Measurement precision bounds on aberrated single-molecule emission patterns.

Single-molecule localization microscopy (SMLM) has revolutionized the study of biological phenomena by providing exquisite nanoscale spatial resolution. However, optical aberrations induced by sample and system imperfections distort the single-molecule emission patterns (i.e. PSFs), leading to reduced precision and resolution of SMLM, particularly in three-dimensional (3D) applications. While various methods, both analytical and instrumental, have been employed to mitigate these aberrations, a comprehensive analysis of how different types of commonly encountered aberrations affect single-molecule experiments and their image formation remains missing. In this study, we addressed this gap by conducting a quantitative study of the theoretical precision limit for position and wavefront distortion measurements in the presence of aberrations. Leveraging Fisher information and Cramér-Rao lower bound (CRLB), we quantitively analyzed and compared the effects of different aberration types, including index mismatch aberrations, on localization precision in both biplane and astigmatism 3D modalities as well as 2D SMLM imaging. Furthermore, we studied the achievable wavefront estimation precision from aberrated single-molecule emission patterns, a pivot step for successful adaptive optics in SMLM through thick specimens. This analysis lays a quantitative foundation for the development and application of SMLM in whole-cells, tissues and with a large field of view, providing in-depth insights into the behavior of different aberration types in single-molecule imaging and thus generating theoretical guidelines for developing highly efficient aberration correction strategies and enhancing the precision and reliability of 3D SMLM.