Utilizing Gaussian-Schell model beams to mitigate atmospheric turbulence in free space optical communications / by Kyle R. Drexler.

Turbulence affects traditional free space optical communication by causing speckle to appear in the received beam profile. This occurs due to changes in the refractive index of the atmosphere that are caused by fluctuations in temperature and pressure, resulting in an inhomogeneous medium. The Gaussian-Schell model of partial coherence has been suggested as a means of mitigating these atmospheric inhomogeneities on the transmission side. This dissertation analyzed the Gaussian-Schell model of partial coherence by verifying the Gaussian-Schell model in the far-field, investigated the number of independent phase control screens necessary to approach the ideal Gaussian-Schell model, and showed experimentally that the Gaussian-Schell model of partial coherence is achievable in the far-field using a liquid crystal spatial light modulator. A method for optimizing the statistical properties of the Gaussian-Schell model was developed to maximize the coherence of the field while ensuring that it does not exhibit the same statistics as a fully coherent source. Finally a technique to estimate the minimum spatial resolution necessary in a spatial light modulator was developed to effectively propagate the Gaussian-Schell model through a range of atmospheric turbulence strengths. This work showed that regardless of turbulence strength or receiver aperture, transmitting the Gaussian-Schell model of partial coherence instead of a fully coherent source will yield a reduction in the intensity fluctuations of the received field. By measuring the variance of the intensity fluctuations and the received mean, it is shown through the scintillation index that using the Gaussian-Schell model of partial coherence is a simple and straight forward method to mitigate atmospheric turbulence instead of traditional adaptive optics in free space optical communications.

Hermitian curve interpolation for CT-data re-sampling

Purpose: Development of an interpolation algorithm for re‐sampling spatially distributed CT‐data with the following features: global and local integral conservation, avoidance of negative interpolation values for positively defined datasets and the ability to control re‐sampling artifacts. Method and Materials: The interpolation can be separated into two steps: first, the discrete CT‐data has to be continuously distributed by an analytic function considering the boundary conditions. Generally, this function is determined by piecewise interpolation. Instead of using linear or high order polynomialinterpolations, which do not fulfill all the above mentioned features, a special form of Hermitian curve interpolation is used to solve the interpolation problem with respect to the required boundary conditions. A single parameter is determined, by which the behavior of the interpolation function is controlled. Second, the interpolated data have to be re‐distributed with respect to the requested grid. Results: The new algorithm was compared with commonly used interpolation functions based on linear and second order polynomial. It is demonstrated that these interpolation functions may over‐ or underestimate the source data by about 10%–20% while the parameter of the new algorithm can be adjusted in order to significantly reduce these interpolation errors. Finally, the performance and accuracy of the algorithm was tested by re‐gridding a series of X‐ray CT‐images. Conclusion: Inaccurate sampling values may occur due to the lack of integral conservation. Re‐sampling algorithms using high order polynomialinterpolation functions may result in significant artifacts of the re‐sampled data. Such artifacts can be avoided by using the new algorithm based on Hermitian curve interpolation

The Isothermal Transformation Curve for S.A.E. 6150

More than 3000 years ago, men began quenching and tem­pering tools to improve their physical properties. The an­cient people found that iron was easier to shape and form in a heated condition. Charcoal was used as the fuel, and when the shaping process was completed, the smiths cooled the piece in the most obvious way, quenching in water. Quite un­intentionally, these people stumbled on the process for im­proving the properties of iron, and the art of blacksmithing began.

On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series

Fossil pollen data from stratigraphic cores are irregularly spaced in time due to non-linear age-depth relations. Moreover, their marginal distributions may vary over time. We address these features in a nonparametric regression model with errors that are monotone transformations of a latent continuous-time Gaussian process Z(T). Although Z(T) is unobserved, due to monotonicity, under suitable regularity conditions, it can be recovered facilitating further computations such as estimation of the long-memory parameter and the Hermite coefficients. The estimation of Z(T) itself involves estimation of the marginal distribution function of the regression errors. These issues are considered in proposing a plug-in algorithm for optimal bandwidth selection and construction of confidence bands for the trend function. Some high-resolution time series of pollen records from Lago di Origlio in Switzerland, which go back ca. 20,000 years are used to illustrate the methods.

Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models

Several methods based on Kriging have recently been proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such a level set—and not solely its volume—and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.

A Nonstationary Space-Time Gaussian Process Model for Partially Converged Simulations

In the context of expensive numerical experiments, a promising solution for alleviating the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at the price of precision in the response. This work addresses the issue of fitting a Gaussian process model to partially converged simulation data for further use in prediction. The main challenge consists of the adequate approximation of the error due to partial convergence, which is correlated in both design variables and time directions. Here, we propose fitting a Gaussian process in the joint space of design parameters and computational time. The model is constructed by building a nonstationary covariance kernel that reflects accurately the actual structure of the error. Practical solutions are proposed for solving parameter estimation issues associated with the proposed model. The method is applied to a computational fluid dynamics test case and shows significant improvement in prediction compared to a classical kriging model.