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 J 45 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 J 180 component and oblique astigmatism component J 45 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, J 180, J 45 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 J 180 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 J 180 of 5.8 D (∼12-D range in cylinder terms).
Generally, ranges of J 45 were small compared with those of J 180. As in other studies,13 J 45 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 J 45 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 J 45 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 J 45 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.
1. Young T. On the mechanism of the eye. Phil Trans Royal Soc Lond 1801;91:23–88.
2. Atchison DA, Charman WN. Thomas Young’s contribution to visual optics: the Bakerian lecture “On the Mechanism of the Eye.” J Vis 2010; 10: 16.
3. Ferree CE, Rand G, Hardy C. Refraction for the peripheral field of vision. Arch Ophthalmol 1931; 5: 717–31.
4. Ferree CE, Rand G, Hardy C. Refractive asymmetry in the temporal and nasal halves of the visual field. Am J Ophthalmol 1932; 15: 513–22.
5. Ferree CE, Rand G. Interpretation of refractive conditions in the peripheral field of vision. Arch Ophthalmol 1933; 9: 925–38.
6. Ferree CE, Rand G, Hardy C. An important factor in space perception in the peripheral field of vision. Am J Psychol 1933; 45: 228–47.
7. Henker O. Apparatus for the objective measurement of the refractive value of the principal point of the eye. US patent 1,475,698. Assigned to Carl Zeiss, Jena, Germany, November 27, 1923.
8. Rempt F, Hoogerheide J, Hoogenboom WP. Peripheral retinoscopy and the skiagram. Ophthalmologica 1971; 162: 1–10.
9. Johnson CA, Leibowitz HW. Practice, refractive error, and feedback as factors influencing peripheral motion thresholds. Percept Psychophys 1974; 15: 276–80.
10. Millodot M. Effect of ametropia on peripheral refraction. Am J Optom Physiol Opt 1981; 58: 691–5.
11. Gustafsson J, Terenius E, Buchheister J, Unsbo P. Peripheral astigmatism in emmetropic eyes. Ophthalmic Physiol Opt 2001; 21: 393–400.
12. Gustafsson J, Terenius E, Buchheister J, Unsbo P. Peripheral astigmatism in emmetropic eyes: erratum. Ophthal Physiol Opt 2001; 21: 491.
13. Atchison DA, Pritchard N, Schmid KL. Peripheral refraction along the horizontal and vertical visual fields in myopia. Vision Res 2006; 46: 1450–8.
14. Mathur A, Atchison DA, Scott DH. Ocular aberrations in the peripheral visual field. Opt Lett 2008; 33: 863–5.
15. Atchison DA, Scott DH, Charman WN. Measuring ocular aberrations in the peripheral visual field using Hartmann-Shack aberrometry. J Opt Soc Am (A) 2007; 24: 2963–73.
16. Atchison DA, Scott DH, Charman WN. Measuring ocular aberrations in the peripheral visual field using Hartmann-Shack aberrometry: erratum. J Opt Soc Am (A) 2008; 25: 2467.
17. Tscherning M. Physiologic Optics: Dioptrics of the Eye, Functions of the Retina, Ocular Movements and Binocular Vision, 4th ed. Philadelpia, PA: The Keystone Publishing Co.; 1924.
18. Stone RA, Flitcroft DI. Ocular shape and myopia. Ann Acad Med Singapore 2004; 33: 7–15.
19. Wallman J, Winawer J. Homeostasis of eye growth and the question of myopia. Neuron 2004; 43: 447–68.
20. Sankaridurg P, Donovan L, Varnas S, Ho A, Chen X, Martinez A, Fisher S, Lin Z, Smith EL 3rd, Ge J, Holden B. Spectacle lenses designed to reduce progression of myopia: 12-month results. Optom Vis Sci 2010; 87: 631–41.
21. Sankaridurg P, Holden B, Smith E 3rd, Naduvilath T, Chen X, de la Jara PL, Martinez A, Kwan J, Ho A, Frick K, Ge J. Decrease in rate of myopia progression with a contact lens designed to reduce relative peripheral hyperopia: one-year results. Invest Ophthalmol Vis Sci 2011; 52: 9362–7.
22. Charman WN, Mountford J, Atchison DA, Markwell EL. Peripheral refraction in orthokeratology patients. Optom Vis Sci 2006; 83: 641–8.
23. Queirós A, Gonzalez-Meijome JM, Jorge J, Villa-Collar C, Gutierrez AR. Peripheral refraction in myopic patients after orthokeratology. Optom Vis Sci 2010; 87: 323–9.
24. Kang P, Swarbrick H. Peripheral refraction in myopic children wearing orthokeratology and gas-permeable lenses. Optom Vis Sci 2011; 88: 476–82.
25. Cho P, Cheung SW, Edwards M. Retardation of myopia in orthokeratology (ROMIO) study: a 2 year randomized clinical trial. Invest Ophthalmol Vis Sci 2012; 53: 7077–85.
26. Kakita T, Hiraoka T, Oshika T. Influence of overnight orthokeratology on axial elongation in childhood myopia. Invest Ophthalmol Vis Sci 2011; 52: 2170–4.
27. Hoogerheide J, Rempt F, Hoogenboom WP. Acquired myopia in young pilots. Ophthalmologica 1971; 163: 209–15.
28. Rosén R, Lundström L, Unsbo P, Atchison DA. Have we misinterpreted the study of Hoogerheide et al. (1971)? Optom Vis Sci 2011; 89: 1235–7.
29. Smith EL 3rd, Kee CS, Ramamirtham R, Qiao-Grider Y, Hung LF. Peripheral vision can influence eye growth and refractive development in infant monkeys. Invest Ophthalmol Vis Sci 2005; 46: 3965–72.
30. Smith EL 3rd, Ramamirtham R, Qiao-Grider Y, Hung LF, Huang J, Kee CS, Coats D, Paysse E. Effects of foveal ablation on emmetropization and form-deprivation myopia. Invest Ophthalmol Vis Sci 2007; 48: 3914–22.
31. Smith EL 3rd, Hung LF, Harwerth RS. Effects of optically induced blur on the refractive status of young monkeys. Vision Res 1994; 34: 293–301.
32. Smith EL 3rd. Prentice Award Lecture 2010: a case for peripheral optical treatment strategies for myopia. Optom Vis Sci 2011; 88: 1029–44.
33. Huang J, Hung LF, Smith EL 3rd. Recovery of peripheral refractive errors and ocular shape in rhesus monkeys (Macaca mulatta
) with experimentally induced myopia. Vision Res 2012; 73: 30–9.
34. Mutti DO, Sinnott LT, Mitchell GL, Jones-Jordan LA, Moeschberger ML, Cotter SA, Kleinstein RN, Manny RE, Twelker JD, Zadnik K. Relative peripheral refractive error and the risk of onset and progression of myopia in children. Invest Ophthalmol Vis Sci 2011; 52: 199–205.
35. Sng CC, Lin XY, Gazzard G, Chang B, Dirani M, Lim L, Selvaraj P, Ian K, Drobe B, Wong TY, Saw SM. Change in peripheral refraction over time in Singapore Chinese children. Invest Ophthalmol Vis Sci 2011; 52: 7880–7.
36. Berntsen DA, Mutti DO, Zadnik K. Study of Theories about Myopia Progression (STAMP) design and baseline data. Optom Vis Sci 2010; 87: 823–32.
37. Chen X, Sankaridurg P, Donovan L, Lin Z, Li L, Martinez A, Holden B, Ge J. Characteristics of peripheral refractive errors of myopic and non-myopic Chinese eyes. Vision Res 2010; 50: 31–5.
Keywords:© 2013 American Academy of Optometry
emmetropia; hypermetropia; myopia; peripheral refraction