Session 1
0.15 ± 0.08
0.00
0.933
0.00
[−0.14, 0.14]
0.663
Session 2
0.14 ± 0.08
0.00
0.662
0.00
[−0.12, 0.12]
0.735
Intersession
0.14 ± 0.07
0.00
0.700
0.00
[−0.12, 0.12]
0.724
Spherical
Session 1
0.07 ± 0.07
0.01
0.295
14.29
[−0.09, 0.11]
0.728
Session 2
0.07 ± 0.07
0.00
0.632
0.00
[−0.14, 0.14]
0.555
Intersession
0.07 ± 0.06
0.00
0.845
0.00
[−0.10, 0.10]
0.700
Secondary
Session 1
0.06 ± 0.04
0.00
0.874
0.00
[−0.10, 0.10]
0.537
Session 2
0.06 ± 0.04
−0.01
0.185
16.67
[−0.11, 0.09]
0.483
Intersession
0.06 ± 0.04
0.00
0.527
0.00
[−0.08, 0.08]
0.631
MTF@5cpd
Session 1
0.55 ± 0.18
0.00
0.831
0.00
[−0.30, 0.30]
0.722
Session 2
0.54 ± 0.18
0.04
0.033∗
7.41
[−0.20, 0.28]
0.811
Intersession
0.54 ± 0.17
−0.01
0.570
1.85
[−0.19, 0.17]
0.875
MTF@10cpd
Session 1
0.28 ± 0.13
−0.01
0.358
3.57
[−0.21, 0.19]
0.723
Session 2
0.26 ± 0.12
0.02
0.320
7.69
[−0.24, 0.28]
0.574
Intersession
0.27 ± 0.12
−0.01
0.334
3.70
[−0.17, 0.15]
0.781
MTF@15cpd
Session 1
0.18 ± 0.09
0.00
0.894
0.00
[−0.24, 0.24]
0.339
Session 2
0.17 ± 0.07
0.01
0.256
5.88
[−0.15, 0.17]
0.561
Intersession
0.18 ± 0.07
−0.02
0.087
11.11
[−0.16, 0.12]
0.617
MTF@20cpd
Session 1
0.13 ± 0.06
−0.01
0.237
7.69
[−0.15, 0.13]
0.480
Session 2
0.12 ± 0.05
0.01
0.552
8.33
[−0.09, 0.11]
0.595
Intersession
0.12 ± 0.05
−0.01
0.102
8.33
[−0.09, 0.07]
0.764
MTF@25cpd
Session 1
0.10 ± 0.05
−0.01
0.333
10.00
[−0.11, 0.09]
0.560
Session 2
0.10 ± 0.04
0.01
0.146
10.00
[−0.09, 0.11]
0.538
Intersession
0.10 ± 0.04
0.00
0.443
0.00
[−0.06, 0.06]
0.734
MTF@30cpd
Session 1
0.08 ± 0.04
0.00
0.762
0.00
[−0.08, 0.08]
0.645
Session 2
0.08 ± 0.04
0.01
0.131
12.50
[−0.07, 0.09]
0.563
Intersession
0.08 ± 0.04;
0.00
0.324
0.00
[−0.06, 0.06]
0.701
Note:P: P values of the intrasession difference; 95% LOA: 95% limits of agreement; ICC: intraclass correlation coefficient. ∗Asterisk indicates statistical significance.


### 3.3. Reproducibility of Ocular Aberration Estimated by Using the Pupil Scaling-Down Method

To compare ocular aberrations within the common pupil diameter, the largest integer pupil size of the total four measurements was first determined and then ocular aberration was estimated by using the pupil scaling-down method (Table3). Similar to the data determined by using the true pupil size, the overall intra- and intersession repeatability of the results was generally good. Nevertheless, it is noted that a greater frequency of statistically significant differences and some very low ICCs (e.g., ICC of Trefoil and MTF@15cpd) was detected for estimated ocular aberrations, including total RMS, HOA total RMS, astigmatism, spherical, MTF@5cpd, MTF@15cpd, and MTF@25cpd. In addition, the relative differences of these parameters tended to be greater than those produced by using the true pupil size (e.g., 69.57% relative difference in the 2nd session for HOA total RMS, Table 3).Table 3
The intrasession and intersession repeatability of the estimated ocular aberration using the pupil scaling-down method.
Parameters
Process
Average
Intrasession difference
P
Difference/average (%)
95% LOA
ICC
Total RMS
Session 1
2.93 ± 1.14
0.06
0.565
2.05
[−1.28, 1.40]
0.839
Session 2
2.78 ± 1.09
−0.25
0.015∗
8.99
[−1.57, 1.07]
0.829
Intersession
2.85 ± 1.07
−0.15
0.109
5.26
[−1.39, 1.09]
0.847
LOA total RMS
Session 1
2.83 ± 1.17
0.10
0.502
3.53
[−1.94, 2.14]
0.678
Session 2
2.66 ± 1.16
−0.27
0.069
10.15
[−2.19, 1.65]
0.707
Intersession
2.74 ± 1.11
−0.17
0.137
6.20
[−1.65, 1.31]
0.798
HOA total RMS
Session 1
0.25 ± 0.15
−0.04
0.866
16.00
[−0.32, 0.24]
0.638
Session 2
0.23 ± 0.11
−0.16
0.010∗
69.57
[−0.34, 0.02]
0.739
Intersession
0.24 ± 0.12
−0.15
0.170
62.50
[−0.31, 0.01]
0.804
Defocus
Session 1
2.78 ± 1.13
0.02
0.785
0.72
[−1.94, 1.98]
0.685
Session 2
2.58 ± 1.14
−0.06
0.248
2.33
[−2.22, 2.10]
0.633
Intersession
2.68 ± 1.07
−0.07
0.097
2.61
[−1.61, 1.47]
0.771
Astigmatism
Session 1
0.47 ± 0.34
0.00
0.485
0.00
[−0.36, 0.36]
0.872
Session 2
0.43 ± 0.29
−0.04
0.029∗
9.30
[−0.38, 0.30]
0.849
Intersession
0.45 ± 0.31
−0.02
0.145
4.44
[−0.34, 0.30]
0.873
Coma
Session 1
0.17 ± 0.11
0.01
0.378
5.88
[−0.17, 0.19]
0.713
Session 2
0.17 ± 0.09
−0.02
0.128
11.76
[−0.18, 0.14]
0.723
Intersession
0.17 ± 0.10
0.00
0.699
0.00
[−0.16, 0.16]
0.682
Trefoil
Session 1
0.11 ± 0.07
0.00
0.914
0.00
[−0.14, 0.14]
0.581
Session 2
0.12 ± 0.10
−0.02
0.159
16.67
[−0.22, 0.18]
0.252
Intersession
0.12 ± 0.07
0.01
0.555
8.33
[−0.19, 0.21]
0.262
Spherical
Session 1
0.06 ± 0.05
0.02
0.029∗
33.33
[−0.08, 0.12]
0.549
Session 2
0.06 ± 0.05
−0.01
0.224
16.67
[−0.11, 0.09]
0.570
Intersession
0.06 ± 0.04
0.00
0.730
0.00
[−0.08, 0.08]
0.618
Secondary
Session 1
0.05 ± 0.03
0.00
0.977
0.00
[−0.08, 0.08]
0.570
Session 2
0.05 ± 0.03
−0.01
0.129
20.00
[−0.09, 0.07]
0.484
Intersession
0.05 ± 0.03
0.00
0.275
0.00
[−0.06, 0.06]
0.619
MTF@5cpd
Session 1
0.60 ± 0.20
−0.01
0.478
1.67
[−0.27, 0.25]
0.810
Session 2
0.60 ± 0.18
0.05
0.015∗
8.33
[−0.19, 0.29]
0.797
Intersession
0.60 ± 0.19
0.00
0.994
0.00
[−0.14, 0.14]
0.925
MTF@10cpd
Session 1
0.33 ± 0.16
−0.03
0.071
9.09
[−0.27, 0.21]
0.743
Session 2
0.31 ± 0.15
0.03
0.096
9.68
[−0.23, 0.29]
0.694
Intersession
0.32 ± 0.15
−0.01
0.314
3.13
[−0.21, 0.19]
0.818
MTF@15cpd
Session 1
0.21 ± 0.11
−0.03
0.033∗
14.29
[−0.23, 0.17]
0.680
Session 2
0.21 ± 0.12
0.03
0.234
14.29
[−0.33, 0.39]
0.275
Intersession
0.21 ± 0.10
0.00
0.997
0.00
[−0.22, 0.22]
0.563
MTF@20cpd
Session 1
0.15 ± 0.08
−0.02
0.076
13.33
[−0.18, 0.14]
0.538
Session 2
0.15 ± 0.08
0.01
0.341
6.67
[−0.15, 0.17]
0.599
Intersession
0.15 ± 0.07
−0.01
0.460
6.67
[−0.13, 0.11]
0.698
MTF@25cpd
Session 1
0.12 ± 0.06
−0.02
0.121
16.67
[−0.14, 0.10]
0.555
Session 2
0.11 ± 0.06
0.01
0.048
9.09
[−0.09, 0.11]
0.698
Intersession
0.11 ± 0.06
−0.01
0.230
9.09
[−0.09, 0.07]
0.793
MTF@30cpd
Session 1
0.10 ± 0.05
−0.01
0.240
10.00
[−0.11, 0.09]
0.578
Session 2
0.09 ± 0.05
0.01
0.063
11.11
[−0.07, 0.09]
0.675
Intersession
0.09 ± 0.05
−0.01
0.202
11.11
[−0.07, 0.05]
0.825
Note:P: P values of the intrasession difference; 95%LOA: 95% limits of agreement; ICC: intraclass correlation coefficient. ∗Asterisk indicates statistical significance.


### 3.4. Comparison of the Measurements and Estimations of Ocular Aberrations

To further investigate the difference between the values produced from true pupil sizes and those estimated from the largest integer pupil size of all measurements, every pair of values for each aberration was compared, as shown in Table4. As expected, due to the decrease in pupil diameter (4.36 ± 0.83 mm versus 5.15 ± 0.55 mm, P<0.001), the estimated 2nd- to 4th-order Zernike coefficients were generally smaller than the corresponding measured values. Nevertheless, these differences did not reach statistical significance, except for defocus and coma. There was neither significant difference between all of the MTF values generated from estimated and the true Zernike coefficients. However, both the estimated LOA total and HOA total RMS were significantly smaller than the measured values.Table 4
Comparison of the ocular aberration between the measured and the estimated values.
Parameters
Measured value
Estimated value
Difference
P value
Difference/measured value (%)
Total RMS
3.74 ± 1.18
2.85 ± 1.07
−0.89
0.001∗
−23.80
LOA total RMS
3.69 ± 1.21
2.74 ± 1.11
−0.95
0.001∗
−25.75
HOA total RMS
0.34 ± 0.14
0.24 ± 0.12
−0.10
0.005∗
−29.41
Defocus
3.64 ± 1.14
2.68 ± 1.07
−0.96
0.000∗
−26.37
Astigmatism
0.58 ± 0.37
0.45 ± 0.31
−0.13
0.089
−22.41
Coma
0.24 ± 0.13
0.17 ± 0.10
−0.07
0.008∗
−29.17
Trefoil
0.14 ± 0.07
0.12 ± 0.07
−0.02
0.101
−14.29
Spherical
0.07 ± 0.06
0.06 ± 0.04
−0.01
0.252
−14.29
Secondary
0.06 ± 0.04
0.05 ± 0.03
−0.01
0.091
−16.67
MTF@5cpd
0.54 ± 0.17
0.60 ± 0.19
0.06
0.189
11.11
MTF@10cpd
0.27 ± 0.12
0.32 ± 0.15
0.05
0.111
18.52
MTF@15cpd
0.18 ± 0.07
0.21 ± 0.10
0.03
0.065
16.67
MTF@20cpd
0.12 ± 0.05
0.15 ± 0.07
0.03
0.067
25.00
MTF@25cpd
0.10 ± 0.04
0.11 ± 0.06
0.01
0.161
10.00
MTF@30cpd
0.08 ± 0.04
0.09 ± 0.05
0.01
0.205
12.50
Note: difference: the difference between the measured value and estimated value.P value: P value of the difference between the measured value and estimated value. ∗Asterisk indicates statistical significance.


## 3.1. Variation in Pupil Size

The values of pupil sizes obtained by iTrace under natural scotopic circumstance are illustrated in Table1. There was no statistically significant difference between the results either within sessions or between the sessions. The ICC values of the three comparisons were basically greater than 0.75, suggesting excellent intra- and intersession reliability under such circumstances.Table 1
The intrasession and intersession repeatability of the pupil sizes measured in natural scotopic circumstances.
Parameters
Process
Average
Intrasession difference
P
Difference/average (%)
95% LOA
ICC
Pupil size
Section 1
5.20 ± 0.53
−0.02
0.719
0.38
[−0.84, 0.80]
0.744
Section 2
5.13 ± 0.62
−0.09
0.106
1.75
[−0.83, 0.65]
0.841
Intersession
5.15 ± 0.55
−0.07
0.256
1.36
[−0.90, 0.76]
0.767
Note:P: P values of the intrasession difference; 95% LOA: 95% limits of agreement for the intrasession difference; ICC: intraclass correlation coefficient.


## 3.2. Reproducibility of Ocular Aberration Measurements in Natural Scotopic Circumstances

The Zernike components measured in natural scotopic circumstances are summarized in Table2. The intra- and intersession differences in aberration expressed by RMS, individual Zernike components, or MTF at varied spatial frequencies were generally insignificant, except for the intrasession difference of total RMS, defocus, and MTF@5cpd. However, the relative difference for the three parameters that had statistical significance was rather small (ranging from 4.31% to 7.41%), which suggested mild clinical significance. Similarly, the ICCs for all of the comparisons were generally greater than 0.4, indicating the good to excellent reproducibility of the aberration measured. It is noted, however, that the ICC for MTF@15cpd was only 0.339 in session 1 but was 0.561 in session 2 and 0.617 for both sessions.Table 2
The intrasession and intersession repeatability of ocular aberration measured in natural scotopic circumstances.
Average
Intrasession difference
P
Difference/average (%)
95% LOA
ICC
Total RMS
Session 1
3.78 ± 1.24
−0.07
0.464
1.85
[−1.31, 1.17]
0.883
Session 2
3.71 ± 1.20
−0.16
0.031∗
4.31
[−1.12, 0.80]
0.922
Intersession
3.74 ± 1.18
−0.08
0.390
2.14
[−1.28, 1.12]
0.877
LOA total RMS
Session 1
3.73 ± 1.27
0.00
0.998
0.00
[−1.46, 1.46]
0.847
Session 2
3.65 ± 1.23
−0.09
0.388
2.47
[−1.49, 1.31]
0.852
Intersession
3.69 ± 1.21
−0.08
0.425
2.17
[−1.38, 1.22]
0.863
HOA total RMS
Session 1
0.33 ± 0.16
−0.01
0.654
3.03
[−0.31, 0.29]
0.668
Session 2
0.35 ± 0.15
0.00
0.951
0.00
[−0.38, 0.38]
0.426
Intersession
0.34 ± 0.14
0.01
0.503
2.94
[−0.23, 0.25]
0.712
Defocus
Session 1
3.64 ± 1.20
−0.07
0.644
1.92
[−2.01, 1.87]
0.719
Session 2
3.63 ± 1.18
−0.15
0.038∗
4.13
[−1.09, 0.79]
0.923
Intersession
3.64 ± 1.14
−0.01
0.941
0.27
[−1.43, 1.41]
0.824
Astigmatism
Session 1
0.59 ± 0.40
0.00
0.987
0.00
[−0.38, 0.38]
0.900
Session 2
0.57 ± 0.35
−0.03
0.137
5.26
[−0.33, 0.27]
0.914
Intersession
0.58 ± 0.37
−0.02
0.246
3.45
[−0.28, 0.24]
0.943
Coma
Session 1
0.24 ± 0.14
−0.02
0.403
8.33
[−0.28, 0.24]
0.682
Session 2
0.25 ± 0.13
−0.03
0.128
12.00
[−0.31, 0.25]
0.540
Intersession
0.24 ± 0.13
0.01
0.566
4.17
[−0.19, 0.21]
0.738
Trefoil
Session 1
0.15 ± 0.08
0.00
0.933
0.00
[−0.14, 0.14]
0.663
Session 2
0.14 ± 0.08
0.00
0.662
0.00
[−0.12, 0.12]
0.735
Intersession
0.14 ± 0.07
0.00
0.700
0.00
[−0.12, 0.12]
0.724
Spherical
Session 1
0.07 ± 0.07
0.01
0.295
14.29
[−0.09, 0.11]
0.728
Session 2
0.07 ± 0.07
0.00
0.632
0.00
[−0.14, 0.14]
0.555
Intersession
0.07 ± 0.06
0.00
0.845
0.00
[−0.10, 0.10]
0.700
Secondary
Session 1
0.06 ± 0.04
0.00
0.874
0.00
[−0.10, 0.10]
0.537
Session 2
0.06 ± 0.04
−0.01
0.185
16.67
[−0.11, 0.09]
0.483
Intersession
0.06 ± 0.04
0.00
0.527
0.00
[−0.08, 0.08]
0.631
MTF@5cpd
Session 1
0.55 ± 0.18
0.00
0.831
0.00
[−0.30, 0.30]
0.722
Session 2
0.54 ± 0.18
0.04
0.033∗
7.41
[−0.20, 0.28]
0.811
Intersession
0.54 ± 0.17
−0.01
0.570
1.85
[−0.19, 0.17]
0.875
MTF@10cpd
Session 1
0.28 ± 0.13
−0.01
0.358
3.57
[−0.21, 0.19]
0.723
Session 2
0.26 ± 0.12
0.02
0.320
7.69
[−0.24, 0.28]
0.574
Intersession
0.27 ± 0.12
−0.01
0.334
3.70
[−0.17, 0.15]
0.781
MTF@15cpd
Session 1
0.18 ± 0.09
0.00
0.894
0.00
[−0.24, 0.24]
0.339
Session 2
0.17 ± 0.07
0.01
0.256
5.88
[−0.15, 0.17]
0.561
Intersession
0.18 ± 0.07
−0.02
0.087
11.11
[−0.16, 0.12]
0.617
MTF@20cpd
Session 1
0.13 ± 0.06
−0.01
0.237
7.69
[−0.15, 0.13]
0.480
Session 2
0.12 ± 0.05
0.01
0.552
8.33
[−0.09, 0.11]
0.595
Intersession
0.12 ± 0.05
−0.01
0.102
8.33
[−0.09, 0.07]
0.764
MTF@25cpd
Session 1
0.10 ± 0.05
−0.01
0.333
10.00
[−0.11, 0.09]
0.560
Session 2
0.10 ± 0.04
0.01
0.146
10.00
[−0.09, 0.11]
0.538
Intersession
0.10 ± 0.04
0.00
0.443
0.00
[−0.06, 0.06]
0.734
MTF@30cpd
Session 1
0.08 ± 0.04
0.00
0.762
0.00
[−0.08, 0.08]
0.645
Session 2
0.08 ± 0.04
0.01
0.131
12.50
[−0.07, 0.09]
0.563
Intersession
0.08 ± 0.04;
0.00
0.324
0.00
[−0.06, 0.06]
0.701
Note:P: P values of the intrasession difference; 95% LOA: 95% limits of agreement; ICC: intraclass correlation coefficient. ∗Asterisk indicates statistical significance.


## 3.3. Reproducibility of Ocular Aberration Estimated by Using the Pupil Scaling-Down Method

To compare ocular aberrations within the common pupil diameter, the largest integer pupil size of the total four measurements was first determined and then ocular aberration was estimated by using the pupil scaling-down method (Table3). Similar to the data determined by using the true pupil size, the overall intra- and intersession repeatability of the results was generally good. Nevertheless, it is noted that a greater frequency of statistically significant differences and some very low ICCs (e.g., ICC of Trefoil and MTF@15cpd) was detected for estimated ocular aberrations, including total RMS, HOA total RMS, astigmatism, spherical, MTF@5cpd, MTF@15cpd, and MTF@25cpd. In addition, the relative differences of these parameters tended to be greater than those produced by using the true pupil size (e.g., 69.57% relative difference in the 2nd session for HOA total RMS, Table 3).Table 3
The intrasession and intersession repeatability of the estimated ocular aberration using the pupil scaling-down method.
Parameters
Process
Average
Intrasession difference
P
Difference/average (%)
95% LOA
ICC
Total RMS
Session 1
2.93 ± 1.14
0.06
0.565
2.05
[−1.28, 1.40]
0.839
Session 2
2.78 ± 1.09
−0.25
0.015∗
8.99
[−1.57, 1.07]
0.829
Intersession
2.85 ± 1.07
−0.15
0.109
5.26
[−1.39, 1.09]
0.847
LOA total RMS
Session 1
2.83 ± 1.17
0.10
0.502
3.53
[−1.94, 2.14]
0.678
Session 2
2.66 ± 1.16
−0.27
0.069
10.15
[−2.19, 1.65]
0.707
Intersession
2.74 ± 1.11
−0.17
0.137
6.20
[−1.65, 1.31]
0.798
HOA total RMS
Session 1
0.25 ± 0.15
−0.04
0.866
16.00
[−0.32, 0.24]
0.638
Session 2
0.23 ± 0.11
−0.16
0.010∗
69.57
[−0.34, 0.02]
0.739
Intersession
0.24 ± 0.12
−0.15
0.170
62.50
[−0.31, 0.01]
0.804
Defocus
Session 1
2.78 ± 1.13
0.02
0.785
0.72
[−1.94, 1.98]
0.685
Session 2
2.58 ± 1.14
−0.06
0.248
2.33
[−2.22, 2.10]
0.633
Intersession
2.68 ± 1.07
−0.07
0.097
2.61
[−1.61, 1.47]
0.771
Astigmatism
Session 1
0.47 ± 0.34
0.00
0.485
0.00
[−0.36, 0.36]
0.872
Session 2
0.43 ± 0.29
−0.04
0.029∗
9.30
[−0.38, 0.30]
0.849
Intersession
0.45 ± 0.31
−0.02
0.145
4.44
[−0.34, 0.30]
0.873
Coma
Session 1
0.17 ± 0.11
0.01
0.378
5.88
[−0.17, 0.19]
0.713
Session 2
0.17 ± 0.09
−0.02
0.128
11.76
[−0.18, 0.14]
0.723
Intersession
0.17 ± 0.10
0.00
0.699
0.00
[−0.16, 0.16]
0.682
Trefoil
Session 1
0.11 ± 0.07
0.00
0.914
0.00
[−0.14, 0.14]
0.581
Session 2
0.12 ± 0.10
−0.02
0.159
16.67
[−0.22, 0.18]
0.252
Intersession
0.12 ± 0.07
0.01
0.555
8.33
[−0.19, 0.21]
0.262
Spherical
Session 1
0.06 ± 0.05
0.02
0.029∗
33.33
[−0.08, 0.12]
0.549
Session 2
0.06 ± 0.05
−0.01
0.224
16.67
[−0.11, 0.09]
0.570
Intersession
0.06 ± 0.04
0.00
0.730
0.00
[−0.08, 0.08]
0.618
Secondary
Session 1
0.05 ± 0.03
0.00
0.977
0.00
[−0.08, 0.08]
0.570
Session 2
0.05 ± 0.03
−0.01
0.129
20.00
[−0.09, 0.07]
0.484
Intersession
0.05 ± 0.03
0.00
0.275
0.00
[−0.06, 0.06]
0.619
MTF@5cpd
Session 1
0.60 ± 0.20
−0.01
0.478
1.67
[−0.27, 0.25]
0.810
Session 2
0.60 ± 0.18
0.05
0.015∗
8.33
[−0.19, 0.29]
0.797
Intersession
0.60 ± 0.19
0.00
0.994
0.00
[−0.14, 0.14]
0.925
MTF@10cpd
Session 1
0.33 ± 0.16
−0.03
0.071
9.09
[−0.27, 0.21]
0.743
Session 2
0.31 ± 0.15
0.03
0.096
9.68
[−0.23, 0.29]
0.694
Intersession
0.32 ± 0.15
−0.01
0.314
3.13
[−0.21, 0.19]
0.818
MTF@15cpd
Session 1
0.21 ± 0.11
−0.03
0.033∗
14.29
[−0.23, 0.17]
0.680
Session 2
0.21 ± 0.12
0.03
0.234
14.29
[−0.33, 0.39]
0.275
Intersession
0.21 ± 0.10
0.00
0.997
0.00
[−0.22, 0.22]
0.563
MTF@20cpd
Session 1
0.15 ± 0.08
−0.02
0.076
13.33
[−0.18, 0.14]
0.538
Session 2
0.15 ± 0.08
0.01
0.341
6.67
[−0.15, 0.17]
0.599
Intersession
0.15 ± 0.07
−0.01
0.460
6.67
[−0.13, 0.11]
0.698
MTF@25cpd
Session 1
0.12 ± 0.06
−0.02
0.121
16.67
[−0.14, 0.10]
0.555
Session 2
0.11 ± 0.06
0.01
0.048
9.09
[−0.09, 0.11]
0.698
Intersession
0.11 ± 0.06
−0.01
0.230
9.09
[−0.09, 0.07]
0.793
MTF@30cpd
Session 1
0.10 ± 0.05
−0.01
0.240
10.00
[−0.11, 0.09]
0.578
Session 2
0.09 ± 0.05
0.01
0.063
11.11
[−0.07, 0.09]
0.675
Intersession
0.09 ± 0.05
−0.01
0.202
11.11
[−0.07, 0.05]
0.825
Note:P: P values of the intrasession difference; 95%LOA: 95% limits of agreement; ICC: intraclass correlation coefficient. ∗Asterisk indicates statistical significance.


## 3.4. Comparison of the Measurements and Estimations of Ocular Aberrations

To further investigate the difference between the values produced from true pupil sizes and those estimated from the largest integer pupil size of all measurements, every pair of values for each aberration was compared, as shown in Table4. As expected, due to the decrease in pupil diameter (4.36 ± 0.83 mm versus 5.15 ± 0.55 mm, P<0.001), the estimated 2nd- to 4th-order Zernike coefficients were generally smaller than the corresponding measured values. Nevertheless, these differences did not reach statistical significance, except for defocus and coma. There was neither significant difference between all of the MTF values generated from estimated and the true Zernike coefficients. However, both the estimated LOA total and HOA total RMS were significantly smaller than the measured values.Table 4
Comparison of the ocular aberration between the measured and the estimated values.
Parameters
Measured value
Estimated value
Difference
P value
Difference/measured value (%)
Total RMS
3.74 ± 1.18
2.85 ± 1.07
−0.89
0.001∗
−23.80
LOA total RMS
3.69 ± 1.21
2.74 ± 1.11
−0.95
0.001∗
−25.75
HOA total RMS
0.34 ± 0.14
0.24 ± 0.12
−0.10
0.005∗
−29.41
Defocus
3.64 ± 1.14
2.68 ± 1.07
−0.96
0.000∗
−26.37
Astigmatism
0.58 ± 0.37
0.45 ± 0.31
−0.13
0.089
−22.41
Coma
0.24 ± 0.13
0.17 ± 0.10
−0.07
0.008∗
−29.17
Trefoil
0.14 ± 0.07
0.12 ± 0.07
−0.02
0.101
−14.29
Spherical
0.07 ± 0.06
0.06 ± 0.04
−0.01
0.252
−14.29
Secondary
0.06 ± 0.04
0.05 ± 0.03
−0.01
0.091
−16.67
MTF@5cpd
0.54 ± 0.17
0.60 ± 0.19
0.06
0.189
11.11
MTF@10cpd
0.27 ± 0.12
0.32 ± 0.15
0.05
0.111
18.52
MTF@15cpd
0.18 ± 0.07
0.21 ± 0.10
0.03
0.065
16.67
MTF@20cpd
0.12 ± 0.05
0.15 ± 0.07
0.03
0.067
25.00
MTF@25cpd
0.10 ± 0.04
0.11 ± 0.06
0.01
0.161
10.00
MTF@30cpd
0.08 ± 0.04
0.09 ± 0.05
0.01
0.205
12.50
Note: difference: the difference between the measured value and estimated value.P value: P value of the difference between the measured value and estimated value. ∗Asterisk indicates statistical significance.


## 4. Discussion

Multiple studies [12, 18, 19] have investigated the reliability of aberrometric measurements previously. Most of these studies were based on adults, and they produced controversial results. Different results could be due to different instruments but could also be due to the use of different protocols or the ages of the examined subjects. To the best of our knowledge, there are very few studies that have investigated the reliability of ocular aberration measurements in children. The present study showed that the overall intra- and intersession repeatability of ocular aberrations expressed by Zernike coefficients was satisfactory. Using a scaling-down technique with the largest integer pupil size serving as the common pupil size for different measurements could provide comparable reliability.The influence of accommodation on ocular aberration is well documented. For instance, studies have found that the RMS of the HOAs changed sharply when the accommodation varied [12, 13]. Therefore, an unstable accommodation status would cause a declining measurement repeatability of aberration [11–13, 20, 21]. It is also well known that ocular aberration is dependent on the pupil diameter, with an increased pupil size leading to greater ocular aberration [22–24]. For the HOA profiles, the effect was found to be as high as 54.9% for observed total variability [22]. Since pupil size is influenced by both illuminance and accommodation, stable illuminance and accommodation are therefore critical prerequisites for obtaining reliable measurements of ocular aberrations. To achieve reliable measurements, in the current study, ocular aberration was measured under a scotopic condition with dark adaption in advance. Additionally, iTrace was adopted because it provided a peephole in the center of the placido disk that allowed subjects to look through the device at distant targets, which further relieved accommodation and led to reliable results. With these efforts, it was found that the pupil sizes were very well maintained between measurements both within and between sessions, leading to the overall satisfactory repeatability of the results. However, it should be pointed out that even in the current circumstance, the measurement repeatability of defocus and spherical aberrations was relatively poorer, given that these two types of aberrations are most likely to be influenced by accommodation [25, 26]. This might be also due to the fact that all participants in the present study were Chinese with deep brown iris, whose pupil sizes and the response to scotopic conditions may be significantly different from those observed in Caucasian [27, 28].In clinical practice, it is often required to compare ocular aberrations measured with different pupil sizes at different visits. To facilitate the comparison, one approach is to acquire a common pupil size by using the scaling technique developed by Schwiegerling [29]. Pupil scaling is a mathematical procedure by which the measured Zernike coefficients for a larger pupil size are estimated for a smaller pupil size or vice versa. In the present study, it was shown that the intrasession or intersession differences of the values produced by using the scaling-down technique were not statistically significant for the majority of the Zernike components, which lends credence to using this approach in practice to compare results from different pupil sizes between visits. But how is difference between these estimated values and the truly measured values? A recent study [30] showed that the estimation of ocular aberration coefficients by either scaling down from large to smaller pupils or by scaling up from smaller to large pupils provided comparable results from clinically measured values. Although it might be difficult to directly compare the results produced by different instruments (the previous study used a Harmann-shack-principle-based aberrometer, whereas the current study used a ray-tracing-technique-based aberrometer), the comparison we found were more complicated. Specially, MTF at all spatial frequencies estimated using the scaling-down technique did demonstrate comparable results with the corresponding measured values. The majority of estimated Zernike coefficients were consistent as well with the corresponding ones, but the estimated defocus, coma, and the corresponding total aberrations were found significantly smaller than the measured values. In addition, it was observed that the variation between measurements was greater than those obtained from direct comparison between measured values. Therefore, it is suggested that comparing results by scaling the pupil down to an identical size between visits is only the second-best option, following a direct comparison with true values acquired under the circumstances in the current study. Another point worth noting is that when using the scaling technique, the rescaled magnitude should be minimal, as the present study applied the largest integer pupil size of all measurements. This is because the results from previous studies suggested that a larger scaling range tended to produce greater variability between measurements [30–32].Caution should be taken when applying the findings of our study. First, ocular aberration is a dynamically changing parameter and each measurement actually only provided data for a static snapshot during the dynamic course [33]. To produce a reliable outcome, it is therefore critical to control the influencing factors, including pupil size and accommodation, and to adopt repeated measurements. Further, some unavoidable factors, such as the intrinsic variability of aberrations [12] and the variability associated with blinks [34], may also affect the consistency of repeated measurements. It is therefore important to acquire the aberration data at a very high speed. One advantage of the iTrace used in the study was that it can take a snapshot within 1/8th of a second [35] and thereby minimize the effects that the tear film and accommodation microfluctuations have on optical aberrations. Thus, the instrument adopted is another essential factor in determining the repeatability of ocular aberration measurements. Additionally, subjects in the current study were normal population, in whom aberrations are low to moderate. The results might be not necessarily applicable for highly aberrated eyes. Extrapolation of the current results to the populations who do not fall into the range of the myopia degree or axial length should be also avoided, because ocular aberration has been found to be related to both the refractive error [36] and axial length [37]. Therefore, further investigation in a population with wider demographic characteristics is warranted in the future.In summary, although influencing factors such as pupil size and accommodation status impose challenges to obtaining reliable aberration measurements in children, our study showed that satisfactory intra- and intersession repeatability could be achieved under scotopic conditions by using iTrace. Scaling-down technique with the largest integer pupil size as the common pupil size offers a useful option to compare results obtained from different pupil sizes between visits, but caution should be taken because the estimated Zernike coefficients were not always comparable with the corresponding measured values.



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*Source: 2043718-2018-02-11.xml*