  Measurement of redshifted 21-cm emission from neutral hydrogen promises to be
the most effective method for studying the reionisation history of hydrogen
and, indirectly, the first galaxies. These studies will be limited not by raw
sensitivity to the signal, but rather, by bright foreground radiation from
Galactic and extragalactic radio sources and the Galactic continuum. In
addition, leakage due to gain errors and non-ideal feeds conspire to further
contaminate low-frequency radio obsevations. This leakage leads to a portion of
the complex linear polarisation signal finding its way into Stokes I, and
inhibits the detection of the non-polarised cosmological signal from the epoch
of reionisation. In this work, we show that rotation measure synthesis can be
used to recover the signature of cosmic hydrogen reionisation in the presence
of contamination by polarised foregrounds. To achieve this, we apply the
rotation measure synthesis technique to the Stokes I component of a synthetic
data cube containing Galactic foreground emission, the effect of instrumental
polarisation leakage, and redshifted 21-cm emission by neutral hydrogen from
the epoch of reionisation. This produces an effective Stokes I Faraday
dispersion function for each line of sight, from which instrumental
polarisation leakage can be fitted and subtracted. Our results show that it is
possible to recover the signature of reionisation in its late stages (z ~ 7) by
way of the 21-cm power spectrum, as well as through tomographic imaging of
ionised cavities in the intergalactic medium.
