The subject of this dissertation is the assessment and optimization of image quality for multiple-pinhole, multiple-camera SPECT systems. These systems collect gamma-ray photons emitted from an object using pinhole apertures. Conventional measures of image quality, such as the signal-to-noise ratio or the modulation transfer function, do not predict how well a system's images can be used to perform a relevant task. This dissertation takes the stance that the ultimate measure of image quality is to measure how well images produced from a system can be used to perform a task. Furthermore, we recognize that image quality is inherently a statistical concept that must be assessed for the average task performance across a large ensemble of images.The tasks considered in this dissertation are detection tasks. Namely we consider detecting a known three-dimensional signal embedded in a three-dimensional stochastic object using the Bayesian ideal observer. Out of all possible observers (human or otherwise) the ideal observer sets the absolute upper bound for detection task performance by using all possible information in the image data. By employing a stochastic object model we can account for the effects of object variability, which has a large effect on observer performance.An imaging system whose hardware has been optimized for ideal observer detection task performance is an imaging system that maximally transfers detection task relevant information to the image data.The theory and simulation of image quality, detection tasks, and gamma-ray imaging are presented. Assessments of ideal observer detection task performance are used to optimize imaging hardware for SPECT systems as well as to rank different imaging system designs.

An atomic resonance filter (ARF), composed of a cell containing an absorbing gas and two interference/absorption filter stacks, is designed to be both wide angle and ultra-narrowband. The bandwidth of this filter, in the range of 1-10mA, is determined by the absorption linewidth of the absorbing gas. Light entering the ARF within this bandwidth excites the gas to a highly excited state, and the fluorescence cascade back to the ground state emerges from the gas cell as the detected signal. The interference/absorption filter stacks insure that light not interacting with the gas does not pass through the ARF. The ARF is necessarily wide-angle due to the isotropic absorption properties of the gas. This dissertation models the processes involved in atomic absorption to determine the performance of an ARF that uses cesium as the absorbing gas. This model uses the Voigt absorption profile to obtain a correlation between the frequency of the traveling photon and the velocity of the absorbing atom. Results of computer simulations based on this model are presented along with experimental measurements. The ARF characteristics of importance include its efficiency and the temporal response of the filter. These characteristics are determined as a function of temperature and the input photon frequency. The effect of an additional buffer gas, which is included to decrease the ARF response time is investigated.

In this dissertation, we offer a novel phase-shifting interferometer/ellipsometer. The uniqueness arises from the fact that this study is the consolidation of four distinct ideas drawn from the field of optics and the field of statistics. A conventional four-step phase-shifting interferometer is modified to allow for both TE and TM polarized measurements. Maximum-likelihood estimation theory is then used to extract the three parameters of interest, namely the real and imaginary components of the complex index of refraction and the surface profile. Finally, Cramer-Rao lower bounds serve as a quantitative means of assessing the particular system design at the task of estimating the three parameters in question. As we will show, the unknown parameters n, k and h are related to the measured irradiance in a complicated, nonlinear way. As such, no analytical expressions to estimate the unknown parameters from the measured data have been found. Rather, the unknown parameters are found numerically through a minimization program, developed and optimized specifically for this task. The results from our Monte Carlo simulations will show that conventional designs such as the Twyman-Green interferometer perform poorly at reconstructing n, k and h. The estimates on n and k exhibit bias, where the mean is not equal to the true value, and are non-efficient, where the standard deviation is greater than the Cramer-Rao lower bound. While the estimate of h is unbiased and efficient, the performance is an order of magnitude worse than the case where only h is to be estimated. By incorporating tilt in the design, the performance on all three parameters improves considerably. The estimates on n and k are shown to be unbiased and efficient, and the performance of the h estimator is equivalent to the h-only case. The dissertation culminates with the development of a Mach-Zehnder prototype. We demonstrate the feasibility of the proposed technique, and show how three system parameters, namely the incident amplitude and the relationship between the TE and TM polarized light in terms of amplitude and phase, affect the performance. We also show how quantization of the measured irradiance affects the performance.

Current magnetic data storage technology is encountering certain fundamental limitations that present roadblocks to its scalability to areal densities of 1 Tbit/in^2 and beyond. Next generation magnetic storage technology is expected to use optical near field techniques to heat the magnetic film locally to write data bits. This requires experimental measurement of thermal conductivity of materials with sub--100 nm resolution. This is essential for the tailoring of the thin film stack to optimize the heat transfer of the process. This can be accomplished with a simple modification to a traditional atomic force microscopy (AFM) system. The modification requires the deposition of a thin metal film on the AFM cantilever thus creating a bimetallic cantilever. The curvature of a bimetallic cantilever is sensitive to temperature. Another modification is the use of a heating laser to raise the temperature of the cantilever so that when it scans across a sample with areas of varying thermal conductivity the bimetallic deformation of the heated cantilever is altered. The resulting system is sensitive to local variations in thermal conductivity with nanoscale resolution. Nanoscale thermal conductivity measurements can then be used to optimize the heat transfer properties of the materials used in a heat assisted magnetic recording system. AFM technology can also play a key role in the development of next generation solid-state chemical sensors. An AFM can be used to measure the workfunction of a material with near atomic resolution thus enabling the study of chemical reactions with high spatial resolution. Since chemical sensors typically use a chemical reaction at their front end to monitor the prescience of a gas, an AFM system can thus be used to understand and optimize the properties of the chemical reaction by monitoring the local workfunction. In this thesis, I explain the use of atomic force microscopy in measuring thermal and chemical properties of materials with applications towards the magnetic storage industry and chemical sensing.

Quarter-wave switched oscillators (SWOs) are an important technology for the generation of high-power, moderate bandwidth (mesoband) wave forms. The use of SWOs in high power microwave sources has been discussed for the past 10 years [1-6], but a detailed discussion of the design of this type of oscillators for particular waveforms has been lacking. In this dissertation I develop a design methodology for a realization of SWOs, also known as MATRIX oscillators in the scientific community.A key element in the design of SWOs is the self-breakdown switch, which is created by a large electric field. In order for the switch to close as expected from the design, it is essential to manage the electrostatic field distribution inside the oscillator during the charging time. This enforces geometric constraints on the shape of the conductors inside MATRIX. At the same time, the electrodynamic operation of MATRIX is dependent on the geometry of the structure. In order to generate a geometry that satisfies both the electrostatic and electrodynamic constraints, a new approach is developed to generate this geometry using the 2-D static solution of the Laplace equation, subject to a particular set of boundary conditions. These boundary conditions are manipulated to generate equipotential lines with specific dimensions that satisfy the electrodynamic constraints. Meanwhile, these equipotential lines naturally support an electrostatic field distribution that meets the requirements for the switch operation.To study the electrodynamic aspects of MATRIX, three different (but interrelated) numerical models are built. Depending on the assumptions made in each model, different information about the electrodynamic properties of the designed SWO are obtained. In addition, the agreement and consistency between the different models, validate and give confidence in the calculated results.Another important aspect of the design process is understanding the relationship between the geometric parameters of MATRIX and the output waveforms. Using the numerical models, the relationship between the dimensions of MATRIX and its calculated resonant parameters are studied. Finally, I present a comprehensive design methodology that generates the geometry of a MATRIX system from the desired specification then calculates the radiated waveform.

The thickness and refractive index of thin films determines their performance. Thickness variation due to the deposition process is well understood and correctable. Variation in the refractive index due to the deposition process is a considerably more complex problem. In this work two important members of the class of high index refractory materials: Tantalum pentoxide and Titania are investigated. These materials are known to produce very high quality films. Ion plating of tantalum results in the extremely high quality films, but ion plating of titania results in films with absorption that is too high and the process is now no longer used. Ion assisted deposition of titania, however, results in high quality films. The variation in refractive index due to the columnar microstructure of these materials has been eliminated but the subtler aspects of the thin films behavior is more difficult to improve. It is this aspect that I have investigated. In particular what improvements can be made by post deposition annealing of ion plated and ion assisted deposition of Tantalum pentoxide, and can the ion bombardment of Titania result in films with increased birefringence. If this anisotropy can be increased a number of interesting polarizing elements can be produced. These investigations were performed in distinct methods. The absorption of these films required the design and construction of a specialized highly sensitive waveguide apparatus. The investigation of anisotropy involved examining the evolution of form birefringence in situ by polarimetry. A further parameter of interest, although not as yet widely studied in thin films as the effects are small and difficult to observe is material nonlinearity. In the future the design of dynamic filters or coatings for powerful laser systems will require a good means of determining this kind of behavior in thin films. To this end we have designed our absorption instrument to be able to determine changes in refractive index due to a strong external pump beam. These effects are described in chapter three as an indication of future trends in this area.

A novel nonlinear frequency conversion technique based on intracavity stimulated Raman scattering in solid-state media is discussed. Devices have been built which are based on this technique. Standard first-order resonator eigenmode routines as well as paraxial diffraction-propagation, laser gain and nonlinear conversion routines have been integrated into a generalized laser resonator design software package which can accurately model the growth and evolution of the transverse field distribution in arbitrary intra- or extra-cavity nonlinear frequency converted laser sources. This package has been implemented as a design tool and has been utilized to model intracavity Raman beam cleanup. The macroscopic and microscopic pulse dynamics are modeled by rate equation and roundtrip pulse intensity iterator routines, respectively. A host of dynamical features are predicted theoretically and confirmed by experiment; such as, nonlinear cavity dumping, gain switching, dynamical chaos, and self-mode-locking. A new theory based on probabilistic arguments is developed to describe the spectral properties of intracavity Raman lasers. It is shown that under normal conditions, the Raman gain profile which results from multimode pumping is inhomogeneously broadened. Questions of efficiency, cavity matching, injection seeding and locking are addressed. Phase-matching and conversion efficiency in optically active second-order nonlinear materials is treated theoretically. Also examined are the conditions under which optical activity significantly alters the nonlinear optical properties of a material and show how this mechanism might be used in designing a nonlinear optical device. Corrections to the standard theoretical expressions for birefringent phase-matching angles and conversion efficiency are obtained for application to biaxial crystals with large natural birefringence. A generalized quasi-phase-matching scheme based on optical activity is formulated for three-wave interactions in second-order nonlinear crystals. A technique based on optical parametric generation and amplification is utilized to accurately determine the dispersion of the nonlinear susceptibilities in thin-film samples. Intrinsic pump-energy instabilities are taken into account in the data analysis.

Substantial impacts of aerosols on climate and public health underscore the need for accurate characterization of atmospheric aerosol distributions and microphysical properties. The Multiangle SpectroPolarimetric Imager (MSPI) combines accurate multispectral, multiangle, and polarimetric technologies in a single instrument that images a wide swath on the Earth's surface to advance aerosol remote sensing capabilities. MSPI is required to have 3% radiometric uncertainty and 0.005 degree of linear polarization (DoLP) uncertainty. These are difficult requirements that push the limits of available technologies needed to perform space-based polarimetric imaging. This work examines three topics related to MSPI fabrication and calibration: polarization errors and their correction, achromatic, athermal, quarter wave retarder fabrication, and analysis of a polarization state generator (PSG) for MSPI polarization calibration confirmation.MSPI polarization errors may arise from surface geometry of the optical components, coatings, and quarter wave plates (QWPs). Static polarization errors can be calibrated out, but result in decreased SNR. Polarization errors that drift following calibration cannot be corrected, so a sensitivity analysis is used to set time-varying diattenuation and retardance magnitude tolerances. QWPs are required to work in concert with the PEMs to modulate the linear component of the Stokes vector. A three-material achromatic, athermalized QWP was designed, fabricated and its performance validated. Analysis indicated that the compound QWP was unlikely to meet the requirements if plates were specified by thickness. To address this, a method for QWP fabrication was developed that involves monitoring retardance during polishing. To verify MSPI performance, a PSG was built and calibrated which outputs weakly linearly polarized light with DoLPs varying from 0.0005 to 0.4 with 0.0005 uncertainty by passing nearly unpolarized light through a tilted plane parallel plate. The PSG was intended to act as a calibration standard based on calculated DoLP, but proved difficult to model. Therefore, the DoLP was instead measured to repeatability of 0.0005. Finally, example spectropolarimetric image data taken with MSPI was presented. Work on a follow-on prototype continues that will advance the technologies needed to realize the space-based, fully capable MSPI.

This dissertation investigates the optical design and characterization for two distinct remote sensing applications. The first application is focused on the high precision optical phase correction for the photonic Local Oscillator (LO) designed for the Atacama Large Millimeter Array (ALMA). The phase instability in the original fiber optics design scheme is characterized and a novel, singlemode fiber-based interferometric approach to measure and actively zero out the unwanted Photonic LO phase drift is introduced. The proposed technique is implemented and characterized by using a 16 km baseline with a two element array. In the second application, the first iteration of the quasioptics design used in the ATOMMS instrument is characterized. (ATOMMS-Active Temperature, Ozone and Moisture Microwave Spectrometer-is the pathfinding implementation of an Earth and Space Atmosphere Global Remote Sensing Instrument).The diffraction problems in this design which were limiting the instrument performance were analyzed. Then different design concepts to mitigate these limitations and optimize system performance are presented.

This dissertation investigates mechanisms that influence image formation in near-field scanning optical microscopy (NSOM) performed with tapered fiber aperture probes. Both the generation of optical contrast for transmission mode NSOM and the force interaction between the probe and sample that is the basis for topographic imaging by shear force microscopy (SFM) are studied. A brief introduction and review of the field of NSOM are given. The lack of understanding in the previous work of the optical and force interactions between the probe and sample is cited as the motivation for the present investigation. A theoretical model is developed that describes the linear scattering of the probe's source field by the complex transmittance of the sample. The imaging of subwavelength features is shown to arise from the spatial mixing of the evanescent waves of the probe's source field with the high spatial frequencies of the object. Calculations of the optical transfer function are presented. The shear force servo that regulates the probe-to-sample separation and facilitates the acquisition of SFM imagery is extensively analyzed. The optical detection scheme that measures the dither vibration of the probe is characterized in order to optimize the servo performance. The shear force interaction is then analyzed by modeling the probe as a simple harmonic oscillator. Measurements of the probe's resonant response while interacting with the sample reveal that the shear force is mainly frictional. The magnitude of the force is derived, and limitations on its measurement are established through analysis of the minimum detectable displacement of the probe. The servo performance is shown to be shot noise limited, as opposed to being limited by the thermal vibration noise of the probe. Experimental SFM and NSOM images of various grating structures and optical data storage materials are presented. The optical contrast mechanisms displayed in the images are identified. Linear scattering generally dominates the contrast, but some images exhibit unique near-field effects due to probe-sample interactions that lead to nonlinear imaging behavior. The origin of these interactions is the boundary conditions imposed on the probe's aperture by the sample's composition and structure.