TY - JOUR

T1 - Information bounds in determining the 3D orientation of a single emitter or scatterer using point-detector-based division-of-amplitude polarimetry

AU - Beckwith, Joseph S.

AU - Yang, Haw

N1 - Funding Information:
This project was supported by the Gordon and Betty Moore Foundation (Grant No. 4741). J.S.B. thanks the Fonds National Suisse de la Recherche Scientifique for financial support in the form of an Early Postdoc.Mobility grant (Project No. P2GEP2_191208). Dr. M. Junaid Amin and Dr. Nyssa T. Emerson are warmly thanked for valuable scientific discussions. Finally, we thank the anonymous reviewers for constructive suggestions that brought the work to its present form.
Publisher Copyright:
© 2021 Author(s).

PY - 2021/10/14

Y1 - 2021/10/14

N2 - 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.

AB - 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.

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U2 - 10.1063/5.0065034

DO - 10.1063/5.0065034

M3 - Article

C2 - 34654316

AN - SCOPUS:85117176335

SN - 0021-9606

VL - 155

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 14

M1 - 144110

ER -