1. Introduction

The higher order aberrations (HOA’s) of the eye are produced by the curvature, alignment, and axial separation of the anterior and posterior surfaces of the cornea and crystalline lens, and the refractive indices of the cornea, crystalline lens, and the aqueous and vitreous humour. Typically, the anterior corneal HOA’s are of greater magnitude than the total ocular HOA’s, due to the partial internal “compensation” effect from the internal HOA’s arising from the posterior cornea and crystalline lens surfaces [1–3].

In adults, it is well-established that total ocular HOA’s tend to increase between ∼20 and 80 years [3–7], primarily due to crystalline lens changes [3] with a small contribution from an increase in anterior corneal HOA’s [8–10]. In general, infants [11] and children [12] have been reported to exhibit greater HOA’s than adults. However, the stability or change in HOA’s during childhood and adolescence is less clear. A large study of Chinese children (1634 eyes) reported an increase in HOA’s between 3 and 17 years [13], while a small study of Canadian children (29 eyes) found a reduction between 6 and 20 years [7]. However, the differences in sample size, methodology and instrumentation, refractive error, and ethnicity among these studies limit the ability to compare these results.

Although the literature is inconsistent, whole eye HOA’s may also vary with refractive error in children. Cross-sectional studies of children have suggested that myopic [12,14] and hyperopic children [15] exhibit greater levels of HOA’s than emmetropic and low hyperopic children. Primary spherical aberration ($C_4^0$) has been reported to become more positive with less myopia/more hyperopia [15,16], although other studies have not reported similar trends [17–19].

Few studies have examined refractive error group differences in anterior corneal and internal ocular HOA’s. In adults, Artal et al. [2] reported greater levels of anterior corneal and internal ocular HOA’s in hyperopes than myopes, however myopes displayed slightly greater levels of total ocular HOA’s compared to hyperopes. In adolescents, Philip et al. [20] reported negligible differences in the composition and magnitude of the anterior corneal HOA’s among refractive error groups, however, low hyperopes displayed significantly more negative internal ocular primary spherical aberration ($C_4^0$) and vertical coma ($C_3^{ - 1}$), and less positive primary horizontal coma ($C_3^1$) compared to emmetropes and myopes. These differences in internal ocular HOA’s between refractive error groups resulted in greater levels of total ocular coma and spherical aberration in the low hyperopes compared to emmetropes and myopes, in contrast to findings in adults [2]. However, no other studies to date have explored the composition of anterior corneal, internal ocular, and total ocular HOA’s or the internal compensation effect in children.

HOA’s are known to degrade objective retinal image quality [21–23], which may influence eye growth and refractive error development [24–26], however retinal image quality in children has not been investigated in detail. Little et al. [19] reported that the Visual Strehl (VS) ratio was similar for myopic, emmetropic, and hyperopic children and adolescents, and Philip et al. [27] showed that the VSOTF (VS ratio based on the optical transfer function) derived from HOA’s alone was similar at the baseline visit in adolescents who exhibited a myopic refractive shift (greater than -0.50 D) and those with a stable refraction over five years.

These studies suggest that the internal optics of the eye and less internal ocular compensation may contribute to total ocular HOA and retinal image quality changes over time, which may influence refractive error development [24–26]. A fundamental understanding of the intraocular composition of HOA’s and factors that may influence HOA’s in children is important, yet currently limited. Therefore, the aim of this study was to comprehensively evaluate the composition of anterior corneal, internal ocular, and total ocular HOA’s, retinal image quality, and any internal ocular compensation of HOA’s in non-myopic, school-aged children, and to explore potential associations with age, sex, refractive error, and axial length (AL).

2. Materials and methods

2.1 Participants

Ethics approval was granted by the Queensland University of Technology (QUT) Human Research Ethics Committee and administrative approval was given by the Queensland Department of Education to conduct the study. All participants and their parent or caregiver provided written informed assent and consent, respectively, prior to participation.

One hundred and thirty-three children (66 males and 67 females) aged between 4 and 12 years (mean ± standard deviation (SD), 7.8 ± 1.9 years) were recruited from the student population of a primary school in Brisbane, Australia. Children were eligible for inclusion if their spherical equivalent refraction (SER) was non-myopic (≥ 0.00 D) and had a cylindrical component of 0.75 DC or less, as determined by non-cycloplegic subjective refraction. Participants had visual acuity of 0.1 logMAR or better in both eyes, good systemic and ocular health, and no binocular vision anomalies based on motility and cover testing. Forty-nine children were excluded as they either did not meet the eligibility criteria or were uncooperative during screening or attempted data collection. Reliable corneal topography and wavefront measurements were captured for eighty-four participants (38 males, 46 females) who were included in the analyses and had a mean age and SER (± SD) of 8.3 ± 1.8 years (range, 5 to 12 years) and +0.63 ± 0.35 D (range, 0.00 to +1.75 D), respectively.

2.2 Instrumentation

Anterior corneal topography of the left eye of each participant was captured using the E300 videokeratoscope (Medmont International Inc., Victoria, Australia). The E300 uses the Placido disk technique and is highly repeatable for determining corneal elevation [28] and anterior corneal HOA’s derived from corneal elevation data [29].

Total ocular HOA’s of the left eye were measured using the Complete Ophthalmic Analysis System (COAS-HD, Wavefront Sciences Inc., New Mexico, USA), which is a well-validated wavefront sensor based on the Hartmann-Shack principle [30]. This instrument uses a near-infrared superluminescent diode with a peak wavelength of 850 nm to image a point source at the fovea and captures the reflected light at the pupil plane via a telescopic relay system which samples the pupil at 159 µm increments. All measurements were re-calibrated to a wavelength of 555 nm by the COAS-HD software.

The IOLMaster 700 (Carl Zeiss Meditec AG, Jena, Germany), a highly repeatable ocular biometer [31], was used to measure ocular biometry of the left eye. This biometer uses swept-source optical coherence tomography via a tuneable laser with a central wavelength of 1055 nm and produces six cross-sectional measurements (B-scans) at 30-degree meridional intervals to determine the on-axis dimension of various ocular structures including AL.

A Badal optometer was attached to the COAS-HD and IOLMaster 700 (identical in design) to present a 0 D accommodation stimulus as described previously [32–34]. The Badal optometer (Fig. 1) consisted of a longpass dichroic filter positioned 20 mm from the eye and angled at 45 degrees. In this configuration, > 95% of wavelengths between 680-1200 nm and >97% wavelengths between 400-630 nm were reflected and transmitted, respectively (based on manufacturer specifications). A + 10 D best-form spherical Badal lens was placed 80 mm from the filter (i.e. 100 mm from the corneal plane) and a + 20 D best-form spherical auxiliary lens was fixed 100 mm from a liquid crystal display, on which emoticon targets were displayed to maximise engagement and fixation during measurements. The separation between the Badal and auxiliary lenses was altered to correct the SER and control accommodation stimuli.

 

Fig. 1. Schematic of the Badal optometer, including the emoticon fixation targets. All distances are expressed in millimetres. IR, infrared radiation (>650 nm); V, visible radiation (400-650 nm); LPF, longpass dichroic filter; LCD, liquid crystal display. The four emoticon images that were used as the experimental fixation targets were randomly presented.

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2.3 Methods

Four corneal topography images were captured using the E300 videokeratoscope while the participants fixated the centre of the Placido disk rings. During each acquisition, several images were captured for review and a high quality image with a quality score of >95 (based on centration, focusing, and eye movement) was selected. The review images were cleared, and this process was repeated until four images were acquired.

Wavefront measurements were captured using the COAS-HD, followed by ocular biometry measurements using the IOLMaster 700. For both instruments, the Badal optometer was calibrated to present a 0 D accommodation stimulus. The instruments were moved to the correct position by aligning and focusing the corneal reflex. The emoticon target of the Badal optometer was aligned to the internal fixation target of the instrument based on verbal directions from the participant. The target of the Badal optometer was then blurred by 2-3 D and slowly returned towards the 0 D position, with the participant asked to report when the target was clear. This was undertaken to confirm the SER and relax accommodation prior to measurements. A single measurement was captured with the IOLMaster 700, and 5 captures of 25 individual measurements were taken for the COAS-HD (125 individual measurements in total). For the COAS-HD measurements, each capture lasted 2 seconds. Before each capture, the corneal reflex was refocused, and the instrument realigned to the pupil centre. Each subsequent capture was obtained as soon as practicable after the former capture, with the children remaining in the chin rest between measurements. The mean (± SD) time between captures was 11.5 ± 6.3 seconds, with the mean (± SD) total duration of measurements being 52.1 ± 15.8 seconds.

2.4 Data analysis

Corneal topography images were manually reviewed and excluded from analysis if the mires were significantly distorted due to tear film disruption or poor instrument positioning, if the palpebral aperture was too narrow, or if the E300 software was unable to display accurate topography analysis. Customised software was used to determine the anterior corneal HOA’s from the corneal elevation data (centred on the visual axis based on pupil centre offset relative to the corneal vertex normal taken from the E300) assuming a corneal refractive index of 1.376 and monochromatic incident light of 555 nm [35].

Data for total ocular HOA’s were exported from the COAS-HD and screened using custom-written software, as previously described [32]. In brief, significant outliers due to blinking, fixation loss, or tear film disruption were removed from analyses based on settings that removed any individual wavefront measurements with a cylindrical refraction >1 D from the average, or caused the higher order (HO) root mean square (RMS) SD to exceed 0.5 µm. Wavefronts were rescaled to 4 and 6 mm pupil diameters using the methods of Schwiegerling [36] and the coefficients derived from each individual measurement were averaged to minimise the influence of HOA microfluctuations [37]. Wavefront data were only included if the measured pupil size was larger than the fixed pupil size for analysis, to ensure data were not extrapolated to larger pupil sizes. Total ocular HOA data were also aligned to the pupil centre (aligned during measurement capture). The number of individual measurements of total ocular HOA’s included in the analysis was pupil size-dependent, with a mean (± SD) of 104 ± 25 and 83 ± 42 individual measurements for a 4 and 6 mm pupil, respectively.

An eighth order Zernike polynomial was fitted to both the anterior corneal and total ocular wavefront at the plane of the entrance pupil of the eye for 4 and 6 mm pupil diameters. For each participant, the individual Zernike coefficients for the total ocular and anterior corneal HOA’s were averaged, and the internal ocular HOA’s were calculated as the direct subtraction of the mean individual Zernike coefficients of the anterior corneal HOA’s from the total ocular HOA’s for each pupil size [1]. RMS errors were determined from the mean individual Zernike coefficients for each participant. RMS errors were calculated for HO (combined third to eighth orders), individual radial orders (third to sixth order), coma ($C_3^{ - 1}$, $C_3^1$, $C_5^{ - 1}$ and $C_5^1$), trefoil ($C_3^{ - 3}$, $C_3^3$, $C_5^{ - 3}$ and $C_5^3$) and spherical aberration (SA) ($C_4^0$ and $C_6^0$) for anterior corneal, internal ocular, and total ocular HOA’s, individually for each participant. Although eighth order Zernike expansions were fitted and all radial orders included in calculations of HO RMS and retinal image quality metrics, for simplicity, only RMS variables and individual Zernike coefficients up to and including the sixth radial order were analysed as the magnitude of the seventh and eighth order values were very small.

To determine the degree of internal ocular “compensation” for RMS HOA’s, a “compensation factor” (CF) was calculated according to the following equation [2]:

A value between 0 and 1 indicates partial internal compensation, a value of 1 indicates complete compensation, and a value of 0 demonstrates no compensation. A negative value suggests that the internal optics adds to the anterior corneal HOA’s (i.e. further increases the total ocular HOA’s). Since this equation does not account for the sign of individual Zernike coefficients, the CF for individual Zernike terms was determined using the following equation [38]:

Retinal image quality was quantified using the Visual Strehl ratio based on the optical transfer function in the frequency domain (VSOTF). The VSOTF is calculated as the relative area under the curve of the optical transfer functions of the aberrated eye ($OT{F_{AE}}$) to a diffraction-limited eye ($OT{F_{DL}}$), as weighted by the neural Contrast Sensitivity Function ($CS{F_N}$), using the following equation:

The VSOTF is a common metric used to assess retinal image quality given its high correlation with visual acuity [22]. Values vary between 0 and 1, with a value ≥0.8 considered to approximate a diffraction-limited eye [21]. In this study, the OTF and VSOTF were calculated based on the third to eighth radial orders, to evaluate the retinal image quality attributable only to HOA’s.

2.5 Statistical analyses

A priori sample size calculations were undertaken to ensure all statistical analyses achieved 80% statistical power with an alpha-error probability of 0.05, using G*Power [39]. For correlation analyses, a minimum total sample size of 61 was required to detect a statistically significant Pearson correlation coefficient of 0.35 or greater, and a total sample size of 62 was required to observe any global differences in the HOA profile between males and females based on a multivariate analysis of variance (MANOVA) and a Pillai’s Trace test statistic of 0.5.

Age, SER, AL, all individual Zernike coefficients, all RMS variables, and CFs were first assessed for normality using the Kolmogorov-Smirnov test for both pupil sizes individually, and parametric and non-parametric tests were then applied as appropriate. SER, most individual Zernike coefficients, RMS values, and CFs were not normally distributed for both pupil sizes (p < 0.05). Participant age and AL were normally distributed (p > 0.05).

Individual Zernike coefficients, RMS variables, and CF’s were examined for associations with age, SER, AL, and the VSOTF with bivariate correlation analyses. Pearson correlations were used where both variables were normally distributed, and Spearman rank correlations were performed if one or both variables were not normally distributed. Given the substantial number of correlation analyses performed for age, SER, AL, and the VSOTF, the significance level (P-value) for the correlation analyses was adjusted using the Sidak correction (30 correlations including the individual Zernike coefficients and RMS variables and 15 correlations including the CF’s), with the significance level adjusted to 0.001 for all correlation analyses including the RMS variables and individual Zernike coefficients and 0.003 for correlations including the CF’s.

Sex-based differences in the composition of anterior corneal, internal ocular, and total ocular HOA’s were individually analysed using a MANOVA and the Hotelling’s Trace test statistic for both pupil sizes, as previously described [17]. A MANOVA was run six times (anterior corneal, internal ocular, and total ocular HOA’s for both pupil sizes) with the individual Zernike coefficients included as dependent variables and sex as the independent, fixed factor.

RMS variables, CF’s, and the VSOTF were compared between males and females using a significance level of 0.006 (8 comparisons), 0.001 (32 comparisons), and 0.05, respectively, using independent sample t-tests for normally distributed data, and Mann-Whitney U-tests when data were not normally distributed within each sex. Median CF values were also compared to a median CF value of 1 using a one sample Wilcoxon signed rank test and a significance level of 0.05 to determine the RMS variables and individual Zernike coefficients that exhibited internal ocular compensation.

3. Results

3.1 Participants

All participants were included in the 4 mm pupil size analysis (n = 84), and fifty-eight participants (25 males and 33 females) were included in the 6 mm analysis (excluded due to insufficient pupil size), with a mean age and SER (± SD) of 8.4 ± 1.7 years and +0.62 ± 0.36 D, respectively (n = 58). There was no difference between the two cohorts for age or SER (independent-samples t-test, both p ≥ 0.65).

For the 4 mm and 6 mm pupil size analysis, a reliable measurement for AL was not captured for two and one participant, respectively, and were therefore excluded from the AL analysis (n = 82 for the 4 mm pupil; n = 57 for the 6 mm pupil). Paired t-tests revealed that there was no difference between the AL for the 4 mm (22.78 ± 0.82 mm) and 6 mm (22.79 ± 0.89 mm) cohorts (p = 0.93). There was also no age or SER difference between the cohorts used in the AL analyses and the original cohorts for both pupil sizes (Mann-Whitney U-tests, both p ≥ 0.91).

3.2 RMS aberrations and individual Zernike coefficients

Within-subject SD’s and repeatability coefficients [40] for the anterior corneal and total ocular HOA’s are presented in Table S1, and the median and interquartile ranges (IQR) of the RMS variables and individual Zernike coefficients for the anterior corneal, internal ocular, and total ocular HOA’s are presented in Table S2 for the 4 mm pupil and Table S3 for the 6 mm pupil. For both pupil sizes, the median values for the anterior corneal HOA’s and internal ocular HOA’s were consistently greater than the total ocular HOA’s, except for fourth order and SA RMS across the 4 mm pupil, and trefoil RMS for both pupil sizes (Fig. 2). For most HOA’s, the median value of the total ocular coefficient was reduced compared to the anterior corneal coefficient, however some notable exceptions were trefoil ($C_3^{ - 3}$ and $C_3^3$), quadrafoil ($C_4^{ - 4}$ and $C_4^4$) and secondary spherical aberration ($C_6^0$).

 

Fig. 2. Box plots of the root mean square (RMS) values for anterior corneal, internal ocular, and total ocular higher order aberrations (HOA’s) for the A: 4 mm and B: 6 mm pupil. The box represents the interquartile range (IQR), the central line designates the median value, with the whisker caps and crosses representing the 10th and 90th, and the 5th and 95th percentile, respectively. The green, red and blue boxes indicate anterior corneal, internal ocular, and total ocular HOA’s, respectively. Note that the y-axis scale differs for the 4 and 6 mm pupil data.

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The mean wavefront error maps for the anterior corneal, internal ocular, and total ocular HOA’s for the 4 and 6 mm pupil sizes are displayed in Fig. 3 to aid visualisation of the partial internal ocular compensation effect. The internal ocular HOA’s exhibit a similar magnitude to the anterior corneal HOA’s, but an inverted shape, and the wavefront error of the total ocular HOA’s is reduced compared to the anterior corneal HOA’s.

 

Fig. 3. Mean anterior corneal, internal ocular, and total ocular wavefront error maps based on the higher order aberrations (HOA’s) (third to eighth radial orders) for a A: 4 mm pupil and B: 6 mm pupil, aligned to the pupil centre. Note the different scales on the x-, y-, and z-axes between A and B.

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3.3 Associations between HOA’s and age, SER, and AL

None of the RMS variables or individual Zernike coefficients for the anterior corneal, internal ocular, or total ocular HOA’s were significantly correlated with age, SER, or AL for either pupil size (all p > 0.001).

3.4 Association between the VSOTF and HOA’s, age, SER, and AL

The median (and IQR) VSOTF was 0.867 (0.835–0.919) for the 4 mm pupil, and 0.777 (0.720–0.844) for the 6 mm pupil. The VSOTF was not correlated with age, SER, or AL for either pupil size (all p ≥ 0.22).

Statistically significant negative correlations were observed between the VSOTF and total ocular HO (4 mm: Spearman’s ρ = -0.95; 6 mm: Pearson r = -0.93), third order (4 mm: Spearman’s ρ = -0.86; 6 mm: Pearson r = -0.87), and coma RMS (4 mm: Spearman’s ρ = -0.82; 6 mm: Pearson r = -0.87) for both pupils (all p < 0.0001). Additionally, for the 4 mm pupil, the VSOTF was significantly correlated with total ocular fourth order (Spearman’s ρ = -0.67) and SA RMS (Spearman’s ρ = -0.48) (both p < 0.0001).

For the 6 mm pupil, no individual Zernike coefficients were correlated with the VSOTF. However, for the 4 mm pupil, correlations between the VSOTF and total ocular primary ($C_3^{ - 1}$) (Spearman’s ρ = 0.41) and secondary vertical coma ($C_5^{ - 1}$) (Spearman’s ρ = -0.37), and primary ($C_4^0$) (Spearman’s ρ = -0.46) and secondary spherical aberration ($C_6^0$) (Spearman’s ρ = 0.45) (all p ≤ 0.001) were significant (Fig. 4). Internal ocular primary vertical coma ($C_3^{ - 1}$) (Spearman’s ρ = 0.38) and spherical aberration ($C_4^0$) (Spearman’s ρ = -0.44) were also significantly correlated with the VSOTF for the 4 mm pupil (both p < 0.0001).

 

Fig. 4. Scatterplot showing the correlations between the Visual Strehl ratio based on the optical transfer function (VSOTF) and total ocular primary ($C_3^{ - 1}$) and secondary horizontal coma ($C_5^{ - 1}$) and primary ($C_4^0$) and secondary spherical aberration ($C_6^0$), for the 4 mm pupil. The correlation coefficients are also displayed on the plots (all p ≤ 0.001).

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3.5 Internal ocular compensation factor

The median (and IQR) compensation factor (CF) for each of the RMS variables and individual Zernike coefficients up to the fourth radial order are presented in Table S4 and Fig. 5. For the 4 mm pupil, all median CF values for the RMS variables were significantly different from 1. The greatest internal ocular compensation of anterior corneal HOA’s occurred for coma RMS, and the least occurred for fourth order RMS. The internal optics also appeared to contribute greater levels of trefoil RMS to the total ocular wavefront. For the 6 mm pupil, internal ocular compensation of anterior corneal HOA’s was greatest for SA RMS and least for trefoil RMS.

 

Fig. 5. Compensation factors (CF’s) for RMS variables and individual Zernike terms for the A: 4 and B: 6 mm pupil. Data are presented as the median value and the interquartile range. The dashed horizontal lines indicate partial internal compensation (i.e. CF values between 0 and 1). CF values greater than 1 indicate “over-compensation” and negative CF values indicate additivity of the internal higher order aberrations (HOA’s) to the anterior corneal HOA’s. Asterisks indicate median CF values that were significantly different from 1 (p < 0.05).

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For both pupil sizes, the median CF value for most individual Zernike coefficients did not significantly differ from 1, indicating almost complete internal ocular compensation. The median CF values for primary vertical trefoil ($Z_3^{ - 3}$) and coma ($Z_3^{ - 1}$) were significantly different from 1 for both pupil sizes. For the 4 mm pupil, the median CF value also differed from 1 for primary spherical aberration ($Z_4^0$), and primary oblique ($Z_4^{ - 4}$) and vertical quadrafoil ($Z_4^4$). For the 6 mm pupil, several other Zernike coefficients exhibited median CF values significantly different from 1, including primary oblique trefoil ($Z_3^3$), primary oblique quadrafoil ($Z_4^{ - 4}$), and secondary oblique astigmatism ($Z_4^{ - 2}$).

3.6 Associations between CF and age, SER, AL, and the VSOTF

Age and AL were not correlated with the CF for any RMS variables or individual Zernike coefficients for either pupil size (all p ≥ 0.02). For the 6 mm pupil, there was a significant negative correlation between SER and the CF for primary vertical quadrafoil ($Z_4^4$) (Spearman’s ρ = -0.39, p = 0.002), but no other CF’s were correlated with SER (all p > 0.04).

Positive correlations were observed between the VSOTF and the CF for HO (4 mm: Spearman’s ρ = 0.65; 6 mm: Spearman’s ρ = 0.68), third order (4 mm: Spearman’s ρ = 0.58; 6 mm: Spearman’s ρ = 0.58), and coma RMS (4 mm: Spearman’s ρ = 0.58; 6 mm: Spearman’s ρ = 0.65) which were statistically significant for both pupils (all p < 0.0001). For the 4 mm pupil, the VSOTF was also significantly positively correlated with the CF for fourth order (Spearman’s ρ = 0.48) and SA RMS (Spearman’s ρ = 0.48) (both p < 0.0001).

The VSOTF did not correlate with the CF for most individual Zernike coefficients, however significant positive correlations were observed between VSOTF and the CF for primary spherical aberration ($Z_4^0$) for the 4 mm pupil (Spearman’s ρ = 0.50, p < 0.0001), and the CF for primary vertical coma ($Z_3^{ - 1}$) for the 6 mm pupil (Spearman’s ρ = 0.54, p < 0.0001).

3.7 Sex-based differences

No significant sex-based differences were observed for the anterior corneal, internal ocular, or total ocular HOA RMS variables, individual coefficients, or the VSOTF for either pupil size (all p > 0.005). There were also no significant differences in the CF value for any RMS variables or individual Zernike terms between the sexes for either the 4 mm or 6 mm pupil (all p > 0.01).

3.8 Power analysis

G*Power was used to calculate statistical power based on the included sample size for all analyses. All correlations including data for the 4 mm pupil diameter had statistical power (P) of >0.80 if the absolute magnitude of the correlation coefficient was ≥0.3 (≥0.31 for correlations including AL). For the 6 mm pupil diameter, all correlation coefficients with an absolute magnitude of ≥0.36 (or ≥0.37 for correlations including AL) had statistical power of >0.80.

For the MANOVA exploring sex-based differences, G*Power was used to calculate statistical power based on the calculated Pillai’s Trace test statistic and included sample size. Each analysis had statistical power of ≥0.94 except for the anterior corneal HOA’s for the 6 mm pupil, which had statistical power of 0.30.

4. Discussion

This is the first study to investigate the associations between age, refractive error, sex, and AL, and the intraocular composition of HOA’s and retinal image quality in non-myopic, school-aged children. As previously described in adults [1–3], partial internal “compensation” of HOA’s was observed in this paediatric cohort. In general, for this group of children, the anterior corneal, internal ocular, and total ocular HOA’s were not associated with age, refractive error, AL, and no sex-based differences were observed for internal ocular compensation.

The median values for total ocular HO, third order, and coma RMS, and primary trefoil ($C_3^{ - 3}$ and $\,C_3^3$) and coma ($C_3^{ - 1}$ and $\,C_3^1$) in this study fell within the range of values previously reported in children and adolescents. Although greater levels of total ocular HOA’s (∼0.35 µm for a 6 mm pupil) have been reported in children of a similar age to the present study [13,41], both previous studies had a marked difference in the refractive error range of their cohorts and used different wavefront sensors. Similarly, Kirwan et al. [14] reported higher levels of total ocular HOA’s (0.16 µm) over a 6 mm pupil in a younger cohort with a wider range of refractive errors under cycloplegia. For a 5 mm pupil, both younger children [15,17,19] and adolescents [20,27] have exhibited greater and lesser magnitudes of HOA’s (∼0.16–0.27 µm) under cycloplegia compared to the findings of the present study over the 4 mm (median 0.093 µm) and 6 mm pupil (median 0.239 µm), respectively, however these differences can be explained by the different pupil sizes used for analyses.

A low positive median value was found for total ocular primary spherical aberration ($C_4^0$) (4 mm: 0.020 µm; 6 mm: 0.014 µm), however most previous studies in children [15,17,41] and adolescents [20,27] have reported more positive values, with findings ranging from -0.115 [14] to 0.07 µm [19]. This observation also accounts for the reduced levels of fourth order and SA RMS compared to previous research, which appears to arise from the less positive anterior corneal primary spherical aberration ($C_4^0$). Since accommodation is known to produce a negative shift in primary spherical aberration ($C_4^0$) [32,42–44], it is also possible that the non-cycloplegic measurements obtained in this study resulted in less positive primary spherical aberration ($C_4^0$) compared to previous studies where HOA’s were measured under cycloplegia or with older participants, despite the accommodative control with the Badal optometer. However, the broad range of values reported in previous HOA studies suggests considerable individual variation in HOA’s, which may be exaggerated by the differences between the instrumentation, methodology, participant age, and refractive error ranges, and the pupil size used for analysis.

After scaling previously published adolescent (mean age ± SD, 16.9 ± 0.7 years) [20] and adult data (mean age ± SD, 41 ± 0.9 years) [45] from a 5 mm pupil diameter to 4 mm, the median magnitudes for internal ocular HO, third order, fourth order, coma, trefoil, and SA RMS in this study of children were all greater (up to 2.3 times) than the average magnitudes previously reported for adolescents under cycloplegia [20] and non-cycloplegic measurements in adults [45]. Some notable differences in the internal ocular individual Zernike coefficients were also found after accounting for enantiomorphism. The children in the current study exhibited approximately half the magnitude (but oppositely signed) of primary vertical ($C_3^{ - 3}$) and horizontal trefoil ($C_3^3$) compared to adolescents and adults. Primary horizontal coma ($C_3^1$) in these children was approximately double the magnitude of adults and adolescents, while primary vertical coma ($C_3^{ - 1}$) was approximately 15% of the magnitude, but the same sign as adults (positive) and opposite in sign to the adolescents. Primary spherical aberration ($C_4^0$) was approximately 70% of the magnitude of both adolescents and adults, but negative in both the children and adolescents, while positive for adolescents.

These findings suggest that children have greater overall levels yet a different composition of internal ocular HOA’s compared to adolescents, at which time they develop similar internal ocular HOA’s to adults. It is likely that these differences arise due to the crystalline lens, since structural and optical changes are observed until ∼10 years of age [46], and increasing levels of spherical aberration and coma have been reported during adulthood resulting from crystalline lens changes [47,48]. However, Atchison et al. [45] used different instrumentation and methodologies, and internal ocular HOA’s were calculated by adding the values for the posterior cornea and the crystalline lens, which make it difficult to make direct comparisons.

This study is the first to show the presence of internal ocular “compensation” of HOA’s in school-aged children, similar to adolescents [20] and adults [1–3,45]. All RMS values exhibited a CF between 0 and 1 except for trefoil RMS for the 4 mm pupil where there was internal “additivity” resulting in greater total ocular trefoil. Since individual Zernike coefficients are signed values, examining the CF of RMS variables may mask internal HOA compensation, hence, CF’s for the individual Zernike coefficients were also determined [38].

The median CF for all analysed Zernike terms was positive and between 0 and 1 for both pupil sizes, which suggests that the absolute magnitude for most Zernike terms was partially reduced by the internal optics of the eye. For primary horizontal coma ($Z_3^1$), the median CF was between 1 and 1.5 for both pupil sizes (although not significantly different from 1), which suggests a possible slight “over-compensation” by the internal optics of the eye for this Zernike coefficient, whereby the absolute magnitude decreased, but the sign changed. This “over-compensation” was associated with a large, positive and negative median value for anterior corneal and internal ocular primary horizontal coma ($Z_3^1$), respectively. There are two main factors suggested by Tabernero et al. [49] that could explain these larger magnitudes yet excellent internal ocular compensation; the angular alignment between the cornea and the crystalline lens (i.e. angle kappa, κ), and the shape factor of these ocular structures [49].

Some terms for the 4 mm ($Z_3^{ - 3}$, $Z_3^{ - 1}$, $Z_4^{ - 4}$, $Z_4^0$, and $Z_4^4$) and 6 mm pupil ($Z_3^{ - 3}$, $Z_3^{ - 1}$, $Z_3^3$, $Z_4^{ - 4}$, $Z_4^{ - 2}$, and $Z_4^2$) exhibited a median CF below 0.5, suggesting less than 50% internal ocular compensation. The consistent finding of low internal ocular compensation of primary vertical trefoil ($Z_3^{ - 3}$) and coma ($Z_3^{ - 1}$) across both pupil sizes could potentially be an effect of lid-induced anterior corneal changes, since these have been identified previously associated with near work and result in changes in primary vertical trefoil ($Z_3^{ - 3}$) and coma ($Z_3^{ - 1}$) [50–52]. However, these findings more broadly indicate that partial internal ocular “compensation” is present in children, as previously reported in adults, such that there is some internal modulation of the anterior corneal HOA’s to minimise total ocular HOA’s and maximise retinal image quality.

It remains unclear whether internal ocular compensation is a passive mechanism (i.e. the natural development of the eye simply results in reduced HOA’s) or whether an active process exists (i.e. the internal ocular components change in response to the presence of certain HOA’s in the anterior cornea to minimise the whole eye HOA’s). This latter theory has some support. A recent pilot study using adaptive optics showed that imposing a known level of longitudinal spherical aberration (LSA) resulted in changes in the LSA of the eye, in the opposite direction to the imposed stimulus [53]. Furthermore, after one week of orthokeratology lens wear, a greater change in anterior corneal primary spherical aberration ($C_4^0$) than for the whole eye has been observed, which suggests that there may be some internal adaptation to the orthokeratology-induced anterior corneal HOA change [54]. These studies suggest that the eye may be able to detect and actively adapt to different HOA’s, perhaps through accommodation response changes during orthokeratology [55], or variation in retinal photoreceptor orientation [53]. However, further examination of this potential mechanism for active internal ocular adaptation is required.

For both pupil sizes, the VSOTF showed that retinal image quality attributable to the total ocular HOA’s in this group of non-myopic, school-aged children was excellent and near diffraction-limited (median VSOTF ∼0.8 for both pupil sizes) [21]. Few studies have examined retinal image quality in children, however the median VSOTF was greater than reported by Philip et al. [27] in adolescents (mean VSOTF = 0.621). Little et al. [19] reported an alternative VS metric (VSX) of ∼0.25 in children aged 9-10 years, and adolescents aged 15-16 years, indicating much lower retinal image quality, but likely included lower order terms of defocus and astigmatism.

Several RMS variables and individual Zernike coefficients correlated with the VSOTF. Negative correlations were observed between the VSOTF and total ocular HO, third order, fourth order, coma, and SA RMS (and the compensation factor for each of these RMS variables). These findings indicate that increasing levels and poorer internal ocular compensation of these HOA’s resulted in a reduction in retinal image quality. Several individual Zernike coefficients were also correlated with the VSOTF including total ocular secondary vertical coma ($C_5^{ - 1}$) and spherical aberration ($C_6^0$), and total and internal ocular primary vertical coma ($C_3^{ - 1}$) and spherical aberration ($C_4^0$) for the 4 mm pupil. These Zernike terms typically dominate the HOA profile of the eye, and suggests that they have the greatest influence on retinal image quality, whereby as the value of the coefficient approached 0, the VSOTF approached a value of 1. Although outside of the scope of this investigation, since visual acuity and the VSOTF metric are highly correlated [22], these findings suggest that less internal ocular compensation, and thus higher levels of these HOA’s, are likely to limit visual acuity in children, even with optimal sphero-cylindrical correction.

Age exhibited no significant correlation with the VSOTF for either pupil size. The few studies that have examined retinal image quality in school-aged children present conflicting results. Little et al. [19] reported that retinal image quality (as measured using the VSX, a different Visual Strehl metric) in children (9-10 years) and adolescents (15-16 years) was similar [19]. Based on measurements with the same aberrometer as in the present study, Philip et al. [27] reported the VSOTF in a group of young adolescents (mean age ± SD, 12.6 ± 0.5 years) and found a lower value compared to the present study. This may suggest that retinal image quality reduces between school-age and adolescence. Philip et al. [27] also suggests that retinal image quality continues to decline between the ages of 12 and 17 years, yet Brunette et al. [7] conversely reported that children under 20 years exhibited poorer retinal image quality than middle-aged adults based on the modulation transfer function, which suggests that retinal image quality improves throughout adolescence and early adulthood. However, these studies had marked differences in sample size, with 29 participants in this age group in the study by Brunette et al. [7] while Philip et al. [27] examined 166 participants. Additional longitudinal studies are required to better understand the changes in retinal image quality during childhood and adolescence.

Philip et al. [27] also reported that emmetropic adolescents who became myopic over a five year period showed a greater reduction in retinal image quality than those who remained emmetropic; however, both groups exhibited the same retinal image quality at the beginning of the study, suggesting that retinal image quality degraded in association with myopia development, and was not the cause of myopia development. A study of adults reported that progressing myopes exhibit poorer retinal image quality than emmetropes [56], however these differences in retinal image quality may only exist once the refractive error is established. Given that the current study included non-myopic children only, with a limited range of refractive errors, it is difficult to draw conclusions about the influence of refractive error on retinal image quality. However, the lack of a significant correlation between AL and the VSOTF suggests that longer eyes do not inherently have poorer retinal image quality. Further research in children with a larger range of refractive errors are required to explore this relationship, in addition to longitudinal studies of retinal image quality and refractive error development.

The repeatability coefficients for the anterior corneal HOA’s for a 6 mm pupil in this paediatric cohort were ∼1 to 1.5 times greater compared to a previous study of adults exploring repeatability of anterior corneal HOA’s for a 6 mm pupil derived from the E300 videokeratoscope [29]. Similarly, for total ocular HOA’s determined using the COAS-HD wavefront aberrometer, the within-subject SD’s for the 4 mm pupil for the participants in this study were also ∼1 to 2 times higher than previously reported for a 5 mm pupil in adults [57]. Measurements of children are typically less reliable than adults due to reduced attention and less fixation stability, so it is not surprising that the repeatability metrics of the anterior corneal and total ocular HOA measurements were slightly poorer in this cohort of children compared to adults.

Several limitations of this study may have impacted the results. Although accommodation was controlled by presenting a target at the participant’s far point, the proximity of the longpass filter and the instrument may have induced some proximal accommodation cues and therefore resulted in some accommodation [58]. These cues were minimised by reducing room lighting to be as low as possible, covering the participant-facing surface of the COAS-HD with black material, patching the non-tested eye, and continuously encouraging participants to maintain attention and fixation on the target within the Badal optometer during measurements, in addition to screening data for significant outliers during data analysis.

Misalignment errors due to small illuminance differences at the ocular plane between the videokeratoscope (∼10 lux) and the aberrometer (∼5 lux) may have caused a shift in the location of the pupil centre and thus influenced the realignment and determination of HOA’s as centred on the pupil [59]. However, the illuminance differences were small (<1 log unit) and such pupil centre shifts have been shown to minimally effect HOA measurements [60]. Furthermore, misalignment due to poor participant reliability in accurately aligning the instrument’s internal fixation and Badal target or poor stability in the headrest of the instruments were minimised by regular realignment of the Badal and instrument fixation targets by the investigator, and repeating measurements where excessive movement or poor fixation potentially influenced the results. Misalignment may have induced asymmetric HOA’s such as coma, due to incident light from the aberrometer obliquely entering and exiting the eye. However, since the findings of this study are consistent with previous studies, it appears that these potential errors had negligible influence on the results.

5. Conclusion

This cross-sectional study is the first to comprehensively examine the composition of intraocular HOA’s and retinal image quality of non-myopic, school-aged children. In this cohort, anterior corneal, internal ocular, and total ocular HOA’s were found to be similar between boys and girls, with few associations observed with SER, AL, and age. This study also confirmed that, like adults, the eyes of most children exhibit partial internal compensation of HOA’s, which results in reduced levels of HOA’s for the whole eye, however the internal ocular HOA’s were of greater magnitude than previous studies of adolescents and adults. The retinal image quality for most of the children in this study was excellent, however increased levels of HOA’s and reduced partial internal ocular compensation of HOA’s was associated with diminished retinal image quality. Future studies are required to evaluate the temporal influence of refractive error development and axial eye growth on HOA’s, in addition to studies of HOA’s during accommodation and convergence in children to establish a greater understanding of the potential association between near work and myopia development.