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In this paper we continue to develop the m-mode formalism, a technique forefficient and optimal analysis of wide-field transit radio telescopes, targetedat 21 cm cosmology. We extend this formalism to give an accurate treatment ofthe polarised sky, fully accounting for the effects of polarisation leakage andcross-polarisation. We use the geometry of the measured set of visibilities toproject down to pure temperature modes on the sky, serving as a significantcompression, and an effective first filter of polarised contaminants. We usethe m-mode formalism with the Karhunen-Loeve transform to give a highlyefficient method for foreground cleaning, and demonstrate its success incleaning realistic polarised skies observed with an instrument suffering fromsubstantial off axis polarisation leakage. We develop an optimal quadraticestimator in the m-mode formalism, which can be efficiently calculated using aMonte-Carlo technique. This is used to assess the implications of foregroundremoval for power spectrum constraints where we find that our method can cleanforegrounds well below the foreground wedge, rendering only scales $k_\parallel< 0.02 h \,\mathrm{Mpc}^{-1}$ inaccessible. As this approach assumes perfectknowledge of the telescope, we perform a conservative test of how essentialthis is by simulating and analysing datasets with deviations about our assumedtelescope. Assuming no other techniques to mitigate bias are applied, werecover unbiased power spectra when the per-feed beam width to be measured to0.1%, and amplifier gains to be known to 1% within each minute. Finally, as anexample application, we extend our forecasts to a wideband 400-800 MHzcosmological observation and consider the implications for probing dark energy,finding a medium-sized cylinder telescope improves the DETF Figure of Merit byaround 70% over Planck and Stage II experiments alone.

Coaxing Cosmic 21cm Fluctuations from the Polarized Sky using m-mode Analysis