  We consider a method for obtaining information on polarization of
astronomical objects radiation at diffraction limited resolution - differential
speckle polarimetry. As an observable we propose to use averaged cross spectrum
of two short-exposure images corresponding to orthogonal polarizations,
normalized by averaged power spectrum of one of images. Information on
polarization can be extracted if object under study can be described by model
with several parameters. We consider two examples: point-like source whose
photocenter position depends on orientation of passing polarization and
exozodiacal dust disc around a star. In first case difference between
photocenter positions can be measured with precision of 8 mirco-arcseconds for
2.5-m telescope and 1.2 micro-arcseconds for 6-m telescope for object V=13. For
second example method allows detection of discs around central star of V=1 with
fractional luminosities of 1.8E-5 and 5.6E-6 for 2.5-m and 6-m telescope,
respectively.
