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Atmospheric turbulence limits the resolving power of astronomical telescopes by distorting the paths of light between distant objects of interest and the imaging camera at the telescope. After many light-years of travel, passing through the turbulence in that last 100km of a photon’s journey results in a blurred image in the telescope, no less than 1” (arc-second) in width. To achieve higher resolutions, corresponding to smaller image widths, various methods have been proposed with varying degrees of effectiveness and practicality. Space telescopes avoid atmospheric turbulence completely and are limited in resolution solely by the size of their mirror apertures. However, the design and maintenance cost of space telescopes, which increases prohibitively with size, has limited the number of space telescopes deployed for astronomical imaging purposes. Ground based telescopes can be built larger and more cheaply, so atmospheric compensation schemes using adaptive optical cancellation mirrors can be a cheaper substitute for space telescopes. Adaptive optics is referred to here as the use of electronic control of optical component to modify the phase of an incident ray within an optical system like an imaging telescope. Fast adaptive optics systems operating in real-time can be used to correct the optical aberrations introduced by atmospheric turbulence. To compensate those aberrations, they must first be measured using a wavefront sensor. The wavefront estimate from the wavefront sensor can then be applied, in a closed-loop system, to a deformable mirror to compensate the incoming wavefront. Many wavefront sensors have been proposed and are in used today in adaptive optics and atmospheric turbulence measurement systems. Experimental results comparing the performance of wavefront sensors have also been published. However, little detailed analyses of the fundamental similarities and differences between the wavefront sensors have been performed. This study concentrates on fourmain types of wavefront sensors, namely the Shack-Hartmann, pyramid, geometric, and the curvature wavefront sensors, and attempts to unify their description within a common framework. The quad-cell is a wavefront slope detector and is first examined as it lays the groundwork for analysing the Shack-Hartmann and pyramid wavefront sensors. The quad-cell slope detector is examined, and a new measure of performance based on the Strehl ratio of the focal plane image is adopted. The quad-cell performance based on the Strehl ratio is compared using simulations against the Cramer-Rao bound, an information theoretic or statistical limit, and a polynomial approximation. The effects of quad-cell modulation, its relationship to extended objects, and the effect on performance are also examined briefly. In the Shack-Hartmann and pyramid wavefront sensor, a strong duality in the imaging and aperture planes exists, allowing for comparison of the performance of the two wavefront sensors. Both sensors subdivide the input wavefront into smaller regions, and measure the local slope. They are equivalent in every way except for the order in which the subdivision and slope measurements were carried out. We show that this crucial difference leads to a theoretically higher performance from the pyramid wavefront sensor. We also presented simulations showing the trade-off between sensor precision and resolution. The geometric wavefront sensor can be considered to be an improved curvature wavefront sensor as it uses a more accurate algorithm based on geometric optics to estimate the wavefront. The algorithm is relatively new and has not found application in operating adaptive optics systems. Further analysis of the noise propagation in the algorithm, sensor resolution, and precision is presented. We also made some observations on the implementation of the geometric wavefront sensor based on image recovery through projections.

The purpose of this research was to develop a more convenient method to distinguish bacteria using Fourier transform infrared (FT-IR) spectroscopy. The specular reflectance infrared spectra of bacterial colonies were obtained in-situ, without removing them from the agar growth media. The spectra of a variety of bacterial species were obtained by the infrared microscope and then were analyzed by factor analysis. Using this statistical method in conjunction with in-situ sampling we evaluated how well Grampositive species were sorted from Gram-negative species. Also, how the type of agar used and how the age of bacterial colonies affects the results of Gram stain predictions were evaluated; our experiments showed that the influence of those various conditions can be decreased. The suitability of various sets of standard spectra for predicting Gram stain, including sets constructed with and without Kramers-Kronig transformation and those constructed using partial regions verses the complete mid-infrared region, was evaluated.The effect that water on the surface of the colonies has been studied in distinguishing bacteria. Furthermore, the original method was improved and the method's suitability to differentiate a larger number of different bacterial species was examined. / Department of Chemistry

A mathematical method is developed for the analysis of the electrostatic fields existing within finite, three-dimensional, cylindrically shaped regions which do not contain the axis of revolution. The derived method defines the potential field within such a region provided that the potentials are known at the boundaries, that the insulating media has homogeneous, linear, and isotropic characteristics, and that the region is charge free. The general solution for the potential field involves forms of both the Fourier and the Fourier Bessel series, and the resulting series solution is shown to be uniformly convergent . It is also shoran that this potential field series solution can be integrated and differentiated to yield series solutions for electric fiend and capacitance and that these solutions are also uniformly convergent.

El objetivo general de este trabajo de tesis consiste en investigar la incidencia del formalismo de la transformada de Fourier fraccionaria en el procesamiento óptico de la información, analizar su relación con otras transformadas de interés óptico y desarrollar sus posibles aplicaciones / Asesor académico: Dr. Mario Garavaglia

The wavelet transform technique has been frequently used in time-frequency analysis as a relatively new concept. Compared to the traditional technique Short-time Fourier Transform (STFT), which is theoretically based on the Fourier transform, the wavelet transform has its advantage on better locality in time and frequency domain, but not significant as the solutions in spectrum. Wavelet transform has dynamic ‘window functions’ to represent time-frequency positions of raw signals, and can get better resolutions in time-frequency analysis. In this report, we shall first briefly introduce fuzzy sets and related concepts. And then we will evaluate their similarities and differences by not only the theoretic comparisons between STFT and wavelet transform, but also the process of the de-nosing to a noisy recorded signal.

New techniques in Fourier transform nuclear magnetic resonance spectroscopy are introduced with chemical applications to the study of molecules in the liquid state. Recently a theoretical description of magnetic resonance in terms of single transition operators has been introduced which provides a geometric interpretation of the behaviour of a spin system. This formalism is developed further and extended to the general description of a system of nonequivalent spin-1/2 nuclei. Operator combinations are introduced which allow extension of the convenient geometric representation to the concerted behaviour of coupled spins. The operator formalism is applied to the excitation and detection of multiple quantum transitions, providing a description of the processes in terms of rotating vectors. The process of coherence transfer in two-dimensional Fourier transform experiments is studied in detail and single transition operators are used to derive a general expression for the tip angle dependence of the detection process. A method of discriminating the sense of precession of double quantum coherence is presented and applied to the correlation of chemical shifts of carbon-13 spins in natural abundance. A new technique is presented for the correlation of chemical shift information in coupled proton spin systems in which excitation and indirect detection of double quantum transitions is used to assign coupling patterns in complex spectra. The tip angle dependence of the detection process is used to suppress all but direct correlation of spins. Methods for the measurement of heteronuclear coupling constants in proton spectra are introduced which discriminate the heteronuclear satellites from the parent proton resonance. The technique provides a sensitivity advantage over direct measurement of coupling in the heteronuclear spectrum. Ambiguities are encountered when the protonproton and proton-heteronuclear coupling constants are of the same order of magnitude. This problem is overcome by extension of the basic experiment to its two-dimensional analogue.

As a contribution to increasing the areal density of digital data stored on a magnetic recording medium, this thesis provides mathematical analyses of various magnetic recording heads. Each of the heads considered here is for use in a perpendicular recording system, writing to or reading from a multi-layer medium which includes a high magnetic permeability layer between the data storage layer and the substrate. The exact two-dimensional analysis is performed in each case by one of two methods: either Fourier analysis or conformal mapping. The types of heads analysed include conventional styles but particular emphasis is placed on the effects of the novel idea of potential grading across the pole pieces. Exact head fields are derived for thin film heads with both constant and linearly varying pole potentials, single pole heads with linearly and arbitrarily varying pole potentials and shielded magnetoresistive heads, all in the presence of a magnetic underlayer. These and other published solutions are used to derive output characteristics for perpendicular replay heads, which are compared with published theoretical and experimental results where possible. The Fourier solutions obtained are in the form of infinite series dependent on at least one set of coefficients which are determined by infinite systems of linear equations. Approximations to the potentials in the head face planes, independent of these coefficients, are derived from the exact Fourier solutions. The accuracy of these approximations is demonstrated when they are used to estimate the vertical field components and the spectral response functions. Heads with graded pole potentials are found to have more localised vertical field components than the corresponding constant potential heads. They are also better suited for use with thin media for 'in contact' recording.

In this work, a rapid Fourier transform near infrared (FT-NIR) spectroscopic peroxide value (PV) method was developed and a prototype Continuous Oil Analysis and Treatment (COAT) system was assessed for monitoring and analytical purposes. High erucic acid rapeseed oil, a principle representative of triglyceride based oils suitable for biodegradable lubricating applications and mineral oil were used to test the methodology developed. / The FT-NIR PV method is based on a well defined stoichiometric reaction of triphenylphospine (TPP) with hydroperoxides to form triphenylphospine oxide (TPPO). A partial least squares calibration model for the prediction of PV was developed using the NIR spectral region where TPP and TPPO co-absorb. The resulting calibration was highly linear over the analytical range of 100PV. Validation of the method carried out by comparing the PV of PLS prediction to the results of AOCS iodometric procedures indicated an excellent concurrence between the two methods. By programming the FT-NIR spectrometer, the analytical procedure simply consists of the addition of TPP stock solution to oil sample, mixing, taking its spectrum and predicting PV value. Through selected testing procedures, the prototype COAT system utilizing FTIR spectroscopy, advanced sample handling system designs, and computer programming was proved to be effective in monitoring the oil quality and behavior of antioxidants in real time. / Both approaches offer combined advantages of speed, accuracy, low labor cost, automation, and environmental friendliness mainly derived from FTIR spectroscopy, and can serve as convenient means for routine quality control applications in oils and fats industry. Potential application based on the joint usage of the two methods in the obtaining of true value of oil stability was also presented in this text. (Abstract shortened by UMI.)

The process by which foods are browned during baking and roasting is attributed to the Maillard reaction. The interaction of the $ alpha$-hydroxycarbonyl moiety of a reducing sugar with an amino compound can result in a complex series of changes. The identification and isolation of the key intermediates, known as the Amadori rearrangement product (ARP) and Heyns rearrangement product (HRP), can provide a greater understanding of the browning process. / Fourier transform infrared (FTIR) analysis of 1-hydroxyacetane provided qualitative and quantitative information of the behavior of this $ alpha$-hydroxycarbonyl compound in various aqueous and non-aqueous solutions. / The carbonyl peaks (in the 1750-1700 $ rm cm sp{-1}$ absorption region) due to the keto and aldehydo forms of 1-hydroxyacetone (acetol) in the pure state and in deuterium oxide $ rm(D sb2O)$ were assigned. Upon addition of the acid-base catalysts (triethylamine, 5% NaOD and 5% DCl) additional peaks were detected in the alkene region (1700-1650 $ rm cm sp{-1})$ due to the formation of enediols by enolization. The examination of analogous hydroxycarbonyl structures (1-hydroxy-2-butanone, glyceraldehyde, glycoaldehyde and dihydroxyacetone) provided the means to confirm the assignments of the carbonyl and enediol bands. / The integrated intensity of the carbonyl peak of 1-hydroxyacetone centered at 1720 $ rm cm sp{-1}$ was determined for dilute solutions in $ rm D sb2O.$ The integrated molar absorptivity of the carbonyl band was calculated to be 3674 L/mol/cm. In addition, the effect of concentration and temperature on dimer dissociation was investigated. The effect of solvent and temperature on enolization was also studied. Time run analysis of the carbonyl-amine reaction of 1-hydroxyacetone with pyrrolidine provided the basis for a kinetic study of the rearrangement process in the early stage of Maillard reaction.