Title: The Hydrogen Epoch of Reionization Array Dish III: Measuring Chromaticity of Prototype Element with Reflectometry,
Abstract: The experimental efforts to detect the redshifted 21 cm signal from the Epoch
of Reionization (EoR) are limited predominantly by the chromatic instrumental
systematic effect. The delay spectrum methodology for 21 cm power spectrum
measurements brought new attention to the critical impact of an antenna's
chromaticity on the viability of making this measurement. This methodology
established a straightforward relationship between time-domain response of an
instrument and the power spectrum modes accessible to a 21 cm EoR experiment.
We examine the performance of a prototype of the Hydrogen Epoch of Reionization
Array (HERA) array element that is currently observing in Karoo desert, South
Africa. We present a mathematical framework to derive the beam integrated
frequency response of a HERA prototype element in reception from the return
loss measurements between 100-200 MHz and determined the extent of additional
foreground contamination in the delay space. The measurement reveals excess
spectral structures in comparison to the simulation studies of the HERA
element. Combined with the HERA data analysis pipeline that incorporates
inverse covariance weighting in optimal quadratic estimation of power spectrum,
we find that in spite of its departure from the simulated response, HERA
prototype element satisfies the necessary criteria posed by the foreground
attenuation limits and potentially can measure the power spectrum at spatial
modes as low as $k_{\parallel} > 0.1h$~Mpc$^{-1}$. The work highlights a
straightforward method for directly measuring an instrument response and
assessing its impact on 21 cm EoR power spectrum measurements for future
experiments that will use reflector-type antenna.