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Effects of myopic spectacle correction and radial refractive gradient spectacles on peripheral refraction
Vision Research 49 (2009) 2176–2186
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Effects of myopic spectacle correction and radial refractive gradient spectacles on peripheral refraction Juan Tabernero a,*, Daniel Vazquez b, Anne Seidemann b, Dietmar Uttenweiler b, Frank Schaeffel a a b
Section of Neurobiology of the Eye, Ophthalmic Research Institute, Calwerstrasse 7/1, 72076 Tuebingen, Germany Rodenstock GmbH, Isartalstrasse 43, 80469 Munich, Germany
a r t i c l e
i n f o
Article history: Received 15 August 2008 Received in revised form 26 May 2009
Keywords: Human eye Physiological optics Peripheral refraction Spectacles Myopia Hyperopia
a b s t r a c t The recent observation that central refractive development might be controlled by the refractive errors in the periphery, also in primates, revived the interest in the peripheral optics of the eye. We optimized an eccentric photorefractor to measure the peripheral refractive error in the vertical pupil meridian over the horizontal visual field (from 45° to 45°), with and without myopic spectacle correction. Furthermore, a newly designed radial refractive gradient lens (RRG lens) that induces increasing myopia in all radial directions from the center was tested. We found that for the geometry of our measurement setup conventional spectacles induced significant relative hyperopia in the periphery, although its magnitude varied greatly among different spectacle designs and subjects. In contrast, the newly designed RRG lens induced relative peripheral myopia. These results are of interest to analyze the effect that different optical corrections might have on the emmetropization process. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction There is evidence that different optical correction schemes influence the rate of progression of myopia. Examples are undercorrected prescriptions (Phillips, 2005; but see also Chung, Mohidin, & O’Leary, 2002; reporting the opposite effect), rigid contact lenses (Walline, Jones, Mutti, & Zadnik, 2004), bifocal spectacles (Fulk, Cyert, & Parker, 2002), bifocal soft contact lenses (Aller & Wildsoet, 2008) or progressive addition lenses (Gwiazda et al., 2003; Leung & Brown, 1999). Although there is some controversy regarding the benefit of optical intervention, given the small effects in many cases, recent analyses of subgroups of children treated with progressive addition lenses showed clinically relevant effects with about 50% of inhibition of myopia, and no rebound effect after termination of the treatment (Gwiazda, 2008). It is known from experiments in animal models that the retina releases biochemical signals to control the growth of the underlying sclera, such that an optimal refraction is achieved over time (review: Wallman & Winawer, 2004). Recent experiments in monkeys have also shown that peripheral defocus might affect central refraction development (Smith, Kee, Ramamirtham, Qiao-Grider, & Hung, 2005). In these experiments, the animals had normal foveal vision but the peripheral visual field was deprived of sharp vision. This condition was sufficient to induce foveal myopia. Apparently, peripheral retinal image quality is important for foveal refractive * Corresponding author. E-mail address: [email protected] (J. Tabernero). 0042-6989/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.visres.2009.06.008
development in primates. According to this, correction for myopia should not impose peripheral hyperopia because that might trigger axial elongation. (e.g. Atchison et al., 2005; Seidemann, Schaeffel, Guirao, Lopez-Gil, & Artal, 2002). However, and due to fundamental optical constraints when providing a sharp foveal vision at all angles of gaze, the peripheral vision plays a minor role in the design of current spectacle lenses. An alternative optical design to prevent myopia from progressing would be some spectacle lenses that impose some myopia in the periphery to stop the eye growth, while maintaining a good correction of foveal refractive errors. On one hand primates, including humans, have poor spatial resolution in the periphery (e.g. Williams, Artal, Navarro, McMahon, & Brainard, 1996), hence residual peripheral myopia should not be a major problem. On the other hand, this optical design would limit the range of angles of gaze with a sharp foveal vision. Although there have been attempts to correct the peripheral refractive errors of the eye (Lunström et al., 2007; Smith, Atchison, Avudainayagam, & Avudainayagam, 2002), strikingly little is published on how regular single vision lenses designed to correct myopia affect peripheral refractive state. Other than a preliminary study by Seidemann and Artal (1999) and a recent paper on the theoretical effects of a pantoscopic tilt of the spectacles on peripheral refraction (Bakaraju, Ehrmann, Ho, & Papas, 2008), no data are available. It would be worthwhile to measure the human peripheral refractive errors with accurate and automated refractors with and without the regular spectacle corrections. Besides, current studies on the peripheral optics of the eye have the limitation that they include only a few sampling points across
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the visual field. In the present study, a continuously recording photorefractor was used to sample refractions in the vertical pupil meridian across the horizontal visual field from 45 to 45° of eccentricity. A Purkinje image-based gaze tracker was used to assign the measured refractions to angular positions. Peripheral refractions were measured both with the regular spectacle corrections of the myopic subjects, and with the special spectacle RRG lens developed for the purpose of this study. 2. Methods 2.1. Subjects Eleven student subjects (five myopic, six emmetropic), aged 25 to 30 years, with no known ocular pathologies other than myopia, were refracted either with their spectacle corrections (unknown manufacturers), or without them, or with the RRG spectacle lenses. Informed consent was obtained from each of the subjects by signing a form that explained the rationale and possible consequences of the study. The study was approved by the Ethics Commission of the Medical Faculty of the University of Tuebingen. 2.2. Techniques: eccentric infrared photoretinoscopy and gaze tracking The infrared photoretinoscope used for refractions has been previously described in detail (Schaeffel, Hagel, Eikermann, & Collett,
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1994; Schaeffel, Wilhelm, & Zrenner, 1993). Its combination with a gaze tracker has been used to map out the refractions in the vertical pupil meridian across the visual field (Schaeffel, Weiss, & Seidel, 1999; Seidemann et al., 2002). The advantage of photorefraction is that it can be performed over long distances and that it is, after individual calibration, quite accurate, resolving down to less than 0.25 D (Kasthurirangan & Glasser, 2006; Schaeffel et al., 1993). Another advantage is that it operates at video frequency. In the present study, a USB2 infrared sensitive monochrome video camera (http://www.theimagingsource.com/de/ products/cameras/usb_mono/dmk21au04/) with a frame rate of 60 Hz and a spatial resolution of 640 480 pixels was used. The camera was combined with a 50 mm lens with an f/# of 1.4 (same company, B5014A(KA)), with a 5 mm extension ring to focus at 1 m distance, and an infrared cut-off filter (#093, same company). The photoretinoscope, placed in front of the lens, was custom-build as previously described (Schaeffel, Burkhardt, Howland, & Williams, 2004). The software was programmed in Visual C++. It detected the eye in each video frame and measured the slope of the brightness gradient in the pupil that was generated by the infrared photoretinoscope (Fig. 1). The refraction was measured only along the vertical meridian of the pupil, ignoring astigmatism. We did not perform individual calibrations of the photorefraction technique since our focus was on the comparison of central and peripheral refractions rather than the absolute refractions in different subjects. It was assumed that the conversion factor (the
Fig. 1. Screenshot of the custom-developed software to measure refraction versus the horizontal angle of gaze. Relevant details are pointed by arrows and text in large white font.
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factor converting the slope of the brightness profile in the pupil into refractive error; Schaeffel et al., 1993) is linear and possesses the same slope across the visual field. To test this assumption, the technique was calibrated in an emmetropic subject at several positions in the horizontal visual field (±35°, ±25°, ±15°, 0°) with a set of trial lenses. The resulting conversion factors showed little variation in the slope versus the position in the visual field (average slope of the conversion factor ± standard deviation: 1.51 ± 0.10). With this variability of about 15%, a standard deviation of 0.5 D in the measurement of the peripheral refraction can be expected for a refractive error of 5 D). Since we were just interested in measuring peripheral refractions relative to the center of the visual field, the variation of the independent terms of the conversion factors for every angle of gaze is not important in our calculations. Fig. 2 shows the calibrations for seven angular positions and illustrates the variability of the slopes. Gaze tracking was performed on-line by detecting the first Purkinje image, created by the photoretinoscope in the pupil, and recording its position relative to the pupil center (see Fig. 1). A Hirschberg ratio of 12°/mm was used throughout the study (Barry, Dunne, & Kirschkamp, 2001; Brodie, 1987; Schaeffel, 2002). Since the software could not distinguish between the corneal Purkinje image and the specular reflections that occurred on the sclera for large angles, gaze tracking was limited to ±50° off-axis. 2.3. Experimental procedures To obtain a continuous trace of refractions across the visual field, a ‘‘continuous” stimulus is more advantageous than discrete fixation targets. The subjects read a text from a bar that subtended an angle of ±45° over the horizontal visual field, and was positioned at 1 m distance. Since the bar was straight, the viewing distance was slightly larger for the more peripheral positions (by maximally 0.3 D). If the subjects had relaxed their accommodation accordingly, slightly more hyperopic refractions were possible for the peripheral positions. This factor was not further considered. Ambient illuminance was kept as low as possible (about 10 lux)
Fig. 2. Pupil brightness slope in the vertical pupil meridian measured at different angular positions in the visual field, and with different powers of trial lenses held in front of the eye. The calibration shows that the slopes of the regressions did not vary significantly with the position in the horizontal visual field, making the use of a single conversion factor for all positions acceptable.
to keep the pupil sizes large and, thus, reduce the measurement noise of the photorefraction. A minimum of three scans were performed for each of the subjects. The retinoscope was positioned at a stationary position at one meter distance, at 0°. The head was stabilized by a chin and forehead rest. Only a limited area of the spectacles could be sampled (Fig. 3). With this approach, about 40% of the central spectacle area could be sampled (Fig. 3). To allow the subjects to move their head rather than their eyes would have permitted to measure a larger area. However, it was found that the Purkinje image-based gaze tracker did no longer work reliably. Since the myopic subjects could not read the text without spectacles, the operator used a laser pointer to project a red spot onto the bar and moved it slowly across the visual field. The total measurement procedure took about 2 min. 2.4. Experimental protocols Three experiments were performed: In experiment (1), the peripheral refractions with conventional negative spectacle lenses for correction of myopia were measured. Nine eyes from five myopic subjects were measured, with their regular spectacles and without them. One eye could not reliably be measured because the pupil was too small. In the myopic subjects, foveal refractive errors ranged from 3 to 8 diopters (with astigmatism less than 1 D, according to their prescriptions). The Hirschberg ratio used by the gaze tracker was corrected for the magnification effect of the glasses – it increases linearly with increasing power of the negative lenses due to magnifications (Schaeffel, 2002). The refraction data across the visual field were fitted with fifth order polynomials and normalized to zero for the foveal refractions to facilitate inter-individual comparisons. In experiment (2), the effects of a Radial Refractive Gradient (RRG) spectacle lens on peripheral refractions were studied. These lenses were designed to optimize two optical features: first, clear foveal vision in the optical center and second, a steady increase of positive power in all radial directions. The increase in spherical equivalent refractive power was about one diopter for every 10° to the periphery in the visual field, with a central plano area (astigmatism and spherical equivalent lower than 1/8 D) with a diameter of 6 mm – about the diameter of the pupils of the young subjects under mesopic conditions. Astigmatism could be kept at 1.1 D at 20°, but increased up to 3.5 D at 40°. Details on the refraction profile of the RRG lenses are shown in Fig. 4. Since the lenses were intended to be used in different subjects with potentially different retinal geometries, the refractive profile was designed and measured in relation to the Far Point Sphere and the Vertex Sphere (Jalie, 1977, chap. 18) and not to a given retinal surface. Thus, the 3.6 D of spherical equivalent at 40° of Fig. 4 indicated that when looking foveally with an angle of gaze of 40°, the spherical equivalent power provided by the lens measured in relation to the Vertex Sphere was 3.6 D. RRG lenses were mounted in a frame suited for large glasses (35 mm height, 55 mm length), centered at a height of 19 mm, with an interpupillary distance of 62 mm. Thus, the extreme values of the spherical equivalents ranged between 2.3 and 6.3 diopters at the edges of the lenses. Finally, in experiment (3), results from the previous two experiments were combined. Ideally, one would like to compare the eccentric refractions of each subject when wearing either the own lenses, RRG lenses, or no lenses at all. Since the RRG lenses were designed without optic power in the center, the best way to test them was to use emmetropic subjects as we did in the second experiment. For the sake of completeness, four myopic subjects were also measured wearing these lenses. This allowed us
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Fig. 3. With a stationary head and spectacle position, the rotations of the eye behind the spectacle lenses over ± 45° in the horizontal plane moved the pupil centers laterally by ±19.1 mm (assuming the center of rotation of the eye at 13.5 mm behind the corneal apex). Since the total horizontal spectacle diameter was 55 mm, the relative spectacle area that could be tested was only about 40%. Screenshots from a simulation in Zemax.
to compare the peripheral refractions in all three cases. In addition, the direct measurements of refractions with the RRG lenses provided valuable information on the relationship between predicted refractive profiles and those measured. 2.4.1. Statistics Paired Student t-tests (two tailed) with equal variances were used to test the significances of the differences between the relative peripheral refractions with and without spectacle corrections. 3. Results 3.1. Experiment 1 Examples of peripheral refractions as measured with the photorefractor in different subjects without their spectacle corrections (if applicable) are shown in Fig. 5. The foveal refractive errors of the subjects can be deduced from the refractions at zero degree gaze positions in the horizontal plane (‘‘x gaze”). They ranged from about 1 D to about 8 D.
Refractions in the vertical pupil meridian, measured with (grey symbols) and without spectacle corrections (black symbols), are plotted across the horizontal visual field in Fig. 6. Refractions were normalized to zero in the center to facilitate comparisons. All subjects became more hyperopic in the periphery when measured with their spectacle corrections, versus without correction. The variability among subjects in the amount of relative hyperopia in the periphery was striking. Fig. 7A shows the polynomial fits (fifth order) to the data from all eyes, plotted in the same color code as above. Fig. 7B shows the means of these polynomials with their standard deviations at a few selected angular positions (±41° and ±39°, respectively, for the grey and black curves; as well as at ±21° and ±19°; and 1° and +1°). In Fig. 7, the sign of the horizontal angles were reversed for the left eyes to account for the mirror symmetry when plotting both eyes on top of each other. This allowed presenting data of all eyes in one plot. Paired Student t-tests (two tails) with equal variances were used to test the significances of the differences between the relative peripheral refractions with and without spectacle corrections. High
Fig. 4. Sphere (dotted line), astigmatism (dashed line) and spherical equivalent (solid line) of the radial refractive gradient (RRG) lenses from their center to the periphery.
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Fig. 5. Examples of refraction profiles, as measured across the horizontal visual field in different subjects without their spectacle corrections.
Fig. 6. Refractions in the vertical pupil meridian, as measured at different angular positions across the horizontal visual field, with (grey symbols) and without spectacle corrections (black symbols). The left eye of the 4th subject, plotted in the top of the right panel could not be measured because the pupil was too small.
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Fig. 7. Summary of the effects of conventional spectacles on peripheral refractions. Gray symbols denote refraction profiles with spectacles, and black without. (A) Polynomials fits to each of the refraction profiles of the individual eyes, and (B) Averages of the polynomial fits from all eyes (means and standard deviations) at five angular positions.
statistical significance (P < 0.01) was found for a larger hyperopia when wearing spectacles for all angular positions except for the center (which was normalized to zero in all cases). 3.2. Experiment 2 Similar to Figs. 6 and 8 shows the differences in peripheral refractions with RRG lens versus the ‘‘no lenses” situation, as measured in the emmetropic subjects. Again, refractions were normalized relative to the foveal refractions, which were set to zero. Different from the conventional spectacles, RRG lenses indeed produced more myopic refractions in the periphery. Fig. 9A shows the polynomial fits, once again with the signs of angles reversed in sign to account for the mirror symmetry. Fig. 9B shows the means and standard deviations of the polynomials, as in Fig. 7B. Highly significant differences were found (P < 0.01) for more myopic peripheral values when wearing RRG lenses. To illustrate the variability of the effects of both types of lenses on peripheral refractions, the induced refraction changes were calculated by subtracting polynomials determined with and without glasses. Results are shown in Fig. 10. The opposite effects of the two types of lenses are obvious. 3.3. Experiment 3 Finally, Fig. 11 shows the peripheral refractions in four myopic subjects when they wore no spectacles (black), their own pair of glasses (dark grey), and the radial refractive gradient lenses (light grey). As above, fifth order polynomials were fitted to the data. The patterns are similar in each of the four subjects and consistent with the previous experiments: The peripheral refractions with the conventional spectacles are more hyperopic than without spectacles, and more myopic with the RRG lenses. Differences range from 2 to 4 diopters at 40°. It is also obvious that there is considerable inter-individual variability.
4. Discussion In this study, significant induced hyperopia was found in the vertical pupil meridian when the subjects wore their conventional spectacle correction and were refracted in the periphery of their visual field. Although the amount of induced hyperopia was quite variable, peripheral myopia was seldom induced. In contrast, RRG lenses generally induced relative peripheral myopia as expected from their theoretical design (see Fig. 10). As a draw-back, distortions were also induced by these lenses, a limitation that is physically inherent when constructing lenses with varying power, and a fact also well known from progressive addition lenses used in presbyopia correction. These distortions would probably limit the direct use of the RRG lenses as currently designed. There is evidence supporting the idea that imposing peripheral myopia could slow down the progression of myopia also in humans. Previous studies (e.g. Gwiazda et al., 2003; Leung and Brown, 1999) show a small but statistically significant reduction of the rate of myopia progression when children wore progressive addition lenses, compared to when they wore single vision lenses. Although the initial intention was to reduce accommodation lags by the reading glasses, it is clear that these lenses also impose relative myopia to the upper part of the retina. It is possible that myopia inhibition was, in fact, due to this effect. It is difficult to separate the relative importance of each of these factors. Another optical solution with similar peripheral effects is obtained with rigid contact lenses (orthokeratology). Here, the original idea was that the central corneal power could be temporarily reduced by the rigid contact lenses due to the plasticity of the corneal tissue under mechanical stress. In addition, it was found that orthokeratology also affects the peripheral refractions, imposing more peripheral myopia although there is most likely a large increase in monochromatic aberrations as well (Charman, Mountford, Atchison, & Markwell, 2006). The newly developed RRG lenses tested in this study may have some advantages over rigid contact lenses since they do not interfere with the natural corneal shape. However, as stated above, there is also the
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Fig. 8. Refractions in the vertical pupil meridian, as measured at different angular positions across the horizontal visual field, with RRG lenses (grey symbols) and without lenses (black symbols).
Fig. 9. Summary of the effects of RRG lenses on peripheral refractions. Gray symbols denote refraction profiles with RRG lenses, and black without. (A) Polynomials fits to each of the refraction profiles of the individual eyes, and (B) Averages of the polynomial fits from all eyes (means and standard deviations) at five angular positions.
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Fig. 10. Changes induced in the peripheral refractions in all subjects, by conventional spectacle lenses (A), and by RRG lenses (B).
disadvantage that optical distortions, induced by the refractive gradient, cannot be avoided. It would probably require the subjects to go through some period of adaptation before they can wear them comfortably, and most likely new RRG lens designs with an im-
proved wearability and comfort should be tested (Vazquez, Altheimer, & Uttenweiler, 2009). The new continuous refraction and gaze tracking procedure has provided some new findings. Interesting off-axis refractions pat-
Fig. 11. Refraction profiles in four myopic subjects when they wore no lens (black symbols), their conventional spectacle corrections (dark grey symbols) or the RRG lenses.
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terns became visible. W-shape patterns of refraction versus gaze were observed (for instance see Figs. 5, 7 and 11) in myopic subjects. The retinal shape required to generate this pattern of refractions would be a U-shaped, flat in the central area and steeper starting at some point on the periphery. The small number of subjects precludes studying patterns of eye shape in myopia more generally. It can be assumed that the different refraction profiles originate largely from differences in shape of the posterior globe, since local ‘‘bumps” are difficult to explain by optical designs of lens and cornea.
4.1. Potential limitations of the measurement technique One limitation is that only the vertical pupil meridian was measured, excluding any information on astigmatism. It is well known that astigmatism increases rapidly toward the periphery of the visual field in human eyes (e.g. Atchison, Pritchard, & Schmid, 2006; Ferree, Rand, & Hardy, 1932; Guirao & Artal, 1999; Millodot, 1981; Rempt, Hooger-Heide, & Hoogenboom, 1971; Seidemann et al., 2002). We chose to refract the vertical pupil meridian and to refract the eyes over the horizontal visual field. This setup configuration avoids problems with the horizontal compression of the off-axis image of the pupil, which would tend to generate more experimental noise and would require a correction factor for the pupil brightness as a function of the eccentricity angle. There are also limitations in the calibration of the photorefraction. Since we did not calibrate each subject individually at each position in the visual field, it cannot be excluded that the conversion factors were more variable. This hypothesis was further tested in five eyes of five emmetropic subjects from this study. The conversion factors (Section 2) were determined for each subject at each angular position. The refractions profiles were shown in Fig. 10B were then re-calculated with individual conversion factors. Fig. 12 shows the results. With one common conversion factor for all subjects (A), the variability was not higher than with individual calibrations (B).
4.2. Can the changes in peripheral refraction be predicted by ray tracing? Conventional spectacle lenses are designed to provide an accurate foveal correction of both sphere and cylinder across the visual field. However, the peripheral refractive errors measured with such lenses were, in some cases, surprisingly high. In Fig. 10A, two eyes are shown that had refractions 4–6 diopters more hyperopic in the vertical pupil meridian at 45° off-axis. Both eyes were from a highly myopic subject (OS 8.5 D. OD 8 D, Fig. 6). However, a high hyperopia could be qualitatively verified by streak retinoscopy. As mentioned, the optical design of regular spectacle lenses for the correction of myopia does not predict such high amounts of peripheral hyperopia. Ray tracing is necessary for a better understanding of its origin. It turns out that the geometrical arrangement of the photorefractor, the spectacle orientation and the eye position can explain the measured refraction. This is illustrated in Fig. 13. One should note the difference in the three settings shown in this figure, although all of them could be claimed to measure the peripheral refraction. However, they are optically different since the spectacle lens modifies astigmatism and spherical equivalent in different ways. In Fig. 13A (which corresponds to the experimental situation in the current study), the eye and the spectacle lens are tilted with respect to each other. In this case, due to the angular magnification, the spectacle generates more astigmatism in the eye (the lens increases the angle between the light and the ocular axis). In Fig. 13B, the eye and the spectacle are aligned, but both are tilted with respect to the direction of the photorefractor. This situation generates the opposite effect as in the geometry shown in Fig. 13A: due to the angular magnification, the spectacle tends to compensate the ocular astigmatism since the angle between the optical axis of the eye and the direction of the light after refraction by the spectacle is smaller. Finally, as shown in Fig. 13C, the peripheral zone of the spectacle is evaluated but in this case with the eye looking at the photorefractor (direction of measurement). This arrangement
Fig. 12. Changes in refractions induced by RRG lenses. (A) Determined with a common conversion factor for all eyes, and (B) determined with individual calibrations of each subject at each angular position. Note that the variability was not reduced by individual calibrations with trial lenses.
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Fig. 13. Three different (and not equivalent) geometrical arrangements to measure peripheral refractions of an eye with a spectacle lens.
is typically used for the design of the commercial spectacles because it leads to the best quality of the foveal correction for different fixation points across the visual field. However, a spectacle optimized for best foveal correction across the visual field does not necessarily minimize the refractive errors imposed in the peripheral retina. Two ray-tracing software packages, ZEMAX (ZEMAX Development Corporation, Bellevue, WA, USA) and OSLO (Lambda Research Corporation, Littleton, MA, USA) were independently used to simulate the three geometrical situations shown in Fig. 13. Refraction was simulated in the vertical pupil meridian, in line with the measured data. Using a plano-hyperbolic spectacle of 8.5 diopters, 3– 4 diopters of hyperopia were calculated at 45° of eccentricity in the situation shown in Fig. 13A. The difference of the calculated and measured values might be attributed to decentration and other experimental deviations. The center of rotation of the eye was set at 13.5 mm behind the corneal apex, as estimated by Le Grand and El Hage (1980). Additional simulations were performed using data of commercial lenses of 3 and 4 diopters. They showed similar hyperopic shifts up to 1–2 diopters at 45°. In summary, the simulations confirm the data obtained by photorefraction under the particular geometry of Fig. 13A, and they also confirmed that very little change occurs in the foveal refractions (normally below the 0.50 diopters) when the subject moves the eye behind a spectacle lens (Fig. 13C) – in line with the postulations of a professional spectacle design. An unexpected observation was that even with perfectly defined RRG lenses, the off-axis refractions were highly variable. Since the measurement noise was much lower (discussed above), this must go back mainly to decentrations when wearing the spectacle lenses. Other factors might be the differences in the individual optical design of the eyes (like different vertex distances, corneal shapes, anterior chamber depths and parameters of the crystalline lens that affect the off-axis refraction in a complex fashion). In the future, two directions emerge: (1) to move the refractor, rather than having the subjects move their eyes behind their glasses and (2) to include measurements of the complete refraction, including astigmatism. Point (1) will be solved by scanning the eye from different angles using a revolving hot mirror (Tabernero and Schaeffel, in press) and (2) will be solved by using a retinoscope which measures in multiple meridians as in the old hardware platform of the PowerRefractor (Choi et al., 2000). In summary, we have measured continuous refraction profiles along the horizontal direction of gaze. We found that peripheral hyperopia was induced in the vertical pupil meridian by conventional negative spectacle lenses. In contrast, a newly designed RRG spectacle lens made subjects more myopic in the periphery. The possibility of measuring in the future the peripheral refractions in multiple meridians is of great interest to analyze the effect
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Millodot, M. (1981). Effect of ametropia on peripheral refraction. American Journal of Optometry and Physiological Optics, 58, 691–695. Phillips, J. R. (2005). Monovision slows juvenile myopia progression unilaterally. British Journal of Ophthalmology, 89, 1196–1200. Rempt, F., Hooger-Heide, J., & Hoogenboom, W. P. H. (1971). Peripheral retinoscopy and the skiagram. Opththalmologica, 165, 1–10. Schaeffel, F. (2002). Kappa and Hirschberg ratio measured with an automated video gaze tracker. Optometry and Vision Science, 79, 329–334. Schaeffel, F., Burkhardt, E., Howland, H. C., & Williams, R. W. (2004). Measurement of refractive state and deprivation myopia in two strains of mice. Optometry and Vision Science, 81, 99–110. Schaeffel, F., Hagel, G., Eikermann, J., & Collett, T. (1994). Lower-field myopia and astigmatism in amphibians and chickens. Journal of the Optical Society of America A-Optics Image Science and Vision, 11, 487–495. Schaeffel, F., Weiss, S., & Seidel, J. (1999). How good is the match between the plane of the text and the plane of focus during reading? Ophthalmic and Physiological Optics, 19, 180–192. Schaeffel, F., Wilhelm, H., & Zrenner, E. (1993). Inter-individual variability in the dynamics of natural accommodation in humans: Relation to age and refractive errors. Journal of Physiology, 461, 301–320. Seidemann, A., Guirao, A., Artal, P., & Schaeffel, F. (1999). Peripheral refraction and myopia development in humans. Investigative Ophthalmology and Visual Science, 40(2362) (ARVO abstract).
Seidemann, A., Schaeffel, F., Guirao, A., Lopez-Gil, N., & Artal, P. (2002). Peripheral refractive errors in myopic, emmetropic, and hyperopic young subjects. Journal of the Optical Society of America A-Optics Image Science and Vision, 19, 2363–2373. Smith, E. L., III, Kee, C., Ramamirtham, R., Qiao-Grider, Y., & Hung, L. F. (2005). Peripheral vision can influence eye growth and refractive development in infant monkeys. Investigative Ophthalmology and Visual Science, 46, 3965–3972. Smith, G., Atchison, D. A., Avudainayagam, C., & Avudainayagam, K. (2002). Designing lenses to correct peripheral refractive errors of the eye. Journal of the Optical Society of America A, 19, 10–18. Tabernero, J., & Schaeffel, F. (in press). Low myopes have more irregular eye shapes than emmetropes. Investigative Ophthalmology and Vision Science. Vazquez, D., Seidemann, A., Altheimer, H., Schaeffel, F., & Uttenweiler, D. (2009). Optical tracking of head movement patterns when wearing spectacle lenses with different radial power profiles. Investigative Ophthalmology and Visual Science, 50(3981) (ARVO abstract). Walline, J. J., Jones, L. A., Mutti, D. O., & Zadnik, K. (2004). A randomized trial of the effects of rigid contact lenses on myopia progression. Archives of Ophthalmology, 122, 1760–1766. Wallman, J., & Winawer, J. (2004). Homeostasis of eye growth and the question of myopia. Neuron, 43, 447–468. Williams, D. R., Artal, P., Navarro, R., McMahon, M. J., & Brainard, D. H. (1996). Offaxis optical quality and retinal sampling in the human eye. Vision Research, 36, 1103–1114.
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Vision Research journal homepage: www.elsevier.com/locate/visres
Effects of myopic spectacle correction and radial refractive gradient spectacles on peripheral refraction Juan Tabernero a,*, Daniel Vazquez b, Anne Seidemann b, Dietmar Uttenweiler b, Frank Schaeffel a a b
Section of Neurobiology of the Eye, Ophthalmic Research Institute, Calwerstrasse 7/1, 72076 Tuebingen, Germany Rodenstock GmbH, Isartalstrasse 43, 80469 Munich, Germany
a r t i c l e
i n f o
Article history: Received 15 August 2008 Received in revised form 26 May 2009
Keywords: Human eye Physiological optics Peripheral refraction Spectacles Myopia Hyperopia
a b s t r a c t The recent observation that central refractive development might be controlled by the refractive errors in the periphery, also in primates, revived the interest in the peripheral optics of the eye. We optimized an eccentric photorefractor to measure the peripheral refractive error in the vertical pupil meridian over the horizontal visual field (from 45° to 45°), with and without myopic spectacle correction. Furthermore, a newly designed radial refractive gradient lens (RRG lens) that induces increasing myopia in all radial directions from the center was tested. We found that for the geometry of our measurement setup conventional spectacles induced significant relative hyperopia in the periphery, although its magnitude varied greatly among different spectacle designs and subjects. In contrast, the newly designed RRG lens induced relative peripheral myopia. These results are of interest to analyze the effect that different optical corrections might have on the emmetropization process. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction There is evidence that different optical correction schemes influence the rate of progression of myopia. Examples are undercorrected prescriptions (Phillips, 2005; but see also Chung, Mohidin, & O’Leary, 2002; reporting the opposite effect), rigid contact lenses (Walline, Jones, Mutti, & Zadnik, 2004), bifocal spectacles (Fulk, Cyert, & Parker, 2002), bifocal soft contact lenses (Aller & Wildsoet, 2008) or progressive addition lenses (Gwiazda et al., 2003; Leung & Brown, 1999). Although there is some controversy regarding the benefit of optical intervention, given the small effects in many cases, recent analyses of subgroups of children treated with progressive addition lenses showed clinically relevant effects with about 50% of inhibition of myopia, and no rebound effect after termination of the treatment (Gwiazda, 2008). It is known from experiments in animal models that the retina releases biochemical signals to control the growth of the underlying sclera, such that an optimal refraction is achieved over time (review: Wallman & Winawer, 2004). Recent experiments in monkeys have also shown that peripheral defocus might affect central refraction development (Smith, Kee, Ramamirtham, Qiao-Grider, & Hung, 2005). In these experiments, the animals had normal foveal vision but the peripheral visual field was deprived of sharp vision. This condition was sufficient to induce foveal myopia. Apparently, peripheral retinal image quality is important for foveal refractive * Corresponding author. E-mail address: [email protected] (J. Tabernero). 0042-6989/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.visres.2009.06.008
development in primates. According to this, correction for myopia should not impose peripheral hyperopia because that might trigger axial elongation. (e.g. Atchison et al., 2005; Seidemann, Schaeffel, Guirao, Lopez-Gil, & Artal, 2002). However, and due to fundamental optical constraints when providing a sharp foveal vision at all angles of gaze, the peripheral vision plays a minor role in the design of current spectacle lenses. An alternative optical design to prevent myopia from progressing would be some spectacle lenses that impose some myopia in the periphery to stop the eye growth, while maintaining a good correction of foveal refractive errors. On one hand primates, including humans, have poor spatial resolution in the periphery (e.g. Williams, Artal, Navarro, McMahon, & Brainard, 1996), hence residual peripheral myopia should not be a major problem. On the other hand, this optical design would limit the range of angles of gaze with a sharp foveal vision. Although there have been attempts to correct the peripheral refractive errors of the eye (Lunström et al., 2007; Smith, Atchison, Avudainayagam, & Avudainayagam, 2002), strikingly little is published on how regular single vision lenses designed to correct myopia affect peripheral refractive state. Other than a preliminary study by Seidemann and Artal (1999) and a recent paper on the theoretical effects of a pantoscopic tilt of the spectacles on peripheral refraction (Bakaraju, Ehrmann, Ho, & Papas, 2008), no data are available. It would be worthwhile to measure the human peripheral refractive errors with accurate and automated refractors with and without the regular spectacle corrections. Besides, current studies on the peripheral optics of the eye have the limitation that they include only a few sampling points across
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the visual field. In the present study, a continuously recording photorefractor was used to sample refractions in the vertical pupil meridian across the horizontal visual field from 45 to 45° of eccentricity. A Purkinje image-based gaze tracker was used to assign the measured refractions to angular positions. Peripheral refractions were measured both with the regular spectacle corrections of the myopic subjects, and with the special spectacle RRG lens developed for the purpose of this study. 2. Methods 2.1. Subjects Eleven student subjects (five myopic, six emmetropic), aged 25 to 30 years, with no known ocular pathologies other than myopia, were refracted either with their spectacle corrections (unknown manufacturers), or without them, or with the RRG spectacle lenses. Informed consent was obtained from each of the subjects by signing a form that explained the rationale and possible consequences of the study. The study was approved by the Ethics Commission of the Medical Faculty of the University of Tuebingen. 2.2. Techniques: eccentric infrared photoretinoscopy and gaze tracking The infrared photoretinoscope used for refractions has been previously described in detail (Schaeffel, Hagel, Eikermann, & Collett,
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1994; Schaeffel, Wilhelm, & Zrenner, 1993). Its combination with a gaze tracker has been used to map out the refractions in the vertical pupil meridian across the visual field (Schaeffel, Weiss, & Seidel, 1999; Seidemann et al., 2002). The advantage of photorefraction is that it can be performed over long distances and that it is, after individual calibration, quite accurate, resolving down to less than 0.25 D (Kasthurirangan & Glasser, 2006; Schaeffel et al., 1993). Another advantage is that it operates at video frequency. In the present study, a USB2 infrared sensitive monochrome video camera (http://www.theimagingsource.com/de/ products/cameras/usb_mono/dmk21au04/) with a frame rate of 60 Hz and a spatial resolution of 640 480 pixels was used. The camera was combined with a 50 mm lens with an f/# of 1.4 (same company, B5014A(KA)), with a 5 mm extension ring to focus at 1 m distance, and an infrared cut-off filter (#093, same company). The photoretinoscope, placed in front of the lens, was custom-build as previously described (Schaeffel, Burkhardt, Howland, & Williams, 2004). The software was programmed in Visual C++. It detected the eye in each video frame and measured the slope of the brightness gradient in the pupil that was generated by the infrared photoretinoscope (Fig. 1). The refraction was measured only along the vertical meridian of the pupil, ignoring astigmatism. We did not perform individual calibrations of the photorefraction technique since our focus was on the comparison of central and peripheral refractions rather than the absolute refractions in different subjects. It was assumed that the conversion factor (the
Fig. 1. Screenshot of the custom-developed software to measure refraction versus the horizontal angle of gaze. Relevant details are pointed by arrows and text in large white font.
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factor converting the slope of the brightness profile in the pupil into refractive error; Schaeffel et al., 1993) is linear and possesses the same slope across the visual field. To test this assumption, the technique was calibrated in an emmetropic subject at several positions in the horizontal visual field (±35°, ±25°, ±15°, 0°) with a set of trial lenses. The resulting conversion factors showed little variation in the slope versus the position in the visual field (average slope of the conversion factor ± standard deviation: 1.51 ± 0.10). With this variability of about 15%, a standard deviation of 0.5 D in the measurement of the peripheral refraction can be expected for a refractive error of 5 D). Since we were just interested in measuring peripheral refractions relative to the center of the visual field, the variation of the independent terms of the conversion factors for every angle of gaze is not important in our calculations. Fig. 2 shows the calibrations for seven angular positions and illustrates the variability of the slopes. Gaze tracking was performed on-line by detecting the first Purkinje image, created by the photoretinoscope in the pupil, and recording its position relative to the pupil center (see Fig. 1). A Hirschberg ratio of 12°/mm was used throughout the study (Barry, Dunne, & Kirschkamp, 2001; Brodie, 1987; Schaeffel, 2002). Since the software could not distinguish between the corneal Purkinje image and the specular reflections that occurred on the sclera for large angles, gaze tracking was limited to ±50° off-axis. 2.3. Experimental procedures To obtain a continuous trace of refractions across the visual field, a ‘‘continuous” stimulus is more advantageous than discrete fixation targets. The subjects read a text from a bar that subtended an angle of ±45° over the horizontal visual field, and was positioned at 1 m distance. Since the bar was straight, the viewing distance was slightly larger for the more peripheral positions (by maximally 0.3 D). If the subjects had relaxed their accommodation accordingly, slightly more hyperopic refractions were possible for the peripheral positions. This factor was not further considered. Ambient illuminance was kept as low as possible (about 10 lux)
Fig. 2. Pupil brightness slope in the vertical pupil meridian measured at different angular positions in the visual field, and with different powers of trial lenses held in front of the eye. The calibration shows that the slopes of the regressions did not vary significantly with the position in the horizontal visual field, making the use of a single conversion factor for all positions acceptable.
to keep the pupil sizes large and, thus, reduce the measurement noise of the photorefraction. A minimum of three scans were performed for each of the subjects. The retinoscope was positioned at a stationary position at one meter distance, at 0°. The head was stabilized by a chin and forehead rest. Only a limited area of the spectacles could be sampled (Fig. 3). With this approach, about 40% of the central spectacle area could be sampled (Fig. 3). To allow the subjects to move their head rather than their eyes would have permitted to measure a larger area. However, it was found that the Purkinje image-based gaze tracker did no longer work reliably. Since the myopic subjects could not read the text without spectacles, the operator used a laser pointer to project a red spot onto the bar and moved it slowly across the visual field. The total measurement procedure took about 2 min. 2.4. Experimental protocols Three experiments were performed: In experiment (1), the peripheral refractions with conventional negative spectacle lenses for correction of myopia were measured. Nine eyes from five myopic subjects were measured, with their regular spectacles and without them. One eye could not reliably be measured because the pupil was too small. In the myopic subjects, foveal refractive errors ranged from 3 to 8 diopters (with astigmatism less than 1 D, according to their prescriptions). The Hirschberg ratio used by the gaze tracker was corrected for the magnification effect of the glasses – it increases linearly with increasing power of the negative lenses due to magnifications (Schaeffel, 2002). The refraction data across the visual field were fitted with fifth order polynomials and normalized to zero for the foveal refractions to facilitate inter-individual comparisons. In experiment (2), the effects of a Radial Refractive Gradient (RRG) spectacle lens on peripheral refractions were studied. These lenses were designed to optimize two optical features: first, clear foveal vision in the optical center and second, a steady increase of positive power in all radial directions. The increase in spherical equivalent refractive power was about one diopter for every 10° to the periphery in the visual field, with a central plano area (astigmatism and spherical equivalent lower than 1/8 D) with a diameter of 6 mm – about the diameter of the pupils of the young subjects under mesopic conditions. Astigmatism could be kept at 1.1 D at 20°, but increased up to 3.5 D at 40°. Details on the refraction profile of the RRG lenses are shown in Fig. 4. Since the lenses were intended to be used in different subjects with potentially different retinal geometries, the refractive profile was designed and measured in relation to the Far Point Sphere and the Vertex Sphere (Jalie, 1977, chap. 18) and not to a given retinal surface. Thus, the 3.6 D of spherical equivalent at 40° of Fig. 4 indicated that when looking foveally with an angle of gaze of 40°, the spherical equivalent power provided by the lens measured in relation to the Vertex Sphere was 3.6 D. RRG lenses were mounted in a frame suited for large glasses (35 mm height, 55 mm length), centered at a height of 19 mm, with an interpupillary distance of 62 mm. Thus, the extreme values of the spherical equivalents ranged between 2.3 and 6.3 diopters at the edges of the lenses. Finally, in experiment (3), results from the previous two experiments were combined. Ideally, one would like to compare the eccentric refractions of each subject when wearing either the own lenses, RRG lenses, or no lenses at all. Since the RRG lenses were designed without optic power in the center, the best way to test them was to use emmetropic subjects as we did in the second experiment. For the sake of completeness, four myopic subjects were also measured wearing these lenses. This allowed us
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Fig. 3. With a stationary head and spectacle position, the rotations of the eye behind the spectacle lenses over ± 45° in the horizontal plane moved the pupil centers laterally by ±19.1 mm (assuming the center of rotation of the eye at 13.5 mm behind the corneal apex). Since the total horizontal spectacle diameter was 55 mm, the relative spectacle area that could be tested was only about 40%. Screenshots from a simulation in Zemax.
to compare the peripheral refractions in all three cases. In addition, the direct measurements of refractions with the RRG lenses provided valuable information on the relationship between predicted refractive profiles and those measured. 2.4.1. Statistics Paired Student t-tests (two tailed) with equal variances were used to test the significances of the differences between the relative peripheral refractions with and without spectacle corrections. 3. Results 3.1. Experiment 1 Examples of peripheral refractions as measured with the photorefractor in different subjects without their spectacle corrections (if applicable) are shown in Fig. 5. The foveal refractive errors of the subjects can be deduced from the refractions at zero degree gaze positions in the horizontal plane (‘‘x gaze”). They ranged from about 1 D to about 8 D.
Refractions in the vertical pupil meridian, measured with (grey symbols) and without spectacle corrections (black symbols), are plotted across the horizontal visual field in Fig. 6. Refractions were normalized to zero in the center to facilitate comparisons. All subjects became more hyperopic in the periphery when measured with their spectacle corrections, versus without correction. The variability among subjects in the amount of relative hyperopia in the periphery was striking. Fig. 7A shows the polynomial fits (fifth order) to the data from all eyes, plotted in the same color code as above. Fig. 7B shows the means of these polynomials with their standard deviations at a few selected angular positions (±41° and ±39°, respectively, for the grey and black curves; as well as at ±21° and ±19°; and 1° and +1°). In Fig. 7, the sign of the horizontal angles were reversed for the left eyes to account for the mirror symmetry when plotting both eyes on top of each other. This allowed presenting data of all eyes in one plot. Paired Student t-tests (two tails) with equal variances were used to test the significances of the differences between the relative peripheral refractions with and without spectacle corrections. High
Fig. 4. Sphere (dotted line), astigmatism (dashed line) and spherical equivalent (solid line) of the radial refractive gradient (RRG) lenses from their center to the periphery.
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Fig. 5. Examples of refraction profiles, as measured across the horizontal visual field in different subjects without their spectacle corrections.
Fig. 6. Refractions in the vertical pupil meridian, as measured at different angular positions across the horizontal visual field, with (grey symbols) and without spectacle corrections (black symbols). The left eye of the 4th subject, plotted in the top of the right panel could not be measured because the pupil was too small.
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Fig. 7. Summary of the effects of conventional spectacles on peripheral refractions. Gray symbols denote refraction profiles with spectacles, and black without. (A) Polynomials fits to each of the refraction profiles of the individual eyes, and (B) Averages of the polynomial fits from all eyes (means and standard deviations) at five angular positions.
statistical significance (P < 0.01) was found for a larger hyperopia when wearing spectacles for all angular positions except for the center (which was normalized to zero in all cases). 3.2. Experiment 2 Similar to Figs. 6 and 8 shows the differences in peripheral refractions with RRG lens versus the ‘‘no lenses” situation, as measured in the emmetropic subjects. Again, refractions were normalized relative to the foveal refractions, which were set to zero. Different from the conventional spectacles, RRG lenses indeed produced more myopic refractions in the periphery. Fig. 9A shows the polynomial fits, once again with the signs of angles reversed in sign to account for the mirror symmetry. Fig. 9B shows the means and standard deviations of the polynomials, as in Fig. 7B. Highly significant differences were found (P < 0.01) for more myopic peripheral values when wearing RRG lenses. To illustrate the variability of the effects of both types of lenses on peripheral refractions, the induced refraction changes were calculated by subtracting polynomials determined with and without glasses. Results are shown in Fig. 10. The opposite effects of the two types of lenses are obvious. 3.3. Experiment 3 Finally, Fig. 11 shows the peripheral refractions in four myopic subjects when they wore no spectacles (black), their own pair of glasses (dark grey), and the radial refractive gradient lenses (light grey). As above, fifth order polynomials were fitted to the data. The patterns are similar in each of the four subjects and consistent with the previous experiments: The peripheral refractions with the conventional spectacles are more hyperopic than without spectacles, and more myopic with the RRG lenses. Differences range from 2 to 4 diopters at 40°. It is also obvious that there is considerable inter-individual variability.
4. Discussion In this study, significant induced hyperopia was found in the vertical pupil meridian when the subjects wore their conventional spectacle correction and were refracted in the periphery of their visual field. Although the amount of induced hyperopia was quite variable, peripheral myopia was seldom induced. In contrast, RRG lenses generally induced relative peripheral myopia as expected from their theoretical design (see Fig. 10). As a draw-back, distortions were also induced by these lenses, a limitation that is physically inherent when constructing lenses with varying power, and a fact also well known from progressive addition lenses used in presbyopia correction. These distortions would probably limit the direct use of the RRG lenses as currently designed. There is evidence supporting the idea that imposing peripheral myopia could slow down the progression of myopia also in humans. Previous studies (e.g. Gwiazda et al., 2003; Leung and Brown, 1999) show a small but statistically significant reduction of the rate of myopia progression when children wore progressive addition lenses, compared to when they wore single vision lenses. Although the initial intention was to reduce accommodation lags by the reading glasses, it is clear that these lenses also impose relative myopia to the upper part of the retina. It is possible that myopia inhibition was, in fact, due to this effect. It is difficult to separate the relative importance of each of these factors. Another optical solution with similar peripheral effects is obtained with rigid contact lenses (orthokeratology). Here, the original idea was that the central corneal power could be temporarily reduced by the rigid contact lenses due to the plasticity of the corneal tissue under mechanical stress. In addition, it was found that orthokeratology also affects the peripheral refractions, imposing more peripheral myopia although there is most likely a large increase in monochromatic aberrations as well (Charman, Mountford, Atchison, & Markwell, 2006). The newly developed RRG lenses tested in this study may have some advantages over rigid contact lenses since they do not interfere with the natural corneal shape. However, as stated above, there is also the
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Fig. 8. Refractions in the vertical pupil meridian, as measured at different angular positions across the horizontal visual field, with RRG lenses (grey symbols) and without lenses (black symbols).
Fig. 9. Summary of the effects of RRG lenses on peripheral refractions. Gray symbols denote refraction profiles with RRG lenses, and black without. (A) Polynomials fits to each of the refraction profiles of the individual eyes, and (B) Averages of the polynomial fits from all eyes (means and standard deviations) at five angular positions.
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Fig. 10. Changes induced in the peripheral refractions in all subjects, by conventional spectacle lenses (A), and by RRG lenses (B).
disadvantage that optical distortions, induced by the refractive gradient, cannot be avoided. It would probably require the subjects to go through some period of adaptation before they can wear them comfortably, and most likely new RRG lens designs with an im-
proved wearability and comfort should be tested (Vazquez, Altheimer, & Uttenweiler, 2009). The new continuous refraction and gaze tracking procedure has provided some new findings. Interesting off-axis refractions pat-
Fig. 11. Refraction profiles in four myopic subjects when they wore no lens (black symbols), their conventional spectacle corrections (dark grey symbols) or the RRG lenses.
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terns became visible. W-shape patterns of refraction versus gaze were observed (for instance see Figs. 5, 7 and 11) in myopic subjects. The retinal shape required to generate this pattern of refractions would be a U-shaped, flat in the central area and steeper starting at some point on the periphery. The small number of subjects precludes studying patterns of eye shape in myopia more generally. It can be assumed that the different refraction profiles originate largely from differences in shape of the posterior globe, since local ‘‘bumps” are difficult to explain by optical designs of lens and cornea.
4.1. Potential limitations of the measurement technique One limitation is that only the vertical pupil meridian was measured, excluding any information on astigmatism. It is well known that astigmatism increases rapidly toward the periphery of the visual field in human eyes (e.g. Atchison, Pritchard, & Schmid, 2006; Ferree, Rand, & Hardy, 1932; Guirao & Artal, 1999; Millodot, 1981; Rempt, Hooger-Heide, & Hoogenboom, 1971; Seidemann et al., 2002). We chose to refract the vertical pupil meridian and to refract the eyes over the horizontal visual field. This setup configuration avoids problems with the horizontal compression of the off-axis image of the pupil, which would tend to generate more experimental noise and would require a correction factor for the pupil brightness as a function of the eccentricity angle. There are also limitations in the calibration of the photorefraction. Since we did not calibrate each subject individually at each position in the visual field, it cannot be excluded that the conversion factors were more variable. This hypothesis was further tested in five eyes of five emmetropic subjects from this study. The conversion factors (Section 2) were determined for each subject at each angular position. The refractions profiles were shown in Fig. 10B were then re-calculated with individual conversion factors. Fig. 12 shows the results. With one common conversion factor for all subjects (A), the variability was not higher than with individual calibrations (B).
4.2. Can the changes in peripheral refraction be predicted by ray tracing? Conventional spectacle lenses are designed to provide an accurate foveal correction of both sphere and cylinder across the visual field. However, the peripheral refractive errors measured with such lenses were, in some cases, surprisingly high. In Fig. 10A, two eyes are shown that had refractions 4–6 diopters more hyperopic in the vertical pupil meridian at 45° off-axis. Both eyes were from a highly myopic subject (OS 8.5 D. OD 8 D, Fig. 6). However, a high hyperopia could be qualitatively verified by streak retinoscopy. As mentioned, the optical design of regular spectacle lenses for the correction of myopia does not predict such high amounts of peripheral hyperopia. Ray tracing is necessary for a better understanding of its origin. It turns out that the geometrical arrangement of the photorefractor, the spectacle orientation and the eye position can explain the measured refraction. This is illustrated in Fig. 13. One should note the difference in the three settings shown in this figure, although all of them could be claimed to measure the peripheral refraction. However, they are optically different since the spectacle lens modifies astigmatism and spherical equivalent in different ways. In Fig. 13A (which corresponds to the experimental situation in the current study), the eye and the spectacle lens are tilted with respect to each other. In this case, due to the angular magnification, the spectacle generates more astigmatism in the eye (the lens increases the angle between the light and the ocular axis). In Fig. 13B, the eye and the spectacle are aligned, but both are tilted with respect to the direction of the photorefractor. This situation generates the opposite effect as in the geometry shown in Fig. 13A: due to the angular magnification, the spectacle tends to compensate the ocular astigmatism since the angle between the optical axis of the eye and the direction of the light after refraction by the spectacle is smaller. Finally, as shown in Fig. 13C, the peripheral zone of the spectacle is evaluated but in this case with the eye looking at the photorefractor (direction of measurement). This arrangement
Fig. 12. Changes in refractions induced by RRG lenses. (A) Determined with a common conversion factor for all eyes, and (B) determined with individual calibrations of each subject at each angular position. Note that the variability was not reduced by individual calibrations with trial lenses.
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Fig. 13. Three different (and not equivalent) geometrical arrangements to measure peripheral refractions of an eye with a spectacle lens.
is typically used for the design of the commercial spectacles because it leads to the best quality of the foveal correction for different fixation points across the visual field. However, a spectacle optimized for best foveal correction across the visual field does not necessarily minimize the refractive errors imposed in the peripheral retina. Two ray-tracing software packages, ZEMAX (ZEMAX Development Corporation, Bellevue, WA, USA) and OSLO (Lambda Research Corporation, Littleton, MA, USA) were independently used to simulate the three geometrical situations shown in Fig. 13. Refraction was simulated in the vertical pupil meridian, in line with the measured data. Using a plano-hyperbolic spectacle of 8.5 diopters, 3– 4 diopters of hyperopia were calculated at 45° of eccentricity in the situation shown in Fig. 13A. The difference of the calculated and measured values might be attributed to decentration and other experimental deviations. The center of rotation of the eye was set at 13.5 mm behind the corneal apex, as estimated by Le Grand and El Hage (1980). Additional simulations were performed using data of commercial lenses of 3 and 4 diopters. They showed similar hyperopic shifts up to 1–2 diopters at 45°. In summary, the simulations confirm the data obtained by photorefraction under the particular geometry of Fig. 13A, and they also confirmed that very little change occurs in the foveal refractions (normally below the 0.50 diopters) when the subject moves the eye behind a spectacle lens (Fig. 13C) – in line with the postulations of a professional spectacle design. An unexpected observation was that even with perfectly defined RRG lenses, the off-axis refractions were highly variable. Since the measurement noise was much lower (discussed above), this must go back mainly to decentrations when wearing the spectacle lenses. Other factors might be the differences in the individual optical design of the eyes (like different vertex distances, corneal shapes, anterior chamber depths and parameters of the crystalline lens that affect the off-axis refraction in a complex fashion). In the future, two directions emerge: (1) to move the refractor, rather than having the subjects move their eyes behind their glasses and (2) to include measurements of the complete refraction, including astigmatism. Point (1) will be solved by scanning the eye from different angles using a revolving hot mirror (Tabernero and Schaeffel, in press) and (2) will be solved by using a retinoscope which measures in multiple meridians as in the old hardware platform of the PowerRefractor (Choi et al., 2000). In summary, we have measured continuous refraction profiles along the horizontal direction of gaze. We found that peripheral hyperopia was induced in the vertical pupil meridian by conventional negative spectacle lenses. In contrast, a newly designed RRG spectacle lens made subjects more myopic in the periphery. The possibility of measuring in the future the peripheral refractions in multiple meridians is of great interest to analyze the effect
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