Quantum limits for precisely estimating the orientation and wobble of dipole emitters

Abstract

Precisely measuring molecular orientation is key to understanding how molecules organize and interact in soft matter, but the maximum theoretical limit of measurement precision has yet to be quantified. We use quantum estimation theory and Fisher information (QFI) to derive a fundamental bound on the precision of estimating the orientations of rotationally fixed molecules. While direct imaging of the microscope pupil achieves the quantum bound, it is not compatible with widefield imaging, so we propose an interferometric imaging system that also achieves QFI-limited measurement precision. Extending our analysis to rotationally diffusing molecules, we derive conditions that enable a subset of second-order dipole orientation moments to be measured with quantum-limited precision. Interestingly, we find that no existing techniques can measure all second moments simultaneously with QFI-limited precision; there exists a fundamental trade-off between precisely measuring the mean orientation of a molecule versus its wobble. This theoretical analysis provides crucial insight for optimizing the design of orientation-sensitive imaging systems.

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Cited by in corpus (6)

• Single-molecule orientation localization microscopy II: a performance comparison
• Single-molecule orientation localization microscopy I: fundamental limits
• Spatio-angular fluorescence microscopy III. Constrained angular diffusion, polarized excitation, and high-NA imaging
• Resolving the Orientations of and Angular Separation between a Pair of Dipole Emitters
• Dipole-Spread Function Engineering for 6D Super-Resolution Microscopy
• Quantum limits to resolution and discrimination of spontaneous emission lifetimes