Simultaneous super-resolution estimation of single-molecule position and orientation with minimal photon fluxes

The orientation of a single molecule provides valuable information on fundamental biological processes. We report a technique for the simultaneous estimation of single-molecule 2D position and 2D orientation with ultra-high localization precision (∼2-nm precision with ∼500 photons under a typical 100-nm diameter of excitation beam pattern), which is also compatible with tracking in living cells. In the proposed method, the theoretical precision limits are calculated, and the localization and orientation performance along with potential applications are explored using numerical simulations. Compared to other camera-based orientation measurement methods, it is confirmed that the proposed method can obtain reasonable estimates even under very weak signals (∼15 photons). Moreover, the maximum likelihood estimator (MLE) is found to converge to the theoretical limit when the total number of photons is less than 100.

Photon efficient orientation estimation using polarization modulation in single-molecule localization microscopy

Combining orientation estimation with localization microscopy opens up the possibility to analyze the underlying orientation of biomolecules on the nanometer scale. Inspired by the recent improvement of the localization precision by shifting excitation patterns (MINFLUX, SIMFLUX), we have adapted the idea towards the modulation of excitation polarization to enhance the orientation precision. For this modality two modes are analyzed: i) normally incident excitation with three polarization steps to retrieve the in-plane angle of emitters and ii) obliquely incident excitation with p-polarization with five different azimuthal angles of incidence to retrieve the full orientation. Firstly, we present a theoretical study of the lower precision limit with a Cramér-Rao bound for these modes. For the oblique incidence mode we find a favorable isotropic orientation precision for all molecular orientations if the polar angle of incidence is equal to arccos ⁡ 2 / 3 ≈ 35 degrees. Secondly, a simulation study is performed to assess the performance for low signal-to-background ratios and how inaccurate illumination polarization angles affect the outcome. We show that a precision, at the Cramér-Rao bound (CRB) limit, of just 2.4 and 1.6 degrees in the azimuthal and polar angles can be achieved with only 1000 detected signal photons and 10 background photons per pixel (about twice better than reported earlier). Lastly, the alignment and calibration of an optical microscope with polarization control is described in detail. With this microscope a proof-of-principle experiment is carried out, demonstrating an experimental in-plane precision close to the CRB limit for signal photon counts ranging from 400 to 10,000.