This study investigates the changes in aberrations with monocular accommodation as a function of age. Second-order and higher order wavefront aberrations and pupil size were measured as a function of accommodation demand over the range of 0–4 D in the right eyes of 47 normal subjects with ages between 17 and 56 years. Higher order ocular Zernike aberrations were analyzed for the natural pupil size in terms of their equivalent defocus and were also determined for fixed pupil diameters of 4.5 mm in the unaccommodated eyes and 2.5 mm in the accommodating eyes. With relaxed accommodation (0 D accommodation stimulus), the major change with age was in the value of *C* _{4} ^{0}, which increased in positive value over the age range studied, although the total higher order RMS wavefront aberration did not increase. When the data were analyzed for natural pupils, spherical aberration was again found to change systematically in the positive direction with age. The equivalent defocus of total higher order RMS error for natural pupils showed no significant correlation with age ( *p* > .05). With active accommodation, spherical aberration was found to decrease and become negative as the accommodative response increased in the younger subjects (<40 years). Near-zero spherical aberration was found at accommodation levels of about 0.50 D in the youngest subjects (<20 years) and at around 2–3 D in subjects between 20 and 39 years. In the older subjects (>40 years), the spherical aberration showed only small changes, some of which were positive, within the limited amplitude of accommodation available. Other higher order aberrations and the RMS of higher order aberrations did not appear to change systematically with accommodation, except in the oldest subjects. The change with age in the relationship between aberration and accommodation is interpreted in terms of the changing gradients of refractive index and surface curvatures of the crystalline lens.

*SD*= −1.48 ± 2.53 D). In all cases, astigmatism was ≤2.00 D. The research followed the tenets of the Declaration of Helsinki. All subjects gave their informed consent after being told of the purpose of the experiment. The project protocol was approved by the Senate Committee on the Ethics of Research on Human Beings of the University of Manchester.

^{2}, set at 0.50 D intervals to provide effective accommodation stimuli over the range from 0 to 4.00 D (strictly, the effective target vergences were negative, but the commonly used convention of treating them as positive was followed). A relatively small dioptric range of stimuli was used due to the limited amplitude of accommodation of the older subjects. Subjects were encouraged to try to keep the letter as clear as possible at all times so that both reflex and voluntary accommodations were employed.

*M*. This is the amount of spherical defocus required to produce the same wavefront variance as that produced by one or more higher order aberrations at the same pupil diameter (Thibos, Hong, Bradley, & Cheng, 2002). The attraction of this metric is that it not only allows for changes in pupil diameter but also permits direct comparison of the importance of the aberrations with that of the lags and leads of accommodation corresponding to the second-order defocus errors of the accommodation response.

*C*

_{ n}

^{ f}for a pupil radius

*r*is determined using the following formula:

*M*is in diopters.

^{2}for spherical aberration, where the mm refers to the zonal pupil radius. These values were calculated using the following formulae:

^{2}means that the shift in focus at the margin of a 2-mm-diameter pupil will be 0.50 D, whereas for a 4-mm pupil, it would be 2.00 D. Equal aberration values for the natural pupil in terms of this metric thus do not imply equal retinal image quality. Note that the dioptric metric for coma combines third-order horizontal and vertical coma and that only the magnitude of the coma is expressed, whereas the dioptric spherical aberration retains its appropriate sign.

*y*= −0.038

*x*+ 6.355,

*R*

^{2}= .186,

*p*< .01).

*C*

_{3}

^{−3}), average to around 0 μm. Spherical aberration (

*C*

_{4}

^{0}) averages to a positive mean value of +0.034 ± 0.05 μm.

*C*

_{4}

^{0}, and total higher order RMS error (third to sixth order) plotted as a function of age for the 4.5-mm pupil. Over the range of ages studied, spherical aberration in the relaxed eye became steadily more positive, whereas total RMS error did not change with age. The correlation between spherical aberration and age was significant (

*R*

^{2}= .25,

*p*< .01). Correlations in the case of the other third- and fourth-order coefficients were not significant. With a pupil diameter of 4.5 mm, an RMS wavefront error of 0.1 μm corresponds to an equivalent defocus of 0.14 D, so that the almost constant total RMS error of about 0.16 μm corresponds to an equivalent defocus of around 0.22 D, close to the limits of clinical significance.

*n*= 8, mean ±

*SD*age = 18.5 ± 0.76 years, mean ±

*SD*refractive error = −3.30 ± 3.86), 20–29 years (

*n*= 14, mean ±

*SD*age = 24.86 ± 3.51 years, mean ±

*SD*refractive error = −0.75 ± 1.45), 30–39 years (

*n*= 9, mean ±

*SD*age = 34.00 ± 3.50 years, mean ±

*SD*refractive error = −1.86 ± 2.82), and >39 years (

*n*= 10, mean ±

*SD*age = 46.00 ± 4.00 years, mean ±

*SD*refractive error = −1.28 ± 2.35). Analysis of variance with the 4.5-mm pupil aberration coefficients as the dependent variables and age group as the independent variable gave the results shown in Table 1. There are significant differences in the case of

*C*

_{3}

^{−1}and

*C*

_{4}

^{0}, but not for the other coefficients.

Aberration coefficient | F(3, 40) | p |
---|---|---|

Trefoil, C _{3} ^{−3} | 1.59 | .207 |

Vertical coma, C _{3} ^{−1} | 3.01 | .043 |

Horizontal coma, C _{3} ^{1} | 1.11 | .357 |

Trefoil, C _{3} ^{3} | 0.97 | .416 |

Quadrafoil, C _{4} ^{−4} | 0.16 | .922 |

Fourth-order astigmatism, C _{4} ^{−2} | 1.37 | .268 |

Spherical aberration, C _{4} ^{0} | 4.25 | .011 |

Fourth-order astigmatism, C _{4} ^{2} | 1.07 | .375 |

Quadrafoil, C _{4} ^{4} | 0.90 | .542 |

*C*

_{4}

^{0}(

*p*= .037) and quadrafoil

*C*

_{4}

^{4}(

*p*= .021). As can be seen from the regression equations, fourth-order spherical aberration tended to be always positive and to increase with age, whereas quadrafoil became less positive with age. The other third- and fourth-order aberrations showed no significant correlation with age.

Aberration coefficient | Regression equation | R ^{2} | p |
---|---|---|---|

Trefoil, C _{3} ^{−3} | y = −0.0016 x − 0.0218 | .0264 | .789 |

Vertical coma, C _{3} ^{−1} | y = 0.0024 x − 0.0419 | .041 | .288 |

Horizontal coma, C _{3} ^{1} | y = −0.0012 x + 0.0141 | .0237 | .324 |

Trefoil, C _{3} ^{3} | y = −0.0006 x + 0.0434 | .0097 | .453 |

Quadrafoil, C _{4} ^{−4} | y = 0.0002 x − 0.0055 | .0033 | .694 |

Fourth-order astigmatism, C _{4} ^{−2} | y = −0.0004 x + 0.0098 | .0497 | .204 |

Spherical aberration, C _{4} ^{0} | y = 0.0016 x + 0.0184 | .022 | .037 |

Fourth-order astigmatism, C _{4} ^{2} | y = 0.0007 x − 0.0226 | .0261 | .312 |

Quadrafoil, C _{4} ^{4} | y = −0.0016 x + 0.0758 | .1219 | .021 |

*n*= 8, mean ±

*SD*age = 18.5 ± 0.76 years, mean ±

*SD*refractive error = −3.30 ± 3.86), 20–29 years (

*n*= 15, mean ±

*SD*age = 24.80 ± 3.53 years, mean ±

*SD*refractive error = −1.38 ± 2.11), 30–39 years (

*n*= 11, mean ±

*SD*age = 33.64 ± 3.29 years, mean ±

*SD*refractive error = −0.18 ± 1.10), and >39 years (

*n*= 13, mean ±

*SD*age = 46.08 ± 4.87 years, mean ±

*SD*refractive error = −1.58 ± 2.34). Analysis of variance was performed with the age group (again <20, 20–29, 30–39, >39 years) as the independent variable and the equivalent defocus of the third- and fourth-order aberrations as the dependent variable. The results showed no significant difference in third-order coma coefficients

*C*

_{3}

^{−1},

*F*(3, 46) = 2.56,

*p*= .067, and

*C*

_{3}

^{1},

*F*(3, 46) = 0.31,

*p*= .817; trefoil coefficients

*C*

_{3}

^{−3},

*F*(3, 46) = 0.69,

*p*= .562, and

*C*

_{3}

^{3},

*F*(3, 46) = 0.29,

*p*= .834; fourth-order spherical aberration

*C*

_{4}

^{0},

*F*(3, 46) = 2.33,

*p*= .093; fourth-order astigmatism

*C*

_{4}

^{−2},

*F*(3, 46) = 0.57,

*p*= .64, and

*C*

_{4}

^{2},

*F*(3, 46) = 0.63,

*p*= .60; and quadrafoil

*C*

_{4}

^{−4},

*F*(3, 46) = 0.03,

*p*= .99, and

*C*

_{4}

^{4},

*F*(3, 46) = 1.97,

*p*= .133, between the four age groups. Thus, only for third-order coma and fourth-order spherical aberration did the differences between the age groups approach (but not reach) statistical significance.

*F*(3, 46) = 1.05,

*p*= .381.

^{2}, as a function of age for the full set of 47 subjects. As noted earlier, quantifying aberrations in these ways allows valid comparisons to be made with different pupil diameters. When expressed in these terms, both spherical aberration and coma appear to increase with age. However, although the correlation between spherical aberration and age was found be statistically significant (

*y*= 0.0047

*x*− 0.0433;

*R*

^{2}= .162,

*p*< .05), that for coma was not (

*y*= 0.0019

*x*+ 0.144;

*R*

^{2}= .024,

*p*> .05). Analysis of variance showed a significant difference in magnitude of spherical aberration between the four age groups,

*F*(3, 46) = 4.17,

*p*= .011. A post hoc test (Tukey's HSD) showed a significant difference in spherical aberration between the group with subjects aged over 39 years and the two groups under 30 years of age (

*p*< .05). No significant difference was found in the magnitude of coma between the four age groups,

*F*(3, 46) = 0.817,

*p*= .491.

^{2}or D/mm, respectively.

*n*= 8, mean ±

*SD*age = 18.5 ± 0.76 years, mean ±

*SD*refractive error = −3.30 ± 3.86), 20–29 years (

*n*= 15, mean ±

*SD*age = 25.13 ± 3.54 years, mean ±

*SD*refractive error = −0.70 ± 1.41), 30–39 years (

*n*= 10, mean ±

*SD*age = 34.10 ± 3.31 years, mean ±

*SD*refractive error = −1.67 ± 2.72), and >39 years (

*n*= 9, mean ±

*SD*age = 45.11 ± 3.48, mean ±

*SD*refractive error = −1.71 ± 2.65).

^{2}, as a function of accommodative response in the four age groups are shown in Figures 6a and 6b, respectively. Although there is considerable intersubject scatter, both plots suggest a general modest tendency for spherical aberration to change from a positive value in the relaxed eye toward a negative value as accommodation increases, although for a few subjects, spherical aberration becomes more positive. When the data are broken down into age groups, in both metrics, the least squares regression line fits indicate that typical spherical aberration in the youngest group (<20 years) changes from positive to negative at quite low levels of accommodation response (around 0.5 D), whereas that for the 20- to 29-year and 30- to 39-year groups makes the transition at a response of about 2.5 D. Subjects aged less than 20 years show the highest rate of change in spherical aberration with accommodation: When expressed by equivalent defocus, the typical rate of change is about −0.042 D per diopter of accommodation. This rate decreases in the older subjects, with the change in spherical aberration being −0.020 D per diopter of accommodation in 20- to 29-year-olds and −0.039 D per diopter of accommodation in 30- to 39-year-olds. Due partly to the highly reduced accommodative amplitudes and responses in the subjects aged over 39 years, the positive regression slope for this age group (+0.039 D per diopter) is not statistically significant (although it is when spherical aberration is expressed in D/mm

^{2}rather than equivalent defocus). Over the limited response range achieved, the oldest subjects tend to show relatively high levels of positive spherical aberration in comparison with the other age groups. Full details of the regression line fits are given in Table 3.

Spherical aberration | Age group (years) | Regression equation | R ^{2} | p |
---|---|---|---|---|

Equivalent defocus (D) | <20 | y = −0.04 x + 0.02 | .1108 | .008 |

20–29 | y = −0.02 x + 0.05 | .0357 | .023 | |

30–39 | y = −0.04 x + 0.08 | .1051 | .001 | |

>39 | y = 0.04 x + 0.11 | .0266 | .211 | |

D/mm ^{2} | <20 | y = −0.05 x + 0.03 | .1757 | .001 |

20–29 | y = −0.02 x + 0.08 | .0324 | .031 | |

30–39 | y = −0.04 x + 0.09 | .0306 | .102 | |

>39 | y = 0.27 x + 0.13 | .1979 | .001 |

^{2}) per diopter of accommodation response, as a function of subject age. Filled symbols show slopes (spherical aberration/accommodative response) where the correlation coefficient for the individual subject was significant at the 5% level, whereas open symbols show those where the correlation was not significant. Although there is considerable scatter in the data and the trends fail to reach statistical significance, the slope of the change in spherical aberration per diopter of accommodation appears to be negative in the younger subjects and tends to become positive in the presbyopic subjects, with the transition at which spherical aberration remains constant with increasing accommodation being somewhere in the mid-thirties. This behavior appears to be similar to that found by Lopez-Gil et al. (2005) for fixed 4-mm pupils. However, analysis of variance with the change in spherical aberration (D/mm

^{2}) per diopter of accommodative response as the dependent variable and age group as the independent variable showed no significant difference between the groups,

*F*(3, 41) = 0.30,

*p*= .82.

*F*(3, 41) = 2.55,

*p*= .069.

Aberration | <20 years | 20–29 years | 30–39 years | >39 years |
---|---|---|---|---|

Trefoil, C _{3} ^{−3} | 0.001 ± 0.045 | −0.009 ± 0.028 | −0.0017 ± 0.033 | 0.018 ± 0.055 |

Vertical coma, C _{3} ^{−1} | 0.041 ± 0.068 | 0.013 ± 0.027 | 0.014 ± 0.048 | 0.023 ± 0.082 |

Horizontal coma, C _{3} ^{1} | 0.125 ± 0.19 | 0.009 ± 0.051 | 0.012 ± 0.043 | 0.252 ± 0.35 |

Trefoil, C _{3} ^{3} | 0.074 ± 0.085 | 0.02 ± 0.031 | 0.023 ± 0.023 | 0.172 ± 0.215 |

Quadrafoil, C _{4} ^{−4} | 0.01 ± 0.022 | 0.004 ± 0.011 | 0.004 ± 0.015 | −0.003 ± 0.042 |

Fourth-order astigmatism, C _{4} ^{−2} | 0.004 ± 0.011 | −0.003 ± 0.009 | −0.002 ± 0.011 | −0.007 ± 0.019 |

Fourth-order astigmatism, C _{4} ^{2} | 0.021 ± 0.06 | 0.001 ± 0.015 | 0.013 ± 0.020 | 0.013 ± 0.073 |

Quadrafoil, C _{4} ^{4} | −0.024 ± 0.055 | −0.005 ± 0.018 | −0.022 ± 0.024 | −0.054 ± 0.081 |

*y*= 0.260

*x*+ 0.413;

*R*

^{2}= .111,

*p*< .05). The 30- to 39-year-old group appears to have a higher variability in RMS error with accommodation when compared with other groups and shows a systematic increase in equivalent defocus with accommodation (

*y*= 0.0837

*x*+ 0.4473;

*R*

^{2}= .0614,

*p*< .05). Subjects in the 20- to 29-year (

*y*= 0.0396

*x*+ 0.3441;

*R*

^{2}= .092,

*p*> .05) and <20-year (

*y*= 0.0268

*x*+ 0.3408;

*R*

^{2}= .0709,

*p*> .05) age groups show no systematic change in total RMS error with accommodation.

*F*(3, 41) = 1.18,

*p*= .328.

*F*(3, 40) = 3.30,

*p*= .03. Post hoc analysis (Bonferroni) showed a significant difference between the oldest age group (>39 years) and the other age groups (

*p*< .05). These differences between the age groups might be linked to the fact that most presbyopic subjects accommodated poorly and had slightly higher regression slopes which were not statistically significant. Analysis of variance with the changes in third-order coma (μm) per diopter of accommodative response as the dependent variable and age group as the independent variable showed no significant difference between the age groups,

*F*(3, 40) = 2.84,

*p*= .052.

^{2}, respectively.

*C*

_{4}

^{0}of about 0.035 μm, equivalent to about 0.07 D/mm

^{2}of undercorrected spherical aberration). Several previous studies at broadly similar pupil diameters have shown a similar distribution of higher order aberrations and magnitude of spherical aberration (Cheng, Bradley, Hong, & Thibos, 2003; Howland & Howland, 1977; Netto et al., 2005; Porter, Guirao, Cox, & Williams, 2001; Smirnov, 1962; Thibos, Bradley, et al., 2002; Thibos, Hong, et al., 2002; Walsh & Charman, 1985; Wang & Koch, 2003). Table 5 gives the mean values of spherical aberration, expressed in D/mm

^{2}. There is no evidence that the use of mydriatics or cycloplegics has any major effect on measured aberrations.

Author | Pupil diameter | Mean value for C _{4} ^{0} (μm) | Spherical aberration (D/mm ^{2}) |
---|---|---|---|

Smirnov ( 1962) | 0.055 | ||

Howland and Howland ( 1977) | 0.039 | ||

Walsh and Charman ( 1985) | 0.040 | ||

Porter et al. ( 2001) | 5.7 (natural) | 0.138 ± 0.103 | 0.112 ± 0.084 |

Thibos, Bradley, et al. ( 2002) | 6.0 (cyclo) | 0.12 ± 0.12 | 0.080 ± 0.80 |

X. Cheng et al. ( 2003) | 6.0 (cyclo) | 0.11 ± 0.11 | 0.073 ± 0.073 |

Wang and Koch ( 2003) | 6.0 (natural) | 0.101 ± 0.103 | 0.067 ± 0.068 |

Netto et al. ( 2005) | 6.0 (natural) | 0.09 ± 0.04 | 0.060 ± 0.027 |

Present data | 4.5 (natural) | 0.035 ± 0.05 | 0.073 ± 0.010 |

*C*

_{4}

^{4}) are found to increase significantly ( Figure 3); spherical aberration also increases with age when expressed in terms of D/mm

^{2}. The regression equations for equivalent defocus against age are given in Table 3.

^{2}per diopter of accommodation (see Figure 6); these values are very similar to the values derived from data with fixed 5-mm pupils for a similar subject age range (H. Cheng et al., 2004), that is, −0.047 D of equivalent defocus per diopter of accommodation and 0.059 D/mm

^{2}per diopter of accommodation. The present data show the change from positive to negative values of spherical aberration occurring at response levels of around 0.5 D in the youngest subjects (<20 years) and around 2.5 D in subjects between 20 and 39 years. This compares with findings of 1.0 to 1.5 D by Jenkins (1963), 2.0 D by Atchison et al. (1995), and 1.7 D by H. Cheng et al. (2004), whereas He et al. (2000) found the transition to occur at a stimulus level of around 3.5 D. This level of agreement appears satisfactory in view of the observed intersubject differences and the variations in age composition and other aspects of the various studies. In case of other higher order aberrations, the large intersubject variations found in the data may mask any trends related to age and accommodation.

- The surface curvatures increase (e.g., Koretz, Cook, & Kaufman, 2001).

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