The Hydrogen Epoch of Reionization Array (HERA) is a radio interferometer aiming to detect the power spectrum of 21 cm fluctuations from neutral hydrogen from the Epoch of Reionization (EOR). Drawing on lessons from the Murchison Widefield Array (MWA) and the Precision Array for Probing the Epoch of Reionization (PAPER), HERA is a hexagonal array of large (14 m diameter) dishes with suspended dipole feeds. Not only does the dish determine overall sensitivity, it affects the observed frequency structure of foregrounds in the interferometer. This is the first of a series of four papers characterizing the frequency and angular response of the dish with simulations and measurements. We focus in this paper on the angular response (i.e., power pattern), which sets the relative weighting between sky regions of high and low delay, and thus, apparent source frequency structure. We measure the angular response at 137 MHz using the ORBCOMM beam mapping system of Neben et al. We measure a collecting area of 93 m^2 in the optimal dish/feed configuration, implying HERA-320 should detect the EOR power spectrum at z~9 with a signal-to-noise ratio of 12.7 using a foreground avoidance approach with a single season of observations, and 74.3 using a foreground subtraction approach. Lastly we study the impact of these beam measurements on the distribution of foregrounds in Fourier space.
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