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.
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