ABSTRACT

This chapter follows closely the results where the dihedral groups are used to describe and interpret certain linear operators used in optics and to relate those operators with the statistical analysis of their experimental data. It interprets the coherence matrices as points in the dihedral group algebra realized as specialized compensators including rotators and polarizers. The decompositions were also applied to the study of monochromatic plane waves and to refractive power matrices. The practical fact that the resolution J=∑Skσk of a coherence matrix J determines and is determined by the Stokes Sk parameters finds its analogy in the one-to-one correspondence between a scalar data (xτ) indexed by the elements (τ) of a dihedral group G, and real-coefficient linearization ∑τxτβτ constructed with the two-dimensional irreducible representations βτ of G realized as specialized compensators.