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Data analysis techniques useful for the detection of B-mode polarisation of the Cosmic Microwave Background.
Wallis, Christopher George Roy
[Thesis]. Manchester, UK: The University of Manchester; 2015.
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Abstract
Asymmetric beams can create significant bias in estimates of the power spectra from cosmic microwave background (CMB) experiments. With the temperature power spectrum many orders of magnitude stronger than the B-mode power spectrum any systematic error that couples the two must be carefully controlled and/or removed.In this thesis, I derive unbiased estimators for the CMB temperature and polarisation power spectra taking into account general beams and scan strategies. I test my correction algorithm on simulations of two temperature-only experiments and demonstrate that it is unbiased. I also develop a map-making algorithm that removes beam asymmetry bias at the map level. I demonstrate its implementation using simulations.I present two new map-making algorithms that create polarisation maps clean of temperature-to-polarisation leakage systematics due to differential gain and pointing between a detector pair. Where a half wave plate is used, I show that the spin-2 systematic due to differential ellipticity can also be removed using my algorithms. The first algorithm is designed to work with scan strategies that have a good range of crossing angles for each map pixel and the second for scan strategies that have a limited range of crossing angles. I demonstrate both algorithms by using simulations of time ordered data with realistic scan strategies and instrumental noise.I investigate the role that a scan strategy can have in mitigating certain common systematics by averaging systematic errors down with many crossing angles. I present approximate analytic forms for the error on the recovered B-mode power spectrum that would result from these systematic errors. I use these analytic predictions to search the parameter space of common satellite scan strategies to identify the features of a scan strategy that have most impact in mitigating systematic effects.
Layman's Abstract
Gravitational wave from inflation, a brief rapid expansion of the universe, can cause a very specific signal in the Cosmic Microwave Background. Imperfections in a telescope can make the detection of the this signal problematic, therefore these systematic effects must be carefully controlled and/or removed.In this thesis I develop algorithms that allow to remove the bias created be common imperfections. I analysis how a satellite-based telescope should best scan the sky in order to mitigate these systematic effects.