2-D Peripheral image quality metrics with different types of multifocal contact lenses

To evaluate the impact of multifocal contact lens wear on the image quality metrics across the visual field in the context of eye growth and myopia control. Two-dimensional cross-correlation coefficients were estimated by comparing a reference image against the computed retinal images for every location. Retinal images were simulated based on the measured optical aberrations of the naked eye and a set of multifocal contact lenses (centre-near and centre-distance designs), and images were spatially filtered to match the resolution limit at each eccentricity. Value maps showing the reduction in the quality of the image through each optical condition were obtained by subtracting the optical image quality from the theoretical physiological limits. Results indicate that multifocal contact lenses degrade the image quality independently from their optical design, though this result depends on the type of analysis conducted. Analysis of the image quality across the visual field should not be oversimplified to a single number but split into regional and groups because it provides more insightful information and can avoid misinterpretation of the results. The decay of the image quality caused by the multifocal contacts alone, cannot explain the translation of peripheral defocus towards protection on myopia progression, and a different explanation needs to be found.

Over 140 million people use contact lenses globally as regular optical wear 1 . Single vision contact lenses provide a safe and effective mean for correcting myopia, but they do fail to reduce the eye growth and the consequences that might appear with that 2,3 . The fast-growing prevalence of myopia has resulted in different optical design solutions that not only corrects the refractive error but also attempts to arrest its progression. Reported treatments are ranging from orthokeratology to bifocal or multifocal contact lenses, passing by radial refractive gradient spectacle lenses or progressive addition spectacle lenses and reported efficacies managing the progression of myopia, between 17% to 70% 4-6 . Among these novel optical treatments, multifocal contact lenses which induce defocus in the peripheral retina have shown a moderate but constant effect in slowing the eye growth 2,7 . However, whereas non-optical treatments (such as atropine) usually have their working pathways well-defined 8 ; the underlying mechanisms that translates the induced peripheral defocus into a reduction of the myopia progression, are still uncharted 9 .
A closed feedback loop between the level of retinal blur and the subsequent growth of the eye is widely described in the literature (for review see Wallman and Winawer 2004) 10 . The leading hypothesis also assumes, that outside of the emmetropization process, eye growth is driven by the level of blur in the periphery [10][11][12][13] . The peripheral aberrations that comprise peripheral blur, are known to be dominated by astigmatism even when no astigmatism is present in the fovea 14,15 . This astigmatism together with comma and trefoil varies rapidly across angles while the rest of the high order aberrations remains mainly independent of the angle 16,17 . As a result of this angular dependence, asymmetrical aberrations increase with eccentricity and results in an oriented point spread function (PSF) with a decrease in the image quality. However, as a result of the reduced resolution found in the periphery 16 , the changes on the visual quality promoted by the defocus alone might be subtle and not high enough to be perceived by the visual system 18 . So, defocus alone might not explain why those contact lenses deter the progression of myopia 19 .
Two main hypotheses may still grant to a certain extent a role to defocus in the progression of myopia. The first one proposes the conflict in the spatially oriented ganglion cells [20][21][22][23] and its selectivity that can act as myopigenic clues 24 . Thus, eye growth might be prompted in case a large anisotropy is present in the periphery 25 , and the underlying mechanism of multifocal contact lenses may be related to a reduction of the ratio of radial to azimuthal contrast 25 . Nonetheless, this anisotropic or directional blur has been reported to match neuronally, suggesting a coupling between the two systems [25][26][27][28][29] . Thus, this hypothesis can not explain why some contact lenses still report some effect slowing myopia even after two years of wear 7,30 . Meanwhile, another hypothesis suggests that the ebb in the image quality might be a possible indicator for the retina to react to the presence of blur, deploying signals that are related to the growth of the eye 30 . Nowadays, wave-front technologies allow us to recompose refractive errors and aberrations of the eye at different eccentricities 31 and thus, image quality metrics can be computed readily across the visual field.
In this study, the image quality metrics while wearing contact lenses are mapped and estimated for a visual field of 20 degrees surrounding the fovea. The visual field is segmented for further analysis, and the possible implications of the image quality crumble through multifocal contact lenses are discussed in detail.

Results
The core findings are split into three main groups: (A) the analysis of the root mean square errors (RMSE), where a single number reports the differences against the achievable limit for each image quality conditions, (B) the full-field data-sets analysis, where all the points from the maps were analysed, and finally (C) the sub-analysis by regions and groups (peripheral refractive patterns and optical states), where points are analysed by taking into account their location and the refractive pattern of the subject.
Root mean square errors. While analysing the RMSE, the naked eye condition obtained the highest similarity to the ideal image quality (RMSE = 0.3139). The multifocal centre-near design contact lens significantly degraded the overall quality metric (RMSE = 0.3912; Mann-Whitney-U; p = 0.0010) from the naked eye, while the centre-distance design contact lens did degradate the image quality as well, but without reaching a statistical significance (RMSE = 0.3601; Mann-Whitney-U; p = 0.0183). These results were also replicated with the "Lenna image" at a 5% significance level. Table 1 provides a clear overview of the variance of the results owed to the image used, for direct comparison, the results obtained with the "Lenna image" are kept in a public repository (check Data availability section), and the choice of the "Pirate or Male image" is discussed in the Methods section.
Full difference maps datasets. Comparison between optical conditions. The results of the full difference maps data-sets revealed that, independently of the optical condition (naked eye, centre-near or centre-distance contact lens), each classified type of peripheral refraction behaved significantly different (Kruskal-Wallis; p < 0.01) as it is shown in Fig. 1. Multiple pairwise comparisons reported also significant differences between all groups (Scheffé's correction; p < 0.05).
Comparison between peripheral refractive patterns. As it can be observed in the Fig. 2, the optical treatments showed significant differences (Kruskal-Wallis; p < 0.01). However, the multiple pairwise comparisons found no difference in the image quality between the naked eye and centre-distance contact lens for the case of the positive temporal skew profile (Scheffé's correction; p > 0.05). Additionally, no differences were found between the two

Discussion
Currently, several optical treatments have shown a reduction in the progression of myopia, but the underlying mechanisms on which these treatments rely, still, remain unclear. As one theory supports the influence of the peripheral refractive error of the eye, the current study obtained similar results as reported earlier 32,33 . Looking beyond peripheral refraction, a global approach describing the retinal defocus patterns 34 can explain the inter-subject variability regarding the efficacy of myopia interventions 2 . While the question remains, as to how the retina distinguishes lower order as well as higher order aberrations, a more in-depth analysis of the full image quality is required. Indicators that allow describing the image quality with such treatments will then, facilitate the understanding of the progression of myopia or the development of more efficient optical treatments to control the progression of myopia. Image quality metrics were computed across a large visual field, not only for the naked eye but additionally for two different optical designs of multifocal contact lenses. Other authors have published prior work on image quality and contact lenses 18,35-37 , but to the best of our knowledge, this study reports for first-time results for a wider visual field (not only the horizontal meridian) and relies on real aberration measurements rather than theoretical simulations 18 .
In congruence with the published literature 38,39 , results indicate that image quality across the visual field is reduced when multifocal contact lenses are worn. However, the overall results presented some inconsistencies, depending on the analysis. On the one hand, with the RMSE full-field comparison, the image quality from the naked eye did not decay significantly when the multifocal centre-distance design was present. In contradiction, and when analysing the local or full-field grouped data, this optical design of the contact lens did promote significant differences against the naked eye.
Results of the RMSE, where only the centre-near design deteriorate the image quality, cannot explain why several authors found that centre-distance contact lenses show a better efficacy on the control of myopia progression 40,41 . Nonetheless, when assessing a more detailed test, the centre-distance design seemed also capable of promoting differences in every peripheral refractive group, except for the positive temporal skew (PTS) pattern. The absence of significant changes in this group might be the underlying reason why the RMSE comparison failed to find significant differences.
In the grouped/ranked analysis, the mean of the groups did not present differences between centre-near and centre-distance, which precludes from concluding that there are high differences in the reduction of image quality between contact lenses. The regional analysis of the different optical solutions indicated that the inferior field www.nature.com/scientificreports www.nature.com/scientificreports/ might be the main contributor for the non-significant changes between the different contact lens designs (as in the full-field analysis). Although no pattern can be established in the pairwise regional differences between peripheral refractive groups, it appears that image quality worsens on a similar manner for relative peripheral hyperopia (RPH), relative peripheral myopia (RPM) and positve nasal skew (PNS) groups in the central area (0 to 5 degrees). Namely, the positive nasal skew (PNS) and the relative peripheral myopia (RPM) full inferior visual field presented a similar behaviour. Contrarily to the pure defocus analysis 34 , the deterioration of the image quality when contact lenses are worn, does not seem to rely on the skewness of the peripheral refraction. Only PTS (positive temporal skew) appears to overtake the optical treatments and be less receptive to changes produced by multifocal centre-distance lenses.
The use of cross-correlation values as a full-reference image quality metric 42 was by no means trivial. Most of the studies analysing the image quality metrics over the peripheral visual field tend to use the modulation transfer function (MTF) or the Visual Strehl ratio (VSOTF) 43,44 . While in general, these metrics are appropriate parameters  www.nature.com/scientificreports www.nature.com/scientificreports/ to evaluate the quality of any optical system, the use of such metrics in the context of myopia research, limits the interpretability of the results, given the point that neuronal factors are not taken into account. Essentially, the retinal image quality is not only limited by the optical components but also by the distribution of the photoreceptors 45 , as well as the size and location of the receptive ganglion fields across the retina [46][47][48] , and both factors are known to contributing to reduce peripheral sensitivity to contrast. Interference fringes 49 or adaptive optics systems 50 can measure this change in the neural CSF by surpassing the optical system and testing the angular resolution on specific contrast and frequencies gratings, that are influenced by the neural factors alone. However, given the retrospective nature of this study, rather than measure the cut-off frequency of the NCSF (f cuttoff NCSF) for each subject, and in every eccentricity, the values of the spatial frequency cut-off were interpolated from values reported earlier in the literature [51][52][53] .
The authors acknowledge several limitations to this study that needs to be mentioned. First of all, the measurements of aberrometry while subjects are wearing contact lenses can induce errors, for example due to a displacement of the contact lens. To limit the influence of the potential error input, the coefficients were averaged from four scans, and the visual field estimation was only interpolated for a smaller visual field than the measurements allows. Even though measurements were carried out while the subject fixated a target in three meters distance to avoid any accommodative effect, residual accommodative changes could happen, affecting the image quality as well 54 . The number of subjects may have limited the definition of the peripheral power profiles (especially in the case of PTS) and the conclusions of the grouped analysis, since some groups were represented only by few subjects. Furthermore, in this study, only two contact lenses were tested. Due to the differences in the optical designs of multifocal contact lenses from different manufacturers, this limitation may prevent the findings to be extrapolated to contact lenses from other suppliers. Measurements of the neural contrast sensitivity function (NCSF) in the periphery that are reported in the literature are limited just to a few subjects or a few eccentricities 36,52 . This limitation occurs since such measurements are exhaustive and time consuming for the subject. Given the fact that spatial frequency cut-offs were extrapolated from the literature rather than real measurements for each subject, the obtained results might be less precise. However, the piecewise linear surface function that defines the spatial frequency cut-off can be improved in future studies, by adding more values.
To conclude, regional and groups segmentation of the data can prevent the misinterpretation of results. Hence, the analysis of root mean square errors (RMSE) or the simplification of the image quality over the whole retinal field to a single number can lead to controversial results, and should therefore not be recommended as a benchmark. Although slight differences are shown between contact lenses, the differences are small and not constant over the different analysed segments or the different conducted analysis. On the other hand, image quality decrease caused by multifocal contact lenses alone does not seem to be the underlying reason for the myopia control that these contact lenses can achieve. Future research needs to study other hypotheses to explain how multifocal contact lenses achieve myopia control.

Methods
Data acquintance. Earlier acquired data from thirteen subjects were retrospectively analysed 34   Refraction from the right eyes (OD) of the subjects were objectively measured using a Hartmann-Shack sensor (VAO device, AOVIS-1, VOptica SL, Murcia, Spain) 56,57 and subjectively measured using the same device by a trained optometrist (author MGG). Axial length was obtained using a standard optical biometer (Lenstar LS900; Haag-Streit AG, Köniz, Switzerland). All the subjects were usual contact lens wearers with spherical equivalent refractive errors below −7 dioptres and without any medical or ocular pathologies record.
Measurements were performed with no lens in front of the eye (naked eye) and while wearing two different optical designs of multifocal contact lenses, one with centre-near design and one with the centre-distance design. The contact lens used in this study were the hydrogel Xtensa, Filcon IV 1 55%, by Mark' ennovy, with centre-near and centre-distance optical designs. The central refractive power was −0.25 dioptres for the distance focus and an additional power of +2.25 and +2.50 dioptres for the near-centre and distance-centre designs respectively. Further information regarding these contact lenses can be found here 34 .
The aberration coefficients of the right eyes were recorded using an open-view peripheral wave-front sensor (Voptica SL, Murcia, Spain) as described by Jaeken et al. 35,58 . During the measurements, subjects were fixating a laser target in 3 meters distance while the instrument scanned over a wide range of horizontal arc (80°); recording 81 high-resolution Hartmann-Shack (HS) images within 1.8 seconds. The obtained images were processed up to the sixth order of Zernike polynomials with a 3 mm pupil diameter, rendering full aberrometry data for every point by using the software provided by the manufacturer.
After measuring the mean horizontal meridian or equator, the subjects were asked to fixate at +10°, +20°, −10° and −20 degrees. Four scans (equivalent to 324 HS images) in each vertical fixation point were averaged to define the peripheral refraction and aberrometry profiles. Data analysis. The point spread function was computed using Matlab r2018a (The MathWorks Inc, Natick, MA, USA) for every point (in 5-degrees stepwise), using the Zernike coefficients obtained within the wavefront measurements. In all the computations, low order aberrations (defocus, oblique and vertical astigmatism) were normalised to the error found in the fovea 16 , being the remaining coefficients computed at the wavelength of 532 nm.
Similarly to the theoretical approach from Ji et al. 18 , a grey-scaled 512 × 512 pixels image was used as a reference image. The image was located subtending 2 degrees on every retinal location, and the resolution of the same was 0.2344 m/pixel. At each peripheral angle, this reference image was convolved with the point spread function (PSF). After this, convolved images passed through a low-pass filter to match the image with the spatial frequency domain where the eye can still operate for the corresponding eccentricity. See Figs. 5 and 6.
Owing to the controversial origin of 'Lenna or Lena's image' 59 , in this study, the so known as 'Pirate or Male' image (5.3.01 from the SIPI image database 60 ) was used. This image is according to the literature 61 the most similar picture in terms of features. Nevertheless, owing to the natural variation of the outcomes that using a different image causes, the results obtained with the 'Lena' model remain in the repository to allow a direct comparison with the previous study from Ji et al. 18 . www.nature.com/scientificreports www.nature.com/scientificreports/ Given the retrospective nature of this study, rather than measuring the cut-off frequency of the NCSF (f cuttoff NCSF) for each subject, and in every eccentricity, the values of the spatial frequency cut-off were interpolated from values that were reported in the literature before [51][52][53] . Due to the lack of values for all the required locations, a piecewise linear surface function 62,63 was fitted using the 20 coefficients reported in the literature. Then, using the vertical and horizontal position, an estimation of the cut-off limit was gained and used to match the resolution limit of the convolved images through a 2D Gaussian low-pass filter 64,65 .
Following, the filtered images were cropped to avoid any aliasing effect on the edges 66 and subsequently compared with the original image. Two-dimensional cross-correlation metrics were assessed objectively by allocating Pearson correlation coefficients for every comparison 67 . The resulting coefficients ranged from 0 to 1, where 1 refers to the highest similarity between the images and therefore the best image quality, and 0 to the worse image quality.
On an individual basis (for each subject and each condition), the obtained 2D-cross correlation values were used to interpolate the residuals of the surface fit, covering a range of approximately 40° × 40° (resulting in a matrix/map of 40 × 40 pixels with cross-correlation values at every degree).
Given the neural limitation in the periphery of the eye and the diffraction limit, certain eccentricities would never reach the perfect image quality metric. A direct comparison of the convolved and filtered image against the reference image could provide meaningful information regarding the image quality deterioration due to the peripheral neural factors. Those limitations imposed by the neural factors are not equal in all the retinal locations. Therefore, a more insightful value of how the optical treatment changes the whole field can be observed comparing the difference between the neural limit and the optical paths rather than a direct comparison of the image quality ebb. For this reason, final matrices were remapped with the same spatial distribution and resolution but revealing the changes caused by optical conditions in relation to the neural boundary. These values were achieved by subtracting the two-dimensional cross-correlation values from the neural limited cross-correlation matrix.
Segmentation and grouping. To achieve a more detailed analysis regarding the image quality and to take its location across the visual field in consideration, the significance maps were segmented following a 45° nasal/ temporal/superior/inferior (NTSI) angular division with a complementary annular division every five degrees. Smaller sections resulted in sets of sixteen points while the most larger sections contained above one hundred and forty values.
Moreover, the final maps from every subject were classified attending to their peripheral refractive pattern, under naked eye conditions. Four groups were established, based on the nasal and temporal outer edges compared to the mean refraction in the central area. The profiles were classified as nasal positively skewed (PNS; n = 5), relative peripheral myopia (RPM; n = 4), relative peripheral hyperopia (RPH; n = 3) and temporal positive skewed (PTS; n = 1).
Flow diagram. The scheme in Fig. 7 illustrates how the significance maps were built from the aberrations that were measured with the open-view peripheral Hartmann-Shack sensor and the theoretical resolution limit from the neural factors.
Statistical analysis. The differences between the 2-D significance maps and the limiting spatial frequency cut-off map were used to quantify the overall differences produced by each condition for every subject. The root mean square errors (RMSE) as a single representative value of the full visual field as well as the full-populated maps www.nature.com/scientificreports www.nature.com/scientificreports/ were analysed independently. The non-parametric Mann-Withney-U test was used to test the RMSE from the contact lens conditions against the naked eye. Non-parametric Kruskal-Wallis with multiple pairwise comparisons were performed for the final maps, to test the null hypothesis that there were no differences between groups.
For the analysis of the segmented areas, non-parametric Kruskal-Wallis tests and multiple pairwise comparisons with the Scheffé's correction were performed. Unlike Bonferroni correction, this procedure provides a simultaneous confidence level for comparisons of all linear combinations of the means, and it is conservative for comparisons of simple differences of pairs 68 .