Repeatability of i.Profiler for measuring wavefront aberrations in healthy eyes

To evaluate the repeatability of wavefront aberration measurements and the correlation between corneal aberration and pupil size in normal eyes using a wavefront-based autorefractor (i.ProfilerPlus; Carl Zeiss Vision, Germany). A prospective cross-sectional study. Wavefront aberrations, including spherical aberration (SA) (Z40), coma (Z3−1, Z31), trefoil (Z3−3, Z33) and total higher-order aberrations (tHOA), were measured at different pupil diameters. The repeatability was evaluated using one-way ANOVA method, and statistical indicators including within-subject standard deviation (Sw), test–retest repeatability (TRT), and intra-class correlation coefficient (ICC). The correlations between corneal aberrations and pupil sizes were evaluated by Pearson correlation analysis. A total of 96 healthy young volunteers were enrolled. Corneal and ocular higher-order aberrations (HOA) measured by i.Profiler showed Sw < 0.01 μm, TRT < 0.10 μm, ICC > 0.90. There was a linear positive correlation between the corneal HOA and pupil size. The correlation coefficient between SA and tHOA was the largest (r = 0.996, P < 0.001). The measurements of wavefront aberrations by i.Profiler are highly repeatable. Corneal HOA was significantly dependent on pupil size. SA was the most influential aberration for visual quality in this study.


Introduction
Aberration of the human eyes is the main factor degrading retinal image and visual performance and has been shown to be crucial in many ophthalmic practices, e.g., wavefront-optimized refractive surgery and irregular astigmatism diagnosis [1,2]. It is believed that aberrations also play a role in the development and control of refractive error and eye growth by influencing the retinal image quality and ocular accommodation response, and the relative focal plane of different regions of the entrance pupil [3]. Since the magnitude and type of ocular wavefront aberration vary significantly between individuals, the comprehensive and accurate measurement of both lower-order aberrations (LOAs) and higher-order aberrations (HOAs) is a prerequisite for evaluating

Abstract
Purpose To evaluate the repeatability of wavefront aberration measurements and the correlation between corneal aberration and pupil size in normal eyes using a wavefront-based autorefractor (i.Profiler Plus ; Carl Zeiss Vision, Germany). Methods A prospective cross-sectional study. Wavefront aberrations, including spherical aberration (SA) (Z 4 0 ), coma (Z 3 −1 , Z 3 1 ), trefoil (Z 3 −3 , Z 3 3 ) and total higher-order aberrations (tHOA), were measured at different pupil diameters. The repeatability was evaluated using one-way ANOVA method, and statistical indicators including within-subject standard deviation (S w ), test-retest repeatability (TRT), and intraclass correlation coefficient (ICC). The correlations between corneal aberrations and pupil sizes were evaluated by Pearson correlation analysis. Results A total of 96 healthy young volunteers were enrolled. Corneal and ocular higher-order aberrations (HOA) measured by i.Profiler showed S w < 0.01 μm, refractive error and image quality [3]. However, conventional autorefractors can only quantify LOAs (defocus and astigmatism) but not HOAs (spherical aberration, coma, trefoil, etc.); also, it measures the overall refractive power of the eye confined to a small central area of the pupil. Instead, wavefront autorefractors can provide not only a reasonable refractive accuracy but also a total aberration in wavefront pattern and local variations in refractive power of the entire visual system, and is therefore beginning to gain popularity in clinical applications [4,5].
The i.Profiler Plus (Carl Zeiss Vision, Germany) is a novel wavefront aberrometer autorefractor based on Hartmann-Shack microlens array sensor. Due to the distorted wavefront, namely the aberrated wavefront generated by an eye, the central ray of the infrared laser beam tends to tilt as it passes through each lenslet in the array. Through the analysis of these tilts, the refractive error was calculated and the optical aberrations were quantified by Zernike coefficients up to the 7th radial order over a range of pupil size. Lebow et al. [6] compared the noncycloplegic subjective refractive output of i.Profiler Plus with that of Canon RK-F2, a ray deflecting principle autorefractor, suggesting that both instruments can provide equivalent sphero-cylindrical refractive data. A previous study has demonstrated the repeatability of cycloplegic and noncycloplegic measurements for i.Profiler Plus in terms of the autorefraction function [7]. However, there is paucity of literature available on the repeatability of this instrument with respect to wavefront aberration measurements. The purpose of this study provides a reference for clinical applications by evaluating the repeatability of i.Profiler Plus on the ocular and corneal HOA measurements, and the correlations between HOAs and pupil diameters for the first time in normal eyes.

Subjects
In this prospective study, young volunteers with normal eyes were consecutively recruited at the Affiliated Hospital of North Sichuan Medical College from May to July 2018. Inclusion criteria were healthy eyes with a corrected distance visual acuity ≥ 20/20. Exclusion criteria consisted of ocular pathology or systemic disease with ocular symptoms, a recent history of contact lens wearing or dry eye, and a previous history of intraocular and corneal surgery or trauma. The targeted total sample size is 96 with 3 repeated measurements and within 10% confidence level [8]. All participants were provided a written informed consent document to be signed prior to enrollment. All procedures were conducted on the basis of the approval of the hospital's Ethics Committee [2018ER(A)036] and followed the guidelines of Helsinki Declaration.

Procedures
Routine examinations included distance uncorrected visual acuity (UCVA), best corrected visual acuity (BCVA), manifest refraction, non-contact tonometry, slit-lamp biomicroscopy and ophthalmoscopy. A well-trained examiner was involved in the experimental procedure. The i.Profiler device was used to obtain the following measurements: the corneal and ocular vertical coma (Z 3 3 ), spherical aberration abbreviated SA (Z 4 0 ) and total highorder aberration (tHOA). Pupil was dilated to more than 7 mm using a mixture of 0.5% tropicamide and 0.5% phenylephrine (Mydrin P, Santen Pharmaceutical, Osaka, Japan), and data was collected at an entry pupil diameter of 2 mm to 7 mm (2, 3, 4, 5, 6, 7 mm, respectively). Only the right eye was used for the analysis because data from both eyes is similar in a healthy population. The subjects placed their heads on the chin rest and fixated on the test mark during the measurement period. For each subject, three consecutive mydriatic measurements were made with the i.Profiler under repeatable conditions. For each measurement, the subjects blinked to allow an optically smooth tear film to spread over the cornea. The instrument automatically aligned the pupil center with the optical axis of the device to ensure that the spot of the measuring laser hits the macular fovea accurately.

Statistical analysis
Statistical analyses were performed using the statistics software SPSS 25.0 (IBM Corp., USA). The demographic characteristics were summarized using descriptive statistics. The normality of data was evaluated by means of the Kolmogorov-Smirnov test (P > 0.05). The results of the parameters were reported as means and standard deviations (SD). The repeatability of the measurements was described in terms of within-subject standard deviation (S w ), and repeatability limits or test-retest repeatability (TRT ). One-way analysis of variance (ANOVA) was performed to determine S w . Considering the 95% confidence interval (CI) of S w , the repeatability limit was calculated as 1.96√2 × S w or 2.77 × S w , which provides an estimate of the limits within which 95% of measurements should be [8]. The intra-class correlation coefficient (ICC) of test-retest reliability was also calculated, which represents the consistency of measurement [9]. The correlation between corneal aberrations and pupil sizes was evaluated by Pearson correlation analysis. A P value less than 0.05 was considered to denote statistical significance.

Results
Ninety-six eyes of 96 healthy subjects (48% males and 52% females) were included in the study. Their mean age was 21 ± 1.9 years (range 18-28 years), the average spherical refraction was − 1.40 ± 1.00 D (range 0.00 to − 3.00 D), and the average cylindrical refraction was − 0.50 ± 0.50 D (range 0.00 to − 1.00 D). All subjects' pupils can be dilated to 7 mm or larger. No participants were withdrawn or dropped out.

Repeatability of corneal high order aberration
The i.Profiler provided highly repeatable measurements for corneal high order aberration (ICC > 0.9, S w < 0.01 μm, TRT < 0.1 μm). Table 1 summarizes the mean values and repeatability metrics for corneal high order aberration at 2 mm ~ 7 mm pupil diameter. ICCs of corneal Z 3 −1 and Z 3 1 at 6 mm pupil diameter were 1.0, showing an excellent consistency of measurements. The TRT values were all less than 0.02 μm with one exception of 0.22 μm at 6 mm pupil diameter SA (Z 4 0 ); a lower TRT value represents a higher repeatability. At 3 mm pupil diameter, the values of corneal tHOA and SA were 0.050 ± 0.022 μm and 0.016 ± 0.007 μm, respectively; at 5 mm pupil diameter, 0.220 ± 0.059 μm and 0.116 ± 0.031 μm, respectively. Repeatability of ocular high order aberration Table 2 summarizes the mean values and repeatability metrics for ocular high order aberration at 3 mm and 5 mm pupil diameter. Measurement of ocular high order aberration also provided the highest repeatability as ICC higher than 0.9, S w and TRT lower than 0.01 μm and 0.10 μm, respectively. The ocular tHOA and SA were 0.050 ± 0.016 μm and 0.010 ± 0.008 μm respectively at 3 mm pupil diameter, and 0.240 ± 0.090 μm and 0.073 ± 0.052 μm respectively at 5 mm pupil diameter.

Discussion
It is essential to know about the repeatability of instruments under normal conditions to establish its validity in clinical practices and studies. The i.Profiler Plus , as a wavefront autorefractor, can provide the quantification of both objective refraction and wavefront aberration [10][11][12]. More information about this device is needed as growing interest in image quality assessment for refractive surgery design, intraocular lens selection, contact lenses evaluation, corneal diseases diagnose, and so forth [13][14][15][16]. The present study might provide evidence to help learn more about this wavefront-based device.
The present study showed a high repeatability for measuring corneal and ocular HOAs by i.Profiler, with ICC (both greater than 0.9) and S w (both less than 0.01 μm). Meanwhile, this study verified that the values of corneal HOA [SA (Z 4 0 ), coma (Z 3 −1 , Z 3 1 ), and trefoil (Z 3 −3 , Z 3 3 )] and tHOA significantly depended on the pupil diameters; at 2-7 mm pupil diameter, these values all rose with the increase of pupil diameter. At 3 mm pupil diameter, the amount of ocular HOAs was found to be comparable to the previous studies [17]. When the pupil diameter was ≥ 5 mm, the increase amplitude of SA became the largest. It implied that SA plays an important role in the factors influencing visual quality. Randazzo [18] pointed out that when the pupil diameter was ≥ 5 mm, SA doubled for every 1 mm increase, which was consistent with the results of this study. Raymond et al. [19] also compared the corneal HOAs at 3-7 mm pupil size, and found that HOAs increased with the pupil dilation, among which the corneal SA had the largest variation. SA, as the variation of focus with aperture, has a great impact on the image quality. With the increase of pupil size, the diffuse spot centered on the optical axis becomes larger and the visual quality becomes worse. In this study, the cornea and ocular SA showed larger ICC and smaller S w values under different pupil diameters. The TRT values of SA at all pupil diameters were not more than 0.020 μm, except for the TRT of corneal SA (Z 4 0 ) with 0.022 μm at 7 mm pupil, indicating that the repeatability of measuring corneal and ocular SA with i.Profiler was excellent. The results also showed that the corneal SA was 0.049 ± 0.016 μm and 0.270 ± 0.040 μm at 4 mm and 6 mm pupil diameters respectively, which were close to our previous measurements of 0.05 ± 0.03 μm and 0.28 ± 0.07 μm by a wavefront aberration instrument KR-1 W based on Hartmann-Shack principle [20]. Similarly, Beiko et al. [21] also obtained a corneal SA value of 0.270 ± 0.089 μm at pupil diameter of 6 mm by measuring 696 healthy subjects earlier.
Unlike SA, coma and trefoil is not on-axis aberration with axial symmetry. The decentration of pupil increases coma and trefoil, so pupil size is associated with both. In this study, ICC and S w of the coma and trefoil are similar to these of SA at different pupil. ICC values of negative vertical coma (Z 3 −1 ) even reached 1.0 at 6 mm pupil diameter. Likewise, all the TRT values of coma and trefoil were not more than 0.020 μm, except for ocular trefoil (Z 3 3 ) 0.022 μm at 5 mm pupil diameter. These data all indicated that the repeatability was excellent in measuring the coma  and trefoil of cornea and oculi with i.Profiler. It was also found that the corneal and ocular Z 3 −1 was larger than Z 3 1 , and this trend increased with the increase of pupil diameter. Studies have shown that a vertical coma increased the depth of field on the vertical meridian and helps improve reading [22,23]. This feature was used in the optical surface of rotationally asymmetric multifocal IOL (intraocular lens) and was correlated with postoperative visual acuity corresponding to near defocus [24]. In addition, Omaret al. [25] compared the HOAs in keratoconus before and after CXL (corneal collagen cross-linking), and suggested that the corneal vertical coma and trefoil could add value beside keratometric readings.
Ocular aberrations consist of corneal and intraocular (mainly lenticular) aberrations. In this study, the corneal SA at 3 mm (mesopic) and 5 mm (scotopic) pupil diameter were 0.016 ± 0.007 μm and 0.116 ± 0.031 μm respectively, while the ocular SA were 0.010 ± 0.008 μm and 0.073 ± 0.052 μm respectively. The ocular SA was smaller than corneal SA at the same pupil diameters, thus intraocular SA in young adults is negative. Just like the coupling of two optical systems, the corneal positive aberration and lenticular negative aberrations tend to neutralize each other, thereby achieving optimal image quality and visual function. In our previous studies, it was also confirmed that aspheric IOL can compensate corneal SA and reduce ocular SA, and improve the postoperative visual quality in the darkness [20]. Moreover, the i.Profiler Plus is capable of obtaining measurements for pupil sizes of 2-7 mm. As shown by the measurements, the aberrations are pupil size dependent. This needs to be taken into special consideration when measuring different participants or under different conditions, especially when the measurements are used for clinical applications such as corneal refractive surgery and refractive cataract surgery.
In the present study, a few deficiencies were found in the i.Profiler Plus . For example, only corneal and ocular aberrations but not intraocular aberrations could be directly measured; further, ocular aberrations were provided only with the pupil diameter of 3 mm and 5 mm. The values of Kappa angle and Alpha angle were also not available. The improvement in these aspects will facilitate the device to be widely used in clinical practice. This study also had its limitations. Firstly, the included subjects were all normal young volunteers, so the accuracy of the device in measuring diseases affecting the refractive transparency (e.g., cataract) remains to be determined. Secondly, the inclusion criteria did not include moderate to severe refractive errors, so the measurement accuracy of the device in this case is not quite clear. In subsequent studies, the sample should be expanded to these participants of different ages, refractive status, and eye diseases.
In summary, the i.Profiler comprehensively evaluated visual quality by measuring both refraction and wavefront aberrations, and the results demonstrated that measurements of wavefront aberrations by i.Profiler are highly repeatable. The present study could serve as an initial approach to a deeper understanding of the novel instrument.