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.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Variation of the Stiles-Crawford effect with accommodation and myopia

Background: Mechanical forces either due to accommodation or myopia may stretch the retina and/or cause shear between the retina and choroid. This can be investigated by making use of the Stiles-Crawford effect (SCE), which is the phenomenon of light changing in apparent brightness as it enters through different positions in the pupil. The SCE can be measured by psychophysical and objective techniques, with the SCE parameters being directionality (rate of change across the pupil), and orientation (the location of peak sensitivity in the pupil). Aims: 1. To study the changes in foveal SCE with accommodation in emmetropes and myopes using a subjective (psychophysical) technique. 2. To develop and evaluate a quick objective technique of measuring the SCE using the multifocal electroretinogram. Methods: The SCE was measured in 6 young emmetropes and 6 young myopes for up to 8 D accommodation stimulus with a psychophysical technique and its variants. An objective technique using the multifocal electroretinogram was developed and evaluated with 5 emmetropes. Results: Using the psychophysical technique, the SCE directionality increased by similar amounts in both emmetropes and myopes as accommodation increased, with an increase of 15-20% with 6 D of accommodation. However, there were no significant orientation changes. Additional measurements showed that most of the change in the directionality was probably an artefact of optical factors such as higher-order aberrations and accommodative lag rather a true effect of accommodation. The multifocal technique demonstrated the presence of the SCE, but results were noisy and too variable to detect any changes in SCE directionality or orientation with accommodation. Conclusion: There is little true change in the SCE with accommodation responses up to 6 D in either emmetropes or myopes, although it is possible that substantial changes might occur at very high accommodation levels. The objective technique using the multifocal electroretinogram was quicker and less demanding for the subjects than the psychophysical technique, but as implemented in this thesis, it is not a reliable method of measuring the SCE.

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.

Modeling corneal surfaces with three-dimensional basis functions

Purpose: To ascertain the effectiveness of object-centered three-dimensional representations for the modeling of corneal surfaces. Methods: Three-dimensional (3D) surface decomposition into series of basis functions including: (i) spherical harmonics, (ii) hemispherical harmonics, and (iii) 3D Zernike polynomials were considered and compared to the traditional viewer-centered representation of two-dimensional (2D) Zernike polynomial expansion for a range of retrospective videokeratoscopic height data from three clinical groups. The data were collected using the Medmont E300 videokeratoscope. The groups included 10 normal corneas with corneal astigmatism less than −0.75 D, 10 astigmatic corneas with corneal astigmatism between −1.07 D and 3.34 D (Mean = −1.83 D, SD = ±0.75 D), and 10 keratoconic corneas. Only data from the right eyes of the subjects were considered. Results: All object-centered decompositions led to significantly better fits to corneal surfaces (in terms of the RMS error values) than the corresponding 2D Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters (2, 4, 6, and 8 mm), and model orders (4th to 10th radial orders) The best results (smallest RMS fit error) were obtained with spherical harmonics decomposition which lead to about 22% reduction in the RMS fit error, as compared to the traditional 2D Zernike polynomials. Hemispherical harmonics and the 3D Zernike polynomials reduced the RMS fit error by about 15% and 12%, respectively. Larger reduction in RMS fit error was achieved for smaller corneral diameters and lower order fits. Conclusions: Object-centered 3D decompositions provide viable alternatives to traditional viewer-centered 2D Zernike polynomial expansion of a corneal surface. They achieve better fits to videokeratoscopic height data and could be particularly suited to the analysis of multiple corneal measurements, where there can be slight variations in the position of the cornea from one map acquisition to the next.

Data collection, storage and retrieval with an underwater sensor network

In this paper we present a novel platform for underwater sensor networks to be used for long-term monitoring of coral reefs and �sheries. The sensor network consists of static and mobile underwater sensor nodes. The nodes communicate point-to-point using a novel high-speed optical communication system integrated into the TinyOS stack, and they broadcast using an acoustic protocol integrated in the TinyOS stack. The nodes have a variety of sensing capabilities, including cameras, water temperature, and pressure. The mobile nodes can locate and hover above the static nodes for data muling, and they can perform network maintenance functions such as deployment, relocation, and recovery. In this paper we describe the hardware and software architecture of this underwater sensor network. We then describe the optical and acoustic networking protocols and present experimental networking and data collected in a pool, in rivers, and in the ocean. Finally, we describe our experiments with mobility for data muling in this network.

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.

Catalyst-free growth and optical properties of vertically aligned ZnO Nanorod Arrays on Si substrates covered with thin buffer layers

Vertically aligned ZnO nanorods have been grown on silicon substrates pre-coated with thin, less than 10 nm, textured ZnO seeding layers via a vapor-solid mechanism. The ZnO seeding layers, which were essential for vertical alignment of ZnO nanorods without using any metal catalyst, were prepared by decomposing zinc acetate. The structure and the luminescence properties of the ZnO nanorods synthesized onto ZnO seeding layers were investigated and their morphologies were compared with those of single-crystalline GaN substrates and silicon substrates covered with sputtered ZnO flms. Patterning of ZnO seed layers using photolithography allowed the fabrication of patterned ZnO-nanorod arrays.

Structural damage identification with noise polluted Frequency Response Functions (FRFs)

Damage detection in structures has become increasingly important in recent years. While a number of damage detection and localization methods have been proposed, very few attempts have been made to explore the structure damage with noise polluted data which is unavoidable effect in real world. The measurement data are contaminated by noise because of test environment as well as electronic devices and this noise tend to give error results with structural damage identification methods. Therefore it is important to investigate a method which can perform better with noise polluted data. This paper introduces a new damage index using principal component analysis (PCA) for damage detection of building structures being able to accept noise polluted frequency response functions (FRFs) as input. The FRF data are obtained from the function datagen of MATLAB program which is available on the web site of the IASC-ASCE (International Association for Structural Control– American Society of Civil Engineers) Structural Health Monitoring (SHM) Task Group. The proposed method involves a five-stage process: calculation of FRFs, calculation of damage index values using proposed algorithm, development of the artificial neural networks and introducing damage indices as input parameters and damage detection of the structure. This paper briefly describes the methodology and the results obtained in detecting damage in all six cases of the benchmark study with different noise levels. The proposed method is applied to a benchmark problem sponsored by the IASC-ASCE Task Group on Structural Health Monitoring, which was developed in order to facilitate the comparison of various damage identification methods. The illustrated results show that the PCA-based algorithm is effective for structural health monitoring with noise polluted FRFs which is of common occurrence when dealing with industrial structures.