Information bounds in determining the 3D orientation of a single emitter or scatterer using point-detector-based division-of-amplitude polarimetry

Determining the 3D orientation of a single molecule or particle, encoded in its polar and azimuthal angles, is of interest for a variety of fields, being relevant to a range of questions in elementary chemical reactivity, biomolecular motors, and nanorheology. A popular experimental method, known as division-of-amplitude polarimetry, for determining the real-time orientation of a single particle is to split the emitted/scattered light into multiple polarizations and to measure the light intensity using point detectors at these polarizations during a time interval.t. Here, we derive the Cramer-Rao lower bounds for this method from the perspective of information theory in the cases of utilizing a chromophore or a scattering particle as a 3D orientation probe. Such Cramer-Rao lower bounds are new for using this experimental method to measure the full 3D orientation in both the scattering case and the fluorescence case. These results show that, for a scatterer, the information content of one photon is 1.16 deg(-2) in the polar and 58.71 deg(-2) in the azimuthal angles, respectively. For a chromophore, the information content of one photon is 2.54 deg(-2) in the polar and 80.29 deg(-2) in the azimuthal angles. In addition, the Cramer-Rao lower bound scales with the square root of the total signal photons. To determine orientation to an uncertainty of one degree requires 7.40 x 10(4) and 2.34 x 10(3) photons for the polar and the azimuthal angles, respectively, for fluorescence, whereas it takes 1.62 x 10(5) and 3.20 x 10(3) photons for scattering. This work provides experimentalists new guidelines by which future experiments can be designed and interpreted. Published under an exclusive license by AIP Publishing.

Automated summary

Determining the 3D orientation of a single molecule or particle using division-of-amplitude polarimetry involves splitting emitted/scattered light into multiple polarizations and measuring light intensity. Cramer-Rao lower bounds are derived for this method, showing different information contents for photons in scattering and fluorescence cases. The study provides guidelines for experimental design and interpretation in the future.