Fundamental limits in determining the orientation of single molecules: An information theoretic approach

Polarisation of light affords the means to perform robust orientational measurements of single molecules and sub-wavelength asymmetric scatterers. The precision with which such measurements can be made can be quantified using Fisher information and the Cramér-Rao lower bound. Specifically, a fundamental limit of 0.5/N radians (on average) is found where N is the number of detected photons. Measurement precision is shown to be lost in many realistic measurement scenarios, particularly for inference from null readings. The severity of these precision losses is however also shown to decrease as redundancy in the measurement is increased. Extraneous sources, such as a second fluorescing molecule, can contaminate measured data subsequently causing a further loss of precision. Results are hence also presented in this vein.