Optimized Beam Sculpting with Generalized Fringe-Rate Filters
We generalize the technique of fringe-rate filtering, whereby visibilities measured by a radio interferometer are re-weighted according to their temporal variation. As the Earth rotates, radio sources traverse through an interferometer's fringe pattern at rates that depend on their position on the sky. Capitalizing on this geometric interpretation of fringe rates, we employ time-domain convolution kernels to enact fringe-rate filters that sculpt the effective primary beam of antennas in an interferometer. As we show, beam sculpting through fringe-rate filtering can be used to optimize measurements for a variety of applications, including mapmaking, minimizing polarization leakage, suppressing instrumental systematics, and enhancing the sensitivity of power-spectrum measurements. We show that fringe-rate filtering arises naturally in minimum variance treatments of many of these problems, enabling optimal visibility-based approaches to analyses of interferometric data that avoid systematics potentially introduced by traditional approaches such as imaging. Our techniques have recently been demonstrated in Ali et al. (2015), where new upper limits were placed on the 21 cm power spectrum from reionization, showcasing the ability of fringe-rate filtering to successfully boost sensitivity and reduce the impact of systematics in deep observations.