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

Joseph S. Beckwith, Haw Yang

Research output: Contribution to journalArticlepeer-review

Abstract

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 Δt. Here, we derive the Cramér-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 Cramér-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 Cramér-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 × 104 and 2.34 × 103 photons for the polar and the azimuthal angles, respectively, for fluorescence, whereas it takes 1.62 × 105 and 3.20 × 103 photons for scattering. This work provides experimentalists new guidelines by which future experiments can be designed and interpreted.

Original languageEnglish (US)
Article number144110
JournalJournal of Chemical Physics
Volume155
Issue number14
DOIs
StatePublished - Oct 14 2021

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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