Higher order aberrations and retinal image quality during short‐term accommodation in myopic and non‐myopic children

Despite the known associations between near work and myopia, and retinal image quality and eye growth, accommodation‐induced changes in higher order aberrations (HOA's) and retinal image quality in children with different refractive errors are poorly understood.

Higher order aberration and retinal image quality changes during accommodation should be considered in the context of the accommodation response (AR). Typically, adults 2,14-17 and children 8,18,19 exhibit a lead of accommodation for low accommodation demands (<2-3 D) and a lag of accommodation for higher accommodation demands (>3 D), with increasing accommodation demands associated with an increasing lag. Myopic adults [20][21][22] and children 18,19 have been reported to exhibit greater lags of accommodation than emmetropes; however, more recent findings have shown minimal differences between refractive error groups in adults 23 and children, 24 although AR's tend to be less stable for myopes compared with emmetropes. 25,26 There remains no consensus regarding refractive error differences in accommodation errors (AE's), likely due to various factors influencing accommodation measurements, including the stability of an individual's myopia, 14 target characteristics, 27 methods for inducing accommodation, 28 and the effect of HOA's, predominantly spherical aberration (SA), on the objective refraction measurements used to calculate AE's. 17,[28][29][30] Studies of adults have consistently reported that accommodation results in minimal changes in higher order (HO) root mean square (RMS) aberrations for accommodation demands <3 D, [1][2][3]7 but an increase for 3-6 D demands for a fixed pupil. 1,2,7 However, only one study has previously examined accommodation-induced HOA changes in children, at demands of 0, 3, 6 and 9 D, and demonstrated that HO RMS values only increased significantly for the 9 D demand for a fixed 4 mm pupil. 8 This 'deferred' increase in HOA's to a higher accommodation demand compared with adults was proposed to be the result of age-related differences in the amplitude of accommodation, 31,32 and possible differences in the required accommodative effort between adults and children.
In both adults 1,3,4,6,7,33 and children, 8 primary SA (C 0 4 ) is typically positive during relaxed accommodation (0 D demand), 1,3,4,6,33 and undergoes a monotonic negative shift with increasing levels of accommodation, resulting in negative values for accommodation demands >3 D. 1,7 Secondary SA ( C 0 6 ) also changes during accommodation; however both a positive 34 and negative shift 5 have been reported for a 2.5 D accommodation demand in adults, and a positive trend was observed in children. 8 One study of adults has also reported significant changes in coma during accommodation, 1 although this finding was inconsistent across individual study participants, and other studies of adults 4,5,7 and children 8 have not shown comatic changes.
Several studies of young adults have demonstrated that retinal image quality also varies during accommodation. For example, the visual Strehl ratio based on the modulation transfer function (VSMTF) 35 and optical transfer function (VSOTF) 16,17 generally declines with increasing accommodation between 0 and 5 D demands across a fixed pupil diameter. However, less accommodation-induced retinal image quality changes have been observed for natural pupil sizes. Lopez-Gil et al. 16 reported negligible change in the VSMTF between 0 and 5 D demands, while Buehren and Collins 17 found a slight improvement in the VSOTF from a 0 to 1 D demand and a steady decline between 1 and 5 D. These findings indicate that HOA changes during accommodation in adults typically result in diminished retinal image quality, which may be moderated by the pupillary miosis associated with accommodation.
Retinal image quality changes during accommodation between refractive error groups and in children remains unclear. Using direct HOA measurements during accommodation, Hughes et al. 8 found that the VSOTF was significantly diminished for a 9 D demand for a fixed 4 mm pupil diameter and natural pupils for non-myopic children. 8 In an earlier study, accommodation-induced changes in the VSOTF were found to be of similar magnitude in young myopic and emmetropic adults, 36 and later research revealed that adults with progressing myopia exhibited a reduced VSOTF compared with emmetropic adults when viewing a near target at their habitual working distance. 37 However, these are the only studies to have examined differences in accommodationinduced changes in HOA's and retinal image quality between refractive error groups in adults, and no studies of children have been undertaken to date. Therefore, the aim of this study was to compare HOA and retinal image quality changes during accommodation between myopic, school-aged children and age-and sex-matched non-myopic children.

METHODS
Approval was obtained from the Queensland University of Technology Human Research Ethics Committee prior to study recruitment, and all children and their parents/

Key points
• Myopic children exhibited greater changes in asymmetric higher order aberrations and with-the rule astigmatism compared with nonmyopes, which was associated with a greater reduction in retinal image quality. • Accommodation-induced optical changes may have implications for the association between myopia development and progression and near work behaviours like short working distances. • Non-myopes underwent greater changes in spherical aberration than myopes, which may increase the depth of focus and lead to a smaller reduction in retinal image quality for high accommodation demands.
guardians gave their written informed assent and consent, respectively.

Participants
Eighteen myopic children (11 males and 7 females) with a mean (SD, standard deviation) age and spherical equivalent refraction (SER) of 10.1 (1.4) years (range 7 to 12 years) and −2.08 (0.92) D (range −0.75 to −3.50 D), respectively, were recruited. All myopic children were habitually corrected with single vision distance spectacles, and none had used orthokeratology, atropine eye drops, myopia control spectacles or soft contact lenses. Eighteen ageand sex-matched non-myopic children who participated in a previous study 8 were also included. The mean (SD) age of the non-myopic participants was 10.0 (1.2) years (range 7 to 12 years), which was not significantly different from the myopic group (independent-samples t-test, p = 0.88). The mean (SD) SER of the non-myopic children was +0.63 (0.25) D (range +0.25 to +0.88 D). All myopic and non-myopic participants were in good general and ocular health, had a cylindrical refraction of ≤0.75 DC, and visual acuity of ≤0.1 logMAR in both eyes. All participants demonstrated a push-up amplitude of accommodation of ≥9 D using an N6 target and had no significant binocular vision anomalies or amblyopia.

Instrumentation
Total ocular HOA's were measured using the COAS-HD (Wavefront Sciences Inc., acquired by Johnson & Johnson, www.jnj.com), a well-validated Hartmann-Shack wavefront aberrometer. 38,39 The COAS-HD uses a near-infrared superluminescent diode light source with a peak wavelength of 850 nm to sample the wavefront at the entrance pupil in 159 μm increments. Accommodation demands were presented using a Badal optometer attached to the COAS-HD as previously described. 8 The Badal optometer consisted of a longpass dichroic filter, angled at 45 degrees and positioned 20 mm from the eye, with reflectance of >97% between wavelengths of 400 and 630 nm, and transmission of >95% between wavelengths of 680 and 1200 nm. A +10 D best-form spherical Badal lens was positioned 80 mm from the filter (100 mm optical path distance from the corneal plane). Fixation targets were presented on a liquid crystal display at a fixed distance of 100 mm from a +20 D auxiliary lens, with the separation between the lenses varied to present accommodation stimuli (ocular vergence range of −15 to +5 D). Four emoticon targets subtending 206 minutes of arc (Snellen equivalent: 6/1236) (smallest spatial detail subtending 7 minutes of arc; Snellen equivalent: 6/42) were used to provide accommodation stimulation and maintain the interest and encourage steady fixation of the paediatric participants. The target presentations were fully randomised for each accommodation demand and participant ( Figure 1).

Data collection procedures
Following an initial 5 min washout period of distance fixation, the right eye of the participants was patched and they were instructed to fixate the emoticon target presented within the Badal optometer monocularly using their left eye (the choice of the left eye for measurements was arbitrary). The COAS-HD was aligned to the pupil centre and the corneal reflex was focused. The Badal optometer was calibrated to present a 0 D accommodation demand (i.e., the participant's wore no refractive correction and their SER was corrected using the Badal optometer) and the emoticon targets were aligned to the COAS-HD internal fixation target following verbal instructions from the participant. The target was then blurred by 2-3 D and slowly returned towards the 0 D position, with the participant asked to report when the target became clear, to ensure relaxed accommodation prior to measurements.
Wavefront aberrations were measured at four accommodation demands (0, 3, 6 and 9 D, based on the participant's SER), which were presented in semi-randomised order to reduce possible systematic effects of ascendingorder stimulus presentation, while minimising the potential loss of data from a single accommodation demand due to task disengagement. The first demand presented was either 0 or 6 D, followed by whichever was not presented first, the third demand was 3 or 9 D, and the final demand was the remaining level. The wavefront measurements at each demand included 25 individual wavefront measurements per capture (each measurement capture lasting 2 s), with five separate captures (i.e., 125 individual measurements). The mean (SD) total wavefront measurement duration for each accommodation demand, averaged across all participants and accommodation demands, was 53.95 (17.71) s. All room lighting was extinguished and F I G U R E 1 Badal optometer schematic, including the emoticon fixation targets. All distances are expressed as millimetres. V, visible radiation (400-650 nm); IR, infrared radiation (>650 nm); LPF, longpass dichroic filter; LCD, liquid crystal display. Figure reproduced from Hughes et al. 8 with permission from Elsevier. illuminance at the ocular plane during measurements was ~5 lux.

Data analysis
Wavefront data for each participant at each accommodation demand were exported into customised software and were screened based on manually-input settings for HO RMS and cylindrical refraction to remove significant outliers due to fixation loss, blinking or tear film disruption, as previously described. 8 Eighth order Zernike polynomials were fitted across fixed pupil diameters, with all individual measurements scaled down to the fixed pupil diameter and averaged. The group mean pupil diameter was determined by calculating the average pupil size at each accommodation demand for each participant based on the measured pupil sizes from the COAS-HD and the group average using each participant's mean pupil size was calculated.
Refractive power vectors, M (spherical power vector), J 180 (astigmatic power vector with axes of 180 and 90) and J 45 (astigmatic power vector with axes of 45 and 135), were determined from the wavefront slope for each participant at each accommodation demand for a 2.3 mm pupil diameter. 40 This diameter is reported as the minimum pupil size by manufacturers of various commercially available, openfield autorefractors commonly used in accommodation research (e.g., Shin-Nippon NVision-k 5001, Grand-Seiko WAM-5500 and Grand-Seiko WR-5100 K), which allowed a more accurate comparison with previous research of the AR in children, in addition to minimising the influence of HOA's, particularly SA, for the determination of refractive power at each accommodation demand. 17,29,30 Using the refractive power data, individual wavefront measurements were screened for active accommodation during each measurement capture, with any individual measurements or whole captures excluded if a marked difference in values of power vector, M was observed, which indicated a poor AR. Once the remaining frames were averaged, the AR for each participant at each accommodation demand was determined using the following equation: where M AD is the power vector, M, determined from the wavefront for a particular accommodation demand (3, 6 or 9 D) and M 0 is the power vector, M, for relaxed accommodation (0 D demand). To ensure only participants who were actively accommodating were included in the analysis, arbitrary criteria for screening of AR were used, with participants presumed to be actively accommodating if their mean AR was greater than 0.25, 0.50 and 0.75 D for the 3, 6 and 9 D accommodation demands, respectively. If the AR was less than the above thresholds, the data were excluded from further analyses for those demands.
Discrepancies between subjective and objective refraction measurements and the method used to stimulate accommodation can affect accommodation measurements captured using autorefractors and wavefront sensors. 41 The accommodation demands presented via the Badal optometer were based on the non-cycloplegic subjective refraction and the AR's and AE's were determined using objective measurements from the COAS-HD, which is affected by 'instrument myopia' such that the objective measurements of M over-estimate the level of myopia at each accommodation demand and, thus, underestimate the AR relative to the stimulus, overestimate the accommodative lag and do not detect accommodative leads. 40 Based on the design of this specific Badal optometer 42 and equations developed by Atchison and Varnas, 41 the 'adjusted' AR and accommodation stimulus (AS) were used to calculate the 'adjusted' AE according to the following equations (where positive and negative values indicate an accommodative lag and lead, respectively) (see Appendix S1 for derivations): where d refers to the separation between the Badal and auxiliary lenses of the Badal optometer, M 0 is the spherical power vector, M, for relaxed accommodation (0 D demand) and M AD is the spherical power vector, M, for a particular accommodation demand (3, 6 or 9 D demand).
Eighth order Zernike polynomials were fitted across a 4 mm pupil diameter for HOA and retinal image quality analyses. Although the seventh and eighth radial orders were included in all refractive power, HOA and retinal image quality analyses, since the magnitude of the seventh and eighth order values were very small, for simplicity, the RMS variables and individual Zernike coefficients for these orders are not presented. The RMS for HO (third to eighth order), third to sixth radial orders, coma (C −1 and SA (C 0 4 and C 0 6 ) were determined for each participant and averaged for each accommodation demand. Retinal image quality was examined using the visual Strehl ratio based on the optical transfer function (VSOTF), which was calculated for each participant at each accommodation demand and averaged. The VSOTF was determined as the area under the curve of the optical transfer function of the aberrated eye (OTF AE ) relative to a diffraction-limited eye (OTF DL ), weighted by the neural contrast sensitivity function (CSF N ), as per this equation: Only the third to eighth radial orders were included in the VSOTF calculation to explore the sole effect of HOA's on retinal image quality during accommodation.
Refractive power maps were generated from the mean wavefront (third to eighth radial orders) at each accommodation demand for the 4 mm pupil, and frequency histograms of the refractive power distribution across the pupil were also generated for each accommodation demand using customised software.

Statistical analyses
Based on preliminary data captured from four participants (two myopes and two non-myopes), a minimum total sample size of 28 (14 in each refractive error group) was required to detect an interaction between refractive error group and accommodation demand for HO RMS and primary SA (C 0 4 ) calculated for a repeated measures analysis of variance assuming an alpha-error probability of 0.05 and power of 0.8 using G*Power. 43 Linear mixed model (LMM) analyses were carried out for the refractive power vectors (M, J 180 and J 45 ), AE, each RMS variable and individual Zernike coefficient, pupil size and the VSOTF, with fixed factors of accommodation demand and refractive error group, and the interaction between these fixed factors. A 'restricted maximum likelihood' strategy was used to account for missing data and a 'variance components' matrix covariance structure was used for the repeated measures and random effects. For any parameters where the LMM revealed a significant effect of accommodation demand, pairwise comparisons using a Sidak correction 44 for multiple comparisons were undertaken. If a significant interaction between refractive error group and accommodation demand was found for any variables, a subsequent LMM analysis with the same fixed factors was undertaken using the change in each variable from the 0 D accommodation demand. Pairwise comparisons with a Sidak adjustment were carried out to examine refractive error group differences for each demand.
Additional LMM analyses were undertaken (using the same matrix covariance structure and strategy) to explore associations between the AE and the HOA's. For the RMS variables and individual Zernike coefficients, an LMM with AE as a covariate and refractive error group as a fixed factor to explore main effects and interactions between the AE and refractive error group.

Participant characteristics
One female myopic participant reported blurring of the stimulus target at all accommodation demands except for 0 D and was excluded from the analyses along with the corresponding age-and sex-matched non-myopic participant; therefore, 17 participants in each refractive error group remained in the analyses. The mean (SD) age for the myopic and non-myopic children was similar (10.2 (1.4) and 10.1 (1.2) years, respectively) (independent-sample two-tail t-test, t (31) = 0.217, p = 0.83).
For some participants, unreliable data, a measured pupil size below 4 mm or poor AR's were observed at some accommodation demands, which resulted in a smaller sample size for some demands. The group mean SER and age of the included participants was similar for all accommodation demands (SER: F 3,108 = 0.311, p = 0.82; age: F 3,108 = 0.069, p = 0.98) and there were no differences in the mean SER or age between any of the accommodation demands for either refractive error group (accommodation demand by refractive error group interaction, SER: F 3,108 = 0.191, p = 0.90; age: F 3,108 = 0.180, p = 0.91). On average, across all accommodation demands, there was no significant difference in age between the refractive error groups (F 1,108 = 1.674, p = 0.20; Table 1).

Change in accommodation error, pupil size and refractive power during accommodation
The AE varied significantly with accommodation demand (F 3,80.697 = 89.613, p < 0.0001) ( Table 2). Both refractive groups showed a lead of accommodation for the 0 D demand, with an increasing lag of accommodation observed with increasing accommodation demand. The AE was significantly different between all accommodation demands (all pairwise comparisons p ≤ 0.04) except 6 and 9 D (pairwise comparison p = 0.41). There was no significant interaction between refractive error group and accommodation demand (F 3,80.697 = 1.596, p = 0.20), but the myopic group exhibited a slightly greater lag of accommodation (i.e., reduced AR) compared with the non-myopic group for the 9 D accommodation demand.
The spherical equivalent refractive power vector, M, was significantly more negative in the myopic group than the non-myopic group (F 1,32.740 = 102.211, p < 0.0001), as expected. The astigmatic power vector, J 180 was significantly more positive for the myopes on average across all accommodation demands compared with the non-myopes (F 1,32.479 = 4.422, p = 0.04), but there was no difference between the groups for J 45  demand compared with all other demands (all pairwise comparisons p ≤ 0.01), and the astigmatic power vector, J 45 , was significantly greater at the 6 and 9 D demands than the 0 D demand, and the 9 D demand was significantly greater than the 3 D demand (all pairwise comparisons p ≤ 0.01).
The variation of M and J 45 with accommodation was similar in the two refractive error groups (M: F 3,78.142 = 1.422, p = 0.24; J 45 : F 3,77.795 = 2.025, p = 0.12); however the interaction between accommodation demand and refractive error group was significant for with-therule astigmatism, J 180 (F 3,77.115 = 3.987, p = 0.01), with the myopes exhibiting a larger positive shift in J 180 than the non-myopes (F 3,81.614 = 10.107, p < 0.0001). Pairwise comparisons revealed that the myopes exhibited a significantly greater shift in J 180 than the non-myopes at the 6 and 9 D demands (both pairwise comparisons p ≤ 0.008).  (Table S1). For HO, third order, fourth order, coma and SA RMS, the levels were significantly greater at the 9 D demand compared with all other demands (all pairwise comparisons p ≤ 0.05), and compared with the 3 D demand, the levels of fifth order, sixth order and trefoil RMS were significantly increased for the 9 D demand (all p ≤ 0.006). HO, third order, fifth order, sixth order and trefoil RMS were also significantly greater for the 6 D demand compared with 0 D (all pairwise comparisons p ≤ 0.05).

Change in root mean square variables during accommodation
On average across all accommodation demands, the refractive error groups exhibited similar magnitudes for all RMS variables, except SA RMS, where the non-myopic children exhibited greater levels compared with the myopes (F 1,108.000 = 7.516, p = 0.007); however, the pattern of change in SA RMS with accommodation was similar between the groups (F 3,108.000 = 1.456, p = 0.23). A significant interaction between refractive error group and accommodation demand was observed for HO (F 3,79.522 = 3.316, p = 0.02) and third order RMS (F 3,78.737 = 3.667, p = 0.02). The myopic group exhibited a greater increase in HO (F 3,76.578 = 3.192, p = 0.03) and third order RMS (F 3,76.049 = 3.550, p = 0.02) than the non-myopic group with pairwise comparisons revealing that the change in HO and third order RMS at the 9 D demand was significantly different between the refractive error groups (both p = 0.001) (Figure 2).

Change in individual Zernike coefficients during accommodation
Significant changes during accommodation were observed for primary vertical coma (C  monotonic positive trend, becoming significantly more positive at the 9 D demand compared with the 0 D demand (p = 0.002) (Table S1). Primary horizontal coma (C 1

3
) was more negative at the 9 D demand compared with all other accommodation demands (all pairwise comparisons p ≤ 0.001) and primary vertical coma (C −1 3 ) was more positive at the 9 D demand compared with the 0 D demand only (p = 0.03). Compared with all other accommodation demands, secondary vertical astigmatism (C 2 4 ) was more positive at the 9 D demand (all pairwise comparisons p < 0.0001), and tertiary vertical astigmatism (C 2 6 ) was more negative at the 6 and 9 D demands compared with 0 and 3 D (all pairwise comparisons p ≤ 0.01). Primary oblique (C −4 4 ) and vertical quadrafoil (C 4 4 ) changed significantly during accommodation (p ≤ 0.03), with vertical quadrafoil (C 4 4 ) becoming more negative at the 9 D demand compared with 0 D (p = 0.01).

Differences between refractive error groups for individual Zernike coefficients during accommodation
Various Zernike coefficients were significantly different on average across all accommodation demands between the refractive error groups. The myopic children displayed a more positive value for primary vertical coma (C −1 3 ) (F 1,32.359 = 5.296, p = 0.03) and secondary horizontal coma (C 1 5 ) (F 1,35.763 = 8.088, p = 0.007) and a more negative value for tertiary vertical astigmatism (C 2 6 ) compared with the non-myopes (F 1,33.615 = 6.098, p = 0.02).
There was a significant refractive error group by accommodation demand interaction for several individual Zernike coefficients, including primary SA (C accommodation than the myopic group (F 3,76.477 = 5.184, p = 0.003), with significant refractive error group differences at the 6 and 9 D demands (both pairwise comparisons p ≤ 0.02). The non-myopic group also exhibited a greater change in secondary SA (C 0 6 ) with increasing accommodation than the myopic group (F 3,77.936 = 4.745, p = 0.004), with a significantly greater positive shift at the 6 and 9 D demands compared with the myopic children (both pairwise comparisons p ≤ 0.05).
A greater change in secondary oblique quadrafoil (C −4 6 ) was observed in the non-myopic group than the myopic group (F 3,76.299 = 4.347, p = 0.007), with a negative shift at the 9 D demand found to be significantly different to the myopic group (pairwise comparison p = 0.006). For all other Zernike coefficients that exhibited different patterns of change with accommodation in the two refractive error groups, the differences arose due to the myopic group exhibiting greater changes than the non-myopic group (all p ≤ 0.01). There was a significant difference between the myopes and non-myopes for the change in primary oblique quadrafoil (C −4 4 ) at the 6 and 9 D demands (both pairwise comparisons p ≤ 0.02), secondary vertical trefoil (C −3 5 ) at the 6 D demand (pairwise comparison p < 0.0001), and secondary horizontal coma (C 1 5 ) at the 9 D demand (pairwise comparison p < 0.0001), where the myopic group exhibited positive shifts. A significant negative shift in the myopic group was observed for secondary vertical astigmatism (C 2 4 ) at the 6 and 9 D demands (both pairwise comparisons p ≤ 0.02), tertiary vertical astigmatism (C 2 6 ) at the 3, 6 and 9 D demands (all pairwise comparisons p ≤ 0.05), and secondary oblique trefoil (C 3 5 ) at the 9 D demand (pairwise comparison p = 0.001) compared with the non-myopic group.
To illustrate the refractive error group differences, mean refractive power maps were generated from the group mean wavefronts (third to eighth radial order) for each accommodation demand, using customised software based on Zernike power polynomials described by Iskander et al. 40 (Figure 4). Each map demonstrates the range of dioptric powers distributed across the entrance pupil plane for each accommodation demand, based on Snell's law. Note the symmetry of the refractive power across the pupil for the non-myopic children and the asymmetry for the myopic children and that the trend from 0 to 9 D is for the refractive power near the pupil centre to become more positive while the pupil periphery becomes more negative. Histograms displaying the frequency of these refractive powers across the range of refractive powers within the pupil for each accommodation demand and refractive error group are presented in Figure 5. Note the greater range of refractive powers present within the pupil and increasing frequency of negative refractive powers for higher accommodation demands, which is more marked for the myopic group.  There was a significant interaction observed between AE and refractive error group for HO RMS (F 1,97.270 = 4.160, p = 0.04), third order RMS (F 1,94.487 = 9.864, p = 0.04) and secondary oblique astigmatism (C −2 4 ) (F 1,94.604 = 5.536, p = 0.02). For each of these variables, the slope was significant for the myopic children (all p < 0.001), with a positive trend for HO and third order RMS and a negative association for secondary oblique astigmatism (C −2 4 ), but the slopes were not significant for the non-myopic children (all p ≥ 0.42) ( Table 3).

Change in the visual Strehl ratio based on the optical transfer function during accommodation
For the 0 D demand, the mean VSOTF (SEM) for a fixed 4 mm pupil was 0.872 (0.014) for all participants combined, and 0.857 (0.025) and 0.886 (0.013) for the non-myopic and myopic children, respectively. The VSOTF decreased with increasing accommodation demand (F 3,80.106 = 30.521, F I G U R E 4 Refractive power maps for each accommodation demand determined from the group mean wavefronts (third to eighth radial orders) across a 4 mm pupil for the (a) non-myopic and (b) myopic children. Positive and negative values indicate relative convergence and divergence of light rays, respectively. Note that the data are for the left eye. The refractive error group by accommodation demand interaction was also significant (F 3,80.106 = 2.704, p = 0.05). The mean change in the VSOTF from 0 D (SEM) was −0.034 (0.021), −0.100 (0.034) and −0.274 (0.048) for the myopic children, and 0.007 (0.013), −0.036 (0.026), and −0.131 (0.052) for the non-myopic children for the 3, 6 and 9 D demands, respectively. The VSOTF change with accommodation was significantly different between the refractive error groups (F 3,77.266 = 2.956, p = 0.04), with the myopic group exhibiting a greater reduction at the 9 D demand compared with the non-myopic group (pairwise comparison p = 0.001; Figure 6).

DISCUSSION
This is the first study to examine differences in accommodation-induced changes in HOA's and retinal image quality between myopic and non-myopic children and must be interpreted in the context of the AR. Consistent with previous studies using open-field autorefractors in adults 14,15 and children, 18,19 and using wavefront sensors in adults 2,16,17 and non-myopic children, 8 the typical accommodation stimulus-response function was observed in both refractive error groups, with a lead of accommodation (−0.79 D) found for the 0 D demand and a trend of an increasing lag of accommodation with increasing levels of accommodation (0.64, 1.00 and 1.27 D at the 3, 6 and 9 D demands, respectively). There was a tendency for the myopes to exhibit a larger lag of accommodation (by ~0.50 D) at the 9 D demand compared with the non-myopes; however, these differences were not statistically significant. Although several previous studies in adults [20][21][22] and children 18,19 have demonstrated that myopes exhibit a reduced AR compared with emmetropes, in this experiment, a 2.3 mm pupil was used to determine the refractive power vectors to minimise the influence of SA on the determination of the spherical power vector, M, and may explain the similarity of the AE's between the two refractive error groups, 17,29,30 in contrast to previous studies.
Significant associations between AE and HO RMS, third order RMS and primary oblique astigmatism (C −2 4 ) were observed for the myopic children, whereby a significantly greater lag of accommodation was associated with increased TA B L E 3 Estimated linear regression slopes and standard error (SE) based on the estimate of fixed effects from the linear mixed model (LMM) analyses for the association between accommodation error (AE) and higher order (HO) and third order root mean square (RMS) and secondary oblique astigmatism (C −2 4 ) for the non-myopic and myopic children. Pearson correlation coefficients (r) and p-values (p) for the associations are also displayed. levels of HO and third order RMS and more negative values of primary oblique astigmatism (C −2 4 ) for the myopes. Although significant, the change in HO and third order RMS explained only ~16% of the variance in AE, and the change in primary oblique astigmatism (C −2 4 ) explained ~11%; hence, these associations are weak and are likely to simply reflect the observed accommodation-induced trends in the data.

RMS variable
Compared with the non-myopic children, the myopic children exhibited a greater increase in with-the-rule astigmatism, J 180 during accommodation at the 6 and 9 D demands. As shown in chicks [45][46][47] and rhesus monkeys, 48 imposed astigmatic blur may disrupt emmetropisation and normal eye growth, although a consistent response has not been observed, 49 with some studies showing that eyes adjust their growth towards the more myopic (i.e., reduced eye growth) 45 or less myopic meridian (i.e., increased eye growth), 47,48 or shift towards the circle of least confusion. 46 Against-the-rule astigmatism has also been linked with increased myopia prevalence, 50 and higher rates of myopia progression in children. 51 A recent study in young adults also reported that imposed with-the-rule (+3 DC × 180) and against-the-rule myopic astigmatic defocus (+3 DC × 90) resulted in a small, but statistically significant increase and decrease in choroidal thickness, respectively. 52 Therefore, the differences in the astigmatic changes during higher levels of accommodation between the myopes and nonmyopes may have implications for refractive error development and eye growth and requires further study.
For all participants, all RMS variables across a 4 mm pupil increased significantly at the 6 and/or 9 D demand compared with the 0 D demand. Consistent with a previous study of non-myopic children, 8 most of the HO RMS changes were considerably lower than for adults for the same accommodation demand [3][4][5]7 and this may be due to reduced biomechanical effort by the children to produce the same AR. Similarly in adults, it has been reported that increasing age is associated with greater changes in HO RMS during accommodation for a fixed 4 mm pupil. 33 The non-myopic group exhibited approximately twice the negative shift in primary SA (C 0 4 ) compared with the myopic group at the 6 and 9 D demands. The non-myopes also exhibited a significant positive shift in secondary SA (C 0 6 ) at the 6 and 9 D demands compared with negligible change for the myopes. Only one study has examined refractive error group differences in accommodation-induced HOA changes and reported that the magnitude of change in longitudinal SA during accommodation was similar in myopic and nonmyopic young adults up to a 3 D stimulus; however the myopes exhibited more negative values than the non-myopes at each AS (0, 1.5 and 3 D). 36 Similarly, the mean level of primary SA (C 0 4 ) was less positive for the myopes at the 0 and 3 D demands in the present study, but in contrast for higher accommodation stimuli, the non-myopes displayed more negative primary SA (C 0 4 ) on average at the 6 and 9 D demands. The myopic children underwent a 10-fold greater positive shift in primary vertical coma (C −1 3 ) compared with the non-myopes at the 9 D stimulus, and a substantial negative shift in primary horizontal coma (C 1 3 ) at the 6 and 9 D demands compared with negligible change in the nonmyopic children. These changes were also reflected in the 3.5 times greater increase in third order RMS at the 9 D stimulus in the myopic group compared with the nonmyopic group. Previous studies have reported associations between changes in coma and axial elongation and refractive error shifts in children during normal myopia progression and orthokeratology treatment. In a retrospective analysis of children with myopia (presumably wearing single vision spectacles), fast progressors (≤−0.50 D per year) exhibited significantly greater levels of third order and coma RMS and more negative levels of primary vertical coma (C −1 3 ) compared with slow progressors (>−0.50 D per year). 53 More positive values of primary vertical coma (C −1 3 ) and more negative values of horizontal coma (C 1 3 ) have also been associated with reduced axial elongation and myopia progression in a longitudinal study of single vision spectacle-corrected myopic children. 54 Recent studies have also reported that an increase in third order 55,56 and coma RMS 55 during orthokeratology were associated with reduced axial elongation during treatment; however, these findings do not provide any information regarding the sign of the coefficients. These studies suggest that the more positive primary vertical coma (C −1 3 ) and more negative primary horizontal coma (C 1 3 ) that arose during accommodation in the myopic group, after accounting for enantiomorphism, may be a factor that could contribute to greater axial elongation and myopia development associated with near work. For all other Zernike coefficients, where the patterns of accommodation-induced change differed between the refractive error groups, except for secondary oblique quadrafoil (C −4 6 ), the myopic group exhibited larger-magnitude changes than the non-myopic group, mostly for the 6 and 9 D demands. Several of these individual Zernike aberrations, including coma, trefoil, quadrafoil and astigmatism, are those that produce wavefronts that have mirror asymmetry across the vertical or horizontal midlines and produce meridional differences in the optical vergence variations across the pupil. Conversely, although the nonmyopic group also had poorer retinal image quality at the high accommodation demands compared with lower stimuli, they exhibited greater changes in symmetrical aberrations such as SA, which may have improved the depth of focus (DoF) at the 6 and 9 D demands for the non-myopes more than for the myopes, since combinations of oppositely signed primary (C 0 4 ) and secondary SA (C 0 6 ) have been shown to considerably improve the DoF of the eye. [57][58][59] The accommodation-induced changes observed in the myopic group in this study provide some evidence for a potential role for refractive power, HOA and retinal image quality changes during accommodation as an underlying mechanism for childhood myopia development associated with near work. Although near work has been linked with higher myopia prevalence, 60,61 recent studies have demonstrated that particular behaviours indicative of greater near work intensity are more strongly associated with myopia prevalence, including continuous near work or reading without breaks and the use of working distances of <30 cm. [11][12][13] The difference in the accommodation-induced changes between the myopes and non-myopes occurred predominantly for the 6 and 9 D accommodation demands, which corresponds to working distances of <17 cm; therefore, it is possible that the observed optical changes could play a role in possible near work-associated myopia development and progression.
There are several possible mechanisms by which refractive error development and eye growth could be influenced by the observed differences in the accommodationinduced changes between the refractive error groups. Firstly, the degradation of the retinal image due to the greater levels of HOA's, particularly asymmetric HOA's like coma, could provide a form deprivation-like stimulus that produces axial elongation. Secondly, the ocular growth response to imposed defocus in chicks has been shown to be due to the detection of optical vergence within the retinal image. 62 Since HOA's produce optical vergence variations across the pupil, it may be possible for the retina to detect these optical vergence variations, which could trigger changes in eye growth; however, further studies are required to explore these theories more fully. Furthermore, given that the paradigm in most animal studies was the constant imposition of a form deprivation or defocus stimulus, 63,64 consideration must be given to the working distances and time duration that children spend performing continuous near work tasks comparable with the 6 and 9 D demands in this study.
Short working distances have been reported to be used by children in China 12,65 and Australia 66 when performing near tasks, ranging from <10 cm to ~25 cm. Bao et al. 65 also reported that the working distance during reading and writing tasks can also reduce by ~5 cm within 3 min of task commencement. Studies of Australian children have estimated near work totals of 27-30 h/week (3.9-4.3 h/day), 67 and from 1.6 to 2.8 h/day in Singaporean children. 68 During school hours on a typical Australian school day, the mean duration of continuous near tasks is ~23 min/task, and cumulative totals of near work averaged ~2 h/day; however these observations do not account for additional time engaged in near work outside of school. 66 Therefore, it is possible that children spend many hours per day engaged in sustained near tasks, at working distances much shorter than the 17 cm corresponding to the 6 D demand in this study, which potentially exposes the retina to such HOA increases and degraded image quality for considerable durations of time. It should be noted that the short-term accommodation task utilised in this experiment does not accurately reflect the dynamic nature of near work tasks encountered on a typical day by children, and further studies examining HOA and retinal image changes during prolonged accommodation tasks are required.

CONCLUSION
This study evaluated differences in HOA's and retinal image quality in school-aged non-myopic and myopic children during accommodation. Myopic children exhibited substantially greater changes in with-the-rule astigmatism (J 180 ), primary vertical (C −1 3 ) and horizontal coma (C 1 3 ), and many other individual Zernike terms with accommodation. Non-myopic children displayed a significantly greater negative and positive shift in primary (C 0 4 ) and secondary SA (C 0 6 ), respectively. Retinal image quality declined significantly for high levels of accommodation in both refractive error groups, but image quality in myopic children underwent a greater reduction. These findings may have implications for myopia development and the association with near work and accommodation.

AC K N O W L E D G E M E N T S
The authors thank Henry Kricancic for his contributions to the construction of elements of the instrumentation, Pryntha Rajasingam for her assistance with data collection, and Robert Iskander for developing the customised software used in the experiment. Open access publishing facilitated by Queensland University of Technology, as part of the Wiley -Queensland University of Technology agreement via the Council of Australian University Librarians.

FU N D I N G I N FO R M AT I O N
This study was supported by an Australian Government Research Training Program Stipend (Domestic) and a Queensland University of Technology Excellence Top-Up Scholarship.

CO N F L I C T O F I N T E R E S T S TAT E M E N T
The authors report no conflicts of interest and have no proprietary interest in any of the materials mentioned in this article.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data are available from the corresponding author upon request.

I N FO R M E D CO N S E N T
Written informed consent was granted by the parents/ guardians of the participants, and participants provided their informed assent.