Thesis (Ph. D.)--Washington State University, December 2007. / Includes bibliographical references.

The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. In this thesis, the development of a symbolic computer algebra toolbox to compute two dimensional Fourier transforms in polar coordinates is discussed. Among the many operations implemented in this toolbox are different types of convolutions and procedures that allow for managing the toolbox effectively. The implementation of the two dimensional Fourier transform in polar coordinates within the toolbox is shown to be a combination of two significantly simpler transforms. The toolbox is also tested throughout the thesis to verify its capabilities.

Carbon Monoxide (CO) was discovered in the stratosphere of Neptune from the detection of the J=3-2 and J=2-1 rotational transitions in emission at 345.8 and 230.5 GHz respectively. It was conventionally thought that all of the atmospheric carbon should be in its reduced form of methane (CH₄). Two sources of stratospheric CO have been postulated: CO transported from the interior by convection due to Neptune's strong internal heat source (internal source); or, CO produced through photochemical reactions from an external supply of water (external source). <p>In this research project the J=3-2 transition of CO was observed to find the CO profile in Neptune's atmosphere and determine the mechanism producing CO. Three instruments were used at the James Clerk Maxwell Telescope (JCMT) to measure the CO line: the heterodyne receiver B3; the University of Lethbridge Fourier Transform Spectrometer (FTS); and, the Submillimeter Common User Bolometer Array (SCUBA). <p>The high resolution (1.25 MHz) of the heterodyne observations over a large frequency range (~20 GHz) produced a very powerful result because the narrow emission core from the stratosphere and the broad absorption feature arising in the lower atmosphere were measured simultaneously. The CO abundance profile was determined using a model of the J=3-2 CO transition in Neptune's atmosphere developed for this project. Calculations indicate a CO abundance of 1.9^+0.5_-0.3x10^-6 in the upper stratosphere and (0.8±0.2)x10^-6 in the lower stratosphere and troposphere. <p>The moderate resolution of the FTS data allowed the broad absorption feature to be measured. Uranus was originally chosen as the calibration source, but the discovery of CO in Uranus by Encrenaz et al. (2004), while this project was in progress, prompted both Neptune and Uranus to be examined for CO absorption. Two data sets (1993 and 2002) were analyzed and it was found that the 1993 spectra produced superior results, giving a CO mole ratio in the lower atmosphere between 0.8x10^-6 and 2x10^-5; this agrees, within the uncertainty limit, with the lower atmosphere heterodyne result. A tentative detection of CO in Uranus was also obtained from the 1993 data, with a CO abundance profile constrained to pressures greater than 0.5 bar with an abundance between 5x10^-7 and 1x10^-5. The 2002 data were found to be inferior to the 1993 data because of imperfect cancellation of thermal emission from the terrestrial atmosphere. <p> The 850ìm SCUBA filter profile is well matched to the width of the CO feature. Photometric observations of Neptune and Uranus were used to determine if the reduction in integrated flux due to CO absorption could be detected using SCUBA. A CO mole ratio in the range (1.2-1.7) x10^-6 was found for Neptune, calibrated against Uranus and assuming no CO in Uranus. Calibration of the Neptune and Uranus SCUBA data against Mars to produce an independent estimate of the CO abundance in both planets did not produce a useful result because of large calibration errors. <p>Comparison of the results from the three techniques determined that the heterodyne measurement was superior and the derived CO profile was used to determine the source of neptunian CO. It was concluded that the source of CO in Neptune is both internal and external. The lower atmosphere result indicates an interior dominated by water ice. The most likely mechanism for the upper atmosphere CO involves meteoritic ablation, photolysis of H₂O, and chemical reaction with by-products of methane photochemistry. The required H₂O influx for this mechanism is at least two orders of magnitude higher than previously observed, indicating either that the observed H₂O abundance is too small or that CO is produced by a different mechanism.

The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. In this thesis, the development of a symbolic computer algebra toolbox to compute two dimensional Fourier transforms in polar coordinates is discussed. Among the many operations implemented in this toolbox are different types of convolutions and procedures that allow for managing the toolbox effectively. The implementation of the two dimensional Fourier transform in polar coordinates within the toolbox is shown to be a combination of two significantly simpler transforms. The toolbox is also tested throughout the thesis to verify its capabilities.

Content-based image retrieval (CBIR) is still in its early stages, although several attempts have been made to solve or minimize challenges associated with it. CBIR techniques use such visual contents as color, texture, and shape to represent and index images. Of these, shapes contain richer information than color or texture. However, retrieval based on shape contents remains more difficult than that based on color or texture due to the diversity of shapes and the natural occurrence of shape transformations such as deformation, scaling and orientation. This thesis presents an approach for fusing several shape-based image retrieval techniques for the purpose of achieving reliable and accurate retrieval performance. An extensive investigation of notable existing shape descriptors is reported. Two new shape descriptors have been proposed as means to overcome limitations of current shape descriptors. The first descriptor is based on a novel shape signature that includes corner information in order to enhance the performance of shape retrieval techniques that use Fourier descriptors. The second descriptor is based on the curvature of the shape contour. This invariant descriptor takes an unconventional view of the curvature-scale-space map of a contour by treating it as a 2-D binary image. The descriptor is then derived from the 2-D Fourier transform of the 2-D binary image. This technique allows the descriptor to capture the detailed dynamics of the curvature of the shape and enhances the efficiency of the shape-matching process. Several experiments have been conducted in order to compare the proposed descriptors with several notable descriptors. The new descriptors not only speed up the online matching process, but also lead to improved retrieval accuracy. The complexity and variety of the content of real images make it impossible for a particular choice of descriptor to be effective for all types of images. Therefore, a data- fusion formulation based on a team consensus approach is proposed as a means of achieving high accuracy performance. In this approach a select set of retrieval techniques form a team. Members of the team exchange information so as to complement each other’s assessment of a database image candidate as a match to query images. Several experiments have been conducted based on the MPEG-7 contour-shape databases; the results demonstrate that the performance of the proposed fusion scheme is superior to that achieved by any technique individually.

Content-based image retrieval (CBIR) is still in its early stages, although several attempts have been made to solve or minimize challenges associated with it. CBIR techniques use such visual contents as color, texture, and shape to represent and index images. Of these, shapes contain richer information than color or texture. However, retrieval based on shape contents remains more difficult than that based on color or texture due to the diversity of shapes and the natural occurrence of shape transformations such as deformation, scaling and orientation. This thesis presents an approach for fusing several shape-based image retrieval techniques for the purpose of achieving reliable and accurate retrieval performance. An extensive investigation of notable existing shape descriptors is reported. Two new shape descriptors have been proposed as means to overcome limitations of current shape descriptors. The first descriptor is based on a novel shape signature that includes corner information in order to enhance the performance of shape retrieval techniques that use Fourier descriptors. The second descriptor is based on the curvature of the shape contour. This invariant descriptor takes an unconventional view of the curvature-scale-space map of a contour by treating it as a 2-D binary image. The descriptor is then derived from the 2-D Fourier transform of the 2-D binary image. This technique allows the descriptor to capture the detailed dynamics of the curvature of the shape and enhances the efficiency of the shape-matching process. Several experiments have been conducted in order to compare the proposed descriptors with several notable descriptors. The new descriptors not only speed up the online matching process, but also lead to improved retrieval accuracy. The complexity and variety of the content of real images make it impossible for a particular choice of descriptor to be effective for all types of images. Therefore, a data- fusion formulation based on a team consensus approach is proposed as a means of achieving high accuracy performance. In this approach a select set of retrieval techniques form a team. Members of the team exchange information so as to complement each other’s assessment of a database image candidate as a match to query images. Several experiments have been conducted based on the MPEG-7 contour-shape databases; the results demonstrate that the performance of the proposed fusion scheme is superior to that achieved by any technique individually.

Carbon Monoxide (CO) was discovered in the stratosphere of Neptune from the detection of the J=3-2 and J=2-1 rotational transitions in emission at 345.8 and 230.5 GHz respectively. It was conventionally thought that all of the atmospheric carbon should be in its reduced form of methane (CH₄). Two sources of stratospheric CO have been postulated: CO transported from the interior by convection due to Neptune's strong internal heat source (internal source); or, CO produced through photochemical reactions from an external supply of water (external source). <p>In this research project the J=3-2 transition of CO was observed to find the CO profile in Neptune's atmosphere and determine the mechanism producing CO. Three instruments were used at the James Clerk Maxwell Telescope (JCMT) to measure the CO line: the heterodyne receiver B3; the University of Lethbridge Fourier Transform Spectrometer (FTS); and, the Submillimeter Common User Bolometer Array (SCUBA). <p>The high resolution (1.25 MHz) of the heterodyne observations over a large frequency range (~20 GHz) produced a very powerful result because the narrow emission core from the stratosphere and the broad absorption feature arising in the lower atmosphere were measured simultaneously. The CO abundance profile was determined using a model of the J=3-2 CO transition in Neptune's atmosphere developed for this project. Calculations indicate a CO abundance of 1.9^+0.5_-0.3x10^-6 in the upper stratosphere and (0.8±0.2)x10^-6 in the lower stratosphere and troposphere. <p>The moderate resolution of the FTS data allowed the broad absorption feature to be measured. Uranus was originally chosen as the calibration source, but the discovery of CO in Uranus by Encrenaz et al. (2004), while this project was in progress, prompted both Neptune and Uranus to be examined for CO absorption. Two data sets (1993 and 2002) were analyzed and it was found that the 1993 spectra produced superior results, giving a CO mole ratio in the lower atmosphere between 0.8x10^-6 and 2x10^-5; this agrees, within the uncertainty limit, with the lower atmosphere heterodyne result. A tentative detection of CO in Uranus was also obtained from the 1993 data, with a CO abundance profile constrained to pressures greater than 0.5 bar with an abundance between 5x10^-7 and 1x10^-5. The 2002 data were found to be inferior to the 1993 data because of imperfect cancellation of thermal emission from the terrestrial atmosphere. <p> The 850ìm SCUBA filter profile is well matched to the width of the CO feature. Photometric observations of Neptune and Uranus were used to determine if the reduction in integrated flux due to CO absorption could be detected using SCUBA. A CO mole ratio in the range (1.2-1.7) x10^-6 was found for Neptune, calibrated against Uranus and assuming no CO in Uranus. Calibration of the Neptune and Uranus SCUBA data against Mars to produce an independent estimate of the CO abundance in both planets did not produce a useful result because of large calibration errors. <p>Comparison of the results from the three techniques determined that the heterodyne measurement was superior and the derived CO profile was used to determine the source of neptunian CO. It was concluded that the source of CO in Neptune is both internal and external. The lower atmosphere result indicates an interior dominated by water ice. The most likely mechanism for the upper atmosphere CO involves meteoritic ablation, photolysis of H₂O, and chemical reaction with by-products of methane photochemistry. The required H₂O influx for this mechanism is at least two orders of magnitude higher than previously observed, indicating either that the observed H₂O abundance is too small or that CO is produced by a different mechanism.

Thin films are used in many energy conversion applications, ranging from photodetectors to solar cells. Accurately predicting the radiative properties of thin films when they possess rough surfaces is critical in many instances, but can be challenging due to the complexity arising from light scattering and interferences at the microscale. This work describes measurements of the spectral transmittance and reflectance of several thin-film materials (including crystalline silicon wafers and a polycrystalline diamond film) in the mid-infrared spectral region (2 20 m) using a Fourier-transform infrared (FT-IR) spectrometer. The transmittance and reflectance were calculated using thin-film optics for the double-side polished samples and scalar scattering theory for the single-side polished samples. The effects of partial coherence are considered using a fringe smoothing technique. The interval used for fringe smoothing was assumed to be linearly dependent on the wavenumber. Good agreement between the predicted and measured transmittance was achieved for the double-side polished silicon wafers and for the diamond film. The disagreement for some single-side polished silicon wafers may be inherently related to their surface microstructures, as suggested from surface topographic data and images obtained from surface profilometry and microscopy. By comparing the intervals used for fringe smoothing with the instrumental resolution, beam divergence in the spectrometer was found to be a major factor contributing to the partial coherence. Future research is proposed to investigate the correlation between the detailed surface characteristics and the conical-conical transmittance and reflectance.

Using Graphic Processor Unit (GPU) to process the parallel operation via Compute Unified Device Architecture (CUDA) is a new technology in recent years. In the past, the GPU has been used in parallel operation but it was not easy for programming so that it couldn¡¦t be widely used in applications. CUDA is the newly-developed environment based on C language mainly for improving the complexity in programming with CUDA. The applications of GPU with CUDA has been expending to various fields gradually due to support of IEEE floating point as well as its lower cost in hardware while comparing to the super computers. Magnetic Resonance Spectroscopy (MRS) has the feature of non-invasive to probe the concentration distributed of metabolites in vivo. It can assist doctor in clinical diagnosis. The Magnetic Resonance Spectroscopy Imaging (MRSI) is imaging by many Signal Voxel Spectroscopy (SVS) to become multi-dimension MRS image. In MRSI, it can offer more information than SVS. CUDA are applied to MR image widely such as accelerating the image reconstruction and promoting the image quality, but in MRS it is seldom for the related application. In this paper, we using the CUDA to applied in MRS, the MRSI data pre-processing, to accelerate the spatial location in MRSI. In this work, we firstly use random data with different dimensions: 1D (one-dimension), 2D and 3D to evaluate the performance of Fourier transformation by using CUDA. We also finally apply some GE 2D/3D MRSI data to see how the acceleration of using CUDA works. Our results show that the acceleration rate of Fastest Fourier Transform (FFT) with CUDA in 1D, 2D and 3D random data largely increases as the data size increases. In the experiment of 2D/3D MRSI data, we find that using CUDA for accelerating the MRSI RAW-file generating procedure would avoid the data moving times, and it is not good for CUDA 1D FFT with parallel architecture while too small data amount processing in kernel. Therefore, how to solve the relationship between MRSI data format with CUDA FFT library and how to decrease the data moving time will discuss in the study.

The main advantage of wavelet transform relative to its Fourier analysis counterpart is its suitability to deal with transient signals. Furthermore, wavelet packet transform has very good frequency analytic ability with the result that it is developing in very fast speed and widespread researched and used in industry and academia. We study the characteristics of fiber optic sensors by applying wavelet transform. Hence, in this paper, the traditional Fourier analysis is taken as a basis, and the wavelet packet analysis is taken as a comparison. The major objects include: (1) calibration of hydrophones; (2) vibration measurement. In calibration of hydrophones, the experimental results show a 2.72 dB re V/£gPa inaccuracies and a 5.3 dB re V/£gPa standard deviation by Fourier analysis, but 0.5 dB inaccuracies and 1.6 dB re V/£gPa standard deviation by wavelet packet analysis. It shows that the wavelet packet analysis has better analytic ability than that of traditional Fourier analysis. In vibration measurement, we utilize FBG interferometers to measure stable vibration. The experimental results denote that wavelet packet analysis has excellent frequency analytic ability as Fourier analysis. Besides, in obtaining transient characteristic signals induced by falling stones, the results appear that wavelet packet analysis has better resolution and identification capability relative to Fourier analysis.