  In polarimetry, a superposition of internal quantal states is exposed to a
single Hamiltonian and information about the evolution of the quantal states is
inferred from projection measurements on the final superposition. In this
framework, we here extend the polarimetric test of Pancharatnam's relative
phase for spin$-{1/2}$ proposed by Wagh and Rakhecha [Phys. Lett. A {\bf 197},
112 (1995)] to spin $j\geq 1$ undergoing noncyclic SO(3) evolution. We
demonstrate that the output intensity for higher spin values is a polynomial
function of the corresponding spin$-{1/2}$ intensity. We further propose a
general method to extract the noncyclic SO(3) phase and visibility by rigid
translation of two $\pi /2$ spin flippers. Polarimetry on higher spin states
may in practice be done with spin polarized atomic beams.
