  New-generation X-ray polarimeters currently under development promise to open
a new window in the study of high-energy astrophysical sources. Among them,
neutron stars appear particularly suited for polarization measurements.
Radiation from the (cooling) surface of a neutron star is expected to exhibit a
large intrinsic polarization degree due to the star strong magnetic field
($\approx 10^{12}-10^{15}$ G), which influences the plasma opacity in the
outermost stellar layers. The polarization fraction and polarization angle as
measured by an instrument, however, do not necessary coincide with the
intrinsic ones derived from models of surface emission. This is due to the
effects of quantum electrodynamics in the highly magnetized vacuum around the
star (the vacuum polarization) coupled with the rotation of the Stokes
parameters in the plane perpendicular to the line of sight induced by the
non-uniform magnetic field. Here we revisit the problem and present an
efficient method for computing the observed polarization fraction and
polarization angle in the case of radiation coming from the entire surface of a
neutron star, accounting for both vacuum polarization and geometrical effects
due to the extended emitting region. Our approach is fairly general and is
illustrated in the case of blackbody emission from a neutron star with either a
dipolar or a (globally) twisted magnetic field.
