This chapter introduces the tools used by astronomers and instrument designers in describing the action of a medium on the polarization of the radiation passing through it. In the majority of situations encountered in astronomy, the phase of the wave is unimportant, and we need a way to describe the transformation of Stokes parameters, i.e. the changing polarization forms which support the flow of radiant energy. For cases where the phase of the polarized radiation is important (e.g. polarization effects within an optical interferometer, the focusing of a plane wave by a radio telescope, or the amplification of polarized radiation within an astronomical maser), an alternative formulation will be introduced (in section 4.2) that describes the transformation (including phase) of the electric field vibrations of two orthogonal 100% polarized waves (usually linear polarization). In this formulation, partial polarization cannot be handled, and we must make separate calculations for two orthogonal polarizations of the incident radiation, constructing the incoherent sum at the end. Shurcliff (1962, sections 8.6, 8.7, 8.9) details the early history of these two calculi and compares their fields of use; a concise statement of the relationship between the two calculi may be found in Stenflo (1994, section 2.6).

Mueller matrices

As discussed in chapter 2, the four Stokes parameters denote the flow of radiant energy in specific vibrations of the electromagnetic field, and all four are expressed in the same units.