Search

The purpose of this research has been to develop technology necessary for Low-Cost Magnetic Resonance Imaging (LC-MRI) machines. This dissertation describes an overview of the tradeoffs necessary for LC-MRI machines and focuses on compensating for magnetic field inhomogeneity. The trade-offs for allowing inhomogeneous fields is examined. The equations describing inhomogeneity are derived for both one and two dimensions. Two methods of image compensation are compared, one from the literature and a new, proposed method. Both methods are demonstrated and analyzed on one-dimensional and two-dimensional images. The robustness of each method to uncompensated quantization errors and field mis-measurement is also examined. The computational complexity of each method is also investigated. The appendix of the dissertation covers background on MRI. The classical model of MRI is explained as well as the meaning of the time constants T1, T2, and T2*. Two fundamental pulse sequences (Field Echo and Spin Echo) are explained in detail, along with a description of k-space.

In wavelength division multiplexed (WDM) optical communication networks, signals are amplified periodically by optical amplifiers. Since the gain profiles of optical amplifiers are not flat, equalizers are usually used to maintain signal powers at different wavelengths in equal to avoid crosstalk and data loss. However, fixed attenuation can only compensate fixed input power and amplification. In active network, input power and amplifier gain change with time. Active level compensation at each wavelength is needed. An adaptive attenuator is a device with a chromatically variable transmissivity used to equalize channel powers in wavelength-division multiplexing (WDM) fiber-optic communication lines. In this thesis, a method of Fourier analysis of multi-beam interference is developed. It is shown that the total electric field and relative phase delay of each beam form a Fourier transform pair. Thus methods and properties of Fourier analysis are applicable in multi-beam interference analysis and design. Fourier transform based design is presented. Novel devices that apply such design principles are introduced. Principles and structures of novel adaptive attenuators based on various technologies such as segment deformable mirror, liquid crystal, phase modulation array are given. Simulation results for segment deformable mirror based adaptive attenuator are presented.

Infrared radiative cooling of vibrationally excited n-butylbenzene ions was studied in chapter III. This was done by a technique called ion thermometry, where the internal energy of the ions could be probed by the branching ratio of two competitive photoproducts. The infrared radiative cooling rate constant was observed to be 0.8 s-1 for ions with energies of only 0.3 eV above room temperature.Confidence in the thermometric data depended on the reliability of the measured branching ratios. In chapter IV a computer simulation was used to show that erroneous peak height ratios were produced by the Coulombic repulsion between ions during ion excitation, and reliable ratios could be obtained by working at low excitation, and reliable ratios could be obtained by working at low ion densities and using a short excitation pulse.Chapter V discussed our first attempt to describe infrared multiphoton dissociation (IRMPD) of trapped ions in a thermal framework. Using a computer simulation the laser intensity was associated with an internal ion temperature for ions undergoing continuous laser irradiation. An Arrhenius type plot was constructed, and the activation energy obtained from it seemed reasonable within the expectations from Tolman’s theorem.To pursue the feasibility of the thermal analysis of IRMPD kinetics, the thermometric technique was used in chapter VI to observe the CO2 laser pumping process for n-butylbenzene ions. The data showed that the steady state distribution of the ion energies reached during laser pumping is very dependent on the rate of photon absorption and emission. The generalized thermal analysis which was done in chapter V was found to be unfeasible.Ion thermometry was also used in chapter V to observe the rate of photon emission from n-butylbenzene ions heated by the cw-CO2 laser. Although the ions contained 0.3 eV more energy than the ions studied in chapter 2, the observed rate of cooling was the same.Chapter VII describes the association reactions between silicon ions and a series of aromatic molecules (benzene, naphthalene, and anthracene). These reactions are mediated by the emission of an infrared photon, thereby termed radiative association reactions. In all three cases the silicon ion inserted into the C-H bond of the molecules as shown by the collision induced dissociation spectra of the association product ions.

Objective methods of fold shape analysis are necessary to better understand the behavior of folds and the folding process. I examined two methods of analysis, and used a method based on the Fourier Transform to show that the method based on the Fourier Series was insufficient for identifying shape characteristics of aperiodic natural fold trains. I also showed that the Fourier Transform method accessed information that was inaccessible using the Fourier Series method.

Knowledge of how an image is changed by a given modification of its Fourier transform is important when attempting to find solutions to problems in image processing. Several types of filters were used to modify the Fourier transforms of an edge and a bartarget. The images were reconstructed from the modified transforms to determine the change produced by a given modification. Various regions of the Fourier transform determine specific characteristics of the image. The amplitude of the low frequencies controls the form and average level of the image, while the amplitude of the high frequencies effects sharp transitions and noise.

Digital Image Processing techniques have become increasingly popular in the last few years. Conventional silver halide photography continues to be used by the large amateur market, but not without "imperfect" images. There is almost always a need for enhancement or subsequent improvement after the photograph is made. This study dealt with computer image enhancement of such "imperfect" photographs using homomorphic (non-linear) and linear frequency-domain digital filtering (on a VAX-11/785) and a comparison in effectiveness was determined, using a subjective criteria for image quality. It was found that, in general, linear filtering is to be the preferred method of choice when implementing image enhancement on amateur type photographs. Differences in "image quality improvement" by the two techniques was minimal, when the image was subjected to histogram equalization after processing. Homomorphic filtering requires substantial post processing without which it is a potential failure. Linear filtering was both computationally less demanding and subjectively more pleasing.

The fast Fourier transform is used in two-dimensions to calculate the apodizing effect of a center opening pupil shutter. Two shutter models are investigated and compared, a circular shutter with diameter a function of time, and a five-bladed leaf-type shutter. The influence of shutter shape, defocus, and third and fifth order spherical aberration on the time-averaged optical transfer function is investigated. The results indicate that there is only a small effect on resolution and depth of focus due to shutter motion in a well corrected optical system.

A new method for determining the modulation transfer function (MTF) for photographic films is described. The MTF and corresponding line spread function are approximated by carefully chosen models which are uniquely specified by a few parametric constants. By estimating the parameters in space and frequency simultaneously, the interactions between the two domains result in improved estimates over those provided by either domain alone. A computer algorithm has been written to determine the parameter constants that define the best-fit model for the emulsion MTF.

An electronic dot generating scanner is a complex machine. This complexity is based in the photographic methods which the scanner is designed to duplicate. This study addresses the mathematical principles of the entire scanner system. This paper was intended to provide an improved understanding of the scanner system. The hypothesis states that a mathematical analysis with experimental verification can be developed to accurately model the internal optics, tone reproduction, and output dot characteristics of an electronic dot generating scanner. The analysis begins with a functional block diagram, which shows the information flow through the scanner. This diagram breaks the process into its smaller components and provides the framework for the mathematical analysis. The diagram has an accompanying word description for each section of the scanner. The basic function of the scanning optics, data compression, gradation, color correction, digitization, halftone screening, and film exposure is discussed for the scanner system. The system characterization develops a mathematical analysis based on the functional block diagram. It details the theory behind each section of the scanner. Fourier optics, electrical engineering, and photographic tone reproduction theories are applied to the various scanner functions. The scanning optical system is analyzed using Fourier transform techniques to describe the effect of the imaging system on image transmission. Modulation Transfer Functions (MTFs) are used to show the output frequency spectrum of the scanning aperture. The electronic unsharp masking is modeled by using an optically equivalent process. The photomultiplier and associated data compression's effect on the reproduction of shadow detail is demonstrated graphically. The improvement in the photomultiplier response is noted due to logarithmic compression. The flexibility of the gradation processing is demonstrated through a graphical representation of the treatment of a typical signal. The gradation selection provides the operator with the ability to tailor the output to the reproduction requirements of each transparency. This flexibility is a great advantage, if properly utilized, because it allows customization of each separation. The color computer is described in general terms. The subjective manner, which color correction is determined is not addressed in this paper. Digitization is described with its associated compromises in signal integrity. The sampling and quantization processes are detailed. The screening computer and linearization together effectively transform a digitized gray level into a dot on film. The linearization sets up the scanner for its processing environment. The output signal from the screening computer drives a laser modulator, which controls the light traveling through the fiber optic cables to expose the film. The film is developed to produce the final separation. An experimental tone reproduction curve was produced. The type of curve produced versus the expected is discussed. The input/output characteristics are examined through the scanning of a UGRA resolution wedge. The UGRA wedge input and separation film output is analyzed using microphotographic methods to examine structure. This hypothesis was not proven because of the many assumptions required by the scope of this project, which made the prediction of overall systems results not possible. Although, each function (minus color correction) of the scanner is analyzed. This model of the entire scanning system from input optics through the final film exposure can be utilized to improve understanding of the entire scanner system.

Error diffusion is well-known adaptive quantization technique used in halftoning for quantizing data from a larger to a smaller number of gray levels. A method for creating cell-oriented computergenerated holograms using a modified error diffusion approach is proposed. Error diffusion is also a flexible tool for incorporating constraints of the printing device into the calculation of cell-oriented CGHs. The advantage of the proposed scheme is that the printability constraints are not applied in the calculation of the complex wave amplitude, but are incorporated in the subsequent quantization step for the CGH. The robustness of the quantization process has been investigated for varying aperture sizes, quantization conditions, and printer characteristics. The ability of error diffusion to reconstruct objects without adding a random phase and using a form of nonuniform quantization is also discussed.

The phase retrieval problem arises when a signal must be reconstructed from only the magnitude of its Fourier transform; if the phase information were also available, the signal could simply be synthesized using the inverse Fourier transform. The phase retrieval problem occurs in several areas of engineering and applied physics such as antenna array design, optical astronomy, electron microscopy, and x-ray crystallography. Although a unique relationship exists between a signal and its Fourier transform, the same cannot be said for a signal and the intensity of its Fourier transform. Given certain a priori information about the signal, the magnitude and phase of its Fourier transform are no longer independent functions. Compact support, real-valuedness, and non-negativity are some of the constraints that are often used to reconstruct the signal. In this thesis we describe our research concerning the solution of one- and two-dimensional, discrete and continuous time phase retrieval problems. In discrete phase retrieval we formulate the problem as a linear system of equations; our methods do not require polynomial rooting, tracking zero curves of algebraic functions, or any sort of iteration like previous methods. In continuous phase retrieval, most previous solutions rely on simply discretizing the problem and then employing an iterative algorithm. We avoid this approximation by using wavelet expansions to transform this uncountably infinite problem into a linear system of equations. The wavelet bases provide the following advantages: they easily allow incorporation of the a priori signal information; they provide a structured system of equations which permits a fast algorithm; and, they represent signals which are self-similar across scales (e.g. fractals) efficiently. Our solutions obviate the stagnation problems associated with iterative algorithms and our solutions are computationally simpler and more stable than alternative non-iterative algorithms. Moreover, our algorithms can accommodate noisy Fourier magnitude information and their performance with signals corrupted by noise is explored.