Optimization of localization-based microscopy methods with structured illumination

The complex structures and molecular interactions of biological systems are of central interest in the biosciences. Insight into the structure and dynamics of the nanometer-scale building blocks of these systems can be achieved in many ways, e.g., with fluorescence microscopy. Here, fluorescent particles (fluorophores) are attached to molecules of interest to allow them to be observed in a light microscope, via the diffraction-limited spots they produce. The individual fluorophores can be localized with high precision, which is utilized by a group of methods known commonly as localization-based microscopy. Conventional localization of fluorophores involves fitting a mathematical model of the intensity distribution to the recorded images, known as the point spread function (PSF). This allows for estimating the position of the fluorophore with a precision better than the size of the diffraction-limited spots they produce. Recently it was demonstrated that by illuminating fluorophores with a structured illumination, individual fluorophores could be localized relative to the structured illumination with much greater precision than the conventional approach of fitting a PSF to an image, introducing a new paradigm of fluorophore localization. However, this demonstration, known as MINFLUX, utilized a scanning approach, thus limiting throughput. In this thesis, we demonstrate that the approach of fitting a PSF to images can be combined with localization relative to a structured illumination in a wide-field setting, thus allowing simultaneous, optimal localization of multiple fluorophores across the field-of-view of a microscope. We demonstrate, theoretically and experimentally, that this approach allows for optimal utilization of all localization information encoded in the collected photons, in the sense that the method satisfies the precision limit set by the Cramér-Rao lower bound. We use this to demonstrate that a calibrated structured illumination can be employed to double the localization precision of the lateral x, y coordinates of fluorophores, compared to the conventional approach. This is done with a slightly modified wide-field microscope and a simple data analysis. Furthermore, we demonstrate theoretically that this approach can be utilized to localize fluorophores in 3D with microscopy modalities that use axially structured illumination for optical sectioning. We show this theoretically with the state-of-the-art lattice light sheet microscope, and show that C-MELM can be used to increase the localization precision of both the lateral x-coordinate and the axial z-coordinate, to obtain a near-isotropic localization precision in 3D. Lastly, we discuss the possibilities of utilizing structured illumination in the studies of dynamic fluorophores, demonstrating theoretically that this allows the diffusion coefficients for freely diffusing particles to be estimated with increased precision in low-signal conditions, compared to conventional methods.