The field of adaptive optics (AO) and laser-beacon AO has been successfully implemented in the last part of the 20th century. Adaptive optics greatly improves the resolution capabilities of ground-based telescopes by correcting for atmospheric turbulence. The initial implementation of laser-beacon AO was done on relatively small telescopes, on the order of 1.5 m. However, with larger aperture telescopes being built, such as the 8-m class Gemini telescopes, there is much room for improvement. Errors resulting from laser-beacon AO, such as focus anisoplanatism, become worse with an increase in aperture diameter. Tilt anisoplanatism is also a problem, regardless of the size of telescope, and also needs to be reduced to enhance the resolution of the objects being observed. This dissertation investigates alternate laser-beacon AO configurations, to reduce the effects of focus and tilt anisoplanatism for larger aperture telescopes. The configurations investigated include single and multiple laser beacons at single altitudes and single and multiple laser beacons at multiple altitudes. These second configurations are referred to as hybrid beacon systems and consist of Rayleigh beacons at altitudes of 10 to 20 km and sodium beacons at about 90 km, the location of the sodium layer. Hybrid systems are shown to reduce both focus and tilt anisoplanatism as opposed to the first configurations which only aid in reducing focus anisoplanatism. An addition to the hybrid systems with multiple beacons, the use of multiple deformable mirrors (DM's) is investigated. These additional DM's are placed conjugate to atmospheric altitudes with predominant turbulence, beyond the traditional conjugate location of the primary mirror. They correct for turbulence at these atmospheric layers and are referred to as multi-conjugate adaptive optical (MCAO) systems. The purpose of MCAO configurations is to increase the corrected field of view. For the types of systems investigated in this dissertation, radiometric characteristics are calculated. These include the optimum range-gate at the minimum noise equivalent angle (NEA) for several laser pulse energies, wavefront sensor sampling rate as a function of bandwidth, and the optimum system bandwidth for several laser powers. These characteristics can be used to further define a practical AO system that will enhance performance.

Dynamic refocus, DR, for adaptive optics has been proposed as a process that, over a given range, will maintain a sharp image of the Rayleigh backscatter due to a laser pulse rising in the atmosphere. Sharp focus is important when the backscatter from an artificial star is used for wavefront sensing. The wavefront variance associated with a Shack Hartmann wavefront sensor is inversely related to the photon return (in the shot noise limited case) and is dependant on the square of the beacon image's angular size. For the same spot size the photon return of a dynamically refocused Rayleigh beacon is increased by a factor of twelve over a system without DR. Here we present the implementation and results of the first operational Rayleigh beacon DR system. The DR system is designed for use on the MMT with five Rayleigh laser beacons projected on a 120arcsec regular pentagon. It was tested on the Mt. Bigelow 61" telescope, configured to act as an off-axis MMT subaperture. The results show the simultaneous DR of five Rayleigh beacons where a beacon image is dynamically refocused from 7arcsec FWHM to 2.7arcsecFWHM.

This dissertation describes the design and manufacturing techniques of antireflection coatings for the optical components of the MAESTRO spectrograph. This work was motivated by the need for a high-performance, robust and inexpensive anti-reflection (AR) coating for deep-space, faint object astronomical observations. I have created a new line of AR-filters, optimal for several different glass substrates, with a small number of layers. The possible ease of mass-manufacture of the CoyoteRTM coating is also illustrated here. I also describe a possible new technique for overcoating aluminum and silver reflective films on glass substrates, as well as future directions for research.

The James Webb Space Telescope (JWST) is an anastigmatic, segmented cryogenic telescope. The stability of the primary mirror back-plane is a major concern in co-phasing the telescope and in the longer term stability of its image quality. The back-plane is a 6.6 meter structure constructed of carbon fiber, and is therefore a "diffuse" object, an object with surface roughness larger than the wavelength of the light. For this reason classical interferometeric measurements will not work. The objective is to design and characterize a Simultaneous phase shifted Digital Speckle Pattern Interferometer (SDSPI) that has the most potential to measure the JWST back plane structure within the required accuracy (15 nm RMS out-of-plane motion). SDSPI interferometry is a method of measuring the back-plane deformations that has the potential of reaching the required accuracy in the presence of vibrations within cryogenic chambers. 4D Technology Corporation, in Tucson, Arizona has an instantaneous phase shifted interferometer (PhaseCam) that is modified to a SDSPI interferometer. Repeatability, dynamic range, and accuracy of the SDSPI is characterized by measuring a 5cm x 5cm back-plane structure made of carbon fiber.

A method is presented for finding coordinate transformations (warpings) of "objects" and "images," related by a shift-variant linear system model, such that the warped objects and images are approximately related by a shift-invariant linear system model. Such warps have utility for inverse solutions to linear problems, in which solution times for shift-invariant systems are less than the solution times for shift-variant systems. To this end, a measure of shift-variance for sampled linear systems is proposed. This measure allows for a variability in the sampling locations, as well as separable multipliers in the object and image domains (collectively called warping parameters), so that the measure may be used as the objective function for an optimization problem. Properties of the desired solution, which includes adequate field coverage and limits on the allowable warps, are also proposed. These features are combined in a formally stated optimization problem, which will search for a set of sample locations and multipliers to minimize the shift-variance of the warped system. The performance of a number of optimization algorithms which were directed at this task are presented. Also reported are results for finding the optimal warpings for some example one-dimensional systems. Inverse solutions, using both linear and non-linear techniques, are obtained using this warping method, and these results are compared to related inverse solutions which directly perform shift-variant inversion.

The error-handling capability of the Compact Disc Error Correction Code (ECC) is influenced by the statistical distribution of the errors that contaminate the recorded data. Error measurement hardware and software are developed to examine the recorded data on Compact Discs and report the locations of the erroneous data with single-byte resolution. A sample population of 8 read-only and 8 write-once Compact Discs are subjected to error measurement and the recovered error statistics are compared for the two types of media. A novel Markov state machine is developed to quantitatively characterize the measured errors and produce block-error probability rates at the input of the ECC decoder. These probability rates are used to obtain reliability estimates for the recovered data bytes at the output of the ECC decoder. The capability of the Compact Disc's ECC decoder to detect and subsequently correct the erroneous data bytes is greatly influenced by the particular decoding strategy used by the ECC decoder. The performance of seven different ECC decoding strategies that are applied to the recovered data from read-only and write-once Compact Discs are evaluated. In addition, the ECC decoder performance of a newly proposed Compact Disc recording format known as the Compact Disc-Direct Access Storage Disc (CD-DASD) is investigated. Reliability estimates for the data occurring at the output of the CD-DASD ECC decoder is compared to that of conventional CD-ROM's Cross-Interleaved Reed-Solomon Code decoder.

Integrated optics-based approaches to beam steering, beam shaping, beam collimation, and quasi-phasematched (QPM) second harmonic generation (SHG) of light offer significant advantages over conventional approaches based on bulk optics. The research in this dissertation addresses the analysis and design of optical guided-wave devices for both efficient quasi-phasematched second harmonic generation in diffused channel waveguides, as well as Bragg deflection of beams in planar waveguides. It is known that the normalized SHG efficiency depends on the linear properties of the waveguide through the overlap of the modal fields at the fundamental and second harmonic wavelengths. To analyze the linear modal properties, a fast and accurate modeling tool, based on an improved, semi-vector, Fourier method of analysis, is presented. The tool incorporates the Wentzel-Kramers-Brillouin (WKB) and effective index methods to accurately determine the computational parameters required for the numerical calculation in the Fourier method so that automatic variation of the waveguide parameters is permitted. Using the modeling tool, the dependence of the SHG process on the waveguide parameters is investigated in detail, leading to waveguide designs with improved mode confinement, and consequently higher SHG efficiency. The phasematching characteristics of these improved designs are also calculated, and it is found that non-critical phasematching, or phasematching with wide tolerances to variations in the waveguide parameters, is possible in certain cases. The analysis of the waveguide-SHG process also indicates that efficiency can be improved by utilizing thin films on the waveguide surface to ensure that the peaks of the fundamental and second harmonic modes are coincident. This contributes to higher SHG efficiency through improved mode overlap as well, but it is demonstrated that this approach is clearly distinct from and independent of the mode-confinement approach. The analysis of planar overlays is based on recursion relations for the phase shift upon reflection at interfaces. The significance of this approach is demonstrated through the "matching" of the diffused waveguide to an independently-designed, multilayer overlay for the purposes of obtaining specific modal characteristics in the "integrated" structure. On a different note but incorporating similar approaches for analysis and design, beam shaping, steering, and collimation in planar waveguides, using Bragg gratings with finite area and non-uniform depth variation, are also discussed.

Nonlinear optical phenomena in both semiconductor microcavities and sodium vapor are investigated. Systems displaying atomic and excitonic coupling are studied in detail in order to unravel underlying physical principles. Possible applications for these systems are evaluated where appropriate. Normal-mode coupling (NMC) in a semiconductor microcavity is achieved when a narrow-linewidth quantum well exciton resonance is coincident with the cavity mode of a high-finesse microcavity. This interaction leads to a double-peaked spectrum in either transmission, reflection, or photoluminescence (PL). The high-quality microcavities studied here at liquid-Helium temperatures reveal intensity dependent behavior that has not previously been observed. Nonlinear saturation of the exciton leads to a spectral broadening of the excitonic absorption without a significant loss in oscillator strength. This results in a reduction of the two transmission peaks with almost no change in the splitting between the peaks. Such behavior is easily explained using phenomenological nonlinear dispersion theory. In this nonlinear regime, the luminescence from the microcavity shows a gradual transition from the nonperturbative regime of NMC to lasing with increasing excitation. The observed behavior is explained by density-dependent changes in both the transmission of the microcavity and the bare-exciton emission, rather than a boson-condensation of excitons which has been previously proposed. An intermediate-finesse microcavity also modifies the emission distribution from a bulk-semiconductor at room temperature. Angularly resolved emission spectra and quantum efficiency measurements show the PL is strongly dependent on the reflectivity of the microcavity. Unfortunately, the enhancement in the decay rate of excitons due to high-reflectivity mirrors seen previously by our group does not result in an increased quantum efficiency. High-gain optical-wavefront amplification in atomic sodium vapor is demonstrated via both the three-photon effect and stimulated Raman scattering (SRS). In both cases, single-pass weak-field gain of nearly 400 is achieved with only 800 mW of pump power near 589 nm. In the case of SRS, phase preservation of the amplified wavefront, which is necessary in adaptive imaging applications, is also demonstrated.

Surface-relief, submicron period transmission gratings are fabricated in fused silica. A rigorous vector diffraction code, based on the coupled-wave analysis technique, is used to design and analyze the surface relief gratings. When light with wavelength greater than the grating period encounters such element, only zeroth order transmitted and reflected beams propagate, all other diffracted orders are evanescent. These surface-relief gratings act as homogeneous thin film layers of equivalent refractive indices. The equivalent refractive indices depend on grating characteristics, angle of incidence, and incident light polarization. These gratings can be used as equivalent anti-reflection coatings and as polarization elements. Since the grating structures are etched into the substrate material, these optical elements are durable and chemically resistant compared to resist gratings. Subwavelength elements may play a critical role in high power laser systems where damage resistant antireflection and birefringent materials may not exist. By gaining an understanding and being able to control the many variables involved in the grating fabrication process, one-dimensional and two-dimensional submicron period surface-relief resist gratings with rectangular profiles and precisely controlled dimensions are generated. Subsequent pattern transfer etch into underlying substrate layer resulted in one and two-dimensional gratings in fused silica. One-dimensional gratings fabricated in fused silica behaves as polarization elements, giving a maximum measured phase retardation of 50 degrees. To create a polarization insensitive antireflection structure, two-dimensional surface relief gratings are fabricated. These elements exhibited reflectivities near zero percent. The AR structures also showed broadband performance. Application of two-dimensional AR structures on a 16-level diffractive phase plate reduces the surface reflectance of the multilevel phase plate to 0.2%, from 3.3% of that of a bare fused silica surface. Subwavelength grating elements were found to damage when exposed to 45 mJ/cm² and 13 mJ/cm² of laser radiation at 1064 nm and 351 nm wavelength, respectively. The subwavelength gratings have laser damage thresholds comparable to that of bare fused silica. Initial effort on replicating the subwavelength grating structures in polymers yielded promising results, demonstrating the potential for mass production. Replicated elements exhibited no stress birefringence.

High-power laser systems, such as the National Ignition Facility (NIF) project at Lawrence Livermore National Laboratories (LLNL), require optics of extremely high quality. Surface errors, especially periodic surface relief structures, can lead to focal spot degradation at best and serious damage to downstream optics at worst. The optics in these systems must be characterized with a high degree of accuracy to ensure proper operation. To provide system optics of sufficient quality, the testing apparatus must measure surface structure with high fidelity and cannot introduce significant errors into the measurements. This paper deals with measurements taken on two WYKO phase-shifting laser Fizeau interferometers to optimize their ability to meet the measurement requirements for optics in high-power laser systems. Increasingly, tolerances on optics are being specified with the power spectral density function (PSD) of the surface height data, and thus the power spectrum is used to characterize the measurement system. The system transfer function, which is the ratio of the measured amplitude of frequency components to the actual, is calculated using several methods. The effects of various parameters on the calculated system transfer function are studied. First, the use of the finite Fourier transform to estimate the power spectrum from surface profile data was studied. Next, simulated measurements were analyzed to determine the effects of rotation, feature location, noise, windowing, and other variables on the calculated power spectral density. After the theoretical analysis, the interferometer transfer function was calculated using two techniques. The effects of wavefront propagation on the measurements were also studied. Measurements were first taken on a 150mm laser Fizeau system where the effect of changing various parameters was studied. Final measurements were taken on the 600mm system to verify system performance. The large aperture laser Fizeau interferometer as built had a system transfer that surpassed the system requirements with regards to transfer function and measurement noise. The system measured frequency amplitudes with 70% fidelity up to half the Nyquist frequency. In addition, the power spectrum of the noise plots was below the system specification of 0.1ν⁻¹·⁵⁵nm²mm over the spatial frequencies ν of interest,¹ more than ten times lower than the specification on the parts to be measured.