  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.
