Relationships between elements of the Stokes matrix.

Although there are sixteen elements of the Stokes matrix, they are constructed from basically four amplitudes and three phase differences. This of course implies that there exist nine independent relationships connecting the elements. These relationships are equalities for scattering by a single particle in a fixed orientation and in a fixed direction. When Stokes matrices from an ensemble of particles differing in size, orientation, morphology, or optical properties are added incoherently, only six equalities become one-way inequalities. These relations will prove to be very useful for providing consistency checks on experimental measurements of all sixteen elements.