Control algorithms for large scale adaptive optics

In this dissertation, the problem of creating effective large scale Adaptive Optics (AO) systems control algorithms for the new generation of giant optical telescopes is addressed. The effectiveness of AO control algorithms is evaluated in several respects, such as computational complexity, compensation error rejection and robustness, i.e. reasonable insensitivity to the system imperfections. The results of this research are summarized as follows: 1. Robustness study of Sparse Minimum Variance Pseudo Open Loop Controller (POLC) for multi-conjugate adaptive optics (MCAO). The AO system model that accounts for various system errors has been developed and applied to check the stability and performance of the POLC algorithm, which is one of the most promising approaches for the future AO systems control. It has been shown through numerous simulations that, despite the initial assumption that the exact system knowledge is necessary for the POLC algorithm to work, it is highly robust against various system errors. 2. Predictive Kalman Filter (KF) and Minimum Variance (MV) control algorithms for MCAO. The limiting performance of the non-dynamic Minimum Variance and dynamic KF-based phase estimation algorithms for MCAO has been evaluated by doing Monte-Carlo simulations. The validity of simple near-Markov autoregressive phase dynamics model has been tested and its adequate ability to predict the turbulence phase has been demonstrated both for single- and multiconjugate AO. It has also been shown that there is no performance improvement gained from the use of the more complicated KF approach in comparison to the much simpler MV algorithm in the case of MCAO. 3. Sparse predictive Minimum Variance control algorithm for MCAO. The temporal prediction stage has been added to the non-dynamic MV control algorithm in such a way that no additional computational burden is introduced. It has been confirmed through simulations that the use of phase prediction makes it possible to significantly reduce the system sampling rate and thus overall computational complexity while both maintaining the system stable and effectively compensating for the measurement and control latencies.

MITEP: REFLECTIVE JOURNEY

This research looks at the use of the Interactive Student Notebook (ISN) in the math classroom and the impact on student achievement as part of the MiTEP program. A reflective critical analysis of the MiTEP program discusses impact on teacher pedagogy, leadership, and connections to people and resources. The purpose of the study stemmed from the lack of student retention, poor organizational skills, and the students’ inability to demonstrate college readiness skills such as how to study, completing homework, and thinking independently. Motivation also stemmed from teacher frustration. The research was conducted at Linden Grove Middle School in Kalamazoo Michigan in a strategic math class. Twenty-two sixth graders, thirty-two seventh graders, and forty eighth graders were part of the study.Students were given the Strategic Math Inventory (SMI) test in week 1 of the class and again at the end of a 12 week marking period. Students participated in an attitude survey to record their feelings about the use of the ISN in the strategic math classroom. The data compared the control group (the previous year’s [2012-2013] growth data) to the experimental group, the current year’s (2013-2014) growth data. Both groups were statistically similar in that the mean average was about a 4th grade level equivalency and the groups had similar numbers of grade level students. The significant findings were in the amount of growth made using the ISN. The control group started with a mean average of 586.6 and ended with a mean average of 697.1, making about one year’s growth from a 4th to a 5th grade level equivalency. The experimental group started with a mean average of 585.2 and ended with a mean average of 744.2, making about two years growth from a 4th to a 6th grade level equivalency. This is double the growth of the control group. The Cohen’s test resulted in a score of 0.311 which describes that the teaching method, the use of the ISN in the math classroom had a medium impact on student growth.

MULTI-WAVELENGTH SPECKLE REDUCTION FOR LASER PICO-PROJECTORS USING DIFFRACTIVE OPTICS

Personal electronic devices, such as cell phones and tablets, continue to decrease in size while the number of features and add-ons keep increasing. One particular feature of great interest is an integrated projector system. Laser pico-projectors have been considered, but the technology has not been developed enough to warrant integration. With new advancements in diode technology and MEMS devices, laser-based projection is currently being advanced for pico-projectors. A primary problem encountered when using a pico-projector is coherent interference known as speckle. Laser speckle can lead to eye irritation and headaches after prolonged viewing. Diffractive optical elements known as diffusers have been examined as a means to lower speckle contrast. Diffusers are often rotated to achieve temporal averaging of the spatial phase pattern provided by diffuser surface. While diffusers are unable to completely eliminate speckle, they can be utilized to decrease the resultant contrast to provide a more visually acceptable image. This dissertation measures the reduction in speckle contrast achievable through the use of diffractive diffusers. A theoretical Fourier optics model is used to provide the diffuser’s stationary and in-motion performance in terms of the resultant contrast level. Contrast measurements of two diffractive diffusers are calculated theoretically and compared with experimental results. In addition, a novel binary diffuser design based on Hadamard matrices will be presented. Using two static in-line Hadamard diffusers eliminates the need for rotation or vibration of the diffuser for temporal averaging. Two Hadamard diffusers were fabricated and contrast values were subsequently measured, showing good agreement with theory and simulated values. Monochromatic speckle contrast values of 0.40 were achieved using the Hadamard diffusers. Finally, color laser projection devices require the use of red, green, and blue laser sources; therefore, using a monochromatic diffractive diffuser may not optimal for color speckle contrast reduction. A simulation of the Hadamard diffusers is conducted to determine the optimum spacing between the two diffusers for polychromatic speckle reduction. Experimental measured results are presented using the optimal spacing of Hadamard diffusers for RGB color speckle reduction, showing 60% reduction in contrast.