Stokes-based analysis for the estimation of 3D dipolar emission

We provide a general description of the measurement capabilities of systems that probe the 3D state of polarization of light emitted by a dipole or a collection of dipoles. This analysis is based on a generalization of the Stokes parameters for 3D polarization, and its goal is to provide insight into what constitutes a good measurement system under specific circumstances, through the definition of appropriate merit functions. Three cases are considered: the general case of arbitrary states of 3D polarization, the special case of 3D linear full or partial polarization states, and the even more specific case of linear dipoles that wobble with rotational symmetry around a central direction. Note that the latter two cases are of interest in fluorescence microscopy. The analysis presented here is illustrated by applying it to two different approaches used commonly in orientation microscopy: PSF engineering and ratiometric measurements.