  We examine the polarization signal of the cosmic microwave background
radiation associated with distant clusters.
  The polarization is induced by the Thomson scattering of microwave photons
with ionized gas of clusters and contains information of quadrupole temperature
anisotropies observed at the clusters. The three-dimensional map of the signal
are expressed in terms of the spin-weighted harmonics for its angular
dependence. Its radial dependence is expanded perturbatively with respect to
the distances (equivalently redshifts) to the clusters.
  The independent information that we can extract out from the map is clarified
explicitly.
