Non-common path aberrations (NCPA) in an adaptive optics system are static aberrations that appear due to the difference in optical path between light arriving at the wavefront sensor (WFS) and at the science detector. If the adaptive optics are calibrated to output an unaberrated wavefront, then any optics outside the path of the light arriving at the WFS inherently introduce aberrations to this corrected wavefront. NCPA corrections calibrate the adaptive optics system such that it outputs a wavefront that is inverse in phase to the aberrations introduced by these non-common path optics, and therefore arrives unaberrated at the science detector, rather than at the output of the corrective elements. Focal plane sharpening (FPS) is one technique used to calibrate for NCPA in adaptive optics systems. Small changes in shape to the deformable element(s) are implemented and images are taken and analyzed for image quality (IQ) on the science detector. This process is iterated until the image quality is maximized and hence the NCPA are corrected. The work carried out as described in this paper employs two FPS techniques at Gemini North to attempt to mitigate up to 33% of the adaptive optics performance and image quality degradations currently under investigation. Changes in the NCPA correction are made by varying the Zernike polynomial coefficients in the closed-loop correction file for Altair (the facility adaptive optics system). As these coefficients are varied during closed-loop operation, a calibration point-source at the focal plane of the telescope is imaged through Altair and NIRI (the facility near-infrared imager) at f/32 in K-prime (2.12 μm). These images are analyzed to determine the Strehl ratio, and a parabolic fit is used to determine the appropriate coefficient correction that maximizes the Strehl ratio. Historic calibrations of the NCPA file in Altair's control loop were done at night on a celestial point source, and used a separate, high-resolution WFS (with its own inherent aberrations not common to either NIRI nor Altair) to measure phase corrections directly. In this paper it is shown that using FPS on a calibration source negates both the need to use costly time on the night sky and the use of separate optical systems (which introduce their own NCPA) for analysis. An increase of 6% in Strehl ratio is achieved (an improvement over current NCPA corrections of 11%), and discussions of future improvements and extensions of the technique is presented. Furthermore, a potentially unknown problem is uncovered in the form of high spatial frequency degradation in the PSF of the calibration source.

Fisheye lenses refer to ultra-wide angle lenses that have field of view equal or larger than 180 degrees. Such lenses introduce large amount of barrel distortion to capture at least the entire hemisphere in front of the lens. Fisheye lenses were initially designed for scientific use, such as cloud recording and angle measuring, and were widely used for commercial purposes later. The development of photographic fisheye lenses started in 1960s. However, the lack of detailed references on photographic fisheye lens design makes such design challenging. This thesis provides detailed introduction of photographic fisheye lens design for 35mm format DSLR cameras. A discussion on the history of fisheye lenses is provided to describe the development of fisheye lenses. The tangential and sagittal magnifications are mathematically derived for each fisheye lens projection mapping method to show their differences. The special properties and design issues of photographic fisheye lenses are described in detail. Along with each design issue, some solutions suggested by the author are also provided. The performance of the current diagonal fisheye lenses for 35mm DSLR cameras are evaluated in detail. Then a new diagonal fisheye lens designed by the author is presented and compared with the current diagonal fisheye lenses on the market. Finally, a zoom fisheye lens designed for 35mm DSLR cameras is presented and discussed.

A head-mounted-display with an optical combiner may introduce significant amount of distortion to the real world scene. The ability to accurately model the effects of both 2-dimensional and 3-dimensional distortion introduced by thick optical elements has many uses in the development of head-mounted display systems and applications. For instance, the computer rendering system must be able to accurately model this distortion and provide accurate compensation in the virtual path in order to provide a seamless overlay between the virtual and real world scenes. In this paper, we present a ray tracing method that determines the ray shifts and deviations introduced by a thick optical element giving us the ability to generate correct computation models for rendering a virtual object in 3D space with the appropriate amount of distortion. We also demonstrate how a Hartmann wavefront sensor approach can be used to evaluate the manufacturing errors in a freeform optical element to better predict wavefront distortion. A classic Hartmann mask is used as an inexpensive and easily manufacturable solution for accurate wavefront measurements. This paper further suggests two techniques; by scanning the Hartmann mask laterally to obtain dense sampling and by increasing the view screen distance to the testing aperture, for improving the slope measurement accuracy and resolution. The paper quantifies the improvements of these techniques on measuring both the high and low sloped wavefronts often seen in freeform optical-see-through head-mounted displays. By comparing the measured wavefront to theoretical wavefronts constructed with ray tracing software, we determine the sources of error within the freeform prism. We also present a testing setup capable of measuring off-axis viewing angles to replicate how the system would perform when worn by its user.

Surface textures add another dimension to optical design. They can be used to redirect light, isolate spectral bands, and enhance optical fields. They effectively take up no space, so can be applied to any optical surface–from intermediary elements to substrates. Here I present three applications of textured surfaces for light harvesting. The first project places scattering textures inside a film that can be applied to windows to scatter infrared light towards solar cells at the edges. The collected energy is then used to power tinting films. The second project uses modular diffractive structures to increase the absorption in solar cells. Lastly, structured silver surfaces are used to enhance plasmonics fields and increase two-photon excitation fluorescence.

This dissertation demonstrates the usefulness of exactly solvable quantum models in the investigation of light-matter interaction phenomena associated with the propagation of ultrashort laser pulses through gaseous media. This work fits into the larger research effort towards remedying the weaker portions of the standard set of medium modeling equations commonly used in simulations. The ultimate goal is to provide a self-consistent quantum mechanical description that can integrate Maxwell and Schrödinger systems and provide a means to realistically simulate nonlinear optical experiments on relevant scales. The study of exactly solvable models begins with one of the simplest quantum systems available, one with a 1D Dirac-delta function potential plus interaction with the light field. This model contains, in the simplest form, the most important "ingredients" that control optical filamentation, i.e. discrete and continuum electronic states. The importance of both states is emphasized in the optical intensity regime in which filaments form, where both kinds of electronic states simultaneously play a role and may not even be distinguishable. For this model atom, an analytical solution for the time-dependent light-induced atomic response from an arbitrary excitation waveform is obtained. Although this system is well-known and has been studied for decades, this result is probably the most practically useful and general one obtained thus far. Numerical implementation details of the result are also given as the task is far from trivial. Given an efficient implementation, the model is used in light-matter interaction simulations and from these it is apparent that even this toy model can qualitatively reproduce many of the nonlinear phenomena seen in experiments. Not only does this model capture the basic physics of optical filamentation, but it is also well-suited for high harmonic generation simulations. Next, a theoretical framework for using Stark resonant states (or metastable states) to represent the medium's polarization response is presented. Researchers have recognized long ago the utility of Gamow resonant states as a description of various decay processes. Even though a bound electron experiences a similar decay-like process as it transitions into the continuum upon ionization, it was unclear whether field-induced Stark resonant states carry physically relevant information. It is found that they do, and in particular it is possible to use them to capture a medium's polarization response. To this end, two quantum systems with potentials represented by a 1D Dirac-delta function and a 1D square well are solved, and all the necessary quantities for their use as medium models are presented. From these results it is possible to conjecture some general properties that hold for all resonance systems, including systems that reside in higher than one dimensional space. Finally, as a practical application of this theory, the Metastable Electronic State Approach (MESA) is presented as a quantum-based replacement for the standard medium modeling equations.

Molecular beam epitaxy (MBE) grown metal has been a renewed area of interest recently in order to achieve high quality metal films or nanostructures for plasmonics. Recently MBE grown silver films have been shown to possess optical constants closer to that of intrinsic silver leading to lower losses and thus allowing for higher quality plasmonics. MBE has also been used to grow silver nanocrystals and indium droplets, or islands, for plasmonics. These self-assembled nanostructures can be grown in close proximity to quantum confined structures such as InAs/GaAs quantum dots or InGaAs/GaAs quantum wells in a single process, without post-processing and fabrication, allowing for increased plasmonic enhancement due to the improved interface between the semiconductor and plasmonic structures.In this dissertation, widely tunable plasmonic resonances of indium islands will be discussed and plasmonic enhancement results will be presented and compared to those of nanoantennas constructed from standard fabrication processes. The coupling between near-surface quantum confined structures, both fabricated and self-assembled, will be compared to the coupling in typical dielectric cavities, such as photonic crystal nanobeams. Beyond the plasmonic possibilities of indium islands, indium becomes superconducting at 3.4 K. With the proximity effect allowing for electrons in materials in contact with a superconductor to occupy a superconducting like state, allowing for the possibility for a hybrid superconductor/semiconductor optical source. The observation of superconductivity in indium islands will be presented and considerations for a superconductor/semiconductor source will be discussed.

Methods to generate, manipulate, and measure optical and atomic fields with global or local angular momentum have a wide range of applications in both fundamental physics research and technology development. In optics, the engineering of angular momentum states of light can aid studies of orbital angular momentum (OAM) exchange between light and matter. The engineering of optical angular momentum states can also be used to increase the bandwidth of optical communications or serve as a means to distribute quantum keys, for example. Similar capabilities in Bose-Einstein condensates are being investigated to improve our understanding of superfluid dynamics, superconductivity, and turbulence, the last of which is widely considered to be one of most ubiquitous yet poorly understood subjects in physics. The first part of this two-part dissertation presents an analysis of techniques for measuring and manipulating quantized vortices in BECs. The second part of this dissertation presents theoretical and numerical analyses of new methods to engineer the OAM spectra of optical beams. The superfluid dynamics of a BEC are often well described by a nonlinear Schrodinger equation. The nonlinearity arises from interatomic scattering and enables BECs to support quantized vortices, which have quantized circulation and are fundamental structural elements of quantum turbulence. With the experimental tools to dynamically manipulate and measure quantized vortices, BECs are proving to be a useful medium for testing the theoretical predictions of quantum turbulence. In this dissertation we analyze a method for making minimally destructive in situ observations of quantized vortices in a BEC. Secondly, we numerically study a mechanism to imprint vortex dipoles in a BEC. With these advancements, more robust experiments of vortex dynamics and quantum turbulence will be within reach. A more complete understanding of quantum turbulence will enable principles of microscopic fluid flow to be related to the statistical properties of turbulence in a superfluid. In the second part of this dissertation we explore frequency mixing, a subset of nonlinear optical processes in which one or more input optical beam(s) are converted into one or more output beams with different optical frequencies. The ability of parametric nonlinear processes such as second harmonic generation or parametric amplification to manipulate the OAM spectra of optical beams is an active area of research. In a theoretical and numerical investigation, two complimentary methods for sculpting the OAM spectra are developed. The first method employs second harmonic generation with two non-collinear input beams to develop a broad spectrum of OAM states in an optical field. The second method utilizes parametric amplification with collinear input beams to develop an OAM-dependent gain or attenuation, termed dichroism for OAM, to effectively narrow the OAM spectrum of an optical beam. The theoretical principles developed in this dissertation enhance our understanding of how nonlinear processes can be used to engineer the OAM spectra of optical beams and could serve as methods to increase the bandwidth of an optical signal by multiplexing over a range of OAM states.

The Daniel K Inouye Solar Telescope (DKIST), when completed in 2019 will be the largest solar telescope built to date. DKIST will have a suite of first light polarimetric instrumentation requiring broadband polarization modulation and calibration optical elements. Compound crystalline retarders meet the design requirements for efficient modulators and achromatic calibration retarders. These retarders are the only possible large diameter optic that can survive the high flux, 5 arc minute field, and ultraviolet intense environment of a large aperture solar telescope at Gregorian focus. This dissertation presents work performed for the project. First, I measured birefringence of the candidate materials necessary to complete designs. Then, I modeled the polarization effects with three-dimensional ray-tracing codes as a function of angle of incidence and field of view. Through this analysis I learned that due to the incident converging F/13 beam on the calibration retarders, the previously assumed linear retarder model fails to account for effects above the project polarization specifications. I discuss modeling strategies such as Mueller matrix decompositions and simplifications of those strategies while still meeting fit error requirements. Finally, I present characterization techniques and how these were applied to prototype components.

Simulated images can provide insight into the performance of optical systems, especially those with complicated features. Many modern solutions for presbyopia and cataracts feature sophisticated power geometries or diffractive elements. Some intraocular lenses (IOLs) arrive at multifocality through the use of a diffractive surface and multifocal contact lenses have a radially varying power profile. These type of elements induce simultaneous vision as well as affecting vision much differently than a monofocal ophthalmic appliance. With myriad multifocal ophthalmics available on the market it is difficult to compare or assess performance in ways that effect wearers of such appliances. Here we present software and algorithmic metrics that can be used to qualitatively and quantitatively compare ophthalmic element performance, with specific examples of bifocal intraocular lenses (IOLs) and multifocal contact lenses. We anticipate this study, methods, and results to serve as a starting point for more complex models of vision and visual acuity in a setting where modeling is advantageous. Generating simulated images of real- scene scenarios is useful for patients in assessing vision quality with a certain appliance. Visual acuity estimation can serve as an important tool for manufacturing and design of ophthalmic appliances.

Improved imaging and detection of objects through turbid obscurants is a vital problem of current interest to both military and civilian entities. Image quality is severely degraded when obscurant fields such as fog, smoke, dust, etc., lie between an object and the light-collecting optics. Conventional intensity imaging through turbid media suffers from rapid loss of image contrast due to light scattering from particles (e.g. in fog) or random variations of refractive index (e.g. in medical imaging). Intensity imaging does not differentiate between rays scattered off particles in the obscurant field and those reflected off objects within the field. Scattering degrades image quality in all spectral bands (UV, visible, and IR), although the amount of degradation is wavelength dependent. This dissertation features the development of innovative system designs and techniques that utilize scattered radiation's deterministic polarization state evolution to greatly enhance the image contrast of stand-off objects within obscurant fields such as smoke, fog, or dust using active polarized illumination in the visible. The produced sensors acquire and process image data in real time using computationally non-intensive algorithms that differentiate between radiation that scatters or reflects from obscured objects and the radiation from the scattering media, improving image contrast by factors of ten or greater for dense water vapor obscurants.