Symmetry relations for the Mueller scattering matrix integrated over the azimuthal angle

Explicit symmetry relations for azimuthal Fourier components of the Mueller scattering matrix were derived as implications of particular scatterer symmetries. Several types of the latter were considered, including plane symmetries and second- and fourth-order rotational symmetries around the z-axis. Depending on the particular symmetry the integrals of the Mueller matrix over the azimuthal angle either vanish or equal the ones computed over the reduced angular range. Derived relations provide an independent test for any computer code that computes these integrals, which was illustrated by the discrete-dipole-approximation simulations for a number of test particles. Moreover, these relations can be used to reduce the time for computing these integrals for a symmetric particle by several times, which is relevant for several specific applications.

► Symmetry relations for azimuthal integrals of Muller matrix are derived. ► Plane and finite rotational symmetries of a scatterer are considered. ► The relations allow for external tests of results and decrease simulation time. ► The relations were verified by the discrete-dipole-approximation simulations.