  We present recent improvements in polarization analysis with the INTEGRAL SPI
data. The SPI detector plane consists of 19 independent Ge crystals and can
operate as a polarimeter. The anisotropy characteristics of Compton diffusions
can provide information on the polarization parameters of the incident flux. By
including the physics of the polarized Compton process in the instrument
simulation, we are able to determine the instrument response for a linearly
polarized emission at any position angle. We compare the observed data with the
simulation sets by a minimum \chi^2 technique to determine the polarization
parameters of the source (angle and fraction). We have tested our analysis
procedure with Crab nebula observations and find a position angle similar to
those previously reported in the literature, with a comfortable significance.
Since the instrument response depends on the incident angle, each exposure in
the SPI data requires its own set of simulations, calculated for 18
polarization angles (from 0{\deg} to 170{\deg} in steps of 10{\deg}) and
unpolarized emission. The analysis of a large amount of observations for a
given source, required to obtain statistically significant results, represents
a large amount of computing time, but it is the only way to access this
complementary information in the hard X-ray regime. Indeed, major scientific
advances are expected from such studies since the observational results will
help to discriminate between the different models proposed for the high energy
emission of compact objects like X-ray binaries and active galactic nuclei or
gamma-ray bursts.

Instrumentation and Methods for Astrophysics;High Energy Astrophysical Phenomena