  We analyze the generation of polarization cross-talk in Stokes polarimeters
by atmospheric seeing, and its effects on the noise statistics of
spectropolarimetric measurements for both single-beam and dual-beam
instruments. We investigate the time evolution of seeing-induced correlations
between different states of one modulation cycle, and compare the response to
these correlations of two popular polarization modulation schemes in a
dual-beam system. Extension of the formalism to encompass an arbitrary number
of modulation cycles enables us to compare our results with earlier work. Even
though we discuss examples pertinent to solar physics, the general treatment of
the subject and its fundamental results might be useful to a wider community.
