Polarization Transfer Function of an Optical System as a Bilinear Transformation*

The polarization states of light incident on and emerging from an optical system are represented by complex numbers $\overline{\chi }$ and $\overline{\xi }$, respectively, in two different planes. In this representation, the input–output transfer function $\overline{\xi }=f(\overline{\chi })$ is a conformal bilinear transformation with coefficients given by the elements of the system’s Jones matrix. From the known properties of the bilinear transformation, important conclusions can be reached on the response of optical systems to incident light of all possible polarization forms. In addition, the analysis appears to have considerable potential in the synthesis of systems to effect a prescribed polarization transfer. As an example, the ellipsometer is analyzed by use of some of the ideas developed.