The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

The effect of simulated astigmatic refractive error on reading performance

Background: Few studies have specifically investigated the functional effects of uncorrected astigmatism on measures of reading fluency. This information is important to provide evidence for the development of clinical guidelines for the correction of astigmatism. Methods: Participants included 30 visually normal, young adults (mean age 21.7 ± 3.4 years). Distance and near visual acuity and reading fluency were assessed with optimal spectacle correction (baseline) and for two levels of astigmatism, 1.00DC and 2.00DC, at two axes (90° and 180°) to induce both against-the-rule (ATR) and with-the-rule (WTR) astigmatism. Reading and eye movement fluency were assessed using standardized clinical measures including the test of Discrete Reading Rate (DRR), the Developmental Eye Movement (DEM) test and by recording eye movement patterns with the Visagraph (III) during reading for comprehension. Results: Both distance and near acuity were significantly decreased compared to baseline for all of the astigmatic lens conditions (p < 0.001). Reading speed with the DRR for N16 print size was significantly reduced for the 2.00DC ATR condition (a reduction of 10%), while for smaller text sizes reading speed was reduced by up to 24% for the 1.00DC ATR and 2.00DC condition in both axis directions (p<0.05). For the DEM, sub-test completion speeds were significantly impaired, with the 2.00DC condition affecting both vertical and horizontal times and the 1.00DC ATR condition affecting only horizontal times (p<0.05). Visagraph reading eye movements were not significantly affected by the induced astigmatism. Conclusions: Induced astigmatism impaired performance on selected tests of reading fluency, with ATR astigmatism having significantly greater effects on performance than did WTR, even for relatively small amounts of astigmatic blur of 1.00DC. These findings have implications for the minimal prescribing criteria for astigmatic refractive errors.

Prevalence and predictors of refractive error in a genetically isolated population : the Norfolk Island Eye Study

BACKGROUND: We aimed to determine the prevalence and associations of refractive error on Norfolk Island. DESIGN: Population-based study on Norfolk Island, South Pacific. PARTICIPANTS: All permanent residents on Norfolk Island aged ≥ 15 years were invited to participate. METHODS: Patients underwent non-cycloplegic autorefraction, slit-lamp biomicroscope examination and biometry assessment. Only phakic eyes were analysed. MAIN OUTCOME MEASURES: Prevalence and multivariate associations of refractive error and myopia. RESULTS: There were 677 people (645 right phakic eyes, 648 left phakic eyes) aged ≥ 15 years were included in this study. Mean age of participants was 51.1 (standard deviation 15.7; range 15-81). Three hundred and seventy-six people (55.5%) were female. Adjusted to the 2006 Norfolk Island population, prevalence estimates of refractive error were as follows: myopia (mean spherical equivalent ≥ -1.0 D) 10.1%, hypermetropia (mean spherical equivalent ≥ 1.0 D) 36.6%, and astigmatism 17.7%. Significant independent predictors of myopia in the multivariate model were lower age (P < 0.001), longer axial length (P < 0.001), shallower anterior chamber depth (P = 0.031) and increased corneal curvature (P < 0.001). Significant independent predictors of refractive error were increasing age (P < 0.001), male gender (P = 0.009), Pitcairn ancestry (P = 0.041), cataract (P < 0.001), longer axial length (P < 0.001) and decreased corneal curvature (P < 0.001). CONCLUSIONS: The prevalence of myopia on Norfolk Island is lower than on mainland Australia, and the Norfolk Island population demonstrates ethnic differences in the prevalence estimates. Given the significant associations between refractive error and several ocular biometry characteristics, Norfolk Island may be a useful population in which to find the genetic basis of refractive error.

Interocular corneal symmetry in refractive error groups

Purpose: To examine between eye differences in corneal higher order aberrations and topographical characteristics in a range of refractive error groups. Methods: One hundred and seventy subjects were recruited including; 50 emmetropic isometropes, 48 myopic isometropes (spherical equivalent anisometropia ≤ 0.75 D), 50 myopic anisometropes (spherical equivalent anisometropia ≥ 1.00 D) and 22 keratoconics. The corneal topography of each eye was captured using the E300 videokeratoscope (Medmont, Victoria, Australia) and analyzed using custom written software. All left eye data were rotated about the vertical midline to account for enantiomorphism. Corneal height data were used to calculate the corneal wavefront error using a ray tracing procedure and fit with Zernike polynomials (up to and including the eighth radial order). The wavefront was centred on the line of sight by using the pupil offset value from the pupil detection function in the videokeratoscope. Refractive power maps were analysed to assess corneal sphero-cylindrical power vectors. Differences between the more myopic (or more advanced eye for keratoconics) and the less myopic (advanced) eye were examined. Results: Over a 6 mm diameter, the cornea of the more myopic eye was significantly steeper (refractive power vector M) compared to the fellow eye in both anisometropes (0.10 ± 0.27 D steeper, p = 0.01) and keratoconics (2.54 ± 2.32 D steeper, p < 0.001) while no significant interocular difference was observed for isometropic emmetropes (-0.03 ± 0.32 D) or isometropic myopes (0.02 ± 0.30 D) (both p > 0.05). In keratoconic eyes, the between eye difference in corneal refractive power was greatest inferiorly (associated with cone location). Similarly, in myopic anisometropes, the more myopic eye displayed a central region of significant inferior corneal steepening (0.15 ± 0.42 D steeper) relative to the fellow eye (p = 0.01). Significant interocular differences in higher order aberrations were only observed in the keratoconic group for; vertical trefoil C(3,-3), horizontal coma C(3,1) secondary astigmatism along 45 C(4, -2) (p < 0.05) and vertical coma C(3,-1) (p < 0.001). The interocular difference in vertical pupil decentration (relative to the corneal vertex normal) increased with between eye asymmetry in refraction (isometropia 0.00 ± 0.09, anisometropia 0.03 ± 0.15 and keratoconus 0.08 ± 0.16 mm) as did the interocular difference in corneal vertical coma C (3,-1) (isometropia -0.006 ± 0.142, anisometropia -0.037 ± 0.195 and keratoconus -1.243 ± 0.936 μm) but only reached statistical significance for pair-wise comparisons between the isometropic and keratoconic groups. Conclusions: There is a high degree of corneal symmetry between the fellow eyes of myopic and emmetropic isometropes. Interocular differences in corneal topography and higher order aberrations are more apparent in myopic anisometropes and keratoconics due to regional (primarily inferior) differences in topography and between eye differences in vertical pupil decentration relative to the corneal vertex normal. Interocular asymmetries in corneal optics appear to be associated with anisometropic refractive development.

Effect of age and refractive error on the melanopsin mediated Post-Illumination Pupil Response (PIPR)

Melanopsin containing intrinsically photosensitive Retinal Ganglion cells (ipRGCs) mediate the pupil light reflex (PLR) during light onset and at light offset (the post-illumination pupil response, PIPR). Recent evidence shows that the PLR and PIPR can provide non-invasive, objective markers of age-related retinal and optic nerve disease, however there is no consensus on the effects of healthy ageing or refractive error on the ipRGC mediated pupil function. Here we isolated melanopsin contributions to the pupil control pathway in 59 human participants with no ocular pathology across a range of ages and refractive errors. We show that there is no effect of age or refractive error on ipRGC inputs to the human pupil control pathway. The stability of the ipRGC mediated pupil response across the human lifespan provides a functional correlate of their robustness observed during ageing in rodent models.

Differential effects of refractive blur on day and night-time driving performance

Purpose To investigate the effect of different levels of refractive blur on real-world driving performance measured under day and nighttime conditions. Methods Participants included 12 visually normal, young adults (mean age = 25.8 ± 5.2 years) who drove an instrumented research vehicle around a 4 km closed road circuit with three different levels of binocular spherical refractive blur (+0.50 diopter sphere [DS], +1.00 DS, +2.00 DS) compared with a baseline condition. The subjects wore optimal spherocylinder correction and the additional blur lenses were mounted in modified full-field goggles; the order of testing of the blur conditions was randomized. Driving performance was assessed in two different sessions under day and nighttime conditions and included measures of road signs recognized, hazard detection and avoidance, gap detection, lane-keeping, sign recognition distance, speed, and time to complete the course. Results Refractive blur and time of day had significant effects on driving performance (P < 0.05), where increasing blur and nighttime driving reduced performance on all driving tasks except gap judgment and lane keeping. There was also a significant interaction between blur and time of day (P < 0.05), such that the effects of blur were exacerbated under nighttime driving conditions; performance differences were evident even for +0.50 DS blur relative to baseline for some measures. Conclusions The effects of blur were greatest under nighttime conditions, even for levels of binocular refractive blur as low as +0.50 DS. These results emphasize the importance of accurate and up-to-date refractive correction of even low levels of refractive error when driving at night.

Prevalence of refractive errors among schoolchildren in Shiraz, Iran

PURPOSE To determine the prevalence of refractive errors in Shiraz schoolchildren by age and gender. METHODS For this cross-sectional study, random cluster sampling was carried out from students of the 2008-2009 academic year. After the initial interview, ophthalmic examinations including tests of visual acuity, non-cycloplegic and cycloplegic refraction and binocular vision were performed. Myopia was defined as a spherical equivalent < or =-0.50 dioptre (D), hyperopia as > or =+2.0 D, and astigmatism as a cylinder refraction > or =0.75 D. All values for school grade and gender were directly standardized based on the total student population in the 2008-2009 school year. RESULTS A total of 2130 students were sampled, of which 1872 participated in the study (response rate = 87.88%). The prevalence of uncorrected, best-corrected, presenting and spectacle corrected visual acuity of 6/12 or worse in the better eye was 6.46%, 0%, 1.49% and 0.9%, respectively. The prevalence rates of myopia, hyperopia and astigmatism were 4.35% (95% confidence interval [CI]: 2.89-5.82%), 5.04% (95% CI: 3.50-6.58%), and 11.27% (95% CI: 9.81-12.74%), respectively. Anisometropia was detected in 2.58% of schoolchildren. The prevalence of hyperopia significantly decreased with age (P = 0.021). CONCLUSIONS Compared with other reported rates, the prevalence of myopia in the schoolchildren of Shiraz is similar to that in most places excluding East Asian countries, and that of hyperopia is in the mid range.

Prevalence and risk factors of refractive errors among schoolchildren in Shiraz, Iran

Purpose: To determine the prevalence and risk factors of refractive errors among schoolchildren in Shiraz, Iran. Methods: In a cross-sectional study, using random cluster sampling, 3065 Shiraz schoolchildren were selected in this study. The participants totaled 2683; 1872 elementary and middle school and 811 high school students. For the primary and middle schoolchildren, cycloplegic refraction and for the high school students, non-cycloplegic autorefraction was measured. Myopia, defined as spherical equivalent (SE) refraction -0.50 diopter (D) or worse, hyperopia as SE +2.00D and +0.50D or more for cycloplegic and noncycloplegic refractions respectively, and astigmatism as cylinder -0.75D or worse. Results: The prevalence of refractive errors in elementary and middle school students was: myopia 4.35 % (95% confidence interval (CI), 2.89 -5.81), hyperopia 5.04 % (95%CI, 3.49 -6.58) and astigmatism 11.79 % (95%CI, 10.21 -13.38). For high school students, these rates were 22.4 % (95%CI, 18.44 -26.36), 10.52 % (95%CI, 6.75 -14.29) and 20.99% (95%CI, 16.55 -25.44), respectively.The prevalence of myopia increased with age in primary and middle school students (OR=1.15, 95% CI, 0.98 to1.33, p=0.073). Conclusions: The result of this study indicated a relatively low prevalence of refractive errors among schoolchildren in Shiraz according to the protocol by "Refractive Error Study in Children" (RESC) in other investigations.

Visual demands of modern primary classrooms and the impact of refractive anomalies on academic performance

This research investigated the visual demands in modern primary school classrooms and also the impact of common refractive anomalies on a child's ability to perform academic-related tasks. The results showed that relatively high levels of visual acuity, contrast demand and sustained accommodative-convergence are required to perform optimally in the modern classroom environment. It was also demonstrated that relatively low magnitudes of uncorrected refractive error may have a detrimental impact on children's ability to perform academic-related activities at school, with sustained near work further exacerbating this effect. These findings have important implications for both eye care practitioners and education authorities.

Amblyopia treatment : an evidence-based approach to maximising treatment outcome

The basis of treatment for amblyopia (poor vision due to abnormal visual experience early in life) for 250 years has been patching of the unaffected eye for extended times to ensure a period of use of the affected eye. Over the last decade randomised controlled treatment trials have provided some evidence on how to tailor amblyopia therapy more precisely to achieve the best visual outcome with the least negative impact on the patient and the family. This review highlights the expansion of knowledge regarding treatment for amblyopia and aims to provide optometrists with a summary of research evidence to enable them to better treat amblyopia. Treatment for amblyopia is effective, as it reduces overall prevalence and severity of visual loss in this population. Correction of refractive error alone significantly improves visual acuity, sometimes to the point where further amblyopia treatment is not required. Atropine penalisation and patch occlusion are effective in treating amblyopia. Lesser amounts of occlusion or penalisation have been found to be just as effective as greater amounts. Recent evidence has highlighted that occlusion or penalisation in amblyopia treatment can create negative changes in behaviour in children and impact on family life. These complications should be considere when prescribing treatment because they can negatively affect compliance. Studies investigating the maximum age at which treatment of amblyopia can still be effective and the importance of near activities during occlusion are ongoing.

Decentred optical axes and aberrations along principal visual field meridians

Suggestions that peripheral imagery may affect the development of refractive error have led to interest in the variation in refraction and aberration across the visual field. It is shown that, if the optical system of the eye is rotationally symmetric about an optical axis which does not coincide with the visual axis, measurements of refraction and aberration made along the horizontal and vertical meridians of the visual field will show asymmetry about the visual axis. The departures from symmetry are modelled for second-order aberrations, refractive components and third-order coma. These theoretical results are compared with practical measurements from the literature. The experimental data support the concept that departures from symmetry about the visual axis in the measurements of crossed-cylinder astigmatism J45 and J180 are largely explicable in terms of a decentred optical axis. Measurements of the mean sphere M suggest, however, that the retinal curvature must differ in the horizontal and vertical meridians.

Effect of amblyopia on the developmental eye movement test in children

Purpose. To investigate the functional impact of amblyopia in children, the performance of amblyopic and age-matched control children on a clinical test of eye movements was compared. The influence of visual factors on test outcome measures was explored. Methods. Eye movements were assessed with the Developmental Eye Movement (DEM) test, in a group of children with amblyopia (n = 39; age, 9.1 ± 0.9 years) of different causes (infantile esotropia, n = 7; acquired strabismus, n = 10; anisometropia, n = 8; mixed, n = 8; deprivation, n = 6) and in an age-matched control group (n = 42; age, 9.3 ± 0.4 years). LogMAR visual acuity (VA), stereoacuity, and refractive error were also recorded in both groups. Results. No significant difference was found between the amblyopic and age-matched control group for any of the outcome measures of the DEM (vertical time, horizontal time, number of errors and ratio(horizontal time/vertical time)). The DEM measures were not significantly related to VA in either eye, level of binocular function (stereoacuity), history of strabismus, or refractive error. Conclusions. The performance of amblyopic children on the DEM, a commonly used clinical measure of eye movements, has not previously been reported. Under habitual binocular viewing conditions, amblyopia has no effect on DEM outcome scores despite significant impairment of binocular vision and decreased VA in both the better and worse eye.

The effect of Amblyopia on motor and psychosocial skills in children

Background/Aims: In an investigation of the functional impact of amblyopia on children, the fine motor skills, perceived self-esteem and eye movements of amblyopic children were compared with that of age-matched controls. The influence of amblyogenic condition or treatment factors that might predict any decrement in outcome measures was investigated. The relationship between indirect measures of eye movements that are used clinically and eye movement characteristics recorded during reading was examined and the relevance of proficiency in fine motor skills to performance on standardised educational tests was explored in a sub-group of the control children. Methods: Children with amblyopia (n=82; age 8.2 ± 1.3 years) from differing causes (infantile esotropia n=17, acquired strabismus n=28, anisometropia n=15, mixed n=13 and deprivation n=9), and a control group of children (n=106; age 9.5 ± 1.2 years) participated in this study. Measures of visual function included monocular logMAR visual acuity (VA) and stereopsis assessed with the Randot Preschool Stereoacuity test, while fine motor skills were measured using the Visual-Motor Control (VMC) and Upper Limb Speed and Dexterity (ULSD) subtests of the Brunicks-Oseretsky Test of Motor Proficiency. Perceived self esteem was assessed for those children from grade 3 school level with the Harter Self Perception Profile for Children and for those in younger grades (preschool to grade 2) with the Pictorial Scale of Perceived Competence and Acceptance for Young Children. A clinical measure of eye movements was made with the Developmental Eye Movement (DEM) test for those children aged eight years and above. For appropriate case-control comparison of data, the results from amblyopic children were compared with age-matched sub-samples drawn from the group of children with normal vision who completed the tests. Eye movements during reading for comprehension were recorded by the Visagraph infra-red recording system and results of standardised tests of educational performance were also obtained for a sub-set of the control group. Results Amblyopic children (n=82; age 8.2 ± 1.7 years) performed significantly poorer than age-matched control children (n=37; age 8.3 ± 1.3 years) on 9 of 16 fine motor skills sub-items and for the overall age-standardised scores for both VMC and ULSD items (p<0.05); differences were most evident on timed manual dexterity tasks. The underlying aetiology of amblyopia and level of stereoacuity significantly affected fine motor skill performance on both items. However, when examined in a multiple regression model that took into account the inter-correlation between visual characteristics, poorer fine motor skills performance was only associated with strabismus (F1,75 = 5.428; p =0. 022), and not with the level of stereoacuity, refractive error or visual acuity in either eye. Amblyopic children from grade 3 school level and above (n=47; age 9.2 ± 1.3 years), particularly those with acquired strabismus, had significantly lower social acceptance scores than age-matched control children (n=52; age 9.4 ± 0.5 years) (F(5,93) = 3.14; p = 0.012). However, the scores of the amblyopic children were not significantly different to controls for other areas related to self-esteem, including scholastic competence, physical appearance, athletic competence, behavioural conduct and global self worth. A lower social acceptance score was independently associated with a history of treatment with patching but not with a history of strabismus or wearing glasses. Amblyopic children from pre-school to grade 2 school level (n=29; age = 6.6 ± 0.6 years) had similar self-perception scores to their age-matched peers (n=20; age = 6.4 ± 0.5 years). There were no significant differences between the amblyopic (n=39; age 9.1 ± 0.9 years) and age-matched control (n = 42; age = 9.3 ± 0.38 years) groups for any of the DEM outcome measures (Vertical Time, Horizontal Time, Number of Errors and Ratio (Horizontal time/Vertical time)). Performance on the DEM did not significantly relate to measures of VA in either eye, level of binocular function, history of strabismus or refractive error. Developmental Eye Movement test outcome measures Horizontal Time and Vertical Time were significantly correlated with reading rates measured by the Visagraph for both reading for comprehension and naming numbers (r>0.5). Some moderate correlations were also seen between the DEM Ratio and word reading rates as recorded by Visagraph (r=0.37). In children with normal vision, academic scores in mathematics, spelling and reading were associated with measures of fine motor skills. Strongest effect sizes were seen with the timed manual dexterity domain, Upper Limb Speed and Dexterity. Conclusions Amblyopia may have a negative impact on a child’s fine motor skills and an older child’s sense of acceptance by their peers may be influenced by treatment that includes eye patching. Clinical measures of eye movements were not affected in amblyopic children. A number of the outcome measures of the DEM are associated with objective recordings of reading rates, supporting its clinical use for identification of children with slower reading rates. In children with normal vision, proficiency on clinical measures of fine motor skill are associated with outcomes on standardised measures of educational performance. Scores on timed manual dexterity tasks had the strongest association with educational performance. Collectively, the results of this study indicate that, in addition to the reduction in visual acuity and binocular function that define the condition, amblyopes have functional impairment in childhood development skills that underlie proficiency in everyday activities. The study provides support for strategies aimed at early identification and remediation of amblyopia and the co-morbidities that arise from abnormal visual neurodevelopment.

Changes in intraocular pressure and ocular pulse amplitude with accommodation

Aims: To investigate the change that occurs in intraocular pressure (IOP) and ocular pulse amplitude (OPA) with accommodation in young adult myopes and emmetropes. Methods: Fifteen progressing myopic and 17 emmetropic young adult subjects had their IOP and OPA measured using the Pascal dynamic contour tonometer. Measurements were taken initially with accommodation relaxed, and then following 2 min of near fixation (accommodative demand 3 D). Baseline measurements of axial length and corneal thickness were also collected prior to the IOP measures. Results: IOP significantly decreased with accommodation in both the myopic and emmetropic subjects (mean change 1.861.1 mm Hg, p<0.0001). There was no significant difference (p>0.05) between myopes and emmetropes in terms of baseline IOP or the magnitude of change in IOP with accommodation. OPA also decreased significantly with accommodation (mean change for all subjects 0.560.5, p<0.0001). The myopic subjects (baseline OPA 2.060.7 mm Hg) exhibited a significantly lower baseline OPA (p¼0.004) than the emmetropes (baseline OPA 3.261.3 mm Hg),and a significantly lower magnitude of change in OPA with accommodation. Conclusion: IOP decreases significantly with accommodation, and changes similarly in progressing myopic and emmetropic subjects. However, differences found between progressing myopes and emmetropes in the mean OPA levels and the decrease in OPA associated with accommodation suggested some changes in IOP dynamics associated with myopia.