Dual-angle open field wavefront sensor for simultaneous measurements of the central and peripheral human eye

: We have developed a novel dual-angle open ﬁeld wavefront sensor. This device captures real-time foveal and peripheral Zernike aberrations, while providing natural binocular viewing conditions for the subjects. The simultaneous data recording enables accurate analysis of changes in ocular optics with accommodation overcoming any uncertainties caused by accommodative lag or lead. The instrument will be used in myopia research to study central and peripheral ocular optics during near work and to investigate the eﬀects of optical myopia control interventions. Proof of concept measurements, performed on an artiﬁcial eye model and on 3 volunteers, showed good repeatability with foveal-peripheral data synchronization of 65 msec or better. The deviations from subjective cycloplegic refractions were not more than 0.31 D. Furthermore, we tested the dual-angle wavefront sensor in two novel measurement schemes: (1) focusing on a close target, and (2) accommodation step change.


Introduction
Investigation of the peripheral optical errors is of interest in vision science for several reasons. First of all, sufficient quality of the image on the peripheral retina is essential for many everyday activities that utilize high contrast detection and low contrast resolution. These include driving [1][2][3], mobility [4,5], and search tasks [6]. Additionally, it has been shown that there is a link between the peripheral retinal image and myopia [7]. The retinal image, in its turn, is mainly defined by the optical properties of the cornea and the crystalline lens. Thus, during the process of accommodation, when the shape of the crystalline lens changes, the properties of the peripheral retinal image also change [8][9][10][11][12]. Therefore, a device that simultaneously measures peripheral optics and accommodation state of the eye provides a more comprehensive description of the eye's optical system.
The connection between accommodation, retinal image and myopia development is not fully revealed yet. Myopia has been recognized as a global problem several years ago [7]. But its prevalence is still increasing [7,[13][14][15], and the exact mechanisms behind its onset and development are not completely understood yet [13,[16][17][18]. Several authors have reported that prolonged indoor activities, associated with near work and accommodation, can be considered myopia development risk factors [18][19][20][21][22]. However, attempts to prevent myopia with nearaddition spectacles were inefficient, which proved that the possible link between myopia and accommodation is not straight-forward. Studies in guinea pigs [23], monkeys [24][25][26][27] and chickens [28,29] have shown that myopia development can also be driven by inducing defocus either in the foveal or peripheral retinal image. This became the base for developing optical myopia control interventions; currently the most effective of those are multifocal contact lenses, multifocal spectacles, and orthokeratology [30,31]. Also, the recently developed D.I.M.S. spectacles have been reported to be efficient for reducing myopia progression [32]. Even so, the effect of all these treatments is still limited and subject-dependent [30][31][32]. To be able to improve the treatment effect we need a more detailed understanding of the image formed on the retina, particularly under different accommodation demands. This is also supported by previous works showing that the efficient optical myopia control interventions do not only shift the location of the peripheral image, but also have considerable effect on the peripheral image as a whole [30,31,33,34].
The amount of available data on peripheral ocular optics of an accommodating eye is currently rather small. A few previous studies report peripheral optical quality with accommodation [10,11] while the majority of the previous work focus only on peripheral refractive errors for different states of accommodation [8,9,12,[35][36][37]. The studies of the peripheral optical quality are limited to very few accommodation steps (1 excluding the far-away target). The studies of the peripheral refractive errors, even though very thorough, do not agree on the effect of accommodation on the relative peripheral refraction (RPR). The results for both myopes and emmetropes during accommodation vary between myopic shift in RPR [8,10,12], no change in RPR [10,11,[35][36][37], and hypermetropic shift in RPR [9]. Note that the actual accommodation state of the eye was not monitored in any of these experiments (including the peripheral optical quality works). The varying results might therefore be a consequence of accommodative lag, which is subject-dependent and difficult to predict beforehand.
The human eye is a dynamic optical system, and time-dependent fluctuations have to be considered to fully describe this system. Even when fixating on an object, the eye undergoes fluctuations both in gaze direction (microsaccades, drift and tremor) and in its optical characteristics. The dynamics of these optical characteristics in the fovea are known as accommodation microfluctuations, and their magnitude is highly dependent on the accommodation state of the eye [38]. Previous studies of accommodation microfluctuations have shown that myopes tend to have higher magnitude of the microfluctuations compared to emmetropes [39][40][41][42][43]. However, to the best of our knowledge, there are no publications analysing the effect of accommodation microfluctuations on peripheral vision for either relaxed or accommodating eye. Thus, the question whether they have any noticeable effect on the peripheral retinal image remains unanswered. Furthermore, knowing the possible role of peripheral retinal image in myopia development, the comparison of peripheral microfluctuations between myopic and emmetropic subjects can be a valuable contribution to overall understanding of myopia onset and progression mechanisms.
Therefore, in an attempt to reduce these knowledge gaps, we have developed a novel dual-angle open field wavefront sensor. The system consists of two measurements channels, each with a Hartmann-Shack wavefront sensor, providing simultaneous foveal and peripheral measurements. In order to analyse the behavior of the ocular optics, the wavefront data is recorded in real-time. The natural viewing conditions, provided by the open field of view, allow to design experiments in close-to-real-life settings. Potential applications of such a device are rather broad and span from basic investigations of the optical properties of the human eye to comparisons of specific myopia control interventions.

Design of the device
The main features of the dual-angle open field wavefront sensor are listed below: • Open field of view provides natural viewing condition. For an emmetropic subject, the field of view is 50 • horizontally and 60 • vertically through the hot mirror.
• Simultaneous measurements at two horizontal visual field (VF) angles of the same eye. The separation angle can be manually adjusted in the interval between 15 • and 30 • . The chosen angle value is constant during the experiment (for this article, the separation angle was fixed at 20 • ).
• Maximum accepted pupil diameter 9 mm (restricted by the sensor size).
• Theoretical limits for ametropia measurements are ±5.00 D for a 7.5 mm pupil diameter (restricted by the setup).
• Induced accommodation demands of up to 5.00 D.
• The device allows to perform measurements either on the left or right eye of a subject.
• Real-time measurements with an average sampling rate 7.5 ± 0.5 Hz.
• Average synchronization error between the two measurement channels is estimated to 65 msec (half-time of one frame acquisition at 7.5 Hz).
• Custom-developed processing routine (capable of identifying most of the blinks, corneal reflections, and track rapid gaze direction changes) enables the usage of a wide variety of focusing targets, both static and dynamic. Figure 1 shows a photo and a schematic drawing of the developed device. The system includes two measurement channels aligned to the same object plane, but separated by 20 • , to facilitate simultaneous central and peripheral data acquisition on the same eye. Each of these channels consists of the following principal components:

Optical setup
• A 2-lens telescope (L1 + L2; L3 + L4) creates a demagnified (magnification = 0.5) projection of the entrance pupil of the eye onto the lenslet array of the wavefront sensors. In order to minimize the noise from scattering within the ocular media, each of the telescopes have an additional diaphragm located at the back focal plane of the Badal lenses (lenses L1 and L3 respectively). This diaphragm, however, also restricts the extent of ametropia that can be studied without cutting the edges of the measured wavefront. In the current configuration the limits are ±5.00 D for a 7.5 mm pupil diameter.
• Pellicle beam splitters BS2 and BS4 allow the mounting of a pupil camera (PC) in either of the measurement channels. In the current setup the pupil camera is fixed in Channel 1.
• Laser diode light delivery systems consist of laser diodes (LD1 and LD2; λ = 830 nm), collimators (not shown), and pellicle beam splitters (BS1 and BS3). The size of these beam splitters is chosen so that they would not be limiting the field of view of the system (2'' in diameter; all other optical components are 1'' in diameter). The output power of the laser diodes is controlled by the diode drivers (Thorlabs, Inc; not shown on the figure). The diode drivers are also incorporated with a hardware-adjustable upper limit for the diode driving current. This hardware limit is set for the power level 10 times lower than that in the standard of the Swedish Work Environment Authority (Arbetsmiljöverket [44]): 70 µW for each laser diode. The hardware limit of 70 µW per laser diode corresponds to the maximum permittable continuous wave laser exposure during 8 hours (4.45 · 10 4 sec) in the ANSI 136.1-2000 [45]. The typical operation power is in the range 30-35 µW for each diode. Lastly, the system includes a head-chin rest (not shown in the figure) for stabilization of the subjects, and a hot-mirror (HM) that provides open field of view for the subjects. The residual aberrations of the optical systems were compensated by calibrating each channel of the setup with a flat wavefront.

Data post-processing
The implemented data post processing includes recalculation of Zernike coefficients from 830 nm to 550 nm wavelength, and a custom-developed filtering algorithm. The wavelength recalculation is done according to the work of Salmon et al. [46] using ocular dispersion model by Thibos et al. [47]. For subsequent analysis of the temporal behavior of Zernike coefficients, the coefficients are scaled to the same pupil size (equal to or less than the measured one). It is also worth mentioning that peripheral Zernike coefficients are given for a circular area, inscribed in the ellipse of the peripheral pupil. The refractive errors, both for the filtering and subsequent data analysis, are calculated using 2 nd , 4 th and 6 th order Zernike coefficients according to the following formulas: where pupil radius is in mm and Zernike coefficients are in µm.
In order to eliminate measurement artifacts from blinks and corneal reflections, we developed a custom post-processing routine. The main purpose of this filtering algorithm is not only to find the measurement artifacts, but also to avoid smoothing down of the real data fluctuations. In order to achieve this, the algorithm finds individual data points containing artifacts, removes them, and then fills the gaps using linear interpolation through the neighboring data. Thus, the main challenge is the classification of individual data points. In this routine it is done by comparing the measurements to well-known features of accommodation behavior. These include Zernike coefficients as a whole, pupil size, and gaze direction. The raw data is assessed in three steps: 1. Taking away rough artifacts.
(a) The values of mean sphere and pupil diameter are compared to the physically possible boundaries. The pupil diameter should be between 1 mm and 9 mm, and refractive state -between +5.00 D and -10.00 D.
(b) A sudden downward spike in the pupil diameter of more than 0.75 mm, while the neighboring measurements just before and after the spike differ by less than 0.2 mm, is classified as a blink.
(c) A jump in any Zernike coefficient (excluding piston and tilts) of more than 3 µm occurring during one time step (for 7.5 Hz acquisition frequency one time-step corresponds to 0.13 sec) is assumed to be a measurement artifact irrespective of the pupil diameter size.
(d) A data point for which all Zernike coefficients are zero is also classified as a measurement artifact.
2. Fine-filtering routine. This part is based on an assumption that most of the artifacts occur at high temporal frequencies whereas the valuable data is concentrated at lower temporal frequencies. Thus, if we compare the real data to its low-pass filtered copy, the artifacts would appear as a large difference between these data sets. In the suggested routine, the low-pass filtering is implemented by convolving the raw data with a uniform-height window function. Each filtered data point is calculated as: where x denotes the raw data points, y denotes the filtered data points, and n is the index of the raw and filtered data points. The thresholds for classifying the difference between the raw and the low-pass filtered data as an artifact are: (a) Pupil diameter difference of more than 1 mm (concidered a blink).
(b) Mean sphere difference of more than 3.00 D.
3. Additional information extraction. The real-time spotfield image location, provided by the wavefront sensors, can be used to extract additional information about the eye's decentration and rotation dynamics. As shown in the supplementary material, if an eye would change the gaze direction when keeping the lateral position unchanged, it would correspond to a decentration of the spotfield image on the Hartmann-Shack wavefront sensor (see Appendix 1, Fig. 5). If we then make a comparison between the raw and the low-pass filtered data (analogous to the 'Fine-filtering routine'), we can investigate the stability of target fixation for the measured subject (for example during reading). In this case the 'fixation instability' will include both ocular rotation and lateral movements. If the lateral position of a subject is stabilized by a bite bar, the observed fixation deviations, decentring the spotfield image, will be mainly originating from gaze direction changes.
Once the artifacts are identified, the corresponding measurement points are replaced using linear interpolation through the neighboring artifacts-free data. The first reference point for linear interpolation is chosen to be the one right before the artifact. The second reference point is then defined during sequential scanning through the data points within 2 sec span after the artifact. This reference point is chosen as the closest one to the artifact that satisfies one of the additional conditions: (1) difference of the mean sphere between the two reference points should be less than 0.50 D; (2) the difference in the pupil diameter between the two reference points should be less than 1 mm; (3) the difference between the average pupil diameter (throughout the whole measurements set) and the second reference point should be less than 1 mm. If within the two seconds span there are no points satisfying any of the additional conditions, the seconds reference point is set to be that which is two seconds away from the artifact. After the post-processing, raw and filtered data for mean sphere and pupil diameter are manually examined. This allows to identify data sets with too many artifacts, that could not be processed correctly.
The efficacy of the proposed post-processing is demonstrated in Fig. 2 with an example of measured data before and after the processing. The 'raw data' and 'filtered data' curves clearly illustrate that the artifacts are removed while data of interest is intact.

Proof-of-concept measurements
The performance of the dual-angle open field wavefront sensor was assessed in two ways: using an artificial eye model, and collecting central and peripheral (20 • nasal VF) wavefront data for three subjects. In both experiments, the wavefront was reconstructed up to the 6 th order of Zernike polynomials. First, a hypermetropic eye model was sequentially measured on-axis by the two channels separately during 15 sec; the measurements were repeated five times. Average Zernike coefficients for these five measurements are given in Table 1 (Appendix 2). The average mean sphere values were +4.44 ± 0.17 D and +4.63 ± 0.09 D for Channel 1 and Channel 2 respectively. These values demonstrate a good inter-channel and intra-channel repeatability. The standard deviation of individual Zernike coefficients during each measurement set did not exceed 0.003 µm (4 mm pupil diameter) for individual coefficients.
Second, the real-time wavefront data was acquired from the right eye of three volunteers: one emmetropic (28 years old, Spherical Equivalent (SE) +0.25/-0.25 x 165) and two myopic (30 years old, SE -2,75/-0,25 x 175; 41 years old, SE -1.75/-0.50 x 140). The data was acquired during three 30-sec sets for each subject. To avoid distractions, the subjects were in a dark room, fixating on a well-illuminated (photopic conditions) Maltese cross, located at 3.22 m (0.31 D of accommodation demand). The Zernike coefficients, as well as the refractive errors, were then calculated as the average over all of the measured data for each subject. The Zernike coefficients of all subjects are presented in Table 2 (Appendix 2). The measured aberrations agree with subjective refraction and earlier foveal measurements in other instruments (see Table 3, Appendix 2). The differences between foveal and peripheral aberrations are in accordance to previous publications on the population average ocular aberrations [48][49][50][51][52][53]. An example of the variation in central and peripheral Zernike coefficients for the emmetropic subject is given in Fig. 3.
In order to illustrate the potential usage of the proposed system with accommodation, two additional proof-of-concept experiments were conducted on the emmetropic subject. These experiments were (1) real-time wavefront measurements during three 30-sec sessions of accommodation to a 4.00 D target, and (2) real-time wavefront measurements during three 60-sec sessions with accommodation demand step-changes between 0.31 D and 4.00 D. Here, the wavefront was also reconstructed up to the 6 th order of Zernike polynomials. All measurements were performed in a dark room (to avoid distractions) with well illuminated target (photopic conditions). For the far-away viewing, the fixation target was a Maltese cross. For the near-viewing, the target was a black-and-white picture with fine details, subtending 1.5 • in diameter. In the experiment with the accommodation demand step-changes, both far and near targets were visible at the same time, and the subject was altering his fixation between the targets in 15-sec intervals. Results of the first experiment, together with the reference data for a relaxed eye, are given in Table 4 (Appendix 2). Results of the second experiment are demonstrated in Fig. 4. Here, foveal and peripheral mean sphere dynamics as well as RPR behavior during accommodation demand step-changes are shown. The foveal mean sphere curve clearly depicts the change in accommodation state of the eye every 15 sec of the experiment. Analysis of the RPR curve, however, does require some caution. Even though relatively small, the synchronization error (on average, 65 msec) gives rise to some artifacts at the time points of transition between the accommodation states (for example, the peaks at 15 and 30 seconds).

Discussion
In the past years, several devices for multi-angle aberrations measurements have been developed. All of these devices are based on scanning of the VF. Most of them are state-of-the-art and are not available as commercial products. Tabernero and Shaeffel [37] have presented an open-field scanning photoretinoscope, measuring refraction in ±45 • of the horizontal VF in 4 sec. Jaeken et al. [54] introduced a fast scanning open field wavefront sensor, measuring ±40 • of the horizontal VF in 1.8 sec. The BHVI-EyeMapper, described by Fedtke et al. [55], scans ±50 • of the horizontal VF in 10 • increments in less than half a second. This device, however, can measure only relaxed accommodation state due to the absence of fixation target. Finally, Wei and Thibos [56] developed a setup, taking 7 sec to measure 37 discrete locations in the central 30 • of the VF (both horizontal and vertical). Of all the mentioned setups, only two [37,54] have an open field of view providing natural viewing conditions.
The dual-angle open field wavefront sensor presented here uses two wavefront sensors instead of VF scanning. Using one sensor for each eccentricity provides temporal resolution at least 10 times better compared to the scanning devices. The price for this speed is drastically decreased angular resolution: only two VF angles. The separation between these angles is further limited to the interval 15 • -30 • .
High temporal resolution of the novel device enables the charecterization of foveal and peripheral accommodation microfluctuatios. The microflututations are small variations in the optical power of the eye caused by the dynamics of the crystalline lens shape. Previous work on accommodation microfluctuations concluded that they are mainly occurring at temporal frequencies below 2.5 Hz [38]. Therefore, according to the Nyquist sampling theorem, a minimal required frame rate to register the microfluctuations is 5 Hz. The dual-angle wavefront sensor operates at 7.5 ± 0.5 Hz, which is about 1.5 times higher than that threshold.

Summary
In this manuscript we propose a design of a dual-angle open field wavefront sensor. This wavefront sensor allows acquisition of simultaneous foveal and peripheral real-time wavefront data from a fixed eccentricity angle (can be chosen in the range of 15 • -30 • ) at 7.5 ± 0.5 Hz. Such a device enables the analysis of both average and dynamic parameters of the optical system of the human eye. The open field of view in the setup allows a broad spectrum of possible visual tasks as well as experiments in close-to-real-life conditions. The proposed device has many possible applications in myopia research requiring the usage of either static or dynamic accommodation demand.   a Accommodation microfluctuations magnitude is assessed as ± one standard deviation of the foveal mean sphere during one set of measurements. The average through 3 sets is thus the average of these standard deviations.