Describing ocular aberrations with wavefront vergence maps

A common optometric problem is to specify the eye’s ocular aberrations in terms of Zernike coefficients and to reduce that specification to a prescription for the optimum sphero-cylindrical correcting lens. The typical approach is first to reconstruct wavefront phase errors from measurements of wavefront slopes obtained by a wavefront aberrometer. This paper applies a new method to this clinical problem that does not require wavefront reconstruction. Instead, we base our analysis of axial wavefront vergence as inferred directly from wavefront slopes. The result is a wavefront vergence map that is similar to the axial power maps in corneal topography and hence has a potential to be favoured by clinicians. We use our new set of orthogonal Zernike slope polynomials to systematically analyse details of the vergence map analogous to Zernike analysis of wavefront maps. The result is a vector of slope coefficients that describe fundamental aberration components. Three different methods for reducing slope coefficients to a spherocylindrical prescription in power vector forms are compared and contrasted. When the original wavefront contains only second order aberrations, the vergence map is a function of meridian only and the power vectors from all three methods are identical. The differences in the methods begin to appear as we include higher order aberrations, in which case the wavefront vergence map is more complicated. Finally, we discuss the advantages and limitations of vergence map representation of ocular aberrations.

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 higher-order 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.

Influence of spherical intraocular lens implantation and conventional laser in situ keratomileusis on peripheral ocular aberrations

Aim: To measure the influence of spherical intraocular lens implantation and conventional myopic laser in situ keratomileusis on peripheral ocular aberrations. Setting: Visual & Ophthalmic Optics Laboratory, School of Optometry & Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, Australia. Methods: Peripheral aberrations were measured using a modified commercial Hartmann-Shack aberrometer across 42° x 32° of the central visual field in 6 subjects after spherical intraocular lens (IOL) implantation and in 6 subjects after conventional laser in situ keratomileusis (LASIK) for myopia. The results were compared with those of age matched emmetropic and myopic control groups. Results: The IOL group showed a greater rate of quadratic change of spherical equivalent refraction across the visual field, higher spherical aberration, and greater rates of change of higher-order root-mean-square aberrations and total root-mean-square aberrations across the visual field than its emmetropic control group. However, coma trends were similar for the two groups. The LASIK group had a greater rate of quadratic change of spherical equivalent refraction across the visual field, higher spherical aberration, the opposite trend in coma across the field, and greater higher-order root-mean-square aberrations and total root-mean-square aberrations than its myopic control group. Conclusion: Spherical IOL implantation and conventional myopia LASIK increase ocular peripheral aberrations. They cause considerable increase in spherical aberration across the visual field. LASIK reverses the sign of the rate of change in coma across the field relative to that of the other groups. Keywords: refractive surgery, LASIK, IOL implantation, aberrations, peripheral aberrations

Peripheral ocular aberrations in mild and moderate keratoconus

Purpose: To investigate the influence of keratoconus on peripheral ocular aberrations. Methods: Aberrations of 7 mild and 5 moderate keratoconics were determined over a 42°horizontal x 32° vertical visual field with a modified COAS-HD aberrometer. Control data were obtained from an emmetropic group. Results: Most aberrations in keratoconics showed field dependence predominately along the vertical meridian. Mean spherical equivalent M, oblique astigmatism J45 and regular astigmatism J180 refraction components and total root mean square aberrations (excluding defocus) had high magnitudes in the inferior visual field. The rates of change of aberrations were higher in moderate than in mild keratoconics. Coma was the dominant peripheral higher-order aberration in both emmetropes and keratoconics; for the latter it had high magnitudes in the centre and periphery of the visual field. Conclusion: Greater rates of change of aberrations across the visual field occurred for the keratoconic groups than for the emmetropic control group. Moderate keratoconics had more rapid changes in, and higher magnitudes of aberrations across the visual field than mild keratoconics. The dominant higher-order aberration for the keratoconics across the visual field was vertical coma.

Myopia and peripheral ocular aberrations

We measured wave aberrations over the central 42° x 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 were almost constant across the measured field and were more positive in emmetropes (+0.023 ± 0.043 microns) than in myopes (-0.007 ± 0.045 microns). 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.

Effect of accommodation on peripheral ocular aberrations

Changes in peripheral aberrations, particularly higher-order aberrations, as a function of accommodation have received little attention. Wavefront aberrations were measured for the right eyes of 9 young adult emmetropes at 38 field positions in the central 42 x 32 degrees of the visual field. Subjects accommodated monocularly to targets at vergences of either 0.3 or 4.0 D. Wavefront data for a 5 mm diameter pupil were analyzed either in terms of the vector components of refraction or Zernike coefficients and total RMS wavefront aberrations. Relative peripheral refractive error (RPRE) was myopic at both accommodation demands and showed only a slight, not statistically significant, hypermetropic shift in the vertical meridian with the higher accommodation demand. There was little change in the astigmatic components of refraction or the higher-order Zernike coefficients, apart from fourth-order spherical aberration which became more negative (by 0.10 µm) at all field locations. Although it has been suggested that nearwork and the state of peripheral refraction may play some role in myopia development, for most of our adult emmetropes any changes with accommodation in RPRE and aberration were small. Hence it seems unlikely that such changes can be of importance to late-onset myopisation.

Ocular aberrations in the peripheral visual field

We modified a commercial Hartmann-Shack aberrometer and used it to measure ocular aberrations across the central 42º horizontal x 32º vertical visual fields of five young emmetropic subjects. Some Zernike aberration coefficients show coefficient field distributions that were similar to the field dependence predicted by Seidel theory (astigmatism, oblique astigmatism, horizontal coma, vertical coma), but defocus did not demonstrate such similarity.

Effect of age on components of peripheral ocular aberrations

Purpose: To investigate the effect of age on the contributions of the anterior cornea and internal components to ocular aberrations in the peripheral visual field. Methods: Ocular aberrations were measured in 10 young emmetropes and 7 older emmetropes using a modified commercial Hartmann-Shack aberrometer across 42° x 32° of central visual field. Anterior corneal aberrations were estimated from anterior corneal topography using theoretical ray-tracing. Internal aberrations were calculated by subtracting anterior corneal aberrations from ocular aberrations. Results: Anterior corneal aberrations of young subjects were reasonably compensated by the internal aberrations, except for astigmatism for which the internal contribution was small out to the 21° field limit. The internal coma and spherical aberration of the older subjects were considerably smaller in magnitude than those of the young subjects such that the compensation for anterior corneal aberrations was poorer. This can be explained by age-related changes in the lens shape and refractive index distribution. Conclusion: oss of balance between anterior cornea and internal components of higher order aberrations with increasing age, found previously for on-axis vision, applies also to the peripheral visual field.

Through-focus performance with multifocal contact lenses : effect of binocularity, pupil diameter and inherent ocular aberrations

Purpose to evaluate the effects of the wearer’s pupil size and spherical aberration on visual performance with centre-near, aspheric multifocal contact lenses (MFCLs). The advantage of binocular over monocular vision was also investigated. Methods Twelve young volunteers, with an average age of 27±5 years, participated in the study. LogMAR Visual Acuity (VA) was measured under cycloplegia for a range of defocus levels (from +3.0 to -3.0D, in 0.5D steps) with no correction and with three aspheric MFCLs (Air Optix Aqua Multifocal, Ciba Vision, Duluth, GA, US) with a centre-near design, providing correction for “Low”, “Med” and “High” near demands. Measurements were performed for all combinations of the following conditions: i) artificial pupils of 6mm and 3mm diameter, ii) binocular and monocular (dominant eye) vision. Depth-of-focus (DOF) was calculated from the VA vs. defocus curves. Ocular aberrations under cycloplegia were measured using iTrace. Results VA at -3.0D defocus (simulating near performance) was statistically higher for the 3mm than for the 6mm pupil (p=0.006), and for binocular rather than for monocular vision (p<0.001). Similarly, DOF was better for the 3mm pupil (p=0.002) and for binocular viewing conditions (p<0.001, ANOVA). Both VA at –3.0D defocus and DOF increased as the “addition” of the MFCL correction increased. Finally, with the centre-near MFCLs a linear correlation was found between VA at –3.0D defocus and the wearer’s ocular spherical aberration (R2=0.20 p<0.001 for 6mm data), with the eyes exhibiting the higher positive spherical aberration experiencing lower VAs. By contrast, no correlation was found between VA and spherical aberration at 0.00D defocus (distance vision). Conclusions Both near VA and depth-of-focus improve with these MFCLs, with the effects being more pronounced for small pupils and binocular than for monocular vision. Coupling of the wearer’s ocular spherical aberration with the aberration profiles provided by MFCLs affects their functionality.

Diurnal variations in ocular aberrations of human eyes

Purpose: To investigate the diurnal variations in ocular wavefront aberrations over two consecutive days in young adult subjects. Materials and methods: Measurements of both lower-order (sphero-cylindrical refractive powers) and higher-order (3rd and 4th order aberration terms) ocular aberrations were collected for 30 young adult subjects at ten different times over two consecutive days using a Hartmann-Shack aberrometer. Fifteen subjects were myopic and 15 were emmetropic. Five sets of measurements were collected each day at approximately 3 hourly intervals, with the first measurement taken at ~9 am and the final measurement at ~9 pm. Results: Spherical equivalent refraction (p = 0.029) and spherical aberration (p = 0.043) were both found to undergo significant diurnal variation over the two measurement days. The spherical equivalent was typically found to be at a maximum (i.e. most hyperopic) at the morning measurement, with a small myopic shift of 0.37 ± 0.15 D observed over the course of the day. The mean spherical aberration of all subjects (0.038 ± 0.048 μm) was found to be positive during the day and gradually became more negative into the evening, with a mean amplitude of change of 0.036 ± 0.02 μm. None of the other considered sphero-cylindrical refractive power components or higher-order aberrations exhibited significant diurnal variation over the two days of the experiment (p>0.05). Except for the lower-order astigmatism at 90/180 deg (p = 0.040), there were no significant differences between myopes and emmetropes in the magnitude and timing of the observed diurnal variations (p>0.05). Conclusions: Significant diurnal variations in spherical equivalent and spherical aberration were consistently observed over two consecutive days of measurement. Research and clinical applications requiring precise refractive error and wavefront measurements should take these diurnal changes into account when interpreting wavefront data.

Effects of pupil center shift on ocular aberrations

Purpose: To investigate effects of pupil shifts, occurring with changes in luminance and accommodation stimuli, on refraction components and higher-order aberrations. Method: Participants were young and older groups (n=20, 22±2 years, age range 18–25 years; n=19, 49±4 years, 45–58 years). Aberrations/refractions at 4 mm and 3 mm diameters were compared between centered and decentered pupils for low (background 0.01cd/m², 0D), and high (6100cd/m², 4D or 6D) stimuli. Decentration was the difference between pupil centers for low and high stimuli. Clinical important changes with decentration were: M ±0.50D or ±0.25D, J180 and J45 ±0.25D or ±0.125D, HORMS ±0.05m, C(3, 1) ±0.05m, C(4, 0) ±0.05m. Results: Because of small pupil shifts in most participants (mean 0.26mm), there were few important changes in most refraction components and higher-order aberration terms. However, M changed by >0.25 D for a third of participants with 4mm pupils. When determining refractions from 2nd-6th order aberration coefficients, the more stringent criteria gave 76/ 534 (14%) possible important changes. Some participants had large pupil shifts with considerable aberration changes. Comparisons at the high stimulus were possible for only 11 participants because of small pupils. When refractions were determined from 2nd order aberration coefficients only, there were only 35 (7%) important changes for the more stringent criteria. Conclusion: Usually pupil shifts with changes in stimulus conditions have little influence on aberrations, but they can with high shifts. The number of aberrations orders that are considered as contributing to refraction influences the proportion of cases that might be considered clinically important.