  The ~39-m European Extremely Large Telescope (E-ELT) will be the largest
telescope ever built. This makes it particularly suitable for sensitive
polarimetric observations, as polarimetry is a photon-starved technique.
However, the telescope mirrors may severely limit the polarimetric accuracy of
instruments on the Nasmyth platforms by creating instrumental polarisation
and/or modifying the polarisation signal of the object. In this paper we
characterise the polarisation effects of the two currently considered designs
for the E-ELT Nasmyth ports as well as the effect of ageing of the mirrors. By
means of the Mueller matrix formalism, we compute the response matrices of each
mirror arrangement for a range of zenith angles and wavelengths. We then
present two techniques to correct for these effects that require the addition
of a modulating device at the polarisation-free intermediate focus that acts
either as a switch or as a part of a two-stage modulator. We find that the
values of instrumental polarisation, Stokes transmission reduction and cross-
talk vary significantly with wavelength, and with pointing, for the lateral
Nasmyth case, often exceeding the accuracy requirements for proposed
polarimetric instruments. Realistic ageing effects of the mirrors after perfect
calibration of these effects may cause polarimetric errors beyond the
requirements. We show that the modulation approach with a polarimetric element
located in the intermediate focus reduces the instrumental polarisation effects
down to tolerable values, or even removes them altogether. The E-ELT will be
suitable for sensitive and accurate polarimetry, provided frequent calibrations
are carried out, or a dedicated polarimetric element is installed at the
intermediate focus.
