| Summary: | Inflation, which posits an exponential expansion in the early universe, is well motivated since it resolves questions that are left unexplained by standard ΛCDM cosmology, such as the flatness and homogeneity of the universe. The exponential expansion of universe during inflation explains the structure in the universe by freezing out the quantum fluctuations of space. These quantum fluctuations are also expected to generate a background of gravitational waves which would then imprint a B-mode polarization signal on the Cosmic Microwave Background. The BICEP2 and Keck Array experiments search for B-mode polarization from inflationary gravitational waves in the Cosmic Microwave Background. BICEP2 and the Keck Array use small aperture, cold, on-axis refracting optics optimized to target the degree angular scales at which the inflationary B-mode polarization is expected to peak. In this thesis we describe the optical design of B ICEP2 and the Keck Array. The small aperture design allows us to fully characterize the far-field performance of the instrument on site at the South Pole using thermal and amplified sources on the ground. We describe the efforts taken to characterize the main beam shapes of each polarization sensitive bolometer, as well as the differential beam paramters of each co-located orthogonally polarized detector pair. We study the residual temperature to polarization leakage induced by the beam mismatches after the principle modes have been mitigated in the analysis.
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