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.

Zernike radial slope polynomials for wavefront reconstruction and refraction

Ophthalmic wavefront sensors typically measure wavefront slope, from which wavefront phase is reconstructed. We show that ophthalmic prescriptions (in power-vector format) can be obtained directly from slope measurements without wavefront reconstruction. This is achieved by fitting the measurement data with a new set of orthonormal basis functions called Zernike radial slope polynomials. Coefficients of this expansion can be used to specify the ophthalmic power vector using explicit formulas derived by a variety of methods. Zernike coefficients for wavefront error can be recovered from the coefficients of radial slope polynomials, thereby offering an alternative way to perform wavefront reconstruction.

Signs, symptoms and comorbidities in contact lens-related microbial keratitis

Purpose: The aim of this study was to characterize the clinical signs, symptoms, and ocular and systemic comorbidities in a large case series of contact lens-related microbial keratitis. Methods: Two hundred ninety-seven cases of contact lens-related microbial keratitis, aged between 15 and 64 years were detected through surveillance of hospital and community based ophthalmic practitioners in Australia and New Zealand. Full clinical data were available for 190 cases and 90 were interviewed by telephone. Clinical data included the size, location, and degree of anterior chamber response. Symptom data were available from the practitioner and from participant self-report. Associations between symptoms and disease severity were evaluated. Data on ocular and systemic disease were collected from participants and practitioners. The frequency of comorbidities was compared between the different severities of disease and to population norms. Results: More severe disease was associated with greater symptom severity and pain was the most prevalent symptom reported. Ninety-one percent of cases showed progression of ocular symptoms after lens removal, and symptom progression was associated with all severities of disease. Twenty-five percent of cases reported prior episodes requiring emergency attention. Thyroid disease (p 0.05) and self-reported poor health (p 0.001) were more common in cases compared with age-matched population norms. Discussion: Information on the signs, symptoms, and comorbidities associated with contact lens-related microbial keratitis may be useful in patient education and for practitioners involved in the fitting of lenses and management of complications. Although pain was the most common symptom experienced, progression of symptoms despite lens removal was close to universal. Poor general health, particularly respiratory disease and thyroid disease was more common in cases than in the general population, which may prompt practitioners to recommend flexibility in wear schedules when in poor health or the selection of a lower risk wear schedule in at risk patients

Determining the zone of reflection for posterior corneal surface comparison phakometry

Although comparison phakometry has been used by a number of studies to measure posterior corneal shape, these studies have not calculated the size of the posterior corneal zones of reflection they assessed. This paper develops paraxial equations for calculating posterior corneal zones of reflection, based on standard keratometry equations and equivalent mirror theory. For targets used in previous studies, posterior corneal reflection zone sizes were calculated using paraxial equations and using exact ray tracing, assuming spherical and aspheric corneal surfaces. Paraxial methods and exact ray tracing methods give similar estimates for reflection zone sizes less than 2 mm, but for larger zone sizes ray tracing methods should be used.

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

Effect of optical aberrations on the color appearance of small defocused lights

We investigated influences of optics and surround area on color appearance of defocused, small narrow band photopic lights (1’ arc diameter, λmax 510 - 628 nm) centered within a black annulus and surrounded by a white field. Participants included seven normal trichromats with L- or M-cone biased ratios. We controlled chromatic aberration with elements of a Powell achromatizing lens and corrected higher-order aberrations with an adaptive-optics system. Longitudinal chromatic aberrations, but not monochromatic aberrations, are involved in changing appearance of small lights with defocus. Surround field structure is important because color changes were not observed when lights were presented on a uniform white surround.

Thomas Young's contribution to visual optics : the Bakerian lecture "On the mechanism of the eye"

Thomas Young (1773-1829) carried out major pioneering work in many different subjects. In 1800 he gave the Bakerian Lecture of the Royal Society on the topic of the “mechanism of the eye”: this was published in the following year (Young, 1801). Young used his own design of optometer to measure refraction and accommodation, and discovered his own astigmatism. He considered the different possible origins of accommodation and confirmed that it was due to change in shape of the lens rather than to change in shape of the cornea or an increase in axial length. However, the paper also dealt with many other aspects of visual and ophthalmic optics, such as biometric parameters, peripheral refraction, longitudinal chromatic aberration, depth-of-focus and instrument myopia. These aspects of the paper have previously received little attention. We now give detailed consideration to these and other less-familiar features of Young’s work and conclude that his studies remain relevant to many of the topics which currently engage visual scientists.

Inferior visual field reductions are associated with poorer functional status among older adults with glaucoma

Purpose: To examine the relationship between visual impairment and functional status in a community-dwelling sample of older adults with glaucoma. Methods: This study included 74 community-dwelling older adults with open-angle glaucoma (aged 74 ± 6 years). Assessment of central vision included high-contrast visual acuity and Pelli-Robson contrast sensitivity. Binocular integrated visual fields were derived from merged monocular Humphrey Field Analyser visual field plots. Functional status outcome measures included physical performance tests (6-min walk test, timed up and go test and lower limb strength), a physical activity questionnaire (Physical Activity Scale for the Elderly) and an overall functional status score. Correlation and linear regression analyses, adjusting for age and gender, examined the association between visual impairment and functional status outcomes. Results: Greater levels of visual impairment were significantly associated with lower levels of functional status among community-dwelling older adults with glaucoma, independent of age and gender. Specifically, lower levels of visual function were associated with slower timed up and go performance, weaker lower limb strength, lower self-reported physical activity, and lower overall functional status scores. Of the components of vision examined, the inferior visual field and contrast factors were the strongest predictors of these functional outcomes, whereas the superior visual field factor was not related to functional status. Conclusions: Greater visual impairment, particularly in the inferior visual field and loss of contrast sensitivity, was associated with poorer functional status among older adults with glaucoma. The findings of this study highlight the potential links between visual impairment and the onset of functional decline. Interventions which promote physical activity among older adults with glaucoma may assist in preventing functional decline, frailty and falls, and improve overall health and well-being.

Thomas Young’s investigations in gradient-index optics

Purpose: James Clerk Maxwell is usually recognized as being the first, in 1854, to consider using inhomogeneous media in optical systems. However, some fifty years earlier Thomas Young, stimulated by his interest in the optics of the eye and accommodation, had already modeled some applications of gradient-index optics. These applications included using an axial gradient to provide spherical aberration-free optics and a spherical gradient to describe the optics of the atmosphere and the eye lens. We evaluated Young’s contributions. Method: We attempted to derive Young’s equations for axial and spherical refractive index gradients. Raytracing was used to confirm accuracy of formula. Results: We did not confirm Young’s equation for the axial gradient to provide aberration-free optics, but derived a slightly different equation. We confirmed the correctness of his equations for deviation of rays in a spherical gradient index and for the focal length of a lens with a nucleus of fixed index surrounded by a cortex of reducing index towards the edge. Young claimed that the equation for focal length applied to a lens with part of the constant index nucleus of the sphere removed, such that the loss of focal length was a quarter of the thickness removed, but this is not strictly correct. Conclusion: Young’s theoretical work in gradient-index optics received no acknowledgement from either his contemporaries or later authors. While his model of the eye lens is not an accurate physiological description of the human lens, with the index reducing least quickly at the edge, it represented a bold attempt to approximate the characteristics of the lens. Thomas Young’s work deserves wider recognition.

Grading scales for contact lens complications

Purpose. To devise and validate artist-rendered grading scales for contact lens complications Methods. Each of eight tissue complications of contact lens wear (listed under 'Results') was painted by a skilled ophthalmic artist (Terry R. Tarrant) in five grades of severity: 0 (normal), 1 (trace), 2 (mild), 3 (moderate) and 4 (severe). A representative slit lamp photograph of a tissue response of each of the eight complications was shown to 404 contact lens practitioners who had never before used clinical grading scales. The practitioners were asked to grade each tissue response to the nearest 0.1 grade unit by interpolation. Results. The standard deviation (± s.d.) of the 404 responses for each tissue complication is tabulated below:_ing_ 0.5 Endothelial pplymegethisjij-4 0.7 Epithelial microcysts 0.5 Endothelial blebs_ 0.4 Stromal edema_onjunctiva! hyperemia 0.4 Stromal neovascularization 0.4 Papillary conjunctivitis 0.5 The frequency distributions and best-fit normal curves were also plotted. The precision of grading (s.d. x 2) ranged from 0.8 to 1.4, with a mean precision of 1.0. Conclusions. Grading scales afford contact lens practitioners with a method of quantifying the severity of adverse tissue responses to contact lens wear. It is noteworthy that the statistically verified precision of grading (1.0 scale unit) concurs precisely with the essential design feature of the grading scales that each grading step of 1.0 corresponds to clinically significant difference in severity. Thus, as a general rule, a difference or change in grade of > 1.0 can be taken to be both clinically and statistically significant when using these grading scales. Trained observers are likely to achieve even greater grading precision. Supported by Hydron Limited.

Eye shape and retinal shape, and their relation to peripheral refraction

Purpose: We provide an account of the relationships between eye shape, retinal shape and peripheral refraction. Recent findings: We discuss how eye and retinal shapes may be described as conicoids, and we describe an axis and section reference system for determining shapes. Explanations are given of how patterns of retinal expansion during the development of myopia may contribute to changing patterns of peripheral refraction, and how pre-existing retinal shape might contribute to the development of myopia. Direct and indirect techniques for determining eye and retinal shape are described, and results are discussed. There is reasonable consistency in the literature of eye length increasing at a greater rate than height and width as the degree of myopia increases, so that eyes may be described as changing from oblate/spherical shapes to prolate shapes. However, one study indicates that the retina itself, while showing the same trend, remains oblate in shape for most eyes (discounting high myopia). Eye shape and retinal shape are not the same and merely describing an eye shape as being prolate or oblate is insufficient without some understanding of the parameters contributing to this; in myopia a prolate eye shape is likely to involve both a steepening retina near the posterior pole combined with a flattening (or a reduction in steepening compared with an emmetrope) away from the pole.

Corneal nerve structure and function as markers of diabetic neuropathy

Diabetic neuropathy is a significant clinical problem that currently has no effective therapy, and in advanced cases, leads to foot ulceration and lower limb amputation. The accurate detection, characterisation and quantification of this condition are important in order to define at-risk patients, anticipate deterioration, monitor progression and assess new therapies. This thesis evaluates novel corneal methods of assessing diabetic neuropathy. Over the past several years two new non-invasive corneal markers have emerged, and in cross-sectional studies have demonstrated their ability to stratify the severity of this disease. Corneal confocal microscopy (CCM) allows quantification of corneal nerve parameters and non-contact corneal aesthesiometry (NCCA), the presumed functional correlate of corneal structure, assesses the sensitivity of the cornea. Both these techniques are quick to perform, produce little or no discomfort for the patient, and with automatic analysis paradigms developed, are suitable for clinical settings. Each has advantages and disadvantages over established techniques for assessing diabetic neuropathy. New information is presented regarding measurement bias of CCM images, and a unique sampling paradigm and associated accuracy determination method of combinations is described. A novel high-speed corneal nerve mapping procedure has been developed and application of this procedure in individuals with neuropathy has revealed regions of sub-basal nerve plexus that dictate further evaluation, as they appear to show earlier signs of damage than the central region of the cornea that has to date been examined. The discriminative capacity of corneal sensitivity measured by NCCA is revealed to have reasonable potential as a marker of diabetic neuropathy. Application of these new corneal markers for longitudinal evaluation of diabetic neuropathy has the potential to reduce dependence on more invasive, costly, and time-consuming assessments, such as skin biopsy.

Utility of corneal confocal microscopy for assessing mild diabetic neuropathy: baseline findings of the LANDMark study

Background:  For those in the field of managing diabetic complications, the accurate diagnosis and monitoring of diabetic peripheral neuropathy (DPN) continues to be a challenge. Assessment of sub-basal corneal nerve morphology has recently shown promise as a novel ophthalmic marker for the detection of DPN. Methods:  Two hundred and thirty-one individuals with diabetes with predominantly mild or no neuropathy and 61 controls underwent evaluation of diabetic neuropathy symptom score, neuropathy disability score, testing with 10 g monofilament, quantitative sensory testing (warm, cold, vibration detection) and nerve conduction studies. Corneal nerve fibre length, branch density and tortuosity were measured using corneal confocal microscopy. Differences in corneal nerve morphology between individuals with and without DPN and controls were investigated using analysis of variance and correlations were determined between corneal morphology and established tests of, and risk factors for, DPN. Results:  Corneal nerve fibre length was significantly reduced in diabetic individuals with mild DPN compared with both controls (p < 0.001) and diabetic individuals without DPN (p = 0.012). Corneal nerve branch density was significantly reduced in individuals with mild DPN compared with controls (p = 0.032). Corneal nerve fibre tortuosity did not show significant differences. Corneal nerve fibre length and corneal nerve branch density showed modest correlations to most measures of neuropathy, with the strongest correlations to nerve conduction study parameters (r = 0.15 to 0.25). Corneal nerve fibre tortuosity showed only a weak correlation to the vibration detection threshold. Corneal nerve fibre length was inversely correlated to glycated haemoglobin (r = -0.24) and duration of diabetes (r = -0.20). Conclusion:  Assessment of corneal nerve morphology is a non-invasive, rapid test capable of showing differences between individuals with and without DPN. Corneal nerve fibre length shows the strongest associations with other diagnostic tests of neuropathy and with established risk factors for neuropathy.