The lateral and axial localization uncertainty in super-resolution light microscopy

Area of Science:

• Optics and Photonics
• Biophysics
• Computational Biology

Background:

• Super-resolution microscopy enables imaging beyond the diffraction limit.
• Accurate localization of single-molecule emitters is crucial for high-resolution imaging.
• Existing localization methods face challenges with background noise and achieving theoretical limits.

Purpose of the Study:

• To investigate the uncertainty in single-molecule localization for super-resolution microscopy.
• To compare the performance of Maximum Likelihood Estimation (MLE) and least-squares fitting.
• To develop and validate analytical models for predicting localization uncertainty.

Main Methods:

• Theoretical analysis of localization algorithms, including MLE and least-squares fitting.
• Derivation of analytical formulas for the Cramér-Rao lower bound.
• Experimental validation using repeated localization of single-molecule emitters.
• Extension of analysis to axial localization uncertainty for various imaging modalities.

Main Results:

• MLE outperforms least-squares fitting at low background levels.
• Performance difference diminishes to a few percent at practical background levels.
• A concise analytical formula accurately predicts lateral localization uncertainty.
• Experimental results validate the analytical predictions and fitting models.

Conclusions:

• Analytical models provide reliable predictions for lateral localization uncertainty.
• The study verifies the validity of the fitting models and analytical approximations.
• Novel analytical results are presented for axial localization uncertainty across different methods.