The idea of 2D polarisation imaging consists in modification of the basic version of a wide field microscope suited for single molecule detection. For this, two rotating polarisers (more precisely, a λ/2 plate in the excitation channel and a transmission/reflection polarisation analyser in the fluorescence channel) are employed. This allows to record the fluorescence intensity of a single molecule as a function of two arguments: excitation polarisation plane orientation angle φ_ex and allowed emission polarisation plane orientation angle φ_em.

The method has been described thorougly in several publications (and summerized in others not listed here):

• O. Mirzov, R. Bloem, P. R. Hania, D. Thomsson, H. Lin, and I. G. Scheblykin, "2D polarisation single molecule imaging of multichromophoric systems with energy transfer", Small, 5, 1877, 2009.
  
• R. Camacho, D. Thomsson, D. Yadav, I.G. Scheblykin,  "Quantitative characterization of light-harvesting efficiency in single molecules and nanoparticles by 2D polarization microscopy: Experimental and theoretical challenges", Chemical Physics 406, 30 – 40, 2012.
• R. Camacho-Dejay, "Polarization portraits of lightharvesting antennas: from single molecule spectroscopy to imaging" PhD-Thesis, Lund University, 2014.
• D. Täuber, W. Cai, O. Inganäs, I.G. Scheblykin, "Macroscopic Domains within an Oriented TQ1 Film Visualized Using 2D Polarization Imaging " ACS Omega 2, 32-40, 2017. -> Watch the related ACS Live Slide presentation!

Integration of the polarization portrait over the excitation, φex, or emission, φem, angle yields a one dimensional function that contains the modulation depth and phase for fluorescence emission, Mem and θem, or excitation, Mex and θex, respectively.

The difference between the fluorescence excitation and emission phases receives the name of luminescence phase shift, ∆θ = θex − θem. The main axis of orientation of the transition dipole moments that contribute to the fluorescence excitation is given by θex. Therefore, we are able to calculate the fluorescence anisotropy, r, using two points from the polarization portrait: I(θex, θex) and I(θex, θex+ π), resembling III and I⊥.

This calculation assumes that the fluorescence emission is cylindrically symmetric around the 'z' axis of the sample plane.

(taken from supporting information to article: Camacho, R., Meyer, M., Vandewal, K., Tang, Z., Inganäs, O., Scheblykin, I.G., 2014. Polarization Imaging of Emissive Charge Transfer States in Polymer/Fullerene Blends. Chem. Mater. 26, 6695–6704, 2014)

After exciation of a chromophore in some cases, the excitation energy is transferred to another neighbouring site. There are two extremes:

• photoselection: only directly excited molecules/chromophores emit ➡ no energy transfer (NoET)
• energy funnel: all excitation energy is emitted from the same system ➡ emission is independent from polarization in excitation

These extremes will be seen on different parts of the polarization portrait: For the absence of energy transfer, the emission angle is the same as the excitation angle, and the intensity peaks are thus found on the diagonal of the portrait. In contrast, if there is energy transfer (ET), intensity peaks will be off-diagonal. Systems can of course show a mixture of both.

We use a tri-dipolar model to fit the orientation and organization of the excited system, and compare this to the obtained fluorescence emission. It has been found that over 95% of all polarization portraits so far could be fitted by this method.