  The concept of vectorial spin analysis in spin and angle resolved
photoemission is illustrated in this report. Two prototypical systems,
Bi/Ag(111)(sqrt3 x sqrt3)R30 and Pb/Ag(111)(sqrt3 x sqrt3)R30, which show a
large Rashba type spin-orbit splitting, were investigated by means of spin and
angle resolved photoemission. The spin polarization vectors of individual bands
are determined by a two-step fitting routine. First, the measured intensities
are fitted with an appropriate number of suitable peaks to quantify the
contributions of the individual bands, then the measured spin polarization
curves are fitted by varying for each band the polarization direction and its
magnitude. We confirm that the surface states experience a large spin
splitting. Moreover, we find that all surface state bands are 100 percent spin
polarized, and that for some states spin polarization vectors rotate out of the
surface plane.
