Research institutions around the globe are developing phased array feed (PAF) systems for wide-field L-band radio astronomical observations. PAFs offer faster survey speeds and larger fields of view than standard single-pixel feeds, which enable rapid sky surveys and significantly increased scientific capability. Because deep space astronomical signals are inherently weak, PAF systems must meet stringent noise and sensitivity requirements. Meeting these requirements requires detailed modeling of the phased array itself as well as the reflector it is mounted on. This thesis details a novel approach to dual-pol PAF design that models the array and reflector as a complete system in order to achieve a more optimal sensitivity and system noise temperature. The design and construction of two arrays designed using this technique is discussed. The implementation of a data acquisition system to receive data from the first of these arrays is also detailed. Polarization state information plays an important role in understanding cosmological processes for many deep space sources. Because of phase and gain imbalances in the LNAs and receiver chains calibration is required for accurate measurement of polarization by phased array feeds. As a result accurate polarimetric calibration techniques are essential for many observations. Existing polarimetric calibration methods are based on assumptions about the form of the system Mueller matrix that limit the generality of the method or require long observations of a polarized source which is time-consuming for multiple PAF beams. This thesis introduces a more efficient method of calibration that uses only three snapshot observations of bright astronomical calibrator sources, one unpolarized and two partially polarized. The design of an engineering array for the Green Bank Telescope is discussed. Measured results from a prototype element are presented along with simulated on-reflector results for the full array. Simulations predict that the array will be the highest sensitivity dual pol feed built by the Radio Astronomy Systems group at Brigham Young University to date.