The finite difference time domain (FDTD) method has become a main stream analysis tool for engineers solving complex electromagnetic wave interaction problems. Its first principles approach affords it a wide range of applications from radar cross section (RCS) predictions of electrically large structures to molecular scale analysis of complex materials. This wide area of application may be attributed to the coupling of auxiliary differential equations with Maxwell's equations to describe the physical properties of a given problem. Previous extensions have included sub-cell models for describing lumped circuit elements within a single Yee cell, transformation of near-field information to the far-field for the analysis of antenna problems, dispersive material models and mesh truncation techniques. A review of these extensions is presented. What has not been previously developed is the ability to truncate lossy dielectric materials at the boundary of the simulation domain. Such outer boundary conditions (OBCs) are required in simulations dealing with ground penetrating radar, integrated circuits and many microwave devices such as stripline and microstrip structures. We have developed such an OBC by surrounding the exterior of the simulation domain with a lossy dispersive material based on a two time-derivative Lorentz model (L2TDLM). We present the development of the material as an absorber and ultimately as a full 3D OBC. Examples of microstrip, structures are presented to re-enforce the importance of modeling losses in dielectric structures. Finally, validation of the FDTD simulator and demonstration of the L2TDLM OBC's effectiveness is achieved by comparison with measured results from these microwave devices.

Microscopic fluorescence imaging of thick biological tissue has been successfully demonstrated with a fiber-based, slit-scanning, confocal microscope. The system developed under this research consists of an illumination arm, a fiber-optic imaging system, and a detection arm. The illumination arm is an anamorphic optical system that converts a circular, laser beam into a cylindrical beam forming a line image at the proximal face of the fiber-optic relay. This relay system is comprised of a fiber-optic imaging bundle, a miniature objective lens, and a miniature hydraulic positioning mechanism. It delivers illumination to a remote sample and simultaneously collects the fluorescence from the sample. The miniature objective lens and positioning mechanism were specially designed and fabricated for this system, allowing for high resolution imaging and optical sectioning in-vivo. The detection arm relays the fluorescence image at the proximal face of the fiber-optic relay with magnification onto a two-dimensional CCD. Characterization of the system has demonstrated a lateral resolution of three microns. The axial resolution when imaging a point object is 10 microns. When imaging a planar object, the axial resolution is 25 microns. Images are acquired at a rate of 2-4 frames per second and the imaging performance has been evaluated with different biological models including animal peritoneal tissue and human prostate tissue in-vitro. In-vivo images of human skin and rat peritoneum have also been acquired to demonstrate that patient motion does not adversely affect the performance of the system. These in-vitro and in vivo images demonstrate the capability of the system to resolve cell nuclear morphology, to visualize cell density and organization, and to image at selected depths below the tissue surface.

High power, diffraction-limited semiconductor lasers are required for a wide range of applications such as pumping for EDFAs, Raman amplifiers, and for free space optical communications. Unstable resonator has been identified as a very promising concept to develop these lasers. The objective of this research is to investigate and develop tapered cavity unstable resonator grating coupled surface emitting lasers (TCSELs). The laser consists of a ridge section, a tapered gain section and a DBR grating section. The ridge is used to ensure single lateral mode operation. The taper is used to achieve high power from a large aperture. The grating is used to provide feedback and surface outcoupling. This laser design has several key features including high output power, near diffraction-limited beam, low divergence angle, single longitudinal mode operation, and integration with dynamic functionality such as wavelength tuning and beam steering. In this dissertation the design, fabrication and characterization of TCSELs are discussed. The theory of TCSELs is presented. As a theoretical investigation, a comprehensive numerical modeling based on finite difference beam propagation method (FD-BPM) for semiconductor laser is developed. The model includes major parameters affecting device performance such as current spreading, carrier diffusion, nonlinear gain-carrier relation, gain saturation, carrier induced antiguiding and thermal lensing. The simulation results are presented and effects of design parameters on device performance are discussed. TCSELs with different device design and functionality are fabricated. The characterization results are discussed. High power operation is obtained under both pulsed and continuous wave (CW) operation. Collimated near diffraction-limited beam is demonstrated with moderate power. Single longitudinal mode operation with high side mode suppression ratio is observed. Wavelength tuning and beam steering is achieved using current injection to the suitable grating section through indium tin oxide (ITO). Several approaches for the improvement of the laser performance are discussed.

This dissertation is concerned with multiple-frame (multiframe) reconstructions using imagery acquired in dynamic imaging environments. Through several interesting examples, we address and relate the key concepts of information weighting, channel diversity and multiframe processing in the context of producing high resolution estimates from severely degraded imagery. For the problem of space object identification, we look at methods for preprocessing a collection of atmospheric turbulence-degraded short-exposure images to improve the resolving power of estimation algorithms. Specifically, we examine the performance of using frame selection to extract the least degraded subset of images from an ensemble for processing. Several measures of image quality are compared against idealized standards to demonstrate their relative effectiveness for ranking highly the least degraded image frames. We also examine the resolving implication of removing additive background noise, resulting from the sky and telescope. Specifically, we show that background compensation acts as a defacto restoration of the compact object support and leads to furthering the resolving power of estimation algorithms. In the context of dilute aperture imagery, we look at methods for inducing channel diversity into a collection of measurements. With a diverse image set, we compute estimates using both a joint multiframe objective and an aggregated objective. We then examine the implication of using joint or aggregate objectives in any estimation algorithm from a set-theoretic standpoint. Finally, we extend the classic Wiener filter for the multiframe case. The resulting formulation demonstrates that the appropriate weighting of image data allows for the worst frames to be included while improving the restoration. We discuss how this contradicts the earlier idea of frame selection and relates the multiframe Wiener filter to the dual information theoretic concept of "water-filling".

A CCD-camera based system for the retreival of bidirectional reflectance distribution function (BRDF) data has been evaluated for vicarious calibration applications. This evaluation is done by assessing the calibration requirements necessary to retrieve BRDF data for the improvement of the vicarious calibration approach, and then by examining the calibration problem itself. A sensitivity analysis shows that for a top of the atmosphere (TOA) radiance accurate to 0.1%, instrumental biases must be under 5% while pixel-to-pixel gain variations may be as great as 10%. A method for achieving the calibration requirements using a CCD-based BRDF camera system constructed by the Remote Sensing Group (RSG) at the University of Arizona Optical Sciences Center is presented. A relative calibration level of approximately 1% across the camera array is found to be achievable given the laboratory facilities of the RSG. Software designed to extract BRDF data from the BRDF camera system output and convert the data into a form usable in the RSG's radiative transfer code are described and demonstrated on example data sets. A diffuse-light correction algorithm and software to perform the correction on BRDF camera data are described, and the software is tested against several example data sets to evaluate the retrieval accuracy of the code. Retrieval accuracies of better than 0.5% in phase and better than 0.01% in radiance have been achieved with this code using modeled data and at a 45-degree solar zenith angle. Based on these results, CCD-camera based systems can be used to improve the level of accuracy of TOA radiance calculations for vicarious calibration.

The coherent response of a semiconductor three-state system to one or two intense light pulses is investigated experimentally on a 100 fs time scale. Three experiments constitute this dissertation: observation of excitonic Rabi oscillations, measurement of two-exciton coupled Stark shifting, and an attempt to observe dark states. Basic concepts of time-resolved ultrafast semiconductor spectroscopy are explained, followed by an analysis of semiconductor two- and three-state systems. Pure two- and three-state dynamics are derived from first principles, followed by the development of the appropriate semiconductor Bloch equations (SBE). Two-color pump-probe, two-color pump-pump, and pump-pump-probe techniques are explained in the context of three-state semiconductor experiments. The experimental setup is explained in detail. Resonant two-color pump-probe measurements resulted in the first observation of multiple excitonic Rabi oscillations. The common conduction band shared by the light-hole and heavy-hole excitons of an InGaAs multiple quantum well allowed us to measure hh-exciton density (Rabi) oscillations by probing lh-exciton absorption. By studying the intensity dependence of the Rabi frequency, we showed the important role of many-body effects in renormalizing the dipole energy. The shared conduction band also causes the lh-exciton resonance to Stark shift when the hh exciton is Stark shifted. We measured a transient Stark shifting of both resonances due to virtual hh-exciton transitions. We observed that the ratio of the hh-exciton shift to lh-exciton shift was 2:1 at large pump-exciton detuning, as predicted from a simple three-state dressed exciton picture. For smaller detunings we saw an increase in the ratio and a redshift of the non-dipole coupled exciton state. Both of these observations are consistent with the most recent theories and experiments on excitonic Stark shifting. For strong near-resonant pumping of both lh- and hh-exciton transitions, an intervalence-band Raman-type coherence follows from the SBE that results in a transparent eigenstate (dark state) when both pumps are equally detuned from resonance. The existence of this coherence is well-known in atomic-optical systems, but has been elusive in semiconductors. Our inconclusive experimental result is presented along with an evaluation of experimental shortcomings. In brief, the expected change is absorption was too small to see.

Non-rational and rational parametric interpolators are investigated and developed as mathematical entities for describing the geometric propagation of light in optical systems. The Bezier interpolator was chosen over other interpolators to describe extended and point objects and their subsequent mathematical propagation through an optical system primarily because of their superior mathematical stability, convex hull property, and endpoint interpolation, which is especially important for describing wavefront behavior. The limitations of the affine transformation first are exposed for transforming generalized three-dimensional extended Bezier objects ideally or collinearly through an optical system. This limitation necessitated the development of a projective transformation. The perspective projection next was used in a vector derivation of the collinear mapping equations thereby demonstrating that an optical collinear mapping is a special projective transformation. Furthermore, the perspective projection was found to correctly map non-rational and rational Bezier objects through an optical system. Rational Bezier interpolators, because they are inherently projections of n-dimensional functions onto hyperplanes, exist or live in a collinear space and therefore are ideally suited for describing the conjugate relationships found in optical systems. Bezier curves also are shown to describe the behavior of the meridional wavefront as it was refracted and reflected at optical surfaces. Affine maps again proved inadequate for general wavefront propagation necessitating the development of the Bezier ray trace. The Bezier ray trace was developed for both non-rational, rational quadratic, cubic, and piecewise continuous cubic orders by utilizing end control point interpolation and control polygon tangency conditions. In general non-rational quadratic and cubic Bezier curves inaccurately describe wavefront behavior in an optical system whereas their rational counterparts do so accurately. The ability of a rational Bezier curve to accurately describe a meridional wavefront leads to the interpretation that wavefronts and wave aberrations may be considered as projections of n-dimensional functions onto hyperplanes. Finally, the fourth order scalar wave aberration functions were converted into equivalent Bezier representations. This representation leads to a graphical interpretation of individual aberrations in terms of control points, which when uniformly parameterized and degree elevated to the same order, may be added by together to form composite aberrations.

A novel MRI method, DIFRAD-FSE (D̲i̲f̲fusion with R̲adial A̲cquisition of D̲ata with F̲ast S̲pin-E̲cho) is presented that enables rapid, high-resolution, multi-shot diffusion-weighted MRI without significant artifacts due to motion. Following a diffusion-weighted spin-echo preparation, multiple radial lines of Fourier data are acquired using spin-echo refocusing. Data can be acquired in either 2D or 3D Fourier space. Motion correction is accomplished via one of four correction techniques: phase correction, shift correction, a combination of the phase and shift correction, or magnitude. Images from a radial data set are reconstructed with filtered back projection reconstruction. Results from human brain imaging will demonstrate the ability of DIFRAD-FSE to acquire high-resolution images without significant artifacts due to motion in both 2D and 3D. Results from liver and heart imaging demonstrate the versatility of the 2D DIFRAD-FSE.

Super-resolution is the process by which the bandwidth of a diffraction-limited spectrum is extended beyond the optical passband. Many algorithms exist which are capable of super-resolution; however most are iterative methods, which are ill-suited for real-time operation. One approach that has been virtually ignored in super-resolution research is the neural network approach. The Hopfield network has been a popular choice in image restoration applications, however it is also an iterative approach. We consider the feedforward architecture known as a Multilayer Perceptron (MLP), and present results on simulated binary and greyscale images blurred by a diffraction-limited OTF and sampled at the Nyquist rate. To avoid aliasing, the network performs as a nonlinear spatial interpolator while simultaneously extrapolating in the frequency domain. Additionally, a novel use of vector quantization for the generation of training data sets is presented. This is accomplished by training a nonlinear vector quantizer (NLIVQ), whose codebooks are subsequently used in the supervised training of the MLP network using Back-Propagation. The network shows good regularization in the presence of noise.

In recent years astronomers have been pushing to build larger ground-based telescopes with apertures greater than 5 m in order to see deeper into space and resolve smaller objects. Realistically, while a larger telescope aperture allows more light to be collected, atmospheric turbulence caused by thermal gradients in the atmosphere limits the achievable resolution to a level comparable with apertures on the order of half a meter or less. Adaptive optics (AO) can be used to counteract the degrading effects of the atmosphere in real time and recover diffraction-limited resolution. With the help of AO, better science can be done, and as more large ground-based telescopes are built, the need for reliable AO systems grows. The 6.5 m upgrade to the Multiple Mirror Telescope (MMT) on Mt. Hopkins is an example of a large telescope project. An infrared adaptive optics system for this telescope is currently under construction at Steward Observatory in the Center for Astronomical Adaptive Optics. This dissertation reports on the design, construction, and testing of various components of this AO system with which the author was involved. These components include the deformable secondary mirror, the wave front sensor, a laboratory testing system, and wavefront reconstruction algorithms.