Single-molecule orientation localization microscopy I: fundamental limits

TL;DR

This paper establishes fundamental quantum and classical limits on the precision of measuring the position and orientation of single molecules, revealing inherent trade-offs and the impossibility of a universally optimal instrument.

Contribution

It introduces a mathematical framework based on estimation theory to determine the ultimate measurement precision limits for single-molecule localization and orientation.

Findings

Quantum-limited localization precision is 4-8% worse with a vectorial model compared to scalar models.

No single instrument can optimize measurement precision for all localization and orientation tasks.

Fundamental limits depend on the specific measurement task and cannot be universally achieved.

Abstract

Precisely measuring the three-dimensional position and orientation of individual fluorophores is challenging due to the substantial photon shot noise in single-molecule experiments. Facing this limited photon budget, numerous techniques have been developed to encode 2D and 3D position and 2D and 3D orientation information into fluorescence images. In this work, we adapt classical and quantum estimation theory and propose a mathematical framework to derive the best possible precision for measuring the position and orientation of dipole-like emitters for any fixed imaging system. We find that it is impossible to design an instrument that achieves the maximum sensitivity limit for measuring all possible rotational motions. Further, our vectorial dipole imaging model shows that the best quantum-limited localization precision is ~4-8% worse than that suggested by a scalar monopole model. Overall, we conclude that no single instrument can be optimized for maximum precision across all possible 2D and 3D localization and orientation measurement tasks.