Wavefront aberrations and the depth of focus of the human eye

The depth of focus (DOF) can be defined as the variation in image distance of a lens or an optical system which can be tolerated without incurring an objectionable lack of sharpness of focus. The DOF of the human eye serves a mechanism of blur tolerance. As long as the target image remains within the depth of focus in the image space, the eye will still perceive the image as being clear. A large DOF is especially important for presbyopic patients with partial or complete loss of accommodation (presbyopia), since this helps them to obtain an acceptable retinal image when viewing a target moving through a range of near to intermediate distances. The aim of this research was to investigate the DOF of the human eye and its association with the natural wavefront aberrations, and how higher order aberrations (HOAs) can be used to expand the DOF, in particular by inducing spherical aberrations ( 0 4 Z and 0 6 Z ). The depth of focus of the human eye can be measured using a variety of subjective and objective methods. Subjective measurements based on a Badal optical system have been widely adopted, through which the retinal image size can be kept constant. In such measurements, the subject.s tested eye is normally cyclopleged. Objective methods without the need of cycloplegia are also used, where the eye.s accommodative response is continuously monitored. Generally, the DOF measured by subjective methods are slightly larger than those measured objectively. In recent years, methods have also been developed to estimate DOF from retinal image quality metrics (IQMs) derived from the ocular wavefront aberrations. In such methods, the DOF is defined as the range of defocus error that degrades the retinal image quality calculated from the IQMs to a certain level of the possible maximum value. In this study, the effect of different amounts of HOAs on the DOF was theoretically evaluated by modelling and comparing the DOF of subjects from four different clinical groups, including young emmetropes (20 subjects), young myopes (19 subjects), presbyopes (32 subjects) and keratoconics (35 subjects). A novel IQM-based through-focus algorithm was developed to theoretically predict the DOF of subjects with their natural HOAs. Additional primary spherical aberration ( 0 4 Z ) was also induced in the wavefronts of myopes and presbyopes to simulate the effect of myopic refractive correction (e.g. LASIK) and presbyopic correction (e.g. progressive power IOL) on the subject.s DOF. Larger amounts of HOAs were found to lead to greater values of predicted DOF. The introduction of primary spherical aberration was found to provide moderate increase of DOF while slightly deteriorating the image quality at the same time. The predicted DOF was also affected by the IQMs and the threshold level adopted. We then investigated the influence of the chosen threshold level of the IQMs on the predicted DOF, and how it relates to the subjectively measured DOF. The subjective DOF was measured in a group of 17 normal subjects, and we used through-focus visual Strehl ratio based on optical transfer function (VSOTF) derived from their wavefront aberrations as the IQM to estimate the DOF. The results allowed comparison of the subjective DOF with the estimated DOF and determination of a threshold level for DOF estimation. Significant correlation was found between the subject.s estimated threshold level for the estimated DOF and HOA RMS (Pearson.s r=0.88, p<0.001). The linear correlation can be used to estimate the threshold level for each individual subject, subsequently leading to a method for estimating individual.s DOF from a single measurement of their wavefront aberrations. A subsequent study was conducted to investigate the DOF of keratoconic subjects. Significant increases of the level of HOAs, including spherical aberration, coma and trefoil, can be observed in keratoconic eyes. This population of subjects provides an opportunity to study the influence of these HOAs on DOF. It was also expected that the asymmetric aberrations (coma and trefoil) in the keratoconic eye could interact with defocus to cause regional blur of the target. A dual-Badal-channel optical system with a star-pattern target was used to measure the subjective DOF in 10 keratoconic eyes and compared to those from a group of 10 normal subjects. The DOF measured in keratoconic eyes was significantly larger than that in normal eyes. However there was not a strong correlation between the large amount of HOA RMS and DOF in keratoconic eyes. Among all HOA terms, spherical aberration was found to be the only HOA that helped to significantly increase the DOF in the studied keratoconic subjects. Through the first three studies, a comprehensive understanding of DOF and its association to the HOAs in the human eye had been achieved. An adaptive optics system was then designed and constructed. The system was capable of measuring and altering the wavefront aberrations in the subject.s eye and measuring the resulting DOF under the influence of different combination of HOAs. Using the AO system, we investigated the concept of extending the DOF through optimized combinations of 0 4 Z and 0 6 Z . Systematic introduction of a targeted amount of both 0 4 Z and 0 6 Z was found to significantly improve the DOF of healthy subjects. The use of wavefront combinations of 0 4 Z and 0 6 Z with opposite signs can further expand the DOF, rather than using 0 4 Z or 0 6 Z alone. The optimal wavefront combinations to expand the DOF were estimated using the ratio of increase in DOF and loss of retinal image quality defined by VSOTF. In the experiment, the optimal combinations of 0 4 Z and 0 6 Z were found to provide a better balance of DOF expansion and relatively smaller decreases in VA. Therefore, the optimal combinations of 0 4 Z and 0 6 Z provides a more efficient method to expand the DOF rather than 0 4 Z or 0 6 Z alone. This PhD research has shown that there is a positive correlation between the DOF and the eye.s wavefront aberrations. More aberrated eyes generally have a larger DOF. The association of DOF and the natural HOAs in normal subjects can be quantified, which allows the estimation of DOF directly from the ocular wavefront aberration. Among the Zernike HOA terms, spherical aberrations ( 0 4 Z and 0 6 Z ) were found to improve the DOF. Certain combinations of 0 4 Z and 0 6 Z provide a more effective method to expand DOF than using 0 4 Z or 0 6 Z alone, and this could be useful in the optimal design of presbyopic optical corrections such as multifocal contact lenses, intraocular lenses and laser corneal surgeries.

The Glenn A. Fry award lecture 2011 : peripheral optics of the human eye

There has been a low level of interest in peripheral aberrations and corresponding image quality for over 200 years. Most work has been concerned with the second-order aberrations of defocus and astigmatism that can be corrected with conventional lenses. Studies have found high levels of aberration, often amounting to several dioptres, even in eyes with only small central defocus and astigmatism. My investigations have contributed to understanding shape changes in the eye with increases in myopia, changes in eye optics with ageing, and how surgical interventions intended to correct central refractive errors have unintended effects on peripheral optics. My research group has measured peripheral second- and higher-order aberrations over a 42° horizontal × 32° vertical diameter visual field. There is substantial variation in individual aberrations with age and pathology. While the higher-order aberrations in the periphery are usually small compared with second-order aberrations, they can be substantial and change considerably after refractive surgery. The thrust of my research in the next few years is to understand more about the peripheral aberrations of the human eye, to measure visual performance in the periphery and determine whether this can be improved by adaptive optics correction, to use measurements of peripheral aberrations to learn more about the optics of the eye and in particular the gradient index structure of the lens, and to investigate ways of increasing the size of the field of good retinal image quality.

Depth of focus of the human eye

In general optical systems, the range of distances over which the detector cannot detect any change in focus is called the depth-of-field. This may be specified by movement of the object or image planes, with the former being referred to as depth-of-field and the latter as depth-of-focus (DOF). Either term can be used in vision science, where we refer to changes in vergence which have the same value in both object and image space.

Optics of the human eye in diabetes

This study compared optics of eyes in people with diabetes with those age-balanced controls. Relative to the control group, the diabetes group demonstrated greater lens thickness, more curved lens shapes, smaller lens diameters, higher light scatter, greater lens yellowing, and poorer focusing ability. While the optics of the people with diabetes made them appear as older eyes than those of people of the same age without diabetes, the differences did not increase significantly with age. It was concluded that age-related changes in eyes of people with diabetes need not be accelerated if the diabetes is well controlled.

Editorial: Measuring refractive index distribution in the human eye lens

Non-invasive measurements of the age dependence of refractive index distribution in human eye lenses in vitro using a novel X-ray Talbot Interferometry method. In their paper, the authors make frequent reference to our own work in which we employed magnetic resonance imaging (MRI) to make similar non-invasive measurements of the refractive index distribution in the human eye lens [2, 3]. Prior to the current work, ours was the only method for making such measurements both non-invasively and without prior assumptions about the shape of the refractive index distribution. For this reason, the latest work is to be welcomed. However at several points in the paper, Pierscionek et al. [1] make statements about our technique which are factually incorrect...

A Human identification technique using images of the iris and wavelet transform

A new approach for recognizing the iris of the human eye is presented. Zero-crossings of the wavelet transform at various resolution levels are calculated over concentric circles on the iris, and the resulting one-dimensional (1-D) signals are compared with model features using different dissimilarity functions.

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.

Depth of focus and visual acuity with primary and secondary spherical aberration

It is known that the depth of focus (DOF) of the human eye can be affected by the higher order aberrations. We estimated the optimal combinations of primary and secondary Zernike spherical aberration to expand the DOF and evaluated their efficiency in real eyes using an adaptive optics system. The ratio between increased DOF and loss of visual acuity was used as the performance indicator. The results indicate that primary or secondary spherical aberration alone shows similar effectiveness in extending the DOF. However, combinations of primary and secondary spherical aberration with different signs provide better efficiency for expanding the DOF. This finding suggests that the optimal combinations of primary and secondary spherical aberration may be useful in the design of optical presbyopic corrections. © 2011 Elsevier Ltd. All rights reserved.

Assessment of corneal dynamics with high-speed swept source optical coherence tomography combined with an air puff system

We present a novel method and instrument for in vivo imaging and measurement of the human corneal dynamics during an air puff. The instrument is based on high-speed swept source optical coherence tomography (ssOCT) combined with a custom adapted air puff chamber from a non-contact tonometer, which uses an air stream to deform the cornea in a non-invasive manner. During the short period of time that the deformation takes place, the ssOCT acquires multiple A-scans in time (M-scan) at the center of the air puff, allowing observation of the dynamics of the anterior and posterior corneal surfaces as well as the anterior lens surface. The dynamics of the measurement are driven by the biomechanical properties of the human eye as well as its intraocular pressure. Thus, the analysis of the M-scan may provide useful information about the biomechanical behavior of the anterior segment during the applanation caused by the air puff. An initial set of controlled clinical experiments are shown to comprehend the performance of the instrument and its potential applicability to further understand the eye biomechanics and intraocular pressure measurements. Limitations and possibilities of the new apparatus are discussed.

Ocular characteristics of anisometropia

Animal models of refractive error development have demonstrated that visual experience influences ocular growth. In a variety of species, axial anisometropia (i.e. a difference in the length of the two eyes) can be induced through unilateral occlusion, image degradation or optical manipulation. In humans, anisometropia may occur in isolation or in association with amblyopia, strabismus or unilateral pathology. Non-amblyopic myopic anisometropia represents an interesting anomaly of ocular growth, since the two eyes within one visual system have grown to different endpoints. These experiments have investigated a range of biometric, optical and mechanical properties of anisometropic eyes (with and without amblyopia) with the aim of improving our current understanding of asymmetric refractive error development. In the first experiment, the interocular symmetry in 34 non-amblyopic myopic anisometropes (31 Asian, 3 Caucasian) was examined during relaxed accommodation. A high degree of symmetry was observed between the fellow eyes for a range of optical, biometric and biomechanical measurements. When the magnitude of anisometropia exceeded 1.75 D, the more myopic eye was almost always the sighting dominant eye. Further analysis of the optical and biometric properties of the dominant and non-dominant eyes was conducted to determine any related factors but no significant interocular differences were observed with respect to best-corrected visual acuity, corneal or total ocular aberrations during relaxed accommodation. Given the high degree of symmetry observed between the fellow eyes during distance viewing in the first experiment and the strong association previously reported between near work and myopia development, the aim of the second experiment was to investigate the symmetry between the fellow eyes of the same 34 myopic anisometropes following a period of near work. Symmetrical changes in corneal and total ocular aberrations were observed following a short reading task (10 minutes, 2.5 D accommodation demand) which was attributed to the high degree of interocular symmetry for measures of anterior eye morphology, and corneal biomechanics. These changes were related to eyelid shape and position during downward gaze, but gave no clear indication of factors associated with near work that might cause asymmetric eye growth within an individual. Since the influence of near work on eye growth is likely to be most obvious during, rather than following near tasks, in the third experiment the interocular symmetry of the optical and biometric changes was examined during accommodation for 11 myopic anisometropes. The changes in anterior eye biometrics associated with accommodation were again similar between the eyes, resulting in symmetrical changes in the optical characteristics. However, the more myopic eyes exhibited slightly greater amounts of axial elongation during accommodation which may be related to the force exerted by the ciliary muscle. This small asymmetry in axial elongation we observed between the eyes may be due to interocular differences in posterior eye structure, given that the accommodative response was equal between eyes. Using ocular coherence tomography a reduced average choroidal thickness was observed in the more myopic eyes compared to the less myopic eyes of these subjects. The interocular difference in choroidal thickness was correlated with the magnitude of spherical equivalent and axial anisometropia. The symmetry in optics and biometrics between fellow eyes which have undergone significantly different visual development (i.e. anisometropic subjects with amblyopia) is also of interest with respect to refractive error development. In the final experiment the influence of altered visual experience upon corneal and ocular higher-order aberrations was investigated in 21 amblyopic subjects (8 refractive, 11 strabismic and 2 form deprivation). Significant differences in aberrations were observed between the fellow eyes, which varied according to the type of amblyopia. Refractive amblyopes displayed significantly higher levels of 4th order corneal aberrations (spherical aberration and secondary astigmatism) in the amblyopic eye compared to the fellow non-amblyopic eye. Strabismic amblyopes exhibited significantly higher levels of trefoil, a third order aberration, in the amblyopic eye for both corneal and total ocular aberrations. The results of this experiment suggest that asymmetric visual experience during development is associated with asymmetries in higher-order aberrations, proportional to the magnitude of anisometropia and dependent upon the amblyogenic factor. This suggests a direct link between the development of higher-order optical characteristics of the human eye and visual feedback. The results from these experiments have shown that a high degree of symmetry exists between the fellow eyes of non-amblyopic myopic anisometropes for a range of biomechanical, biometric and optical parameters for different levels of accommodation and following near work. While a single specific optical or biomechanical factor that is consistently associated with asymmetric refractive error development has not been identified, the findings from these studies suggest that further research into the association between ocular dominance, choroidal thickness and higher-order aberrations with anisometropia may improve our understanding of refractive error development.

Evaluation of fibroin-based scaffolds for ocular tissue reconstruction

The epithelium of the corneolimbus contains stem cells for regenerating the corneal epithelium. Diseases and injuries affecting the limbus can lead to a condition known as limbal stem cell deficiency (LSCD), which results in loss of the corneal epithelium, and subsequent chronic inflammation and scarring of the ocular surface. Advances in the treatment of LSCD have been achieved through use of cultured human limbal epithelial (HLE) grafts to restore epithelial stem cells of the ocular surface. These epithelial grafts are usually produced by the ex vivo expansion of HLE cells on human donor amniotic membrane (AM), but this is not without limitations. Although AM is the most widely accepted substratum for HLE transplantation, donor variation, risk of disease transfer, and rising costs have led to the search for alternative biomaterials to improve the surgical outcome of LSCD. Recent studies have demonstrated that Bombyx mori silk fibroin (hereafter referred to as fibroin) membranes support the growth of primary HLE cells, and thus this thesis aims to explore the possibility of using fibroin as a biomaterial for ocular surface reconstruction. Optimistically, the grafted sheets of cultured epithelium would provide a replenishing source of epithelial progenitor cells for maintaining the corneal epithelium, however, the HLE cells lose their progenitor cell characteristics once removed from their niche. More severe ocular surface injuries, which result in stromal scarring, damage the epithelial stem cell niche, which subsequently leads to poor corneal re-epithelialisation post-grafting. An ideal solution to repairing the corneal limbus would therefore be to grow and transplant HLE cells on a biomaterial that also provides a means for replacing underlying stromal cells required to better simulate the normal stem cell niche. The recent discovery of limbal mesenchymal stromal cells (L-MSC) provides a possibility for stromal repair and regeneration, and therefore, this thesis presents the use of fibroin as a possible biomaterial to support a three dimensional tissue engineered corneolimbus with both an HLE and underlying L-MSC layer. Investigation into optimal scaffold design is necessary, including adequate separation of epithelial and stromal layers, as well as direct cell-cell contact. Firstly, the attachment, morphology and phenotype of HLE cells grown on fibroin were directly compared to that observed on donor AM, the current clinical standard substrate for HLE transplantation. The production, transparency, and permeability of fibroin membranes were also evaluated in this part of the study. Results revealed that fibroin membranes could be routinely produced using a custom-made film casting table and were found to be transparent and permeable. Attachment of HLE cells to fibroin after 4 hours in serum-free medium was similar to that supported by tissue culture plastic but approximately 6-fold less than that observed on AM. While HLE cultured on AM displayed superior stratification, epithelia constructed from HLE on fibroin maintained evidence of corneal phenotype (cytokeratin pair 3/12 expression; CK3/12) and displayed a comparable number and distribution of ÄNp63+ progenitor cells to that seen in cultures grown on AM. These results confirm the suitability of membranes constructed from silk fibroin as a possible substrate for HLE cultivation. One of the most important aspects in corneolimbal tissue engineering is to consider the reconstruction of the limbal stem cell niche to help form the natural limbus in situ. MSC with similar properties to bone marrow derived-MSC (BM-MSC) have recently been grown from the limbus of the human cornea. This thesis evaluated methods for culturing L-MSC and limbal keratocytes using various serum-free media. The phenotype of resulting cultures was examined using photography, flow cytometry for CD34 (keratocyte marker), CD45 (bone marrow-derived cell marker), CD73, CD90, CD105 (collectively MSC markers), CD141 (epithelial/vascular endothelial marker), and CD271 (neuronal marker), immunocytochemistry (alpha-smooth muscle actin; á-sma), differentiation assays (osteogenesis, adipogenesis and chrondrogenesis), and co-culture experiments with HLE cells. While all techniques supported to varying degrees establishment of keratocyte and L-MSC cultures, sustained growth and serial propagation was only achieved in serum-supplemented medium or the MesenCult-XF„¥ culture system (Stem Cell Technologies). Cultures established in MesenCult-XF„¥ grew faster than those grown in serum-supplemented medium and retained a more optimal MSC phenotype. L-MSC cultivated in MesenCult-XFR were also positive for CD141, rarely expressed £\-sma, and displayed multi-potency. L-MSC supported growth of HLE cells, with the largest epithelial islands being observed in the presence of L-MSC established in MesenCult-XF„¥ medium. All HLE cultures supported by L-MSC widely expressed the progenitor cell marker £GNp63, along with the corneal differentiation marker CK3/12. Our findings conclude that MesenCult-XFR is a superior culture system for L-MSC, but further studies are required to explore the significance of CD141 expression in these cells. Following on from the findings of the previous two parts, silk fibroin was tested as a novel dual-layer construct containing both an epithelium and underlying stroma for corneolimbal reconstruction. In this section, the growth and phenotype of HLE cells on non-porous versus porous fibroin membranes was compared. Furthermore, the growth of L-MSC in either serum-supplemented medium or the MesenCult-XFR culture system within fibroin fibrous mats was investigated. Lastly, the co-culture of HLE and L-MSC in serum-supplemented medium on and within fibroin dual-layer constructs was also examined. HLE on porous membranes displayed a flattened and squamous monolayer; in contrast, HLE on non-porous fibroin appeared cuboidal and stratified closer in appearance to a normal corneal epithelium. Both constructs maintained CK3/12 expression and distribution of £GNp63+ progenitor cells. Dual-layer fibroin scaffolds consisting of HLE cells and L-MSC maintained a similar phenotype as on the single layers alone. Overall, the present study proposed to create a three dimensional limbal tissue substitute of HLE cells and L-MSC together, ultimately for safe and beneficial transplantation back into the human eye. The results show that HLE and L-MSC can be cultivated separately and together whilst maintaining a clinically feasible phenotype containing a majority of progenitor cells. In addition, L-MSC were able to be cultivated routinely in the MesenCult-XF® culture system while maintaining a high purity for the MSC characteristic phenotype. However, as a serum-free culture medium was not found to sustain growth of both HLE and L-MSC, the combination scaffold was created in serum-supplemented medium, indicating that further refinement of this cultured limbal scaffold is required. This thesis has also demonstrated a potential novel marker for L-MSC, and has generated knowledge which may impact on the understanding of stromal-epithelial interactions. These results support the feasibility of a dual-layer tissue engineered corneolimbus constructed from silk fibroin, and warrant further studies into the potential benefits it offers to corneolimbal tissue regeneration. Further refinement of this technology should explore the potential benefits of using epithelial-stromal co-cultures with MesenCult-XF® derived L-MSC. Subsequent investigations into the effects of long-term culture on the phenotype and behaviour of the cells in the dual-layer scaffolds are also required. While this project demonstrated the feasibility in vitro for the production of a dual-layer tissue engineered corneolimbus, further studies are required to test the efficacy of the limbal scaffold in vivo. Future in vivo studies are essential to fully understand the integration and degradation of silk fibroin biomaterials in the cornea over time. Subsequent experiments should also investigate the use of both AM and silk fibroin with epithelial and stromal cell co-cultures in an animal model of LSCD. The outcomes of this project have provided a foundation for research into corneolimbal reconstruction using biomaterials and offer a stepping stone for future studies into corneolimbal tissue engineering.