Effects of age on peripheral ocular aberrations

On-axis monochromatic higher-order aberrations increase with age. Few studies have been made of peripheral refraction along the horizontal meridian of older eyes, and none of their off-axis higherorder aberrations. We measured wave aberrations over the central 42°x32° visual field for a 5mm pupil in 10 young and 7 older emmetropes. Patterns of peripheral refraction were similar in the two groups. Coma increased linearly with field angle at a significantly higher rate in older than in young emmetropes (−0.018±0.007 versus −0.006±0.002 μm/deg). Spherical aberration was almost constant over the measured field in both age groups and mean values across the field were significantly higher in older than in young emmetropes (+0.08±0.05 versus +0.02±0.04 μm). Total root-mean-square and higher-order aberrations increased more rapidly with field angle in the older emmetropes. However, the limits to monochromatic peripheral retinal image quality are largely determined by the second-order aberrations, which do not change markedly with age, and under normal conditions the relative importance of the increased higher-order aberrations in older eyes is lessened by the reduction in pupil diameter with age. Therefore it is unlikely that peripheral visual performance deficits observed in normal older individuals are primarily attributable to the increased impact of higher-order aberration. 0 4 C ©2010 Optical Society of America OCIS codes: Visual optics, accommodation (330.7322); Visual optics, aging changes (330.7323). References and links 1. C. Owsley, R. Sekuler, and D. Siemsen, "Contrast sensitivity throughout adulthood," Vision Res 23, 689-699 (1983). 2. D. B. Elliott, "Contrast sensitivity decline with ageing: a neural or optical phenomenon?," Ophthalmic Physiol Opt 7, 415-419 (1987). 3. D. Elliott, D. Whitaker, and D. MacVeigh, "Neural contribution to spatiotemporal contrast sensitivity decline in healthy ageing eyes," Vision Res 30, 541-547 (1990). 4. D. B. Elliott, K. C. Yang, and D. Whitaker, "Visual acuity changes throughout adulthood in normal, healthy eyes: seeing beyond 6/6," Optom Vis Sci 72, 186-191 (1995). 5. D. G. Pitts, "The effects of aging on selected visual functions: dark adaptation, visual acuity, stereopsis and brightness contrast.," in Aging and Human Visual Function, R. Sekuler, D. Kline, and K. Dismukes, eds. (A.R. Liss, New York, 1982), pp. 131-159. 6. P. Artal, M. Ferro, I. Miranda, and R. Navarro, "Effects of aging in retinal image quality," J Opt Soc Am A 10, 1656-1662 (1993). 7. T. Kuroda, T. Fujikado, S. Ninomiya, N. Maeda, Y. Hirohara, and T. Mihashi, "Effect of aging on ocular light scatter and higher order aberrations," J Refract Surg 18, S598-S602 (2002). 8. T. Oshika, S. D. Klyce, R. A. Applegate, and H. C. Howland, "Changes in corneal wavefront aberrations with aging," Invest Ophthalmol Vis Sci 40, 1351-1355 (1999). 9. R. I. Calver, M. J. Cox, and D. B. Elliott, "Effect of aging on the monochromatic aberrations of the human eye," J Opt Soc Am A 16, 2069-2078 (1999). 10. S. Marcos, "Are changes in ocular aberrations with age a significant problem for refractive surgery?," J Refract Surg 18, S572-S578 (2002). 11. J. S. McLellan, S. Marcos, and S. A. Burns, "Age-related changes in monochromatic wave aberrations of the human eye," Invest Ophthalmol Vis Sci 42, 1390-1395 (2001). 12. R. A. Applegate, W. J. Donnelly III, J. D. Marsack, D. E. Koenig, and K. Pesudovs, "Threedimensional relationship between high-order root-mean-square wavefront error, pupil diameter, and aging," J Opt Soc Am A 24, 578-587 (2007). 13. D. A. Atchison, and E. L. Markwell, "Aberrations of emmetropic subjects at different ages," Vision Res 48, 2224-2231 (2008). 14. S. Plainis, and I. G. Pallikaris, "Ocular monochromatic aberration statistics in a large emmetropic population," J Mod Opt 55, 759 772 (2008). 15. P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J Opt Soc Am A 19, 137-143 (2002). 16. G. Westheimer, and J. Liang, "Influence of ocular light scatter on the eye's optical performance," J Opt Soc Am A 12, 1417-1424 (1995). 17. J. K. IJspeert, P. W. de Waard, T. J. van den Berg, and P. T. de Jong, "The intraocular straylight function in 129 healthy volunteers; dependence on angle, age and pigmentation," Vision Res 30, 699707 (1990). 18. S. L. Elliott, S. S. Choi, N. Doble, J. L. Hardy, J. W. Evans, and J. S. Werner, "Role of high-order aberrations in senescent changes in spatial vision," J Vis 9, 1-16 (2009). 19. F. J. Slataper, "Age norms of refraction and vision," Arch Ophthal 43, 466-481 (1950). 20. H. Saunders, "Age-dependence of human refractive errors," Ophthalmic Physiol Opt 1, 159-174 (1981). 21. H. Saunders, "A longitudinal study of the age-dependence of human ocular refraction-I. Agedependent changes in the equivalent sphere," Ophthalmic Physiol Opt 6, 39-46 (1986). 22. H. C. Fledelius, and M. Stubgaard, "Changes in refraction and corneal curvature during growth and adult life. A cross-sectional study," Acta Ophthalmol. 64, 487-491 (1986). 23. F. A. Young, and G. A. Leary, "Chapter 2. Refractive error in relation to the development of the eye," in Vision and Visual Dysfunction (Macmillan, Basingstoke, 1991), pp. 29-44. 24. J. M. Wood, "Age and visual impairment decrease driving performance as measured on a closed-road circuit," Hum Factors 44, 482-494 (2002). 25. J. M. Wood, and M. A. Bullimore, "Changes in the lower displacement limit for motion with age," Ophthalmic Physiol Opt 15, 31-36 (1995). 26. K. Ball, C. Owsley, M. E. Sloane, D. L. Roenker, and J. R. Bruni, "Visual attention problems as a predictor of vehicle crashes in older drivers," Invest Ophthalmol Vis Sci 34, 3110-3123 (1993). 27. D. W. Kline, T. J. B. Kline, J. L. Fozard, W. Kosnik, F. Schieber, and R. Sekuler, "Vision, aging, and driving: The problems of older drivers," J Gerontol 47, P27-34 (1992). 28. R. Weale, A biography of the eye: development, growth, age (H K Lewis, London, 1982). 29. F. N. Low, "Studies on peripheral visual acuity," Science 97, 586-587 (1943). 30. F. Rempt, J. Hoogerheide, and W. P. Hoogenboom, "Influence of correction of peripheral refractive errors on peripheral static vision.," Int J Ophthalmol 173, 128-135 (1976). 31. M. Millodot, C. A. Johnson, A. Lamont, and H. W. Leibowitz, "Effect of dioptrics on peripheral visual acuity," Vision Res 15, 1357-1362 (1975). 32. R. S. Anderson, "The selective effect of optical defocus on detection and resolution acuity in peripheral vision," Curr Eye Res 15, 351-353 (1996). 33. Y. Z. Wang, L. N. Thibos, and A. Bradley, "Effects of refractive error on detection acuity and resolution acuity in peripheral vision," Invest Ophthalmol Vis Sci 38, 2134-2143 (1997). 34. L. Lundström, J. Gustafsson, and P. Unsbo, "Vision evaluation of eccentric refractive correction," Optom Vis Sci 84, 1046-1052 (2007). 35. L. Lundström, S. Manzanera, P. M. Prieto, D. B. Ayala, N. Gorceix, J. Gustafsson, P. Unsbo, and P. Artal, "Effect of optical correction and remaining aberrations on peripheral resolution acuity in the human eye," Opt Express 15, 12654-12661 (2007). 36. L. Ronchi, "Absolute threshold before and after correction of oblique-ray astigmatism.," J Opt Soc Am 61, 1705-1709 (1971). 37. F. Fankhauser, and J. M. Enoch, "The effects of blur upon perimetric thresholds. A method for determining a quantitative estimate of retinal contour.," Arch Ophthalmol 68, 240-251 (1962). 38. H. W. Leibowitz, C. A. Johnson, and E. Isabelle, "Peripheral motion detection and refractive error," Science 177, 1207-1208 (1972). 39. J. A. Jennings, and W. N. Charman, "Off-axis image quality in the human eye," Vision Res 21, 445455 (1981). 40. P. Artal, A. M. Derrington, and E. Colombo, "Refraction, aliasing, and the absence of motion reversals in peripheral vision," Vision Res 35, 939-947 (1995). 41. R. S. Anderson, D. R. McDowell, and F. A. Ennis, "Effect of localized defocus on detection thresholds for different sized targets in the fovea and periphery," Acta Ophthalmol Scand 79, 60-63 (2001). 42. M. Millodot, "Peripheral refraction in aphakic eyes," Am J Optom Physiol Opt 61, 586-589 (1984). 43. C. T. Scialfa, H. W. Leibowitz, and K. W. Gish, "Age differences in peripheral refractive error," Psychol Aging 4, 372-375 (1989). 44. D. A. Atchison, N. Pritchard, S. D. White, and A. M. Griffiths, "Influence of age on peripheral refraction," Vision Res 45, 715-720 (2005). 45. W. N. Charman, and J. A. Jennings, "Longitudinal changes in peripheral refraction with age," Ophthalmic Physiol Opt 26, 447-455 (2006). 46. A. Mathur, D. A. Atchison, and W. N. Charman, "Myopia and peripheral ocular aberrations," J Vis 9, 1-12 (2009). 47. A. Mathur, D. A. Atchison, and D. H. Scott, "Ocular aberrations in the peripheral visual field," Opt Lett 33, 863-865 (2008). 48. ANSI, "American National Standards Institute. American National Standard for Ophthalmics Methods for reporting optical aberrations of the eye," ANSI Z80.28-2004 (2004). 49. ISO, "International Organization for Standardization. Ophthalmic optics and instruments -Reporting aberrations of the human eye," ISO 24157:2008 (2008). 50. D. A. Atchison, D. H. Scott, and W. N. Charman, "Measuring ocular aberrations in the peripheral visual field using Hartmann-Shack aberrometry," J Opt Soc Am A 24, 2963-2973 (2007). 51. D. A. Atchison, D. H. Scott, and W. N. Charman, "Measuring ocular aberrations in the peripheral visual field using Hartmann-Shack aberrometry: errata," J Opt Soc Am A 25, 2467 (2008). 52. W. N. Charman, and D. A. Atchison, "Decentred optical axes and aberrations along principal visual field meridians," Vision Res 49, 1869-1876 (2009). 53. P. A. Howarth, X. X. Zhang, A. Bradley, D. L. Still, and L. N. Thibos, "Does the chromatic aberration of the eye vary with age?," J Opt Soc Am A 5, 2087-2092 (1988). 54. A. Morrell, H. D. Whitefoot, and W. N. Charman, "Ocular chromatic ab

Less widely studied has been the influence of age on visual and optical performance in the peripheral visual field.This is unfortunate, since many visual tasks, including safe locomotion and driving, depend on efficient peripheral vision.While a number of neural factors may contribute to the reduced ability of older individuals to perform tasks involving peripheral vision (e.g.[24][25][26][27][28]), it is reasonable to postulate that the quality of the image on the peripheral retina might have a significant influence.Studies in which the state of focus is varied in the peripheral retina show that, for normal subjects, changes in spherical focus have little effect on resolution tasks for peripheral angles in the range 10-60 deg [29][30][31][32][33][34][35], although they may in patients with central field defects [34].In contrast, various studies show that detection of pattern, movement, and flicker may be markedly affected by changes in focus of as little as 0.5 D, even at eccentricities of 20-30 degrees (e.g.[33,[36][37][38][39][40][41]).Thus in many real-world visual tasks, peripheral image quality is likely to be of some importance; it is possible that aberrations other than defocus may be of significance here.
The age variation in refractive error across the horizontal visual field has been measured.Although early work showed marked (and conflicting) age differences [42,43], more recent transverse population studies suggest that the changes are small in people with similar refraction ranges [13,44], although there appears to be a systematic change in the nasal/temporal asymmetry, with this reducing in the case of astigmatism at a rate of 1.1° /decade [13].Longitudinal measurements on a handful of eyes suggest that the slow change in mean sphere with age that occurs on axis also occurs across the field [45].No studies have been carried out to compare peripheral higher-order aberrations in older and younger individuals.We have therefore measured refraction and wavefront aberrations across the central fields of groups of young and older emmetropes.

Methods
The study was approved by Queensland University of Technology human ethics committee and complied with tenets of Declaration of Helsinki.Informed consent was obtained from each subject after verbal and written explanation of the risks involved.
Seventeen emmetropic volunteers were recruited and were segregated into 2 groups based on their age.Group 1 contained 10 young emmetropes (mean and standard deviation of spherical equivalent: +0.11 D ± 0.50 D; mean age: 25 ± 3 years; age range: 20-30 years), and group 2 contained 7 older presbyopic emmetropes (mean and standard deviation of spherical equivalent: +0.09D ± 0.60 D; mean age: 63 ± 6 years; age range: 50-71 years).Subject numbers were limited by the constraints of measurement time (2 hours/subject) and analysis time (8 hours/subject).Subjects were screened for any ocular pathology.All the subjects had visual acuity better than 6/6 and < 0.75 D of astigmatism.Right eyes were assessed, while left eyes were occluded during measurement.The same young emmetropes were also used in a study comparing their aberrations to those of young myopes [46].
Wavefront aberration was assessed across the central 42 x 32 degrees of visual field using a COAS-HD Hartmann-Shack aberrometer (Wavefront Sciences Inc., Albuquerque, USA), (see [47], for details).Measuring wavelength was 840 nm, and results were converted to correspond to a wavelength of 555 nm.Fixation was moved successively between each of a matrix of 38 targets produced on a projection screen at 1.2 m from the eye.No mydriatics or cycloplegics were used and the lighting conditions were such that during the measurements the minor diameters of the off-axis elliptical pupils always exceeded 5 mm, as estimated by COAS-HD (some potential subjects whose pupils did not satisfy this condition could not be used in the study).Two recordings were made at each field location and the wavefront data were analyzed to give Zernike coefficients in standard format [48,49] for a 5 mm pupil and the vector components of refraction using Zernike coefficients up to the 6 th order [50,51].The wave aberration coefficients of two sets of measurements were averaged.Typically the higher-order root-mean-squared (HORMS) difference between the two measurements at any point was < 0.03 µm.
Since the fixation targets were at 1.2 m, the younger subjects were accommodating slightly (accommodative demand 0.83 D).The accommodative response was taken as the difference between the axial mean sphere M measured with the internal target and fogging system of the COAS instrument, and the overall mean sphere for the 2 fixation points closest to the visual axis along the vertical field meridian.The mean response was 0.44 ± 0.49 D. The effect of this accommodation on aberrations is likely to be negligible [46].None of the older emmetropes had measurable accommodation (mean response −0.02 ± 0.20 D).
Corneal topography for each subject was measured using a Medmont E300 corneal topographer (Medmont International Pvt.Limited, Australia).The pupil center was used as the reference point.Anterior corneal vertex radius of curvature R and asphericity Q were estimated from corneal height data across 36 meridians for a 6 mm corneal diameter, using least-squares fitting and the equation where the Z axis is the line of sight.The mean estimates from 4 topographic images were used for further analysis.

Results
The refraction components and 3 rd to 4 th order Zernike aberration coefficients were analyzed by repeated measures analyses of variance for the between-group factor of age and the within-group factor of field position (38 positions).Table 1 shows the results.The refraction components are oblique astigmatism J 45 , relative peripheral refractive error (RPRE) which is the change in M relative to axial M, and with/against the rule astigmatism J 180 .Results for the higher-order root-mean-squared aberrations (HORMS) and the total root-mean-squared aberrations except for defocus (Total RMS, i.e.square root of HORMS and astigmatism) are also shown.Age had significant effects on J 180 , , , and .Field position had significant effects on all refraction components and on all coefficients except for Fig. 1 shows the mean refractive components: (a) J 45 , (b) RPRE and (c) J 180 for A) young emmetropes and B) older emmetropes.As found by Mathur et al. [47], the astigmatic components J 45 (Aa, Ba,) and J 180 (Ac, Bc) increased 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 tended to be oriented along the visual field meridian.For both groups, RPRE moved in the negative direction in the periphery, but this change was less pronounced for the older emmetropes than for the younger group (compare Ab, Bb).Note that for both age groups the variations in the refractive components tend to be more symmetrical about a field point approximately 5 degrees temporal rather than about the visual axis, presumably because the approximate optical axis does not coincide with the visual axis [52].Fig. 1C shows the differences between the mean results for the older and younger groups (i.e.B − A).The differences are modest.Those in the J 45 astigmatic components (Ca) appear to have a maximum linear variation along the inferio-nasal to superiotemporal direction (305°-125° meridian) at the rate of 0.013 D/degree and almost no variation along the perpendicular, inferio-temporal to superio-nasal (215°-35°) field meridian.Age did not significantly affect mean J 45 , but there was significant interaction between age and field position (Table 1).The differences in the J 180 component appear to have quasi-linear variation in the approximately vertical inferior to superior (285°-105° meridian) direction at the rate of 0.011 D/degree, with almost no change along the horizontal meridian.The differences in RPRE tended to be generally positive, amounting to around +0.25 D at field angles of about 20°.Fig. 2 shows the mean higher-order wavefront maps across the pupil at each visual field location for (A) young emmetropes and (B) older emmetropes.The combination of horizontal and vertical coma dominated across the visual field of both age groups.Coma increased in magnitude from the center to the periphery of the visual field and changed orientation with the visual field meridian.The increase in coma was most prominent in the older emmetropes, as is evident in the difference plots B − A (Fig. 2c).As for the astigmatism coefficients in Fig. 1, the maps are symmetrical about a field point approximately 5 degrees into the temporal visual field.
Fig. 3 shows some mean higher-order aberration coefficients, HORMS and Total RMS for the 2 groups across the visual field, and the differences between the groups.Other higher-order coefficients are not shown as they were small in magnitude.
Oblique trefoil was more positive in the superior field than in the inferior field (Aa, Ba).The vertical (Ab, Bb) and horizontal coma (Ac, Bc) coefficients were the higher-order coefficients showing the most prominent changes across the field: vertical coma increased linearly from the superior to the inferior visual field and horizontal coma C increased from the nasal to the temporal visual field, in both cases at faster rates for the older emmetropes.For both groups, spherical aberration (Ad, Bd) did not vary across the visual field.Mean spherical aberration was slightly positive (0.02 µm) in the young emmetropic group and more positive in the older emmetropes (0.08 µm) (Cd).HORMS (Ae, Be) and Total RMS (Af, Bf) showed approximately quadratic rates of change across the field with the minimum approximately at the center of the field: rates of change with field angle were higher for the older emmetropes (Ce, Cf).As shown in Fig. 3C, among the mean higher-order aberration coefficients, coma and spherical aberration differed most between the groups.Fig. 4 shows individual vertical coma coefficients and horizontal coma coefficients along the vertical and horizontal visual field meridians, respectively, for the young and older emmetropes.The slopes for the coma coefficients (µm/degree) varied significantly between the groups (Table 2).Vertical and horizontal coma slopes were more than 3 times greater for older emmetropes than for young emmetropes (independent samples t-tests, p ≤ 0.005).Note again that coma values approximated to zero around the center of the field and that the

C
slopes along the horizontal and vertical field meridians were very similar, implying approximate symmetry of coma about the axis.The mean spherical aberration across the field was significantly higher for older emmetropes than for young emmetropes (Table 2, independent samples t-test, p < 0.001)., (e) higher-order root-mean-square aberration (HORMS) and (f) total root-mean-square aberration (Total RMS).The color scales represent the magnitude of aberration coefficient in micrometers (μm) and are the same for a given aberration and both groups.Pupil size is 5 mm.

C
The mean corneal shape data are shown in Table 3. Anterior corneal radii were similar but older emmetropes showed significantly greater negative asphericity than the young emmetropes (independent samples t-test, p < 0.02).

Discussion
As in earlier studies [13,44], these results indicate that the patterns of peripheral refraction do not undergo any major changes with age (Fig. 1).There were, however, substantially higher levels of some peripheral aberration coefficients and of total higherorder wave aberrations in the older subjects.Are these optical differences great enough to produce marked relative degradation in the visual performance of the old as compared to the young?When considering the overall effect on peripheral vision, it must be remembered that the retinal image will be degraded by both the second-order aberrations of defocus and astigmatism and the higher-order aberrations.For both age groups, the former normally tend to be more important over the measured field.However, the effect of the greater levels of higher-order aberration in older eyes may still be detectable.This is illustrated in Fig. 5 which shows theoretical monochromatic point-spread functions at several positions along the horizontal field meridian for eyes having levels of aberration corresponding to the mean values for the younger and older age groups.The pupil diameters are 5 mm in all cases and spherical defocus has been manipulated so that it is zero for the axial case.Although image quality falls with field angle in both age groups, the degrading effects of off-axis coma appear to be noticeably worse in the older eyes, except at −14° in the temporal visual field.Note that the images are asymmetrical about the axis, with images in the temporal field (positive angles) being noticeably worse than the corresponding images in the nasal field.Since average data has been used, images in individual eyes may be substantially worse than those of Fig. 5 due to the effects of those aberrations which are randomly distributed about a mean of zero.The additional effects of increased intraocular scatter in the older eyes will serve to increase these age differences in image quality at constant pupil diameter.Mean aberration coefficients for the groups have been used to derive PSFs.The Zernike defocus coefficient has been altered for each case so that it is zero at fixation for each age group.The color scales have been normalized for each point spread function and the numbers under the functions are the Strehl intensity ratios.As there were no actual horizontal positions, the functions were determined from the mean coefficients at 3.3° above and below the horizontal visual field meridian.The point spread functions were produced with simulations in the optical design package Zemax.
While this suggests that peripheral image quality is worse in the older eye, two effects tend to reduce any differences in normal life.Chromatic aberration, both longitudinal and transverse, causes additional blurring effects which are independent of age [53,54]: these tend to partially mask the effects of the monochromatic aberrations.Moreover, as noted by Calver et al. [9], under normal conditions the reduced pupil diameter of the older eye tends to restrict the effect of any increase in higher-order aberration, although it cannot reduce the effect of increased intra-ocular light scatter.Overall, it seems reasonable to suggest that, although peripheral image quality may be slightly worse, any marked reductions in visual performance for tasks in the peripheral visual field that are observed in older, visually-normal individuals are unlikely to be due to changes in optical imagery but are more likely to be neural in origin.
Considering now the results in more detail, the quasi-linear form of the variation in the differences in the astigmatism components across the visual field (Fig. 1Ca and Cc) is of interest.The components for each age group varied approximately parabolically with field angle but their centre of symmetry was not exactly on the visual axis.The difference between two parabolic variations which are shifted laterally with respect to one another was a linear variation.Thus, the difference data may suggest that the position of the best "optical axis", or centre of optical symmetry, shifts slightly with respect to the visual axis with age [13,52].
Why do aberration levels rise in the older eyes?Among the other age-dependent effects, the different rates of change in the third-order coma coefficients across the visual field, and the difference in fourth-order spherical aberration coefficients are particularly interesting.Are these related to changes in the corneal contour?Earlier investigations found no change in corneal asphericity with increase in age [55], but our older group had significantly more negative asphericity than the young group while their radii of curvature were similar (Table 3).The slope of coma across the horizontal and vertical meridians showed no obvious correlations with the individual corneal radii of curvature of either the young or older emmetropic subjects (Fig. 6a).However there was a positive correlation, which appeared to be common to both groups, between slope and asphericity, with higher negative asphericities being associated with more negative slopes (Fig. 6b).Since average asphericities were more negative in older subjects, this resulted in a negative correlation between slope and age (Fig. 6c).

C
An attempt was made to model the impact of a change in asphericity on the higherorder aberrations, using the Liou and Brennan [56] model eye.This has a gradient index lens and is intended to represent a 45 year old eye, although its lens surface parameters appear to be based on 40 year old parameters [57].Its corneal asphericity was modified to correspond to the values given in Table 3.The retina was given a −12 mm radius of curvature.Out-of-the-eye ray-tracing was performed with Zemax optical design software (Zemax Development Corporation, USA), tracing rays evenly across the 5 mm entrance pupil of the eye (exit pupil as viewed from the retina).Fig. 7 shows the results obtained.Note that, for a constant corneal radius, changing the anterior corneal asphericity Q from −0.08 to −0.16 increases the coma slope from −0.003 to about −0.006 µm/degree.The modeling thus accounts for only 25 % of the observed age-related increase in coma slope (from −0.006 to −0.018 µm/degree, see Table 1).The model predicts a weak parabolic increase in the spherical aberration coefficient with increasing field angle, with values decreasing for higher negative asphericity.These characteristics differ profoundly from the experimentally-observed spherical aberration, which shows little change across the visual fields of both subject groups and reaches a greater mean positive value in the older emmetropes who have the more negative cornea asphericity.
Thus while modeling in terms only of corneal shape change has a partial success in explaining the differences in coma across the field, it fails to explain the observed behavior of spherical aberration.This implies, not surprisingly, that additional lenticular and other factors must contribute to the aberrational differences between the groups.
We therefore turn to recent age-related schematic eyes incorporating gradient-index lenses to see if these better predict the age-related aberration changes that we have found.Goncharov and Dainty [58] designed model eyes with gradient index lenses for ages of 20, 30 and 40 years.There were linear rates of change of corneal radii of curvatures and asphericities, aqueous, lens and vitreous thicknesses, and lens radii of curvature.Smith et al. [57] determined a 60 year old variation of the Liou and Brennan [56] eye.Fig. 8 shows the coma and spherical aberration for the different schematic eyes as a function of visual field angle.For coma and a twenty-year age difference (Fig. 8a), the Goncharov and Dainty and Smith et al. models show age-related slope changes of −0.006 and −0.011 µm/degree, respectively.Since the mean ages of our old and young subjects differed by 38 years, if we make the simplifying assumption that that the slope changes are linear with age, for comparison purposes the slope changes of the earlier models should be multiplied by about two.The Goncharov and Dainty model then predicts our experimental change well (−0.012µm/degree for both), while the Smith et al. model prediction of −0.022 µm/degree is nearly twice our result.For spherical aberration (Fig. 8b), doubling the changes for the model eyes gives +0.10 and +0.22 µm changes for the Goncharov and Dainty and the Smith et al. eyes, respectively: these differences are 1.7 and 3.7 times higher, respectively, than the mean experimental result of +0.06 µm.
Visual field angle (degrees)

C
It can be seen that the aged-related Goncharov and Dainty schematic eye appears to do well at predicting changes in our experimental coma (−0.012 µm/degree for both).However, we argue that this is due largely to exaggerated changes in the cornea with age in their model, which account for half this change.Although some studies have reported, unlike the present study (Table 2), a reduction in anterior corneal radius of curvature with age, they give much smaller changes than the value of 0.18 mm used by Goncharov and Dainty over a 20 year period.Our own earlier study [55] on 101 adult emmetropic eyes across a range of ages did not find significant change in anterior radius of curvature with age (note as compared with the −0.08 change in asphericity here, they did not find a significant change in asphericity).This suggests that the age-related changes in the lens of the Goncharov-Dainty schematic eye are insufficient to account for the change in coma slopes.When its much smaller age-related changes in cornea are disregarded, the Smith et al. eye over-estimates slope changes with age by about 60%.Both the Goncharov and Dainty and Smith et al. model eyes predict much higher spherical aberration than our experimental results.When the likely exaggerated age-related effects of the cornea in the Goncharov and Dainty model are disregarded, this gives similar changes to the experimental data, but the Smith et al. estimate is still over three times greater than our finding even when taking corneal changes are taken into account.Overall, then, current eye models cannot fully reproduce the observed age changes in off-axis aberrations.
Visual field angle (degrees)

Conclusion
Like their axial counterparts, peripheral higher-order ocular aberrations, in particular coma and spherical aberration, increase with age.Coma increases linearly with field angle, at a more rapid rate in older emmetropic than in young emmetropic eyes.Spherical aberration varies little across the field and shows a positive shift with increasing age: currently-available eye models fail to predict these changes.In general, however, the magnitude of the higher-order wavefront errors involved is always small compared with that of second-order aberrations.The latter show only modest changes with age (see also [13,43]).Thus it appears unlikely that any age-related deficits in visual performance in the periphery are primarily attributable to reductions in the quality of the peripheral retinal image.

Acknowledgements
Neil Charman was supported by Australian Research Council International Linkage Fellowship LX0881907.

Fig. 1 .
Fig.1.Mean refractive components (a) oblique astigmatism J 45 , (b) spherical equivalent M relative to the axial value (i.e.relative peripheral refractive error, RPRE) (c) with/against the rule astigmatism J 180 in A) young emmetropes and B) older emmetropes across the visual field.(C) shows the differences B − A between the mean values in the two age groups (note that scales differ from those in A and B).The color scales represent the magnitude of each refractive component in diopters and are same for a given refractive component and for both groups.S, I, N and T represent superior, inferior, nasal and temporal visual fields.Pupil size 5 mm.

CFig. 2 .
Fig. 2. Higher order aberration elliptical wavefront maps at each visual field location for (a) young emmetropes (b) older emmetropes and (c) the difference (b)−(a).Third to sixth Zernike aberrations are included.The minor axis of the elliptical wavefront maps is cosine of visual field angle times the major axis.I, N, S and T represent inferior, nasal, superior and temporal visual fields.Axial pupil diameter 5 mm.

Fig. 3 .
Fig. 3. Individual higher-order aberration coefficients across the visual field for A) young emmetropes, B) older emmetropes and C) the difference between B and A. (a) trefoil coefficient , (b) vertical coma coefficient 3 3 C −

Fig. 4 . 3 −
Fig. 4. Vertical coma coefficient C 1 3 − and horizontal coma coefficient , respectively, along vertical and horizontal visual field meridians for young and older emmetropes.Different symbols represent different subjects.As there were no measurements along the horizontal visual field, horizontal coma for the horizontal visual field was obtained by averaging results at vertical field angles of ± 3.3°. 1 3

Fig. 5 .
Fig. 5. False-color representations of monochromatic point spread functions (PSFs) at different horizontal visual field angles for young emmetropes and older emmetropes.Mean aberration coefficients for the groups have been used to derive PSFs.The Zernike defocus coefficient has been altered for each case so that it is zero at fixation for each age group.The color scales have been normalized for each point spread function and the numbers under the functions are the Strehl intensity ratios.As there were no actual horizontal positions, the functions were determined from the mean coefficients at 3.3° above and below the horizontal visual field meridian.The point spread functions were produced with simulations in the optical design package Zemax.

Fig. 6 .
Fig. 6.Vertical coma coefficient 1 3 C − and horizontal coma coefficient slopes along the vertical and horizontal meridians, respectively, as a function of (a) anterior corneal radius of curvature, (b) corneal asphericity, and (c) age for the individual young and older emmetropes.1 3

Fig. 7 . 3 C
Fig. 7. Theoretical effects of changes in anterior corneal asphericity on (a) coma coefficient and (b) spherical aberration coefficient when the Liou-Brennan model eye is used.Plots derived from the fits to the experimental data for the young and older emmetropes are included; for coma, means of vertical fit for 1 3 C − and horizontal fit for .The observed mean asphericities were −0.08 for the young subjects and −0.18 for the older subjects.

Fig. 8 .
Fig. 8. Aberration coefficients according to some schematic eyes with ageing effects for (a) coma and (b) spherical aberration coefficient.Plots derived from the fits to the young emmetropes (25±3 years) and older emmetropes (63 ± 6 years) are included; for coma, means of vertical fit for

Table 1 .
The p values of repeated measures ANOVA for refraction components, Zernike aberration coefficients and root-mean-squared aberrations for the between-subjects variable of age group and within-subjects factor of field position.The defocus coefficient is relative to its central field value for each subject.Asterisks indicate significant effects.

Table 2 .
Mean values of the rate of change of coma with field angle and of spherical aberration across the visual field in the two age groups (coma slopes are averages for vertical and horizontal meridians).

Table 3 :
Means and SDs of the characteristics of the anterior corneas of the different age groups.