A feature lacking from older studies is the 45-degree/135-degree, or oblique, component of astigmatism in the periphery. The only older study to have attempted this was that of Johnson et al.,11 whose results should be treated with suspicion because of the low cylinders in the periphery. Recent studies at a more restricted range of angles along the horizontal and vertical fields have found the oblique component to change linearly with angle, becoming more positive from the temporal to the nasal field and from the inferior to the superior fields. In the study by Atchison et al.,13 mean rates were +0.004 and +0.011 D/degree out to ± 35 degrees along the horizontal and vertical visual fields, respectively (p < 0.001). Fitting the mean data of Gustafsson et al.11 gives a mean rate of change for J45 along the horizontal visual field of +0.006 ± 0.003 D/degree out to ± 60 degrees (p < 0.001).
To address the issues of hyperopic shift and the oblique component of astigmatism at large angles, we report measures of peripheral refraction out to 60 degrees from fixation along the horizontal visual field in 30 participants with a range of refractions.
The study adhered to the tenets of the Declaration of Helsinki and was approved by the Human Research Ethics Committee of Queensland University of Technology; all participants gave informed consent. The participants consisted of 6 hyperopes with a mean sphere (or spherical equivalent) and SD +1.21 ± 0.64 D and a mean age of 26 ± 5 years, 13 emmetropes (+0.02 ± 0.29 D, 23 ± 6 years), and 11 myopes (−2.87 ± 1.50 D, 27 ± 12 years). Participants with a mean sphere within ± 0.50 D were classified as emmetropes. All participants were screened for any ocular pathology and had best-corrected visual acuities of 6/6 or better.
Measurements were made with a modified COAS-HD Hartmann-Shack aberrometer (Wavefront Sciences Inc., Albuquerque, NM), across ±60 degrees along the horizontal visual field in 5-degree steps, with the nasal side of the field assigned positive values. The COAS-HD aberrometer was modified by replacing its standard 1.4-mm aperture with a 2.5-mm aperture to minimize vignetting of highly aberrated rays. The COAS-HD uses a one-frame tracking algorithm that increases its dynamic range by adjusting the position of the “area of interest” associated with each spot on the Hartmann-Shack image on the CCD camera.14 Participants placed their heads on a rotatable chin rest. The chin rest was kept straight for measurements to ±30 degrees. The chin rest was then rotated by ±30 degrees for measurements from ±35 to ±60 degrees so that eye rotation was limited to 30 degrees. To avoid the aberrometer obstructing most of the visual field, a two-lens relay system (Fig. 4) was built to enable fixation at the targets mounted on the wall 3 m in front of their eye. A pair of infrared light-emitting diodes (LEDs) was part of the relay apparatus for illuminating the pupil to assist alignment. The measurements were done for right eyes with occlusion of left eyes. The participants’ right eyes were dilated with 1% cyclopentolate to avoid accommodation confounding the results. Three measurements were taken for each field angle.
Data and images were exported to be analyzed by a MATLAB (MathWorks) algorithm. Peripheral refraction was estimated as mean sphere M, with/against-the-rule astigmatism J180 component and oblique astigmatism component J45 from Zernike coefficients using the equations given by Atchison et al.15,16 The algorithm compensates for the elliptical shape of the pupil, seen while measuring aberrations in the peripheral field, by stretching it by the cosine of the field angle. Effectively, we were analyzing across elliptical pupils in which the ratio of the minor and major axes was the cosine of the field angle. Zernike aberration coefficients were estimated up to sixth order, at 555-nm wavelength for pupils with 3-mm major axes, but only the second-order coefficients were used to determine refraction. The refraction was taken as the average of the three measures.
Each Hartmann-Shack spot image from the aberrometer was checked by author A.M. for any errors in estimation of pupil center by the algorithm. At high angles, occasionally, the Hartmann-Shack spots from the periphery of the pupil were too faint to be recognized or too blurred for their centroids to be determined accurately by the analysis software. In these cases, the pupil was manually recentered to compensate for these unidentified or poorly identified spots. The correction was required only along the horizontal meridian, and the largest correction required was 0.32 mm. The pupil illumination LEDs caused some spurious spots in the Hartmann-Shack image, which occasionally occurred within the pupillary area (<6 for each LED of about 250 for 3-mm pupils) and were manually deleted before generation of Zernike coefficients.
Most analyses were qualitative. Statistical tests included linear regressions of refraction components against visual field angle and t tests of significance of change of refraction component per degree of visual field angle—all using a significance level of 5%.
We categorized peripheral refraction patterns of our participants according to the types I to V scheme of Rempt et al.8 wherever possible. Some participants showed a rapid hyperopic shift toward the edge of the field, and we have introduced a new pattern IV/I that shows the characteristics of type IV out to an angle of between 40 and 50 degrees before behaving like type I. We placed this pattern between III and IV. Where this shift was found only on one side or at the largest angle only (60 degrees), we classified the refraction pattern as type IV. Results are shown for 12 participants in Fig. 1, with two representatives of each pattern, both in H, V format (see equation 1; on left) and in M, J180, J45 format (on right) (all participants’ results are shown in the Appendix, available at http://links.lww.com/OPX/A112). The representatives of the new type IV/I are shown in Fig. 1G, H). Some readers may disagree with one or more of our classifications.
Peripheral refraction patterns of 9 and 8 of our 30 participants fitted types IV/I and IV, respectively, with smaller numbers in other groups (Table 1). Without applying statistics, the trend was a shift from type I to type V as refraction moved from myopia to hyperopia, consistent with the trend reported by Rempt et al.10
There were considerable contrasts between participants. For example, the type I participant in Fig. 1B had a range of mean sphere of 14.3 D but a range of J180 of 2.2 D, whereas the type IV participant in Fig. 1J had a range of mean sphere of 3.2 D and a range of J180 of 5.8 D (∼12-D range in cylinder terms).
Generally, ranges of J45 were small compared with those of J180. As in other studies,13J45 tended to show a linear variation with angle. The average slope of participants was + 0.0017 ± 0.0088 D/degree, which is not statistically significant from zero and is much smaller than the mean slope of +0.006 D/degree for 20 emmetropes of Gustafsson et al.11,12 The ranges varied from 0.4 to 3.7 D (Figs. 1F and J, respectively). Twenty-four of 30 participants showed a significant linear relation of J45 with angle, ranging from −0.021 to +0.018 D/degree), of which 16 showed the more typical positive slopes (Fig. 1A, C, E, F, G) and 8 showed negative slopes (Fig. 1D, J, K).
We made measurements on the right eyes of 30 adults, having a variety of central refractions, out to ± 60 degrees along the horizontal field using a modern aberrometer. A sizable minority of eyes (30%) showed a pattern that was a combination of type IV and type I patterns of Rempt et al.,8 having the characteristics of type IV (relative hyperopia along the vertical meridian and relative myopia along the horizontal meridian) out to an angle of between 40 and 50 degrees before behaving like type I (both meridians show relative hyperopia). We have classified these as type IV/I.
Our study supports the studies of Millodot10 and Gustafsson et al.11 by finding a tendency for hyperopic shift in the far periphery (≥50 degrees).
As a group, there was no significant variation of oblique astigmatism component J45 with angle (+0.0017 ± 0.0088 D/degree), but about one-half showed significant positive slopes (more positive or less negative values in the nasal field than in the temporal field) and one-fourth showed significant negative slopes. This contrasts with the significant slope of +0.0060 ± 0.003D/degree found by Gustafsson et al.11,12 Several participants showed a change in direction of J45 in the far periphery. When results were analyzed over a ±35-degree range to match that of Atchison et al.,13 the mean slopes were significantly different from zero at +0.0029 ± 0.0069 (p = 0.03) and close to those reported by Atchison et al.13 of +0.004 D/degree. A positive slope is consistent with the visual axis being slightly upward relative to the best fit optical axis in object space (usually by ∼2 to 3 degrees according to Tscherning17).
It is often considered that peripheral refraction is implicated in the development of myopia, with a pattern of relative peripheral hyperopia predisposing to the development of myopia.18,19 On this basis, there have been trials of ophthalmic devices to treat the progression of myopia. These lenses have modifications in the periphery to alter the relative peripheral refraction,20,21 and these have shown some degree of success. Similarly, orthokeratology changes the peripheral refraction pattern in myopes from relative hyperopia to relative myopia, at least along the horizontal meridian,22–24 and this may contribute to the success of this treatment in slowing myopia progression.25,26
The enthusiasm for the role of relative peripheral refractive errors stems from the work of Hoogerheide et al.27 As opposed to the common understanding, it is it likely that they measured peripheral refraction after, rather than before, myopia did or did not develop. Thus, their study has no predictive power in determining peripheral refraction patterns likely to lead to myopia.28 Whereas the animal studies of Smith and colleagues29–33 provide compelling evidence for the importance of the peripheral retina in the development of refractive errors, recent work suggests that peripheral refraction pattern may be a consequence, rather than a cause, of myopia in humans.34,35
This aside, if relative peripheral hyperopia predisposes to the development of myopia, the importance of different visual field meridians and the angle out to which they might influence the development can be considered. There are considerable meridional differences, with the relative peripheral hyperopia of myopes along the horizontal visual field, out to 35 degrees from fixation, not generally being found along the vertical meridian; this suggests that the vertical meridian is not important.13,36,37 Allowing that our results have been taken on adults with stable refractions and along only the horizontal meridian of the visual field, our finding that 7 of 13 emmetropes showed the IV/I pattern with relative peripheral hyperopia rather than the relative peripheral myopia beyond 40 degrees, suggests that it is unlikely that refraction at visual field angles beyond 40 degrees from fixation will contribute to myopia development.
School of Optometry and Institute of Health
& Biomedical Innovation
Queensland University of Technology
60 Musk Ave Kelvin Grove, Queensland 4059
This work was supported by ARC Discovery and ARC Linkage grants to David Atchison and by Carl Zeiss Vision.
Received March 18, 2012; accepted November 6, 2012.
The Appendix, showing peripheral refraction patterns of our participants according to the types I to V scheme of Rempt et al.,8 is available at http://links.lww.com/OPX/A112.
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emmetropia; hypermetropia; myopia; peripheral refraction
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