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.

MINFLUX offers a breakthrough in single molecule localization precision, but is limited in field of view. Here we combine centroid estimation and illumination pattern induced photon count variations in a conventional widefield imaging setup to extract position information over a typical micrometer-sized field of view. We show a near two-fold improvement in precision over standard localization with the same photon count on DNA-origami nanostructures and tubulin in cells, using DNA-PAINT and STORM imaging.

Point spread function (PSF) engineering is used in single emitter localization to measure the emitter position in 3D and possibly other parameters such as the emission color or dipole orientation as well. Advanced PSF models such as spline fits to experimental PSFs or the vectorial PSF model can be used in the corresponding localization algorithms in order to model the intricate spot shape and deformations correctly. The complexity of the optical architecture and fit model makes PSF engineering approaches particularly sensitive to optical aberrations. Here, we present a calibration and alignment protocol for fluorescence microscopes equipped with a spatial light modulator (SLM) with the goal of establishing a wavefront error well below the diffraction limit for optimum application of complex engineered PSFs.We achieve high-precision wavefront control, to a level below 20 mλ wavefront aberration over a 30 minute time window after the calibration procedure, using a separate light path for calibrating the pixel-to-pixel variations of the SLM, and alignment of the SLM with respect to the optical axis and Fourier plane within 3 μm (x/y) and 100 μm (z) error. Aberrations are retrieved from a fit of the vectorial PSF model to a bead z-stack and compensated with a residual wavefront error comparable to the error of the SLM calibration step. This well-calibrated and corrected setup makes it possible to create complex '3D+λ' PSFs that fit very well to the vectorial PSF model. Proof-of-principle bead experiments show precisions below 10 nm in x, y, and λ, and below 20 nm in z over an axial range of 1 μm with 2000 signal photons and 12 background photons.