New massively redundant low frequency arrays allow for a novel investigation
of closure relations in interferometry. We employ commissioning data from the
Hydrogen Epoch of Reionization Array to investigate closure quantities in this
densely packed grid array of 14m antennas operating at 100 MHz to 200 MHz. We
investigate techniques that utilize closure phase spectra for redundant triads
to estimate departures from redundancy for redundant baseline visibilities. We
find a median absolute deviation from redundancy in closure phase across the
observed frequency range of about 4.5deg. This value translates into a
non-redundancy per visibility phase of about 2.6deg, using prototype
electronics. The median absolute deviations from redundancy decrease with
longer baselines. We show that closure phase spectra can be used to identify
ill-behaved antennas in the array, independent of calibration. We investigate
the temporal behavior of closure spectra. The Allan variance increases after a
one minute stride time, due to passage of the sky through the primary beam of
the transit telescope. However, the closure spectra repeat to well within the
noise per measurement at corresponding local sidereal times (LST) from day to
day. In future papers in this series we will develop the technique of using
closure phase spectra in the search for the HI 21cm signal from cosmic
reionization
