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.

Peripheral higher order aberrations in emmetropes and myopes

Purpose: Poor image quality in the peripheral field may lead to myopia. Most studies measuring the higher order aberrations in the periphery have been restricted to the horizontal visual field. The purpose of this study was to measure higher order monochromatic aberrations across the central 42º horizontal x 32º vertical visual fields in myopes and emmetropes. ---------- Methods: We recruited 5 young emmetropes with spherical equivalent refractions +0.17 ± 0.45D and 5 young myopes with spherical equivalent refractions -3.9 ± 2.09D. Measurements were taken with a modified COAS-HD Hartmann-Shack aberrometer (Wavefront Sciences Inc). Measurements were taken while the subjects looked at 38 points arranged in a 7 x 6 matrix (excluding four corner points) through a beam splitter held between the instrument and the eye. A combination of the instrument’s software and our own software was used to estimate OSA Zernike coefficients for 5mm pupil diameter at 555nm for each point. The software took into account the elliptical shape of the off-axis pupil. Nasal and superior fields were taken to have positive x and y signs, respectively. ---------- Results: The total higher order RMS (HORMS) was similar on-axis for emmetropes (0.16 ± 0.02 μm) and myopes (0.17 ± 0.02 μm). There was no common pattern for HORMS for emmetropes across the visual field where as 4 out of 5 myopes showed a linear increase in HORMS in all directions away from the minimum. For all subjects, vertical and horizontal comas showed linear changes across the visual field. The mean rate of change of vertical coma across the vertical meridian was significantly lower (p = 0.008) for emmetropes (-0.005 ± 0.002 μm/deg) than for myopes (-0.013 ± 0.004 μm/deg). The mean rate of change of horizontal coma across the horizontal meridian was lower (p = 0.07) for emmetropes (-0.006 ± 0.003 μm/deg) than myopes (-0.011 ± 0.004 μm/deg). ---------- Conclusion: We have found differences in patterns of higher order aberrations across the visual fields of emmetropes and myopes, with myopes showing the greater rates of change of horizontal and vertical coma.

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.

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.

Peripheral refraction patterns out to large field angles

Purpose To investigate hyperopic shifts and the oblique (or 45-degree/135-degree) component of astigmatism at large angles in the horizontal visual field using the Hartmann-Shack technique. Methods The adult participants consisted of 6 hypermetropes, 13 emmetropes and 11 myopes. Measurements were made with a modified COAS-HD Hartmann-Shack aberrometer across T60 degrees along the horizontal visual field in 5-degree steps. Eyes were dilated with 1% cyclopentolate. Peripheral refraction was estimated as mean spherical (or spherical equivalent) refraction, with/against the rule of astigmatism and oblique astigmatism components, and as horizontal and vertical refraction components based on 3-mm major diameter elliptical pupils. Results Thirty percent of eyes showed a pattern that was a combination of type IV and type I patterns of Rempt et al. (Rempt F, Hoogerheide J, Hoogenboom WP. Peripheral retinoscopy and the skiagram. Ophthalmologica 1971;162:1Y10), which shows the characteristics of type IV (relative hypermetropia along the vertical meridian and relative myopia along the horizontal meridian) out to an angle of between 40 and 50 degrees before behaving like type I (both meridians show relative hypermetropia). We classified this pattern as type IV/I. Seven of 13 emmetropes had this pattern. As a group, there was no significant variation of the oblique component of astigmatism with angle, but about one-half of the eyes showed significant positive slopes (more positive or less negative values in the nasal field than in the temporal field) and one-fourth showed significant negative slopes. Conclusions It is often considered that a pattern of relative peripheral hypermetropia predisposes to the development of myopia. In this context, the finding of a considerable portion of emmetropes with the IV/I pattern suggests that it is unlikely that refraction at visual field angles beyond 40 degrees from fixation contributes to myopia development.

Visual performance with lenses correcting peripheral refractive errors

Purpose To design and manufacture lenses to correct peripheral refraction along the horizontal meridian and to determine whether these resulted in noticeable improvements in visual performance. Method Subjective refraction of a low myope was determined on the basis of best peripheral detection acuity along the horizontal visual field out to ±30° for both horizontal and vertical gratings. Subjective refraction was compared to objective refractions using a COAS-HD aberrometer. Special lenses were made to correct peripheral refraction, based on designs optimized with and without smoothing across a 3 mm diameter square aperture. Grating detection was retested with these lenses. Contrast thresholds of 1.25’ spots were determined across the field for the conditions of best correction, on-axis correction, and the special lenses. Results The participant had high relative peripheral hyperopia, particularly in the temporal visual field (maximum 2.9 D). There were differences > 0.5D between subjective and objective refractions at a few field angles. On-axis correction reduced peripheral detection acuity and increased peripheral contrast threshold in the peripheral visual field, relative to the best correction, by up to 0.4 and 0.5 log units, respectively. The special lenses restored most of the peripheral vision, although not all at angles to ±10°, and with the lens optimized with aperture-smoothing possibly giving better vision than the lens optimized without aperture-smoothing at some angles. Conclusion It is possible to design and manufacture lenses to give near optimum peripheral visual performance to at least ±30° along one visual field meridian. The benefit of such lenses is likely to be manifest only if a subject has a considerable relative peripheral refraction, for example of the order of 2 D.

Influence of eye rotation on peripheral eye length measurement obtained with a partial coherence interferometry instrument

Purpose The eye rotation approach for measuring peripheral eye length leads to concern about whether the rotation influences results, such as through pressure exerted by eyelids or extra-ocular muscles. This study investigated whether this approach is valid. Methods Peripheral eye lengths were measured with a Lenstar LS 900 biometer for eye rotation and no-eye rotation conditions (head rotation for horizontal meridian and instrument rotation for vertical meridian). Measurements were made for 23 healthy young adults along the horizontal visual field (±30°) and, for a subset of eight participants along the vertical visual field (±25°). To investigate the influence of the duration of eye rotation, for six participants measurements were made at 0, 60, 120, 180 and 210 s after eye rotation to ±30° along horizontal and vertical visual fields. Results Peripheral eye lengths were not significantly different for the conditions along the vertical meridian (F1,7 = 0.16, p = 0.71). The peripheral eye lengths for the conditions were significantly different along the horizontal meridian (F1,22 = 4.85, p = 0.04), although not at individual positions (p ≥ 0.10) and were not important. There were no apparent differences between the emmetropic and myopic groups. There was no significant change in eye length at any position after maintaining position for 210 s. Conclusion Eye rotation and no-eye rotation conditions were similar for measuring peripheral eye lengths along horizontal and vertical visual field meridians at ±30° and ±25°, respectively. Either condition can be used to estimate retinal shape from peripheral eye lengths.

Visual field coordinates of pupillary circular axis and optical axis

Purpose: We term the visual field position from which the pupil appears most nearly circular as the pupillary circular axis (PCAx). The aim was to determine and compare the horizontal and vertical co-ordinates of the PCAx and optical axis from pupil shape and refraction information for only the horizontal meridian of the visual field. Method: The PCAx was determined from the changes with visual field angle in the ellipticity and orientation of pupil images out to ±90° from fixation along the horizontal meridian for the right eyes of 30 people. This axis was compared with the optical axis determined from the changes in the astigmatic components of the refractions for field angles out to ±35° in the same meridian. Results: The mean estimated horizontal and vertical field coordinates of the PCAx were (‒5.3±1.9°, ‒3.2±1.5°) compared with (‒4.8±5.1°, ‒1.5±3.4°) for the optical axis. The vertical co-ordinates of the two axes were just significantly different (p =0.03) but there was no significant correlation between them. Only the horizontal coordinate of the PCAx was significantly related to the refraction in the group. Conclusion: On average, the PCAx is displaced from the line-of-sight by about the same angle as the optical axis but there is more inter-subject variation in the position of the optical axis. When modelling the optical performance of the eye, it appears reasonable to assume that the pupil is circular when viewed along the line-of-sight.

Is retinal shape different in Asians and Caucasians? Estimation from peripheral refraction and peripheral eye length methods

Purpose:Race appears to be associated with myopiogenesis, with East Asians showing high myopia prevalence. Considering structural variations in the eye, it is possible that retinal shapes are different between races. The purpose of this study was to quantify and compare retinal shapes between racial groups using peripheral refraction (PR) and peripheral eye lengths (PEL). Methods:A Shin-Nippon SRW5000 autorefractor and a Haag-Streit Lenstar LS900 biometer measured PR and PEL, respectively, along horizontal (H) and vertical (V) fields out to ±35° in 5° steps in 29 Caucasian (CA), 16 South Asian (SA) and 23 East Asian (EA) young adults (spherical equivalent range +0.75D to –5.00D in all groups). Retinal vertex curvature Rv and asphericity Q were determined from two methods: a) PR (Dunne): The Gullstrand-Emsley eye was modified according to participant’s intraocular lengths and anterior cornea curvature. Ray-tracing was performed at each angle through the stop, altering cornea asphericity until peripheral astigmatism matched experimental measurements. Retinal curvature and hence retinal co-ordinate intersection with the chief ray were altered until sagittal refraction matched its measurement. b) PEL: Ray-tracing was performed at each angle through the anterior corneal centre of curvature of the Gullstrand-Emsley eye. Ignoring lens refraction, retinal co-ordinates relative to the fovea were determined from PEL and trigonometry. From sets of retinal co-ordinates, conic retinal shapes were fitted in terms of Rv and Q. Repeated-measures ANOVA were conducted on Rv and Q, and post hoc t-tests with Bonferroni correction were used to compare races. Results:In all racial groups both methods showed greater Rv for the horizontal than for the vertical meridian and greater Rv for myopes than emmetropes. Rv was greater in EA than in CA (P=0.02), with Rv for SA being intermediate and not significantly different from CA and EA. The PEL method provided larger Rv than the PR method: PEL: EA vs CA 87±13 vs 83±11 m-1 (H), 79±13 vs 72±14 m-1 (V); PR: EA vs CA 79±10 vs 67±10 m-1 (H), 71±17 vs 66±12 m-1 (V). Q did not vary significantly with race. Conclusions:Estimates of Rv, but not of Q, varied significantly with race. The greater Rv found in EA than in CA and the comparatively high prevalence rate of myopia in many Asian countries may be related.

Use of partial coherence interferometry in measuring retinal shape

This study concerned development and validation of a simple and inexpensive method involving partial coherence interferometry for measuring retinal shape, and its use in exploring association between retinal shape and myopia. Retinal shapes estimates using partial coherence interferometry were validated against estimates obtained from magnetic resonance imaging. Steeper retinas were found along the horizontal than along the vertical meridian, in myopes than in emmetropes, and in East Asian myopes than in Caucasian myopes. The racial differences, combined with the high prevalence of myopia in East Asia, suggest that retinal shape may play a role in myopia development.

Cone location and correction of keratoconus with rigid gas-permeable contact lenses

Purpose To evaluate the influence of cone location and corneal cylinder on RGP corrected visual acuities and residual astigmatism in patients with keratoconus. Methods In this prospective study, 156 eyes from 134 patients were enrolled. Complete ophthalmologic examination including manifest refraction, Best spectacle visual acuity (BSCVA), slit-lamp biomicroscopy was performed and corneal topography analysis was done. According to the cone location on the topographic map, the patients were divided into central and paracentral cone groups. Trial RGP lenses were selected based on the flat Sim K readings and a ‘three-point touch’ fitting approach was used. Over contact lens refraction was performed, residual astigmatism (RA) was measured and best-corrected RGP visual acuities (RGPVA) were recorded. Results The mean age (±SD) was 22.1 ± 5.3 years. 76 eyes (48.6%) had central and 80 eyes (51.4%) had paracentral cone. Prior to RGP lenses fitting mean (±SD) subjective refraction spherical equivalent (SRSE), subjective refraction astigmatism (SRAST) and BSCVA (logMAR) were −5.04 ± 2.27 D, −3.51 ± 1.68 D and 0.34 ± 0.14, respectively. There were statistically significant differences between central and paracentral cone groups in mean values of SRSE, SRAST, flat meridian (Sim K1), steep meridian (Sim K2), mean K and corneal cylinder (p-values < 0.05). Comparison of BSCVA to RGPVA shows that vision has improved 0.3 logMAR by RGP lenses (p < 0.0001). Mean (±SD) RA was −0.72 ± 0.39 D. There were no statistically significant differences between RGPVAs and RAs of central and paracentral cone groups (p = 0.22) and (p = 0.42), respectively. Pearson's correlation analysis shows that there is a statistically significant relationship between corneal cylinder and BSCVA and RGPVA, However, the relationship between corneal cylinder and residual astigmatism was not significant. Conclusions Cone location has no effect on the RGP corrected visual acuities and residual astigmatism in patients with keratoconus. Corneal cylinder and Sim K values influence RGP-corrected visual acuities but do not influence residual astigmatism.

Regional changes in choroidal thickness associated with accommodation

Purpose. To characterize the changes occurring in choroidal thickness (ChT) across the posterior pole during accommodation using enhanced-depth imaging optical coherence tomography (OCT). Methods. Forty participants (mean age 21 ± 2 years) had measures of ChT and ocular biometry taken during accommodation to 0, 3, and 6 diopter (D) stimuli, with the Spectralis OCT and Lenstar biometer. A Badal optometer and cold mirror system was mounted on both instruments, allowing measurement collection while subjects viewed an external fixation target at varying accommodative demands. Results. The choroid exhibited significant thinning during accommodation to the 6 D stimulus in both subfoveal (mean change, −5 ± 7 μm) and parafoveal regions (P < 0.001). The magnitude of these changes varied by parafoveal meridian, with the largest changes seen in the temporal (−9 ± 12 μm) and inferotemporal (−8 ± 8 μm) meridians (P < 0.001). Axial length increased with accommodation (mean change, +5 ± 11 μm at 3 D, +14 ± 13 μm at 6 D), and these changes were weakly negatively associated with the choroidal changes (r2 = 0.114, P < 0.05). Conclusions. A small, but significant thinning of the choroid was observed at the 6 D accommodation demand, which was greatest in the temporal and inferotemporal parafoveal choroid, and increased with increasing eccentricity from the fovea. The regional variation in the parafoveal thinning corresponds to the distribution of the nonvascular smooth muscle within the uvea, which may implicate these cells as the potential mechanism by which the choroid thins during accommodation.

Association between glaucoma and at–fault motor vehicle collision involvement among older drivers

Objective To examine the association between glaucoma and motor vehicle collision (MVC) involvement among older drivers, including the role of visual field impairment that may underlie any association found. Design A retrospective population-based study Participants A sample of 2,000 licensed drivers aged 70 years and older who reside in north central Alabama. Methods At-fault MVC involvement for five years prior to enrollment was obtained from state records. Three aspects of visual function were measured: habitual binocular distance visual acuity, binocular contrast sensitivity and the binocular driving visual field constructed from combining the monocular visual fields of each eye. Poisson regression was used to calculate crude and adjusted rate ratios (RR) and 95% confidence intervals (CI). Main Outcomes Measures At-fault MVC involvement for five years prior to enrollment. Results Drivers with glaucoma (n = 206) had a 1.65 (95% confidence interval [CI] 1.20-2.28, p = 0.002) times higher MVC rate compared to those without glaucoma after adjusting for age, gender and mental status. Among those with glaucoma, drivers with severe visual field loss had higher MVC rates (RR = 2.11, 95% CI 1.09-4.09, p = 0.027), whereas no significant association was found among those with impaired visual acuity and contrast sensitivity. When the visual field was sub-divided into six regions (upper, lower, left, and right visual fields; horizontal and vertical meridians), we found that impairment in the left, upper or lower visual field was associated with higher MVC rates, and an impaired left visual field showed the highest RR (RR = 3.16, p = 0.001) compared to other regions. However, no significant association was found in deficits in the right side or along the horizontal or vertical meridian. Conclusions A population-based study suggests that older drivers with glaucoma are more likely to have a history of at-fault MVC involvement than those without glaucoma. Impairment in the driving visual field in drivers with glaucoma appears to have an independent association with at-fault MVC involvement, whereas visual acuity and contrast sensitivity impairments do not.

Do small-aperture presbyopic corrections influence the visual field?

Purpose To explore the effect of small-aperture optics, designed to aid presbyopes by increasing ocular depth-of-focus, on measurements of the visual field. Methods Simple theoretical and ray-tracing models were used to predict the impact of different designs of small-aperture contact lenses or corneal inlays on the proportion of light passing through natural pupils of various diameters as a function of the direction in the visual field. The left eyes of five healthy volunteers were tested using three afocal, hand-painted opaque soft contact lenses (www.davidthomas.com). Two were opaque over a 10 mm diameter but had central clear circular apertures of 1.5 and 3.0 mm in diameter. The third had an annular opaque zone with inner and outer diameters of 1.5 and 4.0 mm, approximately simulating the geometry of the KAMRA inlay (www.acufocus.com). A fourth, clear lens was used for comparison purposes. Visual fields along the horizontal meridian were evaluated up to 50° eccentricity with static automated perimetry (Medmont M700, stimulus Goldmann-size III; www.medmont.com). Results According to ray-tracing, the two lenses with the circular apertures were expected to reduce the relative transmittance of the pupil to zero at specific field angles (around 60° for the conditions of the experimental measurements). In contrast, the annular stop had no effect on the absolute field but relative transmittance was reduced over the central area of the field, the exact effects depending upon the natural pupil diameter. Experimental results broadly agreed with these theoretical expectations. With the 1.5 and 3.0 mm pupils, only minor losses in sensitivity (around 2 dB) in comparison with the clear-lens case occurred across the central 10° radius of field. Beyond this angle, sensitivity losses increased, to reach about 7 dB at the edge of the measured field (50°). The field results with the annular stop showed at most only a slight loss in sensitivity (≤3 dB) across the measured field. Conclusion The present theoretical and experimental results support earlier clinical findings that KAMRA-type annular stops, unlike circular artificial pupils, have only minor effects on measurements of the visual field.