Envisioning novel fully monolithic fiber-optical devices, this dissertation investigates four fiber optical devices both, active and passive, that contribute to the goal of further integrating and miniaturizing fiber optics. An all phosphate glass fiber laser was designed in an effort to reduce laser intensity noise by reducing cavity losses and low mechanical strength that arise from intra-cavity fusion splices between silica fiber Bragg gratings (FBG) and phosphate active fiber in state of the art phosphate single frequency fiber lasers. Novel phosphate glass based FBGs have been fabricated utilizing high intensity laser pulses at 193 nm and a phase-mask. Net reflectivities of up to 70 % and a bandwidth of 50 pm have been achieved in the FBGs. The laser design comprised two of the novel FBGs and a short section of Er³⁺Yb³⁺ phosphate fiber to form a distributed Bragg reflector (DBR) laser. The performance of the new laser has been compared to a conventional phosphate fiber laser. Particular focus was put on the laser intensity noise due to its dependence on intra-cavity losses. Relative intensity noise (RIN) amplitudes of -80 dB/Hz have been measured for both lasers when operating at comparable output powers. For similar levels of absorbed pump power the relaxation oscillation frequencies (ROF) were shifted towards lower frequencies in the new laser. ExcessFBG scattering losses and mode-field miss-match between the active and passive fiber limited the output power of the new laser to 16 mW compared to 140 mW in the conventional laser. A monolithic all-phosphate glass fiber laser with up to 550 mW output power that is operating at a single longitudinal mode and exhibiting narrow linewidth is presented. The laser cavity has been formed by inscribing FBGs directly into heavily Er³⁺Yb³⁺ doped phosphate glass fiber using femtosecond laser pulses and a phase mask, completely eliminating the need for intra-cavity fusion splices. A linewidth of less than 60 kHz and relaxation oscillation peak amplitudes below -100 dB/Hz without active suppression of RIN have been measured. The compact form factor and higher output power combined with the low noise and narrow linewidth characteristic make this laser an ideal candidate for ranging, interferometry and sensing applications. Strong and robust Bragg gratings in optical fiber fabricated from highly photosensitive photo-thermo-refractive (PTR) glass are demonstrated. The fibers were drawn at 900 °C from a machined PTR-glass preform. A low power two beam interference pattern from a continuous wave (cw) He-Cd laser with a wavelength of 325 nm was used to write gratings into the fibers, achieving peak grating strengths of 20 dB and a spectral width of 45 pm. The gratings showed no sign of degradation when exposed to a high temperature environment of 425 °C for several hours. This is significantly higher when compared to standard Telecom FBGs which are rated for operation temperatures below 200 °C. A detailed study of novel mode-field adapters (MFA) based on multi-mode interference in graded index multi-mode fibers (GIMF) is presented. MFAs are often used in cases when low coupling losses between single mode fibers with very different mode-field diameters are needed. Here a new type of MFAs has been fabricated and characterized from a selection of commercially available single mode and graded index fibers. Compared to existing techniques the presented MFAs can be fabricated very quickly and are not limited to certain fiber types. Insertion losses of 0:5 dB over a spectral range of several hundred nm have been obtained with an ultra compact MFA with a length of 275 μm.

Mathematical methods have been developed to perform arms-control-treaty verification tasks for enhanced information security. The purpose of these methods is to verify and classify inspected items while shielding the monitoring party from confidential aspects of the objects that the host country does not wish to reveal. Advanced medical-imaging methods used for detection and classification tasks have been adapted for list-mode processing, useful for discriminating projection data without aggregating sensitive information. These models make decisions off of varying amounts of stored information, and their task performance scales with that information. Development has focused on the Bayesian ideal observer, which assumes com- plete probabilistic knowledge of the detector data, and Hotelling observer, which assumes a multivariate Gaussian distribution on the detector data. The models can effectively discriminate sources in the presence of nuisance parameters. The chan- nelized Hotelling observer has proven particularly useful in that quality performance can be achieved while reducing the size of the projection data set. The inclusion of additional penalty terms into the channelizing-matrix optimization offers a great benefit for treaty-verification tasks. Penalty terms can be used to generate non- sensitive channels or to penalize the model's ability to discriminate objects based on confidential information. The end result is a mathematical model that could be shared openly with the monitor. Similarly, observers based on the likelihood probabilities have been developed to perform null-hypothesis tasks. To test these models, neutron and gamma-ray data was simulated with the GEANT4 toolkit. Tasks were performed on various uranium and plutonium in- spection objects. A fast-neutron coded-aperture detector was simulated to image the particles.

This dissertation explores the possibility of using an imaging approach to model classical pharmacokinetic (PK) problems. The kinetic parameters which describe the uptake rates of a drug within a biological system, are parameters of interest. Knowledge of the drug uptake in a system is useful in expediting the drug development process, as well as providing a dosage regimen for patients. Traditionally, the uptake rate of a drug in a system is obtained via sampling the concentration of the drug in a central compartment, usually the blood, and fitting the data to a curve. In a system consisting of multiple compartments, the number of kinetic parameters is proportional to the number of compartments, and in classical PK experiments, the number of identifiable parameters is less than the total number of parameters. Using an imaging approach to model classical PK problems, the support region of each compartment within the system will be exactly known, and all the kinetic parameters are uniquely identifiable. To solve for the kinetic parameters, an indirect approach, which is a two part process, was used. First the compartmental activity was obtained from data, and next the kinetic parameters were estimated. The novel aspect of the research is using listmode data to obtain the activity curves from a system as opposed to a traditional binned approach. Using techniques from information theoretic learning, particularly kernel density estimation, a non-parametric probability density function for the voltage outputs on each photo-multiplier tube, for each event, was generated on the fly, which was used in a least squares optimization routine to estimate the compartmental activity. The estimability of the activity curves for varying noise levels as well as time sample densities were explored. Once an estimate for the activity was obtained, the kinetic parameters were obtained using multiple cost functions, and the compared to each other using the mean squared error as the figure of merit.

Colorectal cancer (CRC) remains the second deadliest cancer in the United States, despite steady reduction in mortality rate over the last three decades. Colonoscopy is the gold-standard screening modality with high sensitivity and specificity to mature polyps. However, the miss rate for small (<5 mm) lesions is estimated to be as high as 26%. Because the five-year survival rate for CRC detected at the local stage is 90%, there is a clear need for a screening procedure that is sensitive to these small lesions. Optical coherence tomography (OCT) has become a major biomedical imaging modality since its invention in 1991. As the optical analog to ultrasound, OCT provides information in both lateral and depth dimensions with resolution < 10 µm and an imaging depth of about 1.5 mm in scattering tissue. In this dissertation, I describe my efforts to develop new uses of OCT for improved early detection of adenoma in the azoxymethane mouse model of CRC. In recent years, commercial OCT systems have reached imaging speeds sufficiently high for in vivo volumeric imaging while laterally sampling the tissue at the Nyquist limit. First, I describe the design of a miniature endoscope and the integration of this probe with a commercial OCT system. Then I describe the development of two OCT imaging methods, one structural and one functional, that could be used for future work in diagnostic or therapeutic studies. The structural method produces en face images of the colon surface showing the colonic crypts, the first such demonstration of crypt visualization in the mouse. Changes in the crypt pattern are correlated with adenoma and are one of the earliest morphological changes. The functional method uses a Doppler OCT algorithm and image processing to detect the colon microvasculature. This technique can be used for vessel counting and blood flow measurements. Angiogenesis occurs at the beginning of tumorigenesis, and the tumor-originated arterioles are incapable of regular vasodilation. This Doppler OCT technique could potentially detect tumors at the earliest stages by measuring the change in local blood flow velocity in response to vasodilatory stimuli.

Ultrasound Current Source Density Imaging (UCSDI) is a noninvasive modality for mapping electrical activities in the body (brain and heart) in 4-dimensions (space + time). Conventional cardiac mapping technologies for guiding the radiofrequency ablation procedure for treatment of cardiac arrhythmias have certain limitations. UCSDI can potentially overcome these limitations and enhance the electrophysiology mapping of the heart. UCSDI exploits the acoustoelectric (AE) effect, an interaction between ultrasound pressure and electrical resistivity. When an ultrasound beam intersects a current path in a material, the local resistivity of the material is modulated by the ultrasonic pressure, and a change in voltage signal can be detected based on Ohm's Law. The degree of modulation is determined by the AE interaction constant K. K is a fundamental property of any type of material, and directly affects the amplitude of the AE signal detected in UCSDI. UCSDI requires detecting a small AE signal associated with electrocardiogram. So sensitivity becomes a major challenge for transferring UCSDI to the clinic. This dissertation will determine the limits of sensitivity and resolution for UCSDI, balancing the tradeoff between them by finding the optimal parameters for electrical cardiac mapping, and finally test the optimized system in a realistic setting. This work begins by describing a technique for measuring K, the AE interaction constant, in ionic solution and biological tissue, and reporting the value of K in excised rabbit cardiac tissue for the first time. K was found to be strongly dependent on concentration for the divalent salt CuSO₄, but not for the monovalent salt NaCl, consistent with their different chemical properties. In the rabbit heart tissue, K was determined to be 0.041 ± 0.012 %/MPa, similar to the measurement of K in physiologic saline: 0.034 ± 0.003 %/MPa. Next, this dissertation investigates the sensitivity limit of UCSDI by quantifying the relation between the recording electrode distance and the measured AE signal amplitude in gel phantoms and excised porcine heart tissue using a clinical intracardiac catheter. Sensitivity of UCSDI with catheter was 4.7 μV/mA (R² = 0.999) in cylindrical gel (0.9% NaCl), and 3.2 μV/mA (R² = 0.92) in porcine heart tissue. The AE signal was detectable more than 25 mm away from the source in cylindrical gel (0.9% NaCl). Effect of transducer properties on UCSDI sensitivity is also investigated using simulation. The optimal ultrasound transducer parameters chosen for cardiac imaging are center frequency = 0.5 MHz and f/number = 1.4. Last but not least, this dissertation shows the result of implementing the optimized ultrasound parameters in live rabbit heart preparation, the comparison of different recording electrode configuration and multichannel UCSDI recording and reconstruction. The AE signal detected using the 0.5 MHz transducer was much stronger (2.99 μV/MPa) than the 1.0 MHz transducer (0.42 μV/MPa). The clinical lasso catheter placed on the epicardium exhibited excellent sensitivity without being too invasive. 3-dimensional cardiac activation maps of the live rabbit heart using only one pair of recording electrodes were also demonstrated for the first time. Cardiac conduction velocity for atrial (1.31 m/s) and apical (0.67 m/s) pacing were calculated based on the activation maps. The future outlook of this dissertation includes integrating UCSDI with 2-dimensional ultrasound transducer array for fast imaging, and developing a multi-modality catheter with 4-dimensional UCSDI, multi-electrode recording and echocardiography capacity.

Overview: Optical concepts as they relate to the ophthalmologic correction of vision in corneal laser vision correction and intraocular lens design was examined. Purpose: The interaction between the excimer laser and residual corneal tissue in laser vision correction produces unwanted side effects. Understanding the origin of these artifacts can lead to better procedures. Furthermore, accommodating intraocular lenses offer a potential for eliminating presbyopia. Understanding the properties of a new accommodating intraocular lens incorporating a deformable interface may lead to advances in cataract surgery. Introduction: Corneal surface irregularities following laser refractive procedures are commonly seen. They regularly result in a patient’s decreased best corrected visual acuity and decreased contrast sensitivity. These changes are only seen in biologic tissue and the etiology has been elusive. A thermal response has been theorized and was investigated in this research. In addition, intraocular lenses using a mechanically deforming interface to change their power in order to duplicate natural accommodation have been developed. The deforming interface(s) induce optical aberrations due to irregular deformations. Design efforts have centered on minimizing these deformations. Both of the ophthalmic applications have been analyzed using finite element analysis (FEA) to understand their inherent optical properties. Methods: FEA modeling of thermal theory has been applied to verify that excimer laser induced collagen contraction creates corneal surface irregularities and central islands. A mathematical model which indicates the viability of the theory was developed. The modeling results were compared to post ablation changes in eyes utilizing an excimer (ArF 193 nm), as well as non-ablative thermal heating in eyes with a CO₂ laser. Addition modeling was performed on an Intraocular lens prototype measuring of actuation force, lens power, interface contour, optical transfer function, and visual Strehl ratio. Prototype verified mathematical models were utilized to optimize optical and mechanical design parameters to maximize the image quality and minimize the required force. Results: The predictive model shows significant irregular central buckling formation and irregular folding. The amount of collagen contraction necessary to cause significant surface changes is very small (0.3%). Uniform scanning excimer laser ablation to corneal stroma produces a significant central steepening and peripheral flattening in the central 3mm diameter. Isolated thermal load from uniform CO₂ laser irradiation without ablation also produces central corneal steepening and paracentral flattening in the central 3mm diameter. The iterative mathematical modeling based upon the intraocular lens prototype yielded maximized optical and mechanical performance through varied input mechanical and optical parameters to produce a maximized visual Strehl ratio and a minimized force requirement. Conclusions: The thermal load created by laser irradiation creates a characteristic spectrum of morphologic changes on the porcine corneal stromal surface which correlates to the temperature rise and is not seen inorganic, isotropic material. The highly similar surface changes seen with both lasers are likely indicative of temperature induced transverse collagen fibril contraction and stress re-distribution. Refractive procedures which produce significant thermal load should be cognizant of these morphological changes. The optimized intraocular lens operates within the physiologic constraints of the human eye including the force available for full accommodative amplitude using the eye’s natural focusing feedback, while maintaining image quality in the space available. Optimized optical and mechanical performance parameters were delineated as those which minimize both asphericity and actuation pressure. The methodology combines a multidisciplinary basic science approach from biomechanics, optical science, and ophthalmology to optimize an intraocular lens design suitable for preliminary trials.

Optical components made of anisotropic materials, such as crystal polarizers and crystal waveplates, are widely used in many complex optical system, such as display systems, microlithography, biomedical imaging and many other optical systems, and induce more complex aberrations than optical components made of isotropic materials. The goal of this dissertation is to accurately simulate the performance of optical systems with anisotropic materials using polarization ray trace. This work extends the polarization ray tracing calculus to incorporate ray tracing through anisotropic materials, including uniaxial, biaxial and optically active materials. The 3D polarization ray tracing calculus is an invaluable tool for analyzing polarization properties of an optical system. The 3×3 polarization ray tracing P matrix developed for anisotropic ray trace assists tracking the 3D polarization transformations along a ray path with series of surfaces in an optical system. To better represent the anisotropic light-matter interactions, the definition of the P matrix is generalized to incorporate not only the polarization change at a refraction/reflection interface, but also the induced optical phase accumulation as light propagates through the anisotropic medium. This enables realistic modeling of crystalline polarization elements, such as crystal waveplates and crystal polarizers. The wavefront and polarization aberrations of these anisotropic components are more complex than those of isotropic optical components and can be evaluated from the resultant P matrix for each eigen-wavefront as well as for the overall image. One incident ray refracting or reflecting into an anisotropic medium produces two eigenpolarizations or eigenmodes propagating in different directions. The associated ray parameters of these modes necessary for the anisotropic ray trace are described in Chapter 2. The algorithms to calculate the P matrix from these ray parameters are described in Chapter 3 for anisotropic ray tracing. This P matrix has the following characteristics: (1) Multiple P matrices are calculated to describe the polarization of the multiple eigenmodes at an anisotropic intercept. (2) Each P matrix maps the orthogonal incident basis vectors (Ê_m, Ê_n, Ŝ) before the optical interface into three orthogonal exiting vectors (a_m Ê'_m, a_n Ê'_n, Ŝ') after the interface, where a_m and a_n are the complex amplitude coefficients induced at the intercept. The ray tracing algorithms described in this dissertation handle three types of uncoated anisotropic interfaces isotropic/anisotropic, anisotropic/isotropic and anisotropic/anisotropic interfaces. (3) The cumulative P matrix associated with multiple surface interactions is calculated by multiplying individual P matrices in the order along the ray path. Many optical components utilize anisotropic materials to induce desired retardance. This important mechanism is modeled as the optical phase associated with propagation. (4) The optical path length OPL of an eigenpolarization along an anisotropic ray path is incorporated into the calculation of each P matrix. Chapter 4 presents the data reduction of the P matrix of a crystal waveplate. The diattenuation is embedded in the singular values of P. The retardance is divided into two parts: (A) The physical retardance induced by OPLs and surface interactions, and (B) the geometrical transformation induced by geometry of a ray path, which is calculated by the geometrical transform Q matrix. The Q matrix of an anisotropic intercept is derived from the generalization of s- and p-bases at the anisotropic intercept; the p basis is not confined to the plane of incidence due to the anisotropic refraction or reflection. Chapter 5 shows how the multiple P matrices associated with the eigenmodes resulting from propagation through multiple anisotropic surfaces can be combined into one P matrix when the multiple modes interfere in their overlapping regions. The resultant P matrix contains diattenuation induced at each surface interaction as well as the retardance due to ray propagation and total internal reflections. The polarization aberrations of crystal waveplates and crystal polarizers are studied in Chapter 6 and Chapter 7. A wavefront simulated by a grid of rays is traced through the anisotropic system and the resultant grid of rays is analyzed. The analysis is complicated by the ray doubling effects and the partially overlapping eigen-wavefronts propagating in various directions. The wavefront and polarization aberrations of each eigenmode can be evaluated from the electric field distributions. The overall polarization at the plane of interest or the image quality at the image plane are affected by each of these eigen-wavefronts. Isotropic materials become anisotropic due to stress, strain, or applied electric or magnetic fields. In Chapter 8, the P matrix for anisotropic materials is extended to ray tracing in stress birefringent materials which are treated as spatially varying anisotropic materials. Such simulations can predict the spatial retardance variation throughout the stressed optical component and its effects on the point spread function and modulation transfer function for different incident polarizations. The anisotropic extension of the P matrix also applies to other anisotropic optical components, such as anisotropic diffractive optical elements and anisotropic thin films. It systematically keeps track of polarization transformation in 3D global Cartesian coordinates of a ray propagating through series of anisotropic and isotropic optical components with arbitrary orientations. The polarization ray tracing calculus with this generalized P matrix provides a powerful tool for optical ray trace and allows comprehensive analysis of complex optical system.

Digital radiography systems are important diagnostic tools for modern medicine. The images are produced when x-ray sensitive materials are coupled directly onto the sensing element of the detector panels. As a result, the size of the detector panels is the same size as the x-ray image. An alternative to the modern DR system is to image the x-ray phosphor screen with a lens onto a digital camera. Potential advantages of this approach include rapid readout, flexible magnification and field of view depending on applications. We have evaluated lens-coupled DR systems for the task of signal detection by analyzing the covariance matrix of the images for three cases, using a perfect detector and lens, when images are affected by blurring due to the lens and screen, and for a signal embedded in a complex random background. We compared the performance of lens-coupled DR systems using three types of digital cameras. These include a scientific CCD, a scientific CMOS, and a prosumer DSLR camera. We found that both the prosumer DSLR and the scientific CMOS have lower noise than the scientific CCD camera by looking at their noise power spectrum. We have built two portable low-cost DR systems, which were used in the field in Nepal and Utah. We have also constructed a lens-coupled CT system, which included a calibration routine and an iterative reconstruction algorithm written in CUDA.

High-power, single-frequency, narrow-linewidth lasers emitting at tailored wavelength are desired for many applications, especially for precision spectroscopy. By way of a free-space resonator, optically pumped semiconductor lasers (OPSLs), a.k.a. vertical external-cavity surface-emitting lasers (VECSELs), can provide near diffraction-limited, high-quality Gaussian beams and are scalable in output power. Free space resonators also allow the insertion of the birefringent filter and the etalon to enforce single-frequency operation. In addition, the emission wavelengths of OPSLs are tailorable through bandgap engineering. These advantages above make OPSL a strong candidate of laser sources for spectroscopic applications including atomic spectroscopy as well as optical lattice clocks. In this research, a single-frequency laser source with high power is demonstrated by applying the injection-locking technique on OPSLs for the first time. The behaviors of the injection-locked OPSL are studied by varying parameters such as output coupling, injection wavelengths and injection power. It was found that the best injection wavelength is by approximately 2 nm shorter than the free-running slave laser at any given pump power. Below the lasing threshold for free-running operation, the laser starts the stimulated emission process as soon as it is pumped, working as a resonant amplifier. With proper parameters, the output power of the injection-locked laser exceeds the output power of its free-running condition. Over 9 W of single-frequency output power at 1015 nm is achieved. The output beam is near-diffraction-limited with Mₓ² = 1.04 and My² = 1.02. By analyzing the surface photoluminescence (PL) and the output performance of the laser, the saturation intensity of OPSLs is estimated to be 100 kW/cm² when the passive loss of 1.4% is assumed. The injection-locked system adds fairly low phase noise to that of the master laser. By measuring the beat note between the master laser and the injection-locked laser, the RMS values of the phase noise are 0.112 rad and 0.081 rad when using the T = 3% and T = 4% output couplers respectively.

Bose-Einstein condensates (BECs), with their superfluid behavior, quantized vortices, and high-level of control over trap geometry and other system parameters provide a compelling environment for studies of quantum fluid dynamics. Recently there has been an influx of theoretical and numerical progress in understanding the superfluid dynamics associated with two-dimensional quantum turbulence, with expectations that complementary experiments will soon be realized. In this dissertation I present progress in the development of an experimental toolkit that will enable such experimental studies of two-dimensional quantum turbulence. My approach to developing this toolkit has been twofold: first, efforts aimed at the development of experimental techniques for generating large disordered vortex distributions within a BEC; and second, efforts directed towards the design, implementation, and characterization of a quantum vortex microscope. Quantum turbulence in a superfluid is generally regarded as a disordered tangle of quantized vortices in three dimensions, or a disordered planar distribution of quantized vortices in two dimensions. However, not all vortex distributions, even large disordered ones, are expected to exhibit robust signatures of quantum turbulence. Identification and development of techniques for controlled forcing or initialization of turbulent vortex distributions is now underway. In this dissertation, I will discuss experimental techniques that were examined during the course of my dissertation research, namely generation of large disordered distributions of vortices, and progress towards injecting clusters of vortices into a BEC. Complimentary to vortex generation is the need to image these vortex distributions. The nondeterministic nature of quantum turbulence and other far-from-equilibrium superfluid dynamics requires the development of new imaging techniques that allow one to obtain information about vortex dynamics from a single BEC. To this end, the first vortex microscope constructed as part of my dissertation research enabled the first in situ images of quantized vortices in a single-component BEC, obtained without prior expansion. I have further developed and characterized a second vortex microscope, which has enabled the acquisition of multiple in situ images of a lattice of vortex cores, as well as the acquisition of single in situ images of vortex cores in a BEC confined in a weak hybrid trap. In this dissertation, I will discuss the state-of-the-art of imaging vortices and other superfluid phenomena in the University of Arizona BEC lab, as indicated by the examined performance of the quantum vortex microscope.