  We introduce a simplified form of Stokes operators for quantum optical fields
that involve the known concept of binning. Behind polarization analyzer photon
numbers (more generally intensities) are measured. If the value obtained in one
of the outputs, say H, is greater the than in the other one, V, then the value
of the simplified Stokes operator is, say, 1, otherwise it is -1. For equal
photon numbers we put 0. Such observables do not have all properties of the
Stokes operators, but surprisingly can be employed in Bell type measurements,
involving polarization analyzers. They are especially handy for states of
undefined number of photons, e.g. squeezed vacuum. We show that surprisingly
they can lead to quite robust violations of associated Bell inequalities.
