The aim of this study was to explore changes in ocular aberration as a function of accommodation and age. In an attempt to maintain as natural conditions as possible, no mydriatic was used. Because accommodation demands photopic levels of target luminance and accommodative miosis occurs, this resulted in some subjects having quite small pupil sizes (<2.5 mm) under some accommodated conditions. Aberrations were then very small, and their measurements were less reliable. Thus, rather than using Zernike coefficients for a fixed pupil diameter to describe the aberrational changes, much of the analysis was carried out for the full natural pupil diameters, which varied with subject and conditions, employing equivalent defocus as the metric to describe the aberration or, in the cases of third-order coma and fourth-order spherical aberration, D/mm or D/mm 2, respectively.
In considering the data of the study, the limited reliability of aberrometer measurements must be borne in mind (e.g., X. Cheng et al.,
2004; Davies, Diaz-Santana, & Lara-Saucedo,
2003; Rodriguez, Navarro, Gonzalez, & Hernandez,
2004). In general, reliability will depend upon the instrument, subject, and measurement conditions. Moreover, it may be expected that a variety of other factors, including small alignment errors, drifts in the measuring equipment, pupil fluctuations, and true short-term variations in the ocular aberrations, will play a role. In the present case, data from the complete presbyopes serve as controls for the aberrometer's estimates of both refraction and higher order aberrations. In the light of the constancy of the Zernike estimates (means for three records) as the accommodation stimulus changed for these nonaccommodating subjects, we believe that the stimulus-dependent changes in the aberrations of younger subjects, as well as their intersubject differences, are real.
The observed distribution of higher order aberrations in relaxed eyes with a fixed pupil diameter (4.5 mm; see
Figure 2) shows that each higher order Zernike coefficient averages to approximately 0 D, except for spherical aberration, which has a positive mean (
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.
With the fixed 4.5-mm pupil, fourth-order spherical aberration is also the only higher order aberration showing significant age dependency, becoming steadily more positive over the age range studied. It is difficult to compare this result with those of earlier workers. Most of them (e.g., Artal et al.,
1993; Brunette et al.,
2003; Calver et al.,
1999; McLellan et al.,
2001; Netto et al.,
2005; Wang & Koch,
2003) found increases with age in most aberrations, but the significance of the trends found depended heavily on the inclusion of subjects aged 60 years or more, when aberrations become obviously higher. Like us, McLellan et al. (
2001) found that the increase in fourth-order spherical aberration correlated significantly with age, whereas that for third-order coma did not. Interestingly, Brunette et al. (
2003) found that aberrations remained almost constant between the ages of 20 and 40 years and only started to increase after the mid-forties. Given the scatter in the results of the different studies, the present data appear to fit within the same broad pattern of age dependence.
If the individual aberrations of the relaxed eye are considered as a function of age for the natural pupil, using the equivalent defocus as the metric, only fourth-order spherical aberration and quadrafoil (
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.
Interestingly, when the RMS of total higher order (third to sixth) aberrations is expressed in terms of the equivalent defocus for the natural pupil, whose diameter tends to decrease with age, no systematic change with age is found (
Figure 4). This supports the view (Calver et al.,
1999) that, under natural observing conditions, the impact on retinal image of the increased level of aberration in the older eye is compensated for by the reduction in its pupil diameter (about 0.035 mm per year under our conditions; see
Figure 1). Earlier work, which generally used mydriatics and larger fixed pupils (around 5 mm) for analysis, has tended to find an increase with age in both individual aberrations and overall higher order RMS wavefront error (Calver et al.,
1999; McLellan et al.,
2001).
When changes with both age and accommodation are considered, it is evident from
Figures 6,
7, and
10 that the age of the subject has a significant effect on the magnitude and direction of change in spherical aberration with accommodation. In most younger subjects, the spherical aberration tends to change from an initially positive value for a zero stimulus to become more negative with accommodation. This finding is in agreement with several previous studies that also show such a shift in spherical aberration with accommodation (H. Cheng et al.,
2004; He et al.,
2000; Ivanoff,
1952,
1956; Jenkins,
1963; Koomen et al.,
1949; Van den Brink,
1962). The rate of change in spherical aberration for our younger subjects (17–40 years) with natural pupils is about −0.05 D of equivalent defocus per diopter of accommodation response or about −0.05 D/mm
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.
In the older (early presbyopic and presbyopic) subjects, the positive spherical aberration shows minimal changes within the limited residual objective amplitude of accommodation and may even show a positive shift in some subjects over 45 years of age. Because the subjects over 45 years of age only accommodated by approximately 1.00 D or less, the regression between changes in aberrations and accommodative response was not significant in most of the older subjects.
Aberrations other than fourth-order spherical aberration, together with total higher order RMS wavefront aberration, when expressed in terms of equivalent defocus for the natural pupil, show no significant changes with accommodation in any age group (
Figures 8 and
9 and
Table 4).
As noted earlier, the need to use a small 2.5-mm pupil, imposed by the small accommodated pupils of some subjects, for the fixed pupil analysis of aberrations made it difficult to demonstrate any strong effects of either age or accommodation under this condition. It has long been known that with such small pupils, the eye is almost diffraction limited (e.g., Berny & Slasky,
1969), so that monochromatic aberrations can only play a very minor role. The observed total higher order RMS aberration for most subjects and conditions was only around 0.05 μm (
Figure 11), corresponding to an equivalent defocus of about 0.20 D, which would be expected to have little effect on retinal image quality with such a pupil diameter. The RMS wavefront error of about 1/10th of a wavelength for the center of the visible spectrum is very close to the value of the Maréchal criterion (1/14th of a wavelength) defining a system whose optical performance is essentially diffraction limited.
How do the present data relate to our knowledge of the optical characteristics of the aging eye? Considering first the case of eyes with relaxed accommodation, it is generally accepted that, in most young eyes, the individual aberrations of the cornea and lens are each larger than those for the complete eye, implying that the cornea and lens have aberrations of opposite signs (e.g., Artal & Guirao,
1998; Artal, Guirao, Berrio, & Williams,
2001; el-Hage & Berny,
1973; Kelly, Mihashi, & Howland,
2004; Tomlinson, Hemenger, & Garriott,
1993). In the case of spherical aberration, for example, the cornea tends to have a positive aberration coefficient, whereas the lens has a negative aberration, leaving a low positive value for the whole eye. As the eye ages and the lens form changes, this compensation breaks down. If corneal spherical aberrations remain approximately constant with age (Guirao, Redondo, & Artal,
2000; Oshika, Klyce, Applegate, & Howland,
1999), our observation of a change with age in total ocular spherical aberration toward more positive values implies that the lenticular aberration must be shifting in the same direction when under conditions of relaxed accommodation (see also Artal et al.,
2001). With aging, several changes occur in the lens due to the addition of new fibers and other factors:
-
The axial thickness increases (e.g., Dubbelman et al.,
2001,
2003; Koretz et al.,
1997).
-
The surface curvatures increase (e.g., Koretz, Cook, & Kaufman,
2001).
-
The axial gradient of refractive index becomes flatter across the central region of the lens and steeper toward the lens surfaces (Jones et al.,
2005; Smith & Pierscionek,
1998), so that the lens behaves more like a body with uniform index.
Thus, it is reasonable to speculate in qualitative terms that, in the young relaxed lens, the positive spherical aberration conferred by its biconvex shape and flatter anterior surface is largely, but not entirely, compensated for by the negative aberration associated with the extended index gradient through the lens volume, with the highest index at the lens center. Because, with aging, the refractive index becomes more constant through most of the lens volume, the compensating effect of the index gradient becomes weaker, and the overall older lens shows more positive spherical aberration. When accommodation occurs, the curvatures of the lens surfaces (particularly that of the anterior surface; e.g., Rosales, Dubbelman, Marcos, & Van der Heijde,
2006) increase. These changes would tend to increase the positive spherical aberration. However, in the young eye, the initially quasi-ellipsoidal iso-index surfaces within the accommodated lenses become more spheroidal, so that the internal refractive index gradients overcompensate for the positive spherical aberration introduced by the surfaces, resulting in an overall change toward negative (overcorrected) spherical aberration in the young accommodated eye. In contrast, the limited extent of the index gradients in the older lens means that it acts more like a lens with homogenous refractive index, so that its initially positive spherical aberration tends to remain constant or even to increase with accommodation. These suggested changes appear to be compatible with the in vitro experimental studies of Glasser and Campbell (
1998).
Because the fourth-order spherical aberration interacts with defocus in determining the image quality of the eye, the stability or increase in spherical aberration with accommodation in the older age group might be advantageous in increasing the depth of focus and allowing the individual to detect a near target despite the presence of a large accommodative lag. In contrast, in the younger groups, the spherical aberration passes through zero at between 0.5 and 2.5 D of accommodation, close to the typical tonic level of accommodation at which accommodative leads and lags are minimal, thus helping to maintain optimal image quality under these conditions.
Although the levels of aberration are generally small, the systematic change in the way spherical aberration is altered with accommodation in different age groups should influence the strategy that should be used for correcting higher order aberrations, especially with refractive surgery. Artal, Fernandez, and Manzanera (
2002) suggest that due to the dynamic nature of ocular optics, a static perfect correction of ocular aberrations performed in customized refractive surgery would not remain perfect for every condition occurring during normal accommodation. H. Cheng et al. (
2004) suggested that, at moderate levels of accommodation (1–3 D), correcting spherical aberration will have no significant effect, but at high accommodative levels, it is advantageous to leave the spherical aberration uncorrected. Our data support their view, as the changes in spherical aberration with accommodation vary greatly with age.