September 2009
Volume 50, Issue 9
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Visual Psychophysics and Physiological Optics  |   September 2009
More Irregular Eye Shape in Low Myopia Than in Emmetropia
Author Affiliations
  • Juan Tabernero
    From the Section of Neurobiology of the Eye, Ophthalmic Research Institute, Tübingen, Germany.
  • Frank Schaeffel
    From the Section of Neurobiology of the Eye, Ophthalmic Research Institute, Tübingen, Germany.
Investigative Ophthalmology & Visual Science September 2009, Vol.50, 4516-4522. doi:10.1167/iovs.09-3441
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      Juan Tabernero, Frank Schaeffel; More Irregular Eye Shape in Low Myopia Than in Emmetropia. Invest. Ophthalmol. Vis. Sci. 2009;50(9):4516-4522. doi: 10.1167/iovs.09-3441.

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      © 2015 Association for Research in Vision and Ophthalmology.

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Abstract

purpose. To improve the description of the peripheral eye shape in myopia and emmetropia by using a new method for continuous measurement of the peripheral refractive state.

methods. A scanning photorefractor was designed to record refractive errors in the vertical pupil meridian across the horizontal visual field (up to ±45°). The setup consists of a hot mirror that continuously projects the infrared light from a photoretinoscope under different angles of eccentricity into the eye. The movement of the mirror is controlled by using two stepping motors. Refraction in a group of 17 emmetropic subjects and 11 myopic subjects (mean, −4.3 D; SD, 1.7) was measured without spectacle correction. For the analysis of eye shape, the refractive error versus the eccentricity angles was fitted with different polynomials (from second to tenth order).

results. The new setup presents some important advantages over previous techniques: The subject does not have to change gaze during the measurements, and a continuous profile is obtained rather than discrete points. There was a significant difference in the fitting errors between the subjects with myopia and those with emmetropia. Tenth-order polynomials were required in myopic subjects to achieve a quality of fit similar to that in emmetropic subjects fitted with only sixth-order polynomials. Apparently, the peripheral shape of the myopic eye is more “bumpy.”

conclusions. A new setup is presented for obtaining continuous peripheral refraction profiles. It was found that the peripheral retinal shape is more irregular even in only moderately myopic eyes, perhaps because the sclera lost some rigidity even at the early stage of myopia.

The observation that central refractive development might be controlled by the quality of the peripheral retinal image 1 revived interest in the peripheral optics of the eye. Different approaches have been used so far to measure the peripheral refractive state of the eye. Streak retinoscopy has been used to characterize the peripheral refraction pattern (skiagrams) in humans 2 and more recently in monkeys. 3 Commercial autorefractors 4 5 6 7 as well as global image quality techniques like the Hartman-Shack wavefront sensor 8 9 10 and the double-pass technique 11 have been frequently used to measure the peripheral refractive errors in different studies in humans. An infrared video-photoretinoscope 12 includes the advantage of measuring from a distance, and it has been used to assess the peripheral refractive state in humans 13 and chickens. 14  
All the techniques described in previous studies have advantages and disadvantages, but all of them include a common methodological pattern: The subject has to fixate different peripheral stimuli so that the visual field will be scanned at a few discrete positions while the operator performs the measurements. A different, but technically equivalent, situation occurs when the operator moves the instrument and scans the field at discrete angular positions. 
To obtain continuous refractions over the visual field and improve the angular resolution of the measurements, an eye-tracker system was attached to an adapted infrared photorefractor. Still, the subject had to turn the eye by reading a text. 15 A limitation was that the Purkinje image–based eye-tracker failed at angles beyond 40° off-axis because the first Purkinje image displayed no clear specular reflections. 
A substantial improvement would be if the subject no longer had to turn the eye and the refractor would still be stationary. To this end, a scanning hot mirror was placed in front of the eye that made it possible to perform infrared photorefraction from −45° to 45° eccentricity. With this method, both the photoretinoscope and the subject’s fixation remained stationary. 
Although the differences in the peripheral refractive errors (and eye shape) of myopic and emmetropic subjects are well documented in the literature 4 5 13 16 for discrete angular positions, continuous data may uncover new details about eye shapes in ammetropia. A better assessment of the peripheral properties of the eye would also have a clear impact on future experiments to control the growth of the peripheral sclera, a factor that seems crucial to understanding emmetropization (Hung L, et al. IOVS 2009;50:ARVO E-Abstract 3934). 
Methods
Design of the Scanning System and Ray Tracing
A hot mirror (which reflects in the infrared but it is transparent to visible light) was used to project the infrared light from the photoretinoscope into the eye under different angles. Ray tracing showed that a simple rotation of a mirror is not enough to scan over the required angles (±45°). In this case, the image of the pupil in the video frame moved out of the field of the camera already for small changes in the angle of the mirror. Therefore, in addition to rotation, translational movements were necessary. Figure 1shows the geometry of the problem. The thickest line represents the reference ray. This reference is defined as the central ray from the photoretinoscope that hits the central point of the mirror. To force the pupil to remain in the field of the camera this ray had to go through the posterior nodal point of the eye (Fig. 1 , N). The angle that the reference ray subtended relative to the fixation line defined the angle of eccentricity (α). A second constraint was imposed by the reflection law (angle of incidence relative to the normal equal to the angle of reflectance). The angle of incidence in Figure 1is denoted γ. Taking these two constraints into account, a rotation of the mirror around the axis (Fig. 1 , angle β) together with a translational movement in the direction of the incoming light (Fig. 1 , Y) permitted refraction at different angles while the pupil remained stationary in the video frame. The equations for the movement of the mirror as a function of eccentricity α were  
\[Y({\alpha}){=}D\ \mathrm{Tan}({\alpha})\]
 
\[{\beta}({\alpha}){=}\frac{1}{2}\left(\frac{{\pi}}{2}{-}{\alpha}\right)\]
 
where D represents the distance from the eye to the mirror when α = 0. With these equations, it can be concluded that, for measurements from −45° to 45°, the mirror had to be moved within the limits of  
\[22.5{^\circ}{\leq}{\beta}{\leq}67.5{^\circ}\ {-}D{\leq}Y{\leq}D\]
 
For a D of 110 mm, Figure 2represents the ray tracing for three positions of the mirror, the central position with eccentricity 0 and the two extreme positions for α = ±45°. 
Experimental Setup
Two stepping motors (PC Control, Ltd., Kettering, UK) were used to translate and rotate a rectangular-shaped hot mirror (5 × 4 in.; Edmund Optics, Barrington, NJ). The angular resolution of each stepping motor was 1.8°. Both motors could be controlled simultaneously via a USB-connected control board (StepperBee+; PC Control, Ltd.). A library written in C++ with all the functions necessary to control the motors was also supplied by the company. One of the stepping motors rotated the hot mirror, and the other controlled its linear translation. Both motors were assembled in a customized screw-driven linear stage approximately 30 cm long. With these dimensions, the device could be placed up to 15 cm away from the eye (equation 2), but a distance of 11 cm was chosen in this study to reduce the dimensions of the setup. Figure 3shows a photograph of the experimental setup. 
The movement of the mirror was programmed with C++, with the functions of the library provided by the manufacturer and the custom written software for photorefraction. The principle of infrared photoretinoscopy is explained in detail elsewhere. 12 17 To maximize sampling speed, the refractions were measured only in the vertical pupil meridian. 
It was necessary to synchronize the frame-by-frame measurements to the position of the mirror. With the motor working at maximum speed (5 ms per step), the number of steps and the number of processed frames were counted while the mirror was moved over a defined distance. This method provided 19 steps per millimeter and 3 steps per video frame. For a scanning distance of 22 cm (with the mirror 11 cm from the eye, see equation 2), 1393 video frames had to be analyzed for a complete scan from −45° to 45°. The scans were programmed in a loop so that the mirror translated back and forth continuously until the numbers of required scans were completed. A complete scan took approximately 23 seconds (1393 frames/60 Hz). 
The final step was to determine the angle of eccentricity in every frame of the scan (from 0 to 1393). Because the angular resolution of the stepping motor was only 1.8°, it was necessary to extrapolate between possible positions to obtain more smooth data. If 45° corresponds to the frame number 0° and −45° corresponds to the frame number 1393, then we obtain the eccentricity from:  
\[\mathrm{Eccentricity({^\circ})}{=}{-}0.0646{\times}\mathrm{Frame_Number}{+}45\ (0{\leq}\mathrm{Frame_Number}{\leq}1393)\]
 
Before a measurement, the operator had to indicate the number of desired scans and to align the hot mirror in the starting position (45°). The measurement procedure itself was fully automated. Refractions with corresponding angles of eccentricity were stored in a file for off-line analysis. 
Subjects and Measurement Procedure
The right eyes of 28 student subjects (11 myopic, 17 emmetropic) with no known ocular disease other than myopia, were measured without their corrections. The average refraction in the myopia group was −4.3 D (SD 1.7). Practices and research adhered to the tenets of the Declaration of Helsinki. Informed consent was obtained from each subject after explanation of the nature and possible consequences of the procedures. Myopia was defined as a spherical equivalent of −0.75 D or less. A green LED, placed at 1 m, was used to keep the subject’s fixation steady. Cycloplegia was not used in the measurements to prevent the peripheral optics from being artificially modified. At least four peripheral scans were performed in each subject. Once the data were collected, a running average (averaging the data of 60 adjacent frames) was calculated in commercial software (Excel; Microsoft, Redmond, WA). Standard deviations from these frames were also computed to estimate the noise of measurement. The possible fluctuations on the accommodation state would show up associated with nosier values. Data from the area of the optic disc were recognized by more myopia and more measurement noise and were removed. The remaining data were fitted to different polynomials, from the 2nd to the 10th order. The error of the fit was computed as the SE of the estimate. Figure 4illustrates the different steps to analyze the data of a myopic subject. Figure 5shows measurements of the refractive state separately for each of the four scans of the hot mirror (from −45° to 45°) in four subjects with different foveal refractions (one emmetropic and three myopic subjects). The noise on the traces was less than 0.5 D and the details of the profiles were reproduced in the repeated scans. Therefore, accommodation drifts can be excluded as a source of variability. Instead, small changes in the horizontal angle of fixation of the subjects can move the curves along the abscissa, and small changes of fixation in the vertical direction can affect their shape. That the noise on the traces increased with increasing refractive error is typical of eccentric photorefraction and is discussed in the Results section. 
Results
Figure 6shows the results from all subjects, divided into myopic or emmetropic. Figure 6Ashows the relative peripheral refraction in the vertical pupil meridian (processed as shown in Fig. 4 ) with respect to the central refraction of the myopic eyes as a function of the eccentricity angle. Figure 6Bshows the same for the emmetropic eyes and Figure 6Crepresents the averages of the data shown in Figure 6A and 6B . Myopia group data are plotted in black and emmetropia group data in gray. Refractions in the vertical pupil meridian became more hyperopic with increasing eccentricity in both groups. Figure 6Cshows also asymmetries between the nasal and the temporal visual fields and also differences between both groups. These differences were more pronounced in the nasal retina. At 40°, there was a difference of almost 1.5 D, with more hyperopia in the myopic subjects. In contrast, there was almost no difference between the myopia and emmetropia groups in the temporal retina. 
Every curve presented on Figures 6A and 6Bwas fitted to polynomials of second, third, fourth, sixth, and tenth order. The residual error of these fits, calculated as the standards error of the estimate is shown in Figure 7 . The abscissa in Figure 7Arepresents the highest order of the polynomial fit, and the vertical axis shows the average residual error in diopters for myopic subjects and emmetropic subjects. Error bars denote the standards errors of the mean. As expected, the residual error decreased as the polynomial order increased. However, the decrease was steeper in the myopia group because they had relatively higher errors for the low-order polynomials. In general, higher order polynomials were necessary for the myopia group than for the emmetropia group to obtain a similar quality of the fit. For instance, to obtain the same error for myopic subjects as the one for the emmetropic subjects at the 6th order, we had to use approximately a 10th-order fit (four orders more). Unpaired Student’s t-tests were performed to compare the fitting errors in myopic and emmetropic eyes for each polynomial order. The tests give significant differences at the P < 0.005 level for all the fitting orders. Even after exclusion of the data from the three more highly myopic subjects, there was still a significant difference in the residual error of the fit between the emmetropic and the myopic groups (for a sixth-order fit, P < 0.03; with all subjects: P < 0.002). Figure 7Bshows the correlation between the fitting error and the refractive central state when the fitting was performed with sixth-order polynomials. It can be seen that the residual error increased with the level of myopia. The dashed straight line represents a linear fit to the data. The correlation coefficient was R 2 = 0.387 (P < 0.001). 
The noise in the measurements was estimated by the standard deviation of the 60 frames taken to compute the moving average of the refraction as a function of the eccentricity. Results are shown in Figure 8for both the myopia and emmetropia study groups. In this case, data also included the refractions in the area of the optic nerve (note the peaks on the nasal side of the retina). It is obvious that the measurements are noisier in the temporal side of the retina, while on the nasal side, they are more constant. However, no difference was detected in noise between the emmetropic and myopic subjects. 
Discussion
Promises of the Scanning Peripheral Photoretinoscope
The scanning system designed for the measurement of the peripheral refraction presents several advantages with respect to previous methodologies. It is clear that a novel feature is that continuous refraction profiles can be recorded. For example, the classic paper by Millodot 4 on peripheral refractions of persons with myopia, emmetropia, or hyperopia presents an angular resolution of 10°. Those details, like the refractive bumps that were detected in the present study remained unresolved. More recent works on peripheral refractions presented similar angular resolutions. For instance, Seidemann et al. 13 used nine fixation positions to scan a visual field from −21° to 21° with the power refractor. Atchison et al. 7 measured the refraction in steps of 5° from −35° to 35° in the horizontal field using a commercial autorefractometer. Similarly, using a commercial Hartmann-Shack instrument, Mathur et al. 9 sampled 42° of the central visual field at seven positions. Previous techniques included a subjective component, since the direction of gaze of the subject could not be verified. In the new scanning setup, the subject had only to keep the fixation at a central stimulus and the time required for a full measurement was reduced, reducing also the risk of changes in the direction of fixation. The central fixation target could be placed at a distant position to avoid accommodation. No gold standard refraction technique was used for comparison to our refraction data. First, our photorefractor was reliable, since it was calibrated with a set of trial lenses. Second, there is currently no other device on the market that can scan refractive state continuously over the visual field, which we could have used for comparison. Preliminary data from the same subjects, obtained with a scanning Hartmann-Shack sensor, showed good agreement (manuscript in preparation). 
A few technical limitations remain in the current device, but they can all be resolved in future versions, because they are related to the mechanics of the mirror. At present, the linear stage could not be moved faster than 23 seconds for a full scan. While 23 seconds were no problem in the laboratory, a study in children or infants would benefit from a faster scanner. Also the vibrations of the mirror associated with each step of rotation generate motion artifacts in the video frame which were removed by off-line filtering. Both problems were solvable by better mechanics. 
Magnitude of the Structural Differences
This study demonstrates a potential advantage of the new scanning method. The fact that peripheral refractive contours in the myopic group required higher order polynomials to achieve a fitting quality similar to that of the emmetropic group (Fig. 7)suggests that myopic persons may either have lower scleral rigidity, or that the “bumps” may reflect early signs of emerging retinal or choroidal lesions. These findings may make continuous scans of peripheral eye shape interesting as a new diagnostic tool. It is known that there may be chorioretinal abnormalities and structural deficiencies in the sclera once myopia has progressed (like retinal breaks, chorioretinal atrophy, Fuchs’s spot, lacquer cracks, pigmentary degeneration, lattice degeneration, posterior staphyloma (see the review by Saw et al. 18 ), but the present study suggests that changes may occur already at early stages in myopia. It could even be that irregularities in the peripheral refraction pattern are detectable before foveal myopia develops. Previous work by Mutti et al. 19 has shown that various optical factors change faster in the years before the onset of myopia. One of these potentially predictive factors was relative peripheral refraction at 30° in the temporal retina. Before the onset of foveal myopia, the peripheral refraction moved faster toward relative hyperopia. An obvious limitation of this work was that refractions were sampled at only one discrete position and this may not identify the full pattern of changes. It should also be noted that the magnitude of the irregularities are too small to be detected with imaging techniques, like magnetic resonance imaging (MRI). 16 20 According to Atchison et al., 20 the measurements of axial length had a mean precision error of 0.3 mm. Given that 1 D represents an axial elongation of 0.37 mm 21 and that the average residual error from a second-order fit was less than 0.4 D in myopic eyes, these irregularities could not be resolved with MRI. It is possible to acquire very high-resolution images of the retina with optical coherence tomography. The resolution may be sufficient to detect local irregularities over the retina, but so far this technique has mostly been used in the central retinal area. 22 23 24 However, the origin of the bumps is unknown and there is the probability that they originated on the scleral surface which is not visualized by OCT. 
The analysis of the noise (Fig. 8)revealed a similar pattern in myopic and emmetropic eyes. Therefore, it can be excluded that the irregularities were due to higher measurement noise in myopia. It is evident that refractions were more variable in the temporal retina for all subjects. The origin of this asymmetry could be due to several factors discussed in the next section. 
Origin of Nasal-Temporal Asymmetries
Different asymmetries were found between the nasal-temporal peripheral refraction (Fig. 6) . On average, refractions were more variable in the temporal retina and there was more relative hyperopia. This observation is in line with previous studies 4 13 and has traditionally been explained by displacement of the fovea into the temporal retina with respect to the optical axis of the globe (the angle α or κ 7 10 21 25 ; illustrated in Fig. 9 ). In the left panel, a hypothetical case is shown where angle κ is 0, resulting in a symmetrical peripheral refraction profile. The right panel shows a more realistic case with a clear deviation of the fixation axis from the optical axis. In this case, the temporal retina is more tilted with respect to the best optical axis (here assumed to be identical with the pupillary axis). As a consequence, more astigmatism is generated in the temporal retina which is in line with previous measurements (see e.g., Seidemann et al. 13 ). 
Also, myopic individuals are more hyperopic than emmetropic persons on the nasal side of the retina but not so clearly on the temporal side. This effect may also be a partial consequence of the alignment. Generally, myopic eyes have smaller angle κ than emmetropic ones, 25 26 which would make the peripheral refraction more symmetric than for emmetropic eyes, which is in fact consistent with our results (Fig. 6) . If the emmetropic retina is generally less hyperopic in the periphery, then an angle κ would have the effect of shifting the refraction curve toward the nasal side (the theoretical minimum should move to the nasal side) increasing the difference with respect to the myopic curve in this side (the myopic curve might be less shifted because of less angle κ) and reducing the distance on the temporal side. This explanation also fits well with our experimental data (Fig. 6)
There is also an asymmetry on the noise of the measurements (Fig. 8) , quantified by the SD of 60 adjacent processed frames. The temporal side is noisier than the nasal side. It could be that the illumination from the nasal field is partially blocked by the nose of the subject during the measurement and generates more complicated images to analyze. Or, as a consequence of the angle κ, the eye could be more tilted when the illumination comes from the nasal field than from the temporal field (Fig. 9) . In this case, the pupil would be more distorted and would be more difficult to analyze. 
Conclusions
It was found that a continuous scan of the peripheral refraction provides new information about the shape of the eye in both myopic and emmetropic individuals. Myopic persons appear to have a more irregular eye shape than do emmetropic individuals. Perhaps these differences exist already before foveal myopia develops and future studies will show whether this information may have any predictive value. Future goals include improving measurement speed and increasing the portability of the device. We also want to add vertical rotation to the mirror through the addition of a third-step motor, so that a 3D-scan can be automatically performed, allowing the construction of a two-dimensional map of the peripheral refraction. Also, animal research may benefit from such new data. 
 
Figure 1.
 
Schematic drawing of the geometry of the scanning mirror that is used to project the light from the retinoscope into the eye under different eccentricity angles. The angle β and the distance Y represent the degrees of freedom of the mirrors movement. Angle α is the eccentricity angle and γ is the incidence and reflected angle of the reference ray. N is the approximate location of the nodal points in the eye, and D is the distance of the eye with respect to the central position of the mirror.
Figure 1.
 
Schematic drawing of the geometry of the scanning mirror that is used to project the light from the retinoscope into the eye under different eccentricity angles. The angle β and the distance Y represent the degrees of freedom of the mirrors movement. Angle α is the eccentricity angle and γ is the incidence and reflected angle of the reference ray. N is the approximate location of the nodal points in the eye, and D is the distance of the eye with respect to the central position of the mirror.
Figure 2.
 
Ray-tracing simulation illustrating three possible positions of the scan: two peripheral locations (±45°) and a central position at 0°.
Figure 2.
 
Ray-tracing simulation illustrating three possible positions of the scan: two peripheral locations (±45°) and a central position at 0°.
Figure 3.
 
The scanning mirror setup with the critical components labeled.
Figure 3.
 
The scanning mirror setup with the critical components labeled.
Figure 4.
 
Postprocessing of the raw data (top left) involves the calculation of the running average (top right), removing the optic nerve area (bottom left), and fitting the data with polynomials of different orders (bottom right).
Figure 4.
 
Postprocessing of the raw data (top left) involves the calculation of the running average (top right), removing the optic nerve area (bottom left), and fitting the data with polynomials of different orders (bottom right).
Figure 5.
 
Refraction as a function of eccentricity in four subjects (one emmetropic, three myopic). In every subject, the measurement consists of four consecutive scans (from −45° to 45°) that are plotted separately to check the experimental noise generated between each scan.
Figure 5.
 
Refraction as a function of eccentricity in four subjects (one emmetropic, three myopic). In every subject, the measurement consists of four consecutive scans (from −45° to 45°) that are plotted separately to check the experimental noise generated between each scan.
Figure 6.
 
The relative peripheral refraction as a function of eccentricity for the myopic (A), emmetropic (B) groups, and the averages of both groups (C).
Figure 6.
 
The relative peripheral refraction as a function of eccentricity for the myopic (A), emmetropic (B) groups, and the averages of both groups (C).
Figure 7.
 
(A) The mean residual error of the polynomial fits plotted as a function of the different polynomial orders. Error bars, SE. (B) The correlation of the fitting error (for a sixth-order polynomial) with the central refractive error (R 2 = 0.387; P < 0.001). The boxes in (B) show the expanded individual data.
Figure 7.
 
(A) The mean residual error of the polynomial fits plotted as a function of the different polynomial orders. Error bars, SE. (B) The correlation of the fitting error (for a sixth-order polynomial) with the central refractive error (R 2 = 0.387; P < 0.001). The boxes in (B) show the expanded individual data.
Figure 8.
 
Average SD of the running average as a function of the eccentricity angle.
Figure 8.
 
Average SD of the running average as a function of the eccentricity angle.
Figure 9.
 
Left: a hypothetical situation in which the optical axis is aligned with the line of sight. Taking this alignment into account, certain symmetry around the line of sight is expected. Right: a more realistic condition is shown. In the presence of an angle κ (formed between the line of sight and the pupillary axis) the line of sight is no longer the axis of symmetry.
Figure 9.
 
Left: a hypothetical situation in which the optical axis is aligned with the line of sight. Taking this alignment into account, certain symmetry around the line of sight is expected. Right: a more realistic condition is shown. In the presence of an angle κ (formed between the line of sight and the pupillary axis) the line of sight is no longer the axis of symmetry.
The authors thank the mechanical workshop of the Ophthalmic Research Institute (Director, Hubert Willmann) for building the mechanical components for the scanning mirror. 
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Figure 1.
 
Schematic drawing of the geometry of the scanning mirror that is used to project the light from the retinoscope into the eye under different eccentricity angles. The angle β and the distance Y represent the degrees of freedom of the mirrors movement. Angle α is the eccentricity angle and γ is the incidence and reflected angle of the reference ray. N is the approximate location of the nodal points in the eye, and D is the distance of the eye with respect to the central position of the mirror.
Figure 1.
 
Schematic drawing of the geometry of the scanning mirror that is used to project the light from the retinoscope into the eye under different eccentricity angles. The angle β and the distance Y represent the degrees of freedom of the mirrors movement. Angle α is the eccentricity angle and γ is the incidence and reflected angle of the reference ray. N is the approximate location of the nodal points in the eye, and D is the distance of the eye with respect to the central position of the mirror.
Figure 2.
 
Ray-tracing simulation illustrating three possible positions of the scan: two peripheral locations (±45°) and a central position at 0°.
Figure 2.
 
Ray-tracing simulation illustrating three possible positions of the scan: two peripheral locations (±45°) and a central position at 0°.
Figure 3.
 
The scanning mirror setup with the critical components labeled.
Figure 3.
 
The scanning mirror setup with the critical components labeled.
Figure 4.
 
Postprocessing of the raw data (top left) involves the calculation of the running average (top right), removing the optic nerve area (bottom left), and fitting the data with polynomials of different orders (bottom right).
Figure 4.
 
Postprocessing of the raw data (top left) involves the calculation of the running average (top right), removing the optic nerve area (bottom left), and fitting the data with polynomials of different orders (bottom right).
Figure 5.
 
Refraction as a function of eccentricity in four subjects (one emmetropic, three myopic). In every subject, the measurement consists of four consecutive scans (from −45° to 45°) that are plotted separately to check the experimental noise generated between each scan.
Figure 5.
 
Refraction as a function of eccentricity in four subjects (one emmetropic, three myopic). In every subject, the measurement consists of four consecutive scans (from −45° to 45°) that are plotted separately to check the experimental noise generated between each scan.
Figure 6.
 
The relative peripheral refraction as a function of eccentricity for the myopic (A), emmetropic (B) groups, and the averages of both groups (C).
Figure 6.
 
The relative peripheral refraction as a function of eccentricity for the myopic (A), emmetropic (B) groups, and the averages of both groups (C).
Figure 7.
 
(A) The mean residual error of the polynomial fits plotted as a function of the different polynomial orders. Error bars, SE. (B) The correlation of the fitting error (for a sixth-order polynomial) with the central refractive error (R 2 = 0.387; P < 0.001). The boxes in (B) show the expanded individual data.
Figure 7.
 
(A) The mean residual error of the polynomial fits plotted as a function of the different polynomial orders. Error bars, SE. (B) The correlation of the fitting error (for a sixth-order polynomial) with the central refractive error (R 2 = 0.387; P < 0.001). The boxes in (B) show the expanded individual data.
Figure 8.
 
Average SD of the running average as a function of the eccentricity angle.
Figure 8.
 
Average SD of the running average as a function of the eccentricity angle.
Figure 9.
 
Left: a hypothetical situation in which the optical axis is aligned with the line of sight. Taking this alignment into account, certain symmetry around the line of sight is expected. Right: a more realistic condition is shown. In the presence of an angle κ (formed between the line of sight and the pupillary axis) the line of sight is no longer the axis of symmetry.
Figure 9.
 
Left: a hypothetical situation in which the optical axis is aligned with the line of sight. Taking this alignment into account, certain symmetry around the line of sight is expected. Right: a more realistic condition is shown. In the presence of an angle κ (formed between the line of sight and the pupillary axis) the line of sight is no longer the axis of symmetry.
Copyright 2009 The Association for Research in Vision and Ophthalmology, Inc.
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