Foreground Cleaning for Cosmic Microwave Background Polarimeters in the Presence of Instrumental Effects

The Cosmic Microwave Background (CMB) B-mode polarization signal offers a direct probe of inflation, a period of exponential expansion in the extreme early universe. The inflationary CMB B-mode polarization signal, however, is subject to the contamination of polarized galactic thermal dust foreground emission. A robust foreground cleaning method is essential for CMB polarimeters targeting the inflationary B-mode signal. In this thesis I present my work on developing foreground cleaning algorithms particularly in the presence of instrumental effects.;One of the instrumental effects I focus on in this work is the frequency dependent polarization rotation effect such as the one caused by an achromatic half-wave plate (AHWP). As an example, I use the AHWP of the E and B Experiment (EBEX) in this work and study the relation between the frequency dependent rotation effect and the characteristic parameters of the AHWP. To address the effect of an AHWP while removing galactic dust foreground contamination, I developed two foreground cleaning algorithms: a simple method that assumes perfect knowledge of the AHWP and a few simplifying assumptions, and a more sophisticated algorithm based on maximum likelihood method. Based on simulation results, the maximum likelihood foreground cleaning algorithm can recover CMB B-mode signal without any bias in the presence of band shape uncertainty, frequency dependent rotation effect and instrumental noise with realistic measurement accuracy of instrumental parameters.;In this thesis I also present my work on calculating the atmospheric loading in the millimeter wave regime for sub-orbital CMB experiments such as EBEX. Having a proper prediction of the atmospheric loading is an important input to detector designs for CMB experiments.