We measured wave aberrations over the central 42° × 32° visual field for a 5-mm pupil for groups of 10 emmetropic (mean spherical equivalent = 0.11 ± 0.50 D) and 9 myopic (MSE = −3.67 ± 1.91 D) young adults. Relative peripheral refractive errors over the measured field were generally myopic in both groups. Mean values of *C* _{4} ^{0} were almost constant across the measured field and were more positive in emmetropes (+0.023 ± 0.043 *μ*m) than in myopes (−0.007 ± 0.045 *μ*m). Coma varied more rapidly with field angle in myopes: modeling suggested that this difference reflected the differences in mean anterior corneal shape and axial length in the two groups. In general, however, overall levels of RMS aberration differed only modestly between the two groups, implying that it is unlikely that high levels of aberration contribute to myopia development.

*M*), with/against-the-rule astigmatism (

*J*

_{180}), and oblique astigmatism (

*J*

_{45}) were calculated from second, fourth, and sixth Zernike-order coefficients, as described by Atchison, Scott, and Charman (2007, 2008). Contour plots representing the magnitude of aberrations at each visual field location were generated using triangle-based interpolation.

*R*and asphericity

*Q*were estimated from corneal height data across 36 equally spaced meridians for a 6-mm corneal diameter using least-squares fitting (Atchison, Markwell, et al., 2008) and the equation

*Z*axis is the line of sight. The means of estimates of

*R*and

*Q*from four topographic images were used for further analysis. For the maximum visual field angle of 21°, the relevant corneal diameter exceeds the fitted 6 mm slightly (for

*R*= 7.8 mm and entrance pupil depth 3.0 mm, the relevant diameter was 6.4 mm).

*M*across the horizontal field for (a) emmetropes and (b) myopes. A few myopes had hyperopic RPRE in at least one semi-meridian. However, there does not appear to be a systematic trend towards a more hyperopic RPRE with increasing axial myopia, with regression analysis failing to show any trends for the myopes as a function of refraction error at any visual field location along either the horizontal or vertical visual field meridians.

*J*

_{45}, (b) change in spherical equivalent

*M*relative to axial spherical equivalent (i.e., RPRE), and (c) with/against the rule astigmatism

*J*

_{180}for (A) emmetropes and B) myopes. In both groups, the astigmatic components

*J*

_{45}(Aa, Ba) and

*J*

_{180}(Ac, Bc) increased approximately quadratically along the 135°–315° meridian and 90°–270° meridians, respectively, and decreased along the meridians perpendicular to these. This implies that, locally, the astigmatism tends to be oriented along the visual field meridian and increases as the square of the field angle. For both groups, RPRE moved generally in the negative direction in the periphery (i.e., relative peripheral myopia). Effects were not the same in all semi-meridians, however, tending to be higher in the nasal field (temporal retina).

*J*

_{45}(linear regression estimate 140 to 320 deg meridian, rate of change 0.013 D/deg of field), along approximately the vertical meridian for RPRE (105 to 285 deg meridian, rate of change 0.023 D/deg of field) and along approximately the inferior/temporal to superior/nasal meridian for

*J*

_{180}(210 to 30 meridian, rate of change 0.008 D/deg of field).

*C*

_{3}

^{−3}decreased from the top to the bottom of the field (Aa, Ba). It was more negative, or less positive, for the myopic group than for the emmetropic group (Aa, Ba). The most prominent differences between the two groups were seen in the vertical

*C*

_{3}

^{−1}(Ab, Bb) and horizontal

*C*

_{3}

^{1}coma (Ac, Bc) coefficients, both of which tended to be relatively large in comparison to the other higher-order coefficients. Vertical coma

*C*

_{3}

^{−1}increased linearly from the superior to the inferior visual field and horizontal coma

*C*

_{3}

^{1}increased from the nasal to the temporal visual field. Emmetropes had slightly lower rates of change in coma coefficients (see below). For each refractive group, spherical aberration

*C*

_{4}

^{0}(Ad, Bd) varied only slightly across the visual field and showed no obvious spatial pattern of variation. Mean spherical aberration was weakly positive in the young emmetropic group and weakly negative in the young myopes. HORMS (Ae, Be) and total RMS excluding defocus (Af, Bf) showed approximately quadratic rates of change across the field with the minimum approximately at the center of the field. The rate of increase in HORMS with field angle was more rapid in myopes, as also was the total RMS, excluding spherical defocus.

*C*

_{3}

^{−3},

*C*

_{3}

^{−1},

*C*

_{3}

^{1}, and

*C*

_{4}

^{0}, with a consequent difference in HORMS and total RMS ( Figures 4Ce and 4Cf, respectively).

*C*

_{3}

^{−1}and horizontal coma coefficients

*C*

_{3}

^{1}along the vertical and horizontal visual field meridians, respectively, for the two refractive groups. The slopes for the coma coefficients (

*μ*m/deg) varied significantly between the groups ( Table 1), using independent sample

*t*-tests. Vertical and horizontal coma slopes were more than two times greater for the myopes than for the emmetropes (

*p*≤ 0.02). Note again that coma values approximate to zero around the center of the field and that the slopes along the horizontal and vertical field meridians are very similar. This implies that, if the horizontal and vertical coma coefficients are combined, the resultant total coma is always oriented approximately radially with respect to the visual axis and its magnitude increases linearly with the field angle in all meridians.

Refractive group | Coma slope ( μm/deg) | Mean C _{3} ^{−3} ( μm) | Mean C _{4} ^{0} ( μm) |
---|---|---|---|

Emmetropes ( N = 10) | −0.006 ± 0.002 | −0.060 ± 0.074 | +0.023 ± 0.043 |

Myopes ( N = 9) | −0.014 ± 0.007 | +0.002 ± 0.052 | −0.007 ± 0.045 |

*C*

_{3}

^{−3}and spherical aberration

*C*

_{4}

^{0}across the field were significantly lower and higher, respectively, for emmetropes than for myopes (repeated measures analysis of variance with field angle as within-subject factor and refractive group as between-subject factor,

*p*< 0.001) ( Table 1). Mean

*C*

_{4}

^{0}was correlated significantly with the mean spherical refraction of the myopes ( Figure 6).

Refractive group | Vertex radius R (mm) | Asphericity Q |
---|---|---|

Emmetropes ( N = 10) | 7.73 ± 0.26 | −0.08 ± 0.04 |

Myopes ( N = 9) | 7.65 ± 0.21 | −0.16 ± 0.09 |

*t*-test (

*p*= 0.04). Although the change in radius of curvature with myopia does not reach significance for the relatively small numbers of subjects involved, its value (−0.020 mm per diopter of myopia) is similar to that found (−0.022 mm per diopter) in a recent large-scale investigation in this laboratory (Atchison, 2006c). However, the latter investigation found no change in asphericity with increase in myopia.

*C*

_{3}

^{−1}and

*C*

_{3}

^{1}showed no significant correlation with either (a) the corneal radius R or (b) the corneal asphericity Q ( Figure 7).

*μ*m for a change in accommodation response of 0.29 ± 0.53 D. Changes in other coefficients were not significant, as was also the case in a study of emmetropes with 0.3 and 4.0 D stimuli (Mathur et al., submitted for publication). It can be concluded that the effects of accommodation on aberrations were negligible and of no consequence to the differences between the groups.

*μ*m/deg is reasonably similar to the mean experimental value of −0.006

*μ*m/deg. The changes in asphericity and vitreous length increase the negative slope to about −0.008

*μ*m/deg: together with a small contribution from a decrease in anterior radius of curvature they result in a slope of about −0.009

*μ*m/deg. Thus, the modeling suggests that the majority of the greater experimental coma slopes of about −0.014

*μ*m/deg with myopes ( Figure 5), as compared to emmetropes (−0.006

*μ*m/deg), can be explained by differences in anterior corneal shape and axial length.

*C*

_{4}

^{0}and with slight increase with field angle. Changing the asphericity from −0.08 to −0.16 decreases the spherical aberration at all field angles with respect to that for the original emmetropic eye by −0.02

*μ*m. The combined length and radius of curvature changes to the myopic eye reduce the aberration difference between the original (

*Q*= −0.08) emmetropic eye and the myopic eye to about −0.01

*μ*m, considerably smaller than the experimental difference of −0.03

*μ*m. The predicted slightly positive change in spherical aberration towards the periphery does not match the experimental results, where spherical aberration changed very little with field angle ( Figures 4Ad and 4Bd). This is presumably because factors other than the anterior cornea, such as the lens, also play an important role.

*μ*m for our myopes who had an overall mean spherical error of −3.7 D (5-mm pupil). In general, however, the magnitude of the higher-order wave aberration was always small compared with that of second-order aberrations.