Information and resolution in electromagnetic optical systems

Quantitative analysis can play a vital role in a number of polarization-based optical systems, yet to date no definition regarding resolution in the polarization domain exists. By adopting a stochastic framework, a suitable metric is developed in this article, allowing a number of polarimetric systems to be assessed and compared. In so doing, the performance dependencies of polarization-based systems are demonstrated and fundamental trends are identified.

Figure 1

Schematic of the (a) Poincaré-sphere and (b) Stokes-cylinder construction illustrated for linearly polarized light (${Š}_3=0$). The axis of the cylinder defines the intensity axis $S_0$. Totally polarized states lie on the outer surface of both the Poincaré sphere and the Stokes cylinder (dark shading), with partially polarized states lying inside (lighter shading).

Figure 2

Schematics of three alternative DOAP designs (see text). Notation is as follows: BS is a beam splitter, WP is a Wollaston prism, QWP is a quarter wave plate, GT is a Glan Thompson polarizer, BBP is a broadband prism, and D is a detector.

Figure 3

Poincaré diagrams showing the polarization-state dependence of accuracy, before Bayesian averaging, for each DOAP configuration shown in Fig. 2. Simulation parameters used were $n_0={10}^4$, $n_b=0$, ${\lambda }_0=c/{\nu }_0=405$ nm, and $c=0.9$. White markers denote the state of polarization at different points on the Poincaré sphere and are shown for reference.

Figure 4

Variation of accuracy and efficiency of observation with mean photon count for different DOAP configurations (see text). Simulation parameters are the same as for Fig. 2