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 - 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 -