  Researchers routinely characterize optical samples by computing the
scattering cross-section. However, the experimental determination of this
magnitude requires the measurement and integration of the components of the
scattered field in all directions. Here, we propose a method to determine the
scattering cross-section and global polarization state of radiation through
measurements of two Stokes parameters at an angle of choice in far-field. The
method applies to cylindrically symmetric samples whose optical response is
well-described by a single multipolar order j. Moreover, the formalism is
applicable for a wide range of different illuminations, and it only requires
the use of a single camera and conventional wave plates. Our findings
significantly reduce the complexity of routine characterization measurements
for cylindrical samples in optical laboratories.
