  The spin dependent reflection at the interface is the key element to
understand the spin transport. By completely solving the scattering problem
based on first principles method, we obtained the spin resolved reflectivity
spectra. The comparison of our theoretical results with experiment is good in a
large energy scale from Fermi level to energy above vacuum level. It is found
that interfacial distortion is crucial for understanding the spin dependence of
the phase gain at the Cu$|$Co interface. Near the Fermi level, image state
plays an important role to the phase accumulation in the copper film.
