  We analyze the instrumental polarization generated by the antenna system
(optics and feed horn) due to the unpolarized sky emission. Our equations show
that it is given by the convolution of the unpolarized emission map
$T_b(\theta, \phi)$ with a sort of instrumental polarization beam $\Pi$ defined
by the co- and cross-polar patterns of the antenna. This result is general, it
can be applied to all antenna systems and is valid for all schemes to detect
polarization, like correlation and differential polarimeters. The axisymmetric
case is attractive: it generates an $E$-mode--like $\Pi$ pattern, the
contamination does not depend on the scanning strategy and the instrumental
polarization map does not have $B$-mode contamination, making axisymmetric
systems suitable to detect the faint $B$-mode signal of the Cosmic Microwave
Background Polarization. The $E$-mode of the contamination only affects the
FWHM scales leaving the larger ones significantly cleaner. Our analysis is also
applied to the SPOrt experiment where we find that the contamination of the
$E$-mode is negligible in the $\ell$-range of interest for CMBP large angular
scale investigations (multipole $\ell < 10$).
