A new device was designed to provide fast measurements (4 s) of the peripheral refraction (90° central horizontal field). Almost-continuous traces are obtained with high angular resolution (0.4°) while the subject is fixating a central stimulus. Three-dimensional profiles can also be measured. The peripheral refractions in 10 emmetropic subjects were studied as a function of accommodation (200 cm, 50 cm, and 25 cm viewing distances). Peripheral refraction profiles were largely preserved during accommodation but were different in each individual. Apparently, the accommodating lens changes its focal length evenly over the central 90° of the visual field.
© 2009 Optical Society of America
It has been hypothesized that hyperopic defocus in the periphery might promote foveal myopia [1, 2]. Therefore, it is of interest to determine under which conditions hyperopic defocus is imposed in the center and in the periphery and how it could be prevented. At present, measurements of peripheral refraction profiles are demanding and provide data at discrete angular positions (streak retinoscopy [3, 4], autorefractometers [5, 6, 7, 8], double-pass method , Hartmann–Shack aberrometry [10, 11, 12], photoretinoscopy [13, 14]). The subject has to fixate at different angular positions across the visual field, imposing some subjectivity, or the operator has to move the instrument to angular different positions.
Recently, a device was introduced to scan the peripheral refraction with a hot mirror in combination with a custom-designed infrared photoretinoscope . The scanning hot mirror projects the light from the infrared photoretinoscope into the eye under different angles, ranging from −45° to 45° from the fovea. The subject has to maintain steady fixation at a central target, which simplifies the procedure and makes it much faster. Still, due to mechanical limitations of the stepping motors that moved the hot mirror, the scanning time was still long (around 22 s for a full scan), which is too slow for measuring the effects of sustained accommodation on peripheral refraction.
Accommodation is assumed to be linked to the etiology of myopia . The lag of accommodation and/or the excess of near work have been associated with the onset of myopia [16, 17]. It is not well known how accommodation affects the peripheral refraction, relative to the fovea, and whether there may be the risk of more relative hyperopia in the periphery during accommodation. With improved mechanics in our scanning photoretinoscope, the measurement time could be reduced to 4 s. This new setup was used to study this question. In addition, the new device was used to measure three-dimensional (3-D) maps of the refraction in the vertical pupil meridian.
2. MATERIALS AND METHODS
2A. Fast Scanning Infrared Photoretinoscope
The principle of the instrument was described in detail in a previous publication . Briefly, a hot mirror (20 × 15 cm) projects the light from an infrared retinoscope into the eye. The mirror is moved using two stepping motors (PC Control, Ltd., Kettering, UK) through a USB-controlled board (StepperBee+, same company). One of the motors translates the mirror while the other performs a rotation around the vertical mirror axis. Theoretically, the rotational and translational movements are nonlinearly related, but in practice, they were linearized between the initial and the final position of the mirror, as previously described . The main improvement in the new version emerges from an optimized linear stage. In this case, we chose to manufacture a belt-driven linear stage that runs with less friction than the previous screw-driven version. A full scan (90°) of the peripheral refraction now takes around 4 s, compared to the 22 s of the first version. In addition, the angular resolution of the rotation of the mirror is increased by a factor of 3 (from 1.2° to 0.4° per step), using a two-gear belt transmission system. The movement of the mirror was combined with the measurement of refraction across the vertical pupil meridian at a frame rate of 62 Hz. The total number of refractions was 226 for a full scan (from −45° to 45°), acquired in steps of 0.4°. The photoretinoscope was calibrated using trial lenses in an emmetropic subject. Calibration of photorefraction is described in detail elsewhere . In line with findings of a previous study , the changes in the calibration factor with angles of eccentricity were negligible, and a single factor was used for all angular positions. Custom software was written in Visual C++ to control the stepping motors and to evaluate the refractions. A small laptop was used to run the software and control mirror and monochrome CCD camera through two USB2 ports. Figure 1 shows a picture of the device with all the components and one of the authors (JT) as a subject.
2B. Subjects and Measurements
Ten young emmetropic students (20–25 years of age) with no ocular pathologies served as subjects for these measurements. Subjects were selected after a detailed subjective refraction performed by an experienced and certified optometrist that proved that they had spherical and cylindrical refractive errors less than 0.5 D. The measurements were approved by the Ethics Commission of the Faculty of Medicine of the Eberhart-Karls-University of Tübingen. In all subjects, peripheral refraction was measured at three accommodation levels (fixation distances 2 m, 0.5 m, and 0.25 m). The fixation target was a Maltese cross subtending 1.5°. Only right eyes were measured. Accommodation was stimulated monocularly through the right eyes (the left eyes were covered with a patch during the measurements). Monocular fixation offered the advantage that the fixation targets could be presented behind one another along a defined axis. Prior to the measurements, the subjects had to align the angular positions of the near and far targets for the right eyes. This procedure guaranteed that the refraction profiles measured for different accommodation levels were normalized to a fixed angular position. At least six full scans (±45°) of the peripheral refraction were performed for every subject at each of the three accommodation levels. In one subject, additional measurements of peripheral refraction were taken while the subject fixated a far stimulus (2 m) at seven different angular elevations (−10°, −8°, −4°, 0°, 4°, 8°, 12°). These data were later used to reconstruct a 3-D map of the peripheral refraction.
In this section, the results of measurements of peripheral refraction, determined in the vertical pupil meridian, from several subjects are presented. Figure 2 shows a 3-D reconstruction of the peripheral refractions from one of the subjects covering a field of 90°V × 22°H. The area of the optic disc head (at around 10° in the nasal retina) shows up as a more myopic region, due to the excavation of the optic disk. Apart from this fact, it seems that across the 22° in elevation the refraction remained similar in this subject.
Effects of accommodation on peripheral refraction patterns are summarized in Fig. 3 . The plots show refraction in diopters (D) (ordinate) versus the angular eccentricity (°) (abscissa) for each of the10 subjects. The three different curves show the refractions for three different accommodation levels: 0.5 D (black), 2 D (red/dark gray), and 4 D (green/light gray). In general, these curves show that with increasing accommodation, the shape of the refraction profile does not change. It is striking that each subject shows a typical pattern of peripheral refractions, from very flat (subjects 3, 4, and 10) to more parabolic (subjects 2 and 5). Other subjects show a centrally flat pattern with a steep increase in hyperopia in the periphery (subjects 1, 6, and 7). Similarly to the 3-D reconstruction map in Fig. 2, the excavation of the optic nerve shows up as the area of more myopia on the nasal side of the retina (positive eccentricity from the fovea).
To determine the gain of accommodation, the baseline refractions at 0.5 D accommodation effort were simply subtracted from the 2 D and 4 D curves. Results are shown in Fig. 4 . The small data points in bright red/dark gray represent the refractive changes from 0.5 D to 2 D, and the data points in light gray represent the changes from 0.5 D to 4 D. Expected changes in accommodation were −1.5 D and −3.5 D. For the sake of comparability, two thick dashed lines were added in Fig. 4 to illustrate these values. Data points above these lines represent a lag of accommodation (more hyperopic refraction), and data below represent a lead of accommodation (more myopic refraction) at a particular angular position. Data plotted in green/light gray filled circles show the averages of the 10 subjects, obtained by clustering the refractions across the field in intervals of 10° from −45° to 45°. The error bars in the circles represent the standard deviation of the average data. No statistically significant differences between expected and measured accommodation were observed. There were higher variations in the case of the 3.5 D accommodation change. This could be attributed to less-stable refractions with higher accommodation efforts or to the fact that photorefraction becomes more variable for higher refractive errors.
4A. Fast Scanning Infrared Photoretinoscope
The instrument presented here shows technical advances, making it attractive for studies on peripheral refractions in larger samples of patients. In general, and with respect to previous methods such as autorefractometers [5, 6, 7, 8], double-pass method , Hartmann–Shack apparatus [10, 11, 12], or classical streak retinoscopy [3, 4], the main advantage is that the acquisition time for a complete and almost continuous scan is reduced to 4 s. Furthermore, the subject has to fixate only to a central stimulus during the measurements. Another approach to measure the peripheral refractive errors was to use an eye tracker in combination with a continuously recording photoretinoscope . In this case, the subject had to look at targets at different positions in the visual field while the gaze tracker linked the measured refractions to angular eye position. However, it is difficult to program a detection algorithm for the first Purkinje image that also works at angles of eccentricity of more than 40°. The advantage of a scanning mirror system is that there is no need for an eye tracker, since the position of the mirror, and hence the measured angle, are known.
At present, the major limitation of the scanning mirror system is that only the vertical meridian is refracted and information on astigmatism is lost. A solution would be to use a rotating photoretinoscope as in the PowerRefractor , although this would also slow down the sampling rate.
Using a mirror that also scans the vertical direction, a complete 3-D map of spheres, cylinders, and axes could be obtained. Again the scanning time would be increased, and in the end, the question remains as to whether such extended data sets would help us to understand the relationship between peripheral refractions and myopia development—currently one of the major goals of such studies.
4B. Inter-Individual Variability of Peripheral Refractions
In 1971, Rempt et al.  published a paper describing how they classified different types of peripheral refraction in a population of 442 subjects. Refractions were measured in both the horizontal and the vertical pupil meridian every 20°, from −60 to 60 across the horizontal visual field. For the refractions in the vertical meridian, the most common condition was increasing hyperopia to the periphery (found in 201 of 217 emmetropes). In the remaining cases, the refractions in the vertical meridian remained “flat” across the visual field. This type of refraction was named type V. Their description would fit to the data of subject 3 and perhaps subjects 4 and 10, shown in Fig. 3. The descriptions by Rempt et al.  were limited by the angular sampling intervals of 20°. Using more-continuous sampling as shown in Fig. 3, it can be seen that, although most of the subjects show more hyperopic refractions in the far periphery, they follow different patterns. Subjects 1, 6, and 7 display a central area with little change in refraction, but hyperopia increases rapidly beyond 30°. In contrast, in subjects 8 and 9 the increase of hyperopia follows a more linear function (V-shape). A different pattern is observed in subjects 2 and 5, where the refraction changes according to a more parabolic function. To evaluate the potential to predict myopia from the peripheral refractions, a more extensive evaluation of the peripheral refraction patterns may become necessary, in a larger sample of subjects.
4C. Changes of Peripheral Refraction with Accommodation
Figures 3, 4 show that a peripheral refraction profile of a subject is largely preserved during accommodation. We performed a ray-tracing simulation using the accommodating Navarro eye model  with a 12 mm spherical retina . The calculations were performed using a ray-tracing package (ZEMAX Development Corporation, Bellevue, Washington, USA). The parameters for the Navarro eye model were for the 0.5 D, 2 D, and 4 D of accommodation levels. The refraction along the vertical meridian (sagittal plane) was calculated from the wavefront map (using up to sixth-order Zernike coefficients) for a 6 mm pupil diameter for 1.5 D and 3.5 D accommodation levels. Results are shown in Fig. 5 (two thick dashed lines). Only small differences are expected between the foveal and peripheral refractions, based on ray tracing (0.5 D at 45° for a 3.5 D accommodation effort). This is in line with our measurements in the 10 subjects. Averaged data are presented as filled circles with error bars denoting standard deviations, normalized to the central refractions for 1.5 D and 3.5 D accommodation efforts. Individual data are also shown as small gray points. Measured data are not significantly different from the predictions derived from ray tracing (although the individual variability can be high).
Previous studies also did not find large differences between the central and peripheral refraction change during accommodation. Smith et al.  found no significant differences up to 40° (N = 11; accommodation up to 5 D). At 50° and 60° they found some differences, but we cannot confirm these findings because this is out of the angular range that we can measure with our current setup. Using the Le Grand eye model, accommodating 7 D, they predicted changes in the myopic direction. Calver et al.  found no changes up to ±30° of eccentricity (N = 10; accommodation up to 2.5 D), similarly to Davies et al.  (N = 21; accommodation up to 3 D). Lundstrom et al.  found a small change toward more myopia (N = 5; accommodation up to 4 D) and differences between the nasal and temporal retina (around 0.3 D on the temporal side and 0.76 D on the nasal side at 40°).
In myopic subjects, the patterns are even more variable. Some found no change [25, 26] in peripheral refraction with accommodation, while others found a small hyperopic shift of around 0.5 D that was restricted to the temporal retina at 30° [24, 27]. Another study found a myopic shift of around 0.5 D at 40° of eccentricity . In conclusion, given that the differences between central and peripheral refraction at different states of accommodation are variable and quite small, it seems unlikely that these differences have a major effect on foveal refractive development and myopia.
Measurements of continuous peripheral refraction profiles in 10 emmetropic subjects did not reveal any changes between center and peripheral refractions during accommodation. The new scanning mirror infrared photoretinoscope proved to be very useful for gathering these data: fast scanning (4 s from −40° to +40°), near-continuous traces (0.4° of angular resolution), and only a single fixation point for the subject. Different types of peripheral refraction profiles were identified, and their high angular resolution will make it possible to further classify peripheral refraction patterns and their potential relationship to myopia progression.
This study was supported by a postdoctoral fellowship of the Marie Curie Research Training Network (RTN) “MyEuropia” of the European Community (http://www. my-europia.net/) to Juan Tabernero. We thank the mechanical workshop of the Ophthalmic Research Institute (Head: Mr. Hubert Willmann) for building the mechanical components for the scanning mirror linear stage.
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