The optical measurement of primary mirrors for astronomical telescopes has become increasingly challenging for two reasons. The mirrors, in addition to being larger, are faster and more aspheric in order to shorten the length of the telescope, and the required accuracy of the optical surfaces is more stringent. This dissertation presents improved methods for measuring these mirrors in the laboratory to the required accuracy. The wire test and the scanning pentaprism test, which measure surface slope errors, were designed and run under computer control. The wire test was used to measure the conic constant of a 3.5-m f/1.75 primary mirror to an accuracy of ±0.003 and the scanning pentaprism test measured the conic constant of a 1.8-m f/1 primary to ±0.003. Improvements in these tests were identified that could increase the accuracy significantly. Interferometric optical testing with null correctors is widely used for measuring aspheric surfaces to high accuracy. A system-level analysis of the null test is given. The test is optimized for wavefront accuracy, imaging distortion, and measurement noise from ghost reflections and diffraction. The optical design and analysis of null correctors, including designs for testing 6.5-m f/1.25 and 8.4-m f/1.14 primary mirrors are given. Several new null corrector designs and a method for performing tolerance analysis using structure functions are given. An error in the null corrector, if not detected, would cause the primary mirror to be polished to the wrong shape. (The primary mirrors for the Hubble Space Telescope and the European New Technology Telescope were misshapen because of faulty null correctors.) A new test of null correctors is presented that uses a computer-generated hologram (CGH) to synthesize a perfect primary mirror. When the CGH is measured through the null corrector, it appears as a perfect primary mirror. Apparent surface errors in this measurement can be attributed to errors in the null corrector. A complete error analysis of this test is given. This method has been proven on null correctors for 3.5-m primary mirrors, where it measured errors as small as 5.1 nm rms and confirmed the conic constants to ±0.000078.

The development of the microcavity laser has opened new vistas for exploration in regard to light-matter interaction. Here, we consider several experimental investigations with these smallest of lasers. Injection of an external optical signal into a vertical cavity surface emitting laser (VCSEL) reveals the weak injection regime of frequency locking and the strong injection regime of asymmetric local modification to the semiconductor gain curve. Above laser threshold linewidth measurements allow us to determine the linewidth enhancement factor, in agreement with theory. Below threshold measurements allow us to deduce carrier density and carrier lifetime. The definition of laser threshold in a microcavity laser has recently come under question. Intensity correlation measurements of the light emitted by a VCSEL exhibit a peak at laser threshold. Theoretical calculations confirm the experimental data and further show that this threshold peak remains even as the spontaneous emission rate into nonlasing modes approaches zero.

This dissertation explores a novel design for a surgical probe, a collimatorless coincidence imaging system designed to aid in tumor detection in nuclear medicine. Surgical probes can be maneuvered close to a suspected tumor site, thereby achieving higher resolution and sensitivity than external gamma cameras. However, conventional probes cannot distinguish between distant background variations and small tumors near the probe. Collimatorless coincidence imaging is a new method for suppressing the effects of variations in the background radiation. This decidedly unconventional imaging system images without a collimator or aperture of any kind. The probe design consists of a 10 x 10 array of collimatorless gamma-ray detectors connected by coincidence circuitry. The probe is used with a radionuclide that emits multiple photons per decay, such as ¹¹¹In. The coincidence circuitry triggers data collection only when two photons strike the detectors within a short time interval. Because the photons are emitted independently, the probability of coincident hits on two detectors is proportional to the product of the solid angles subtended by the two detectors. Therefore distant sources have a very low probability of contributing to the data, making them all but invisible to the probe. Data collection from such a system was simulated using a Monte Carlo routine that included absorption, the slight correlation between the directions of the emitted photons, and the presence of accidental coincidences. The data were reconstructed into object representations using the pseudoinverse obtained by singular value decomposition (SVD). The images showed a significant suppression of distant sources when compared to a probe equipped with a conventional parallel-hole collimator. We confirmed in the laboratory, using a point source of In-111 and two CdTe detectors connected by an AND gate, that the falloff in sensitivity was inversely proportional to the fourth power of the distance to the source and that the proportion of true to accidental coincidences followed the predicted relationship to the source activity. We conclude that collimatorless coincidence imaging is promising approach for tumor detection using surgical probes.

The total wave aberration of an optical system can be broken down into surface contributions. These surface contributions can be further differentiated into induced and intrinsic components. The intrinsic aberration is the aberration introduced by a given surface, based on a perfect incoming wavefront. The induced component is the additional aberration introduced by the surface as a consequence of monochromatic aberrations of the incoming wavefront. This distinction is made without decomposing the aberration or its components into orders. Because no methods have previously been developed to properly analyze this induced component, there is very little known about its significance. As a result, the behavior of lenses is not well understood beyond third order, and designers must depend upon optimization to find solutions with the necessary overall higher-order correction. The first part of this investigation is concerned with developing appropriate methods for separating the surface contributions to the total wave aberration of an optical system into induced and intrinsic components. These systems are limited to rotationally symmetric optical systems with spherical or aspheric surfaces. Three different methods are developed to describe the induced aberrations. These methods emphasize the aberrations of wavefronts rather than rays; rays are simply used for calculation purposes. The first is a numerical approach that determines the true shapes of the wavefront components, without separating the aberrations into orders. A second numerical method, based on a procedure developed by G. W. Hopkins, determines aberration coefficients to seventh order describing the induced, intrinsic, and complete aberrations. Because of the choice of reference surfaces, the third-order aberrations are entirely intrinsic. Thus, the induced component is described only by fifth- and higher-order coefficients. A third method uses an algebraic approach to calculate the fifth-order induced aberration coefficients in terms of third order coefficients. The second part is an exploration of the nature and significance of the induced component. The various analysis methods are used to explore the behavior of induced aberrations in many basic optical systems.

Because atmospheric turbulence causes distortions in stellar wavefronts, passive ground based telescopes, no matter how large, are limited to the resolution limit of a 0.1-0.2m aperture when imaging in the visible. If the new class of large aperture (10 m) telescopes is to reach its resolution potential, adaptive optics must be employed to compensate for the atmospheric wavefront distortions. Vital to an adaptive optics system is the ability to accurately sense the distorted wavefront. Two new methods for wavefront sensing show great promise for the field of adaptive optics. A reflective hybrid of the traditional Shack-Hartmann wavefront sensor has produced near diffraction limited imaging with the Multiple Mirror Telescope, a hexagonal array of six, 1.83 m mirrors. It is also directly applicable to filled aperture telescopes. Another wavefront sensor, the stellar phase shifting interferometer, has produced for the first time ever direct phase map measurements of atmospherically distorted wavefronts. The ability to directly measure the phase of the wavefront at each detector pixel paves the way for a new generation of light efficient and accurate wavefront sensors for adaptive optics.

This dissertation develops and presents an existing but little known method to provide an exact solution to the Wavefront Difference Equation routinely encountered in the reduction of Lateral Shear Interferograms (LSI). The method first suggested by Dr. Roland Shack treats LSI as a convolution of the wavefront with an odd impulse pair. This representation casts the Lateral Shear problem in terms of Fourier optics operators and filters with a simplified treatment of the reduction of the LSI possible. This work extends the original proposal applied to line scans of wavefronts to full two-dimensional recovery of the wavefront along with developing the associated mathematical theory and computer code to efficiently execute the wavefront reduction. Further, a number of applications of the wavefront reduction technique presented here are developed. The applications of the filtering technique developed here include optical imaging systems exhibiting the primary aberrations, a model of residual tool marks after fabrication and propagation of an optical probe through atmospheric turbulence. The computer program developed in this work resides on a PC and produces accurate results to a 1/500 wave when compared to ray traced input wavefronts. The combination of the relatively simple concept providing the basis of the reduction technique with the highly accurate results over a wide range of input wavefronts makes this a timely effort. Finally, the reduction technique can be applied to the accurate testing of aspheric optical components.

Various model observers have been applied to the objective assessment of medical image quality. However, the relevance of this application to clinical efficacy depends largely on how well model observers predict human performance. Attempting to answer this question, this dissertation focuses on the investigation of a linear observer known as the Hotelling observer and a modified version of the Hotelling observer, known as the channelized Hotelling observer. Performances of these observers for a signal-known-exactly detection task are calculated and compared to the performance of the human observer. Several psychophysical studies suggest that the Hotelling observer, formulated on the first- and second-order statistical properties of the images, could predict the human performance very well. To investigate the effect of certain higher-order statistical information on human performance, an experiment was designed in which the mean, variance, and covariance of three groups of images were kept the same, while the shapes of the image grey-level histogram were varied. The results showed little practical difference in the human performance among the three groups; thus the higher-order statistical information represented by the shape of the grey-level histogram did not influence the human observer's signal-detection performance for the task considered in this experiment. Another linear model observer, the nonprewhitening observer has been found in previous work to predict human performance better than the Hotelling observer for images with uniform backgrounds and correlated noise. When the images contain nonuniform background and uncorrelated noise, however, the Hotelling observer is found to be better in predicting human performance. To unify these results, a channelized Hotelling observer was proposed whose performance resembles that of a nonprewhitening observer for images with correlated noise, and that of a Hotelling observer for images with nonuniform background. Moreover, the channelized Hotelling observer is able to predict human performance when images have both the nonuniform background and correlated noise. A nonlinear version of the channelized Hotelling observer has also been found to predict human performance well.

This dissertation presents a study of high density plasma dynamics in semiconductors. Chapter 1 serves as an introduction and presents the basics of how we will use optical nonlinearities in the study of a high density plasma. Chapter 2 develops the necessary femtosecond laser system and techniques utilized in this investigation. The basics of our colliding pulse modelocked femtosecond laser system are presented. A variety of data acquisition systems are also outlined and discussed. A detailed description of our method of chirp measurement and correction rounds out the chapter. Chapter 3 presents a study of plasma dynamics in type I and type II GaAs multiple quantum well samples. First, the samples are compared in the quasi-equilibrium regime. The transfer of carriers from the wells to the barriers in the type II sample is found to profoundly affect the optical nonlinearities. A many-body theory calculation of these nonlinearities is then presented. We also utilize the unique properties of the type II structure to study the picosecond dynamics of a one component (hole) plasma. Finally, the possibility of transient gain in the type II structure is explored and discussed. Chapter 4 describes an investigation into the gain dynamics in an optically inverted semiconductor. Spectral hole burning is observed throughout the gain region, and the dynamics of the hole burning are shown. Since this system is highly inhomogeneously broadened, these results are first modeled by a group of noninteracting, inhomogeneously broadened, two level transitions. This model permits simple insight into the dynamics, but does not do a complete job of modeling the results. So, a full many-body treatment is included to more completely describe the experiment. Chapter 5 presents a study of the dephasing time through the gain region and into the absorption region of an optically excited GaAs multiple quantum well sample. Both spectral and temporal methods for measuring the dephasing time are utilized. A distinct maximum of the dephasing time is observed at the transparency point. A many-body theory calculating the carrier-carrier scattering rate is presented to explain this maximum.

The fundamental limitations on the operation of optical bistable devices in a ring cavity and in GaAs etalons are investigated. Experimental results of spontaneous transitions due to shot noise fluctuations are found in good agreement with various "ladder" models, if one allows the counting rates to vary accordingly. Stability analysis for two-photon homogeneously broadened media reveals single-wavelength instabilities for the laser but not for absorptive optical bistability. Appreciable regions of sidemode gain exist for both problems allowing for multiwavelength instabilities to occur. GaAs bistable devices show attractive features such as low power and high speed at room temperature for optical processing. However, experimental evidence in GaAs confirm the computer simulations of bistability that cavity losses, due to unsaturable background absorption, limit the switching power at room temperature. Methods to overcome the different limitations in GaAs devices toward parallel computation are then addressed from a system approach.

Nonlinear optical transverse effects, which arise from the interaction of a Gaussian beam with a nonlinear medium, are discussed. They are cw on-resonance enhancement (CORE), cw off-resonance rings, crosstalk, intracavity phase switching, self-defocusing of a bistable etalon, and thin-sample-encoding (TSE) self-lensing (i.e., self-focusing or self-defocusing) bistability and instabilities. CORE is the enhancement of the on-axis intensity of an on-resonance laser beam in a two-level medium. We report the first observation of CORE using sodium vapor. Cw off-resonance rings, resulting from a pure phase encoding or from simultaneous phase and amplitude encodings, are observed using sodium vapor. These rings have been observed many time before, but we have made the first careful comparison with numerical calculations. Parallel operation and external switching are two crucial themes for the application of bistable optical devices (BODs). For parallel operation, crosstalk between nearby BODs on the same etalon due to diffraction coupling may need to be avoided. Minimum separations needed to ensure independent operation are computed. For external switching, intracavity phase switching using a plane-wave input can switch on (or off) a BOD using an external pulse. The validity of this concept for a Gaussian input is numerically simulated. Self-defocusing effects, resulting in some interesting effects in the transverse bistable loops, are observed using a GaAs-GaAlAs bistable etalon. The results are confirmed by numerical simulations. TSE self-lensing bistability is observed using a short sodium cell and a single mirror. TSE self-lensing bistability results from an enhancement in the feedback via self-lensing of the beam. The lack of an optical resonator and the use of a thin medium make TSE setup a good candidate to study the Ikeda instability. We report the first observation of the Ikeda instability in this all-optical passive system using a cw input. Numerical simulations show a rich bifurcation sequence not yet fully studied experimentally.