Letter to the editor

We read with interest the article entitled ‘Population spherical aberration: associations with ametropia, age, corneal curvature, and image quality’ by Amanda C Kingston and Ian G Cox (2013). The authors provided higher order aberrations data for a sample of 1124 eyes and performed correlation analyses to compare higher order aberrations with refraction and biometry data, such as spherical equivalent power and corneal curvature. Special attention was drawn to spherical aberration...

Myopic anisometropia : ocular characteristics and aetiological considerations

Anisometropia represents a unique example of ocular development, where the two eyes of an individual, with an identical genetic background and seemingly subject to identical environmental influences, can grow asymmetrically to produce significantly different refractive errors. This review provides an overview of the research examining myopic anisometropia, the ocular characteristics underlying the condition and the potential aetiological factors involved. Various mechanical factors are discussed, including corneal structure, intraocular pressure and forces generated during near work that may contribute to development of anisomyopia. Potential visually guided mechanisms of unequal ocular growth are also explored, including the influence of astigmatism, accommodation, higher-order aberrations and the choroidal response to altered visual experience. The association between binocular vision, ocular dominance and asymmetric refraction is also considered, along with a review of the genetic contribution to the aetiology of myopic anisometropia. Despite a significant amount of research into the biomechanical, structural and optical characteristics of anisometropic eyes, there is still no unifying theory, which adequately explains how two eyes within the same visual system grow to different endpoints.

Comparison of ocular modulation transfer function determined by a ray-tracing aberrometer and a double-pass system in early cataract patients

BACKGROUND: The evaluation of retinal image quality in cataract eyes has gained importance and the clinical modulation transfer functions (MTF) can obtained by aberrometer and double pass (DP) system. This study aimed to compare MTF derived from a ray tracing aberrometer and a DP system in early cataractous and normal eyes. METHODS: There were 128 subjects with 61 control eyes and 67 eyes with early cataract defined according to the Lens Opacities Classification System III. A laser ray-tracing wavefront aberrometer (iTrace) and a double pass (DP) system (OQAS) assessed ocular MTF for 6.0 mm pupil diameters following dilation. Areas under the MTF (AUMTF) and their correlations were analyzed. Stepwise multiple regression analysis assessed factors affecting the differences between iTrace- and OQAS-derived AUMTF for the early cataract group. RESULTS: For both early cataract and control groups, iTrace-derived MTFs were higher than OQAS-derived MTFs across a range of spatial frequencies (P < 0.01). No significant difference between the two groups occurred for iTrace-derived AUMTF, but the early cataract group had significantly smaller OQAS-derived AUMTF than did the control group (P < 0.01). AUMTF determined from both the techniques demonstrated significant correlations with nuclear opacities, higher-order aberrations (HOAs), visual acuity, and contrast sensitivity functions, while the OQAS-derived AUMTF also demonstrated significant correlations with age and cortical opacity grade. The factors significantly affecting the difference between iTrace and OQAS AUMTF were root-mean-squared HOAs (standardized beta coefficient = -0.63, P < 0.01) and age (standardized beta coefficient = 0.26, P < 0.01). CONCLUSIONS: MTFs determined from a iTrace and a DP system (OQAS) differ significantly in early cataractous and normal subjects. Correlations with visual performance were higher for the DP system. OQAS-derived MTF may be useful as an indicator of visual performance in early cataract eyes.

Miniscleral lens wear influences corneal curvature and optics

Purpose Transient changes in corneal topography associated with soft and conventional or reverse geometry rigid contact lens wear have been well documented; however, only a few studies have examined the influence of scleral contact lens wear upon the cornea. Therefore, in this study, we examined the influence of modern miniscleral contact lenses, which land entirely on the sclera and overlying tissues, upon anterior corneal curvature and optics. Methods Anterior corneal topography and elevation data were acquired using Scheimpflug imaging (Pentacam HR, Oculus) immediately prior to and following 8 hours of miniscleral contact lens wear in 15 young healthy adults (mean age 22 ± 3 years, 8 East Asian, 7 Caucasian) with normal corneae. Corneal diurnal variations were accounted for using data collected on a dedicated measurement day without contact lens wear. Corneal clearance was quantified using an optical coherence tomographer (RS-3000, Nidek) following lens insertion and after 8 hours of lens wear. Results Although corneal clearance was maintained throughout the 8 hour lens wear period, significant corneal flattening (up to 0.08 ± 0.04 mm) was observed, primarily in the superior mid-peripheral cornea, which resulted in a slight increase in against-the-rule corneal astigmatism (mean +0.02/-0.15 x 94 for an 8 mm diameter). Higher order aberration terms of horizontal coma, vertical coma and spherical aberration all underwent significant changes for an 8 mm corneal diameter (p ≤ 0.01), which typically resulted in a decrease in RMS error values (mean change in total higher order RMS -0.035 ± 0.046 µm for an 8 mm diameter). There was no association between the magnitude of change in central or mid-peripheral corneal clearance during lens wear and the observed changes in corneal curvature (p > 0.05). However, Asian participants displayed a significantly greater reduction in corneal clearance (p = 0.04) and greater superior-nasal corneal flattening compared to Caucasians (p = 0.048). Conclusions Miniscleral contact lenses that vault the cornea induce significant changes in anterior corneal surface topography and higher order aberrations following 8 hours of lens wear. The region of greatest corneal flattening was observed in the superior-nasal mid-periphery, more so in Asian participants. Practitioners should be aware that corneal measurements obtained following miniscleral lens removal may mask underlying corneal steepening.

Aberrations and pupil location under corneal topography and Hartmann-Shack illumination conditions

PURPOSE. This study was conducted to determine the magnitude of pupil center shift between the illumination conditions provided by corneal topography measurement (photopic illuminance) and by Hartmann-Shack aberrometry (mesopic illuminance) and to investigate the importance of this shift when calculating corneal aberrations and for the success of wavefront-guided surgical procedures. METHODS. Sixty-two subjects with emmetropia underwent corneal topography and Hartmann-Shack aberrometry. Corneal limbus and pupil edges were detected, and the differences between their respective centers were determined for both procedures. Corneal aberrations were calculated using the pupil centers for corneal topography and for Hartmann-Shack aberrometry. Bland-Altmann plots and paired t-tests were used to analyze the differences between corneal aberrations referenced to the two pupil centers. RESULTS. The mean magnitude (modulus) of the displacement of the pupil with the change of the illumination conditions was 0.21 ± 0.11 mm. The effect of this pupillary shift was manifest for coma corneal aberrations for 5-mm pupils, but the two sets of aberrations calculated with the two pupil positions were not significantly different. Sixty-eight percent of the population had differences in coma smaller than 0.05 µm, and only 4% had differences larger than 0.1 µm. Pupil displacement was not large enough to significantly affect other higher-order Zernike modes. CONCLUSIONS. Estimated corneal aberrations changed slightly between photopic and mesopic illumination conditions given by corneal topography and Hartmann-Shack aberrometry. However, this systematic pupil shift, according to the published tolerances ranges, is enough to deteriorate the optical quality below the theoretically predicted diffraction limit of wavefront-guided corneal surgery.

Effect of optical aberrations on the colour appearance of small lights

Purpose: Small red lights (one minute of arc or less) change colour appearance with positive defocus. We investigated the influence of longitudinal chromatic aberration and monochromatic aberrations on the colour appearance of small narrow band lights. Methods: Seven cyclopleged, trichromatic observers viewed a small light (one minute of arc, λmax = 510, 532, 550, 589, 620, 628 nm, approximately 19 per cent Weber contrast) centred within a black annulus (4.5 minutes of arc) and surrounded by a uniform white field (2,170 cd/m2). Pupil size was four millimetres. An optical trombone varied focus. Longitudinal chromatic aberration was controlled with a two component Powell achromatising lens that neutralises the eye’s chromatic aberration; a doublet that doubles and a triplet that reverses the eye’s chromatic aberration. Astigmatism and higher order monochromatic aberrations were corrected using adaptive optics. Results: Observers reported a change in appearance of the small red light (628 nm) without the Powell lens at +0.49 ± 0.21 D defocus and with the doublet at +0.62 ± 0.16 D. Appearance did not alter with the Powell lens, and five of seven observers reported the phenomenon with the triplet for negative defocus (-0.80 ± 0.47 D). Correction of aberrations did not significantly affect the magnitude at which the appearance of the red light changed (+0.44 ± 0.18 D without correction; +0.46 ± 0.16 D with correction). The change in colour appearance with defocus extended to other wavelengths (λmax = 510 to 620 nm), with directions of effects being reversed for short wavelengths relative to long wavelengths. Conclusions: Longitudinal chromatic aberrations but not monochromatic aberrations are involved in changing the appearance of small lights with defocus.

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.

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.

Blur limits for defocus, astigmatism and trefoil

We investigated the limits at which blur due to defocus, crossed-cylinder astigmatism, and trefoil became noticeable, troublesome or objectionable. Black letter targets (0.1, 0.35 and 0.6 logMAR) were presented on white backgrounds. Subjects were cyclopleged and had effectively 5 mm pupils. Blur was induced with a deformable, adaptive-optics mirror operating under open-loop conditions. Mean defocus blur limits of six subjects with uncorrected intrinsic higher-order ocular aberrations ranged from 0.18 ± 0.08 D (noticeable blur criterion, 0.1 logMAR) to 1.01 ± 0.27 D (objectionable blur criterion, 0.6 logMAR. Crossed-cylinder astigmatic blur limits were approximately 90% of those for defocus, but with considerable meridional influences. In two of the subjects, the intrinsic aberrations of the eye were subsequently corrected before the defocus and astigmatic blur were added. This resulted in only minor reductions in their blur limits. When assessed with trefoil blur and corrected intrinsic ocular aberrations, the ratio of objectionable to noticeable blur limits in these two subjects was much higher for trefoil (3.5) than for defocus (2.5) and astigmatism (2.2).

Change in colour appearance of small defocused lights

Small long wavelength lights (≤ 1’ arc) change colour appearance with positive defocus, appearing yellow or white. I investigated influences of longitudinal chromatic aberration and monochromatic aberrations on colour appearance of small narrow band lights. Seven cyclopleged participants viewed a small light (1’ arc diameter, λmax range 510 - 628 nm) centred within a 4.6’ black annulus and surrounded by a uniform white field under photopic light levels. An optical trombone varied focus. Participants were required to vary the focus by moving the optical trombone in either positive or negative direction and report when they noticed a change in appearance of the defocused narrow band light. Longitudinal chromatic aberration was controlled using a Powell achromatizing lens and its doublet and triplet components that neutralized, doubled and reversed the eye’s chromatic aberration, respectively. Changes in colour appearance for a 628 nm light occurred without any lens at +0.5 ± 0.2D defocus and with the doublet at +0.6 ± 0.2 D. The achromatizing lens did not affect appearance and the phenomenon was evident with the triplet for negative defocus (-0.5 ± 0.3 D). Adaptive optics correction of astigmatism and higher order monochromatic aberration did not affect magnitude significantly. Colour changes occurred despite a range of participant L/M cone ratios. Direction of change in colour appearance was reversed for short compared to long wavelengths. We conclude that longitudinal chromatic aberrations, but not monochromatic aberrations, are involved in changing appearance of small lights with defocus. Additional neuronal mechanisms that may contribute to the colour changes are considered.

Thinking critically about critical thinking in higher education

The literature on critical thinking in higher education is constructed around the fundamental assumption that, while regarded as essential, is neither clearly or commonly understood. There is elsewhere evidence that academics and students have differing perceptions of what happens in university classrooms, particularly in regard to higher order thinking. This paper reports on a small-scale investigation in a Faculty of Education at an Australian University into academic and student definitions and understandings of critical thinking. Our particular interest lay in the consistencies and disconnections assumed to exist between academic staff and students. The presumption might therefore be that staff and students perceive critical thinking in different ways and that this may limit its achievement as a critical graduate attribute. The key finding from this study, contrary to extant findings, is that academics and students did share substantively similar definitions and understandings of critical thinking.

Some applications of logic to feasibility in higher types

While it is commonly accepted that computability on a Turing machine in polynomial time represents a correct formalization of the notion of a feasibly computable function, there is no similar agreement on how to extend this notion on functionals, that is, what functionals should be considered feasible. One possible paradigm was introduced by Mehlhorn, who extended Cobham's definition of feasible functions to type 2 functionals. Subsequently, this class of functionals (with inessential changes of the definition) was studied by Townsend who calls this class POLY, and by Kapron and Cook who call the same class basic feasible functionals. Kapron and Cook gave an oracle Turing machine model characterisation of this class. In this article, we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalise the corresponding properties of the class of feasible functions, thus giving further evidence that the notion of feasibility of functionals mentioned above is correctly chosen. We also improve the Kapron and Cook result on machine representation.Our proofs are based on essential applications of logic. We introduce a weak fragment of second order arithmetic with second order variables ranging over functions from NN which suitably characterises basic feasible functionals, and show that it is a useful tool for investigating the properties of basic feasible functionals. In particular, we provide an example how one can extract feasible programs from mathematical proofs that use nonfeasible functions.

An aspect query language model based on query decomposition and high-order contextual term associations

In information retrieval (IR) research, more and more focus has been placed on optimizing a query language model by detecting and estimating the dependencies between the query and the observed terms occurring in the selected relevance feedback documents. In this paper, we propose a novel Aspect Language Modeling framework featuring term association acquisition, document segmentation, query decomposition, and an Aspect Model (AM) for parameter optimization. Through the proposed framework, we advance the theory and practice of applying high-order and context-sensitive term relationships to IR. We first decompose a query into subsets of query terms. Then we segment the relevance feedback documents into chunks using multiple sliding windows. Finally we discover the higher order term associations, that is, the terms in these chunks with high degree of association to the subsets of the query. In this process, we adopt an approach by combining the AM with the Association Rule (AR) mining. In our approach, the AM not only considers the subsets of a query as “hidden” states and estimates their prior distributions, but also evaluates the dependencies between the subsets of a query and the observed terms extracted from the chunks of feedback documents. The AR provides a reasonable initial estimation of the high-order term associations by discovering the associated rules from the document chunks. Experimental results on various TREC collections verify the effectiveness of our approach, which significantly outperforms a baseline language model and two state-of-the-art query language models namely the Relevance Model and the Information Flow model