Quantifying classical and quantum bounds for resolving closely spaced, non-interacting, simultaneously emitting...

Area of Science:

• Optics
• Quantum Metrology
• Microscopy

Background:

• Quantum Fisher information enables super-resolution imaging by estimating source separation.
• Scalar approximation is insufficient for high-numerical-aperture microscopy.
• Dipole emitters are a common model for single-molecule optical beacons.

Purpose of the Study:

• To analyze the estimation of separation between two closely spaced dipole emitters using parameter estimation theory.
• To investigate the impact of emitter orientation (fixed vs. dynamic) on precision limits.
• To explore methods for salvaging super-resolution schemes in the presence of vectorial emission effects.

Main Methods:

• Utilized parameter estimation theory to analyze Fisher information and Cramér-Rao bounds.
• Considered two cases: fixed, equal dipole orientations and freely sampling orientations.
• Investigated the role of azimuthal-radial polarization basis filtering.

Main Results:

• Vectorial emission complicates the estimation of source separation.
• Precision limits were quantified using quantum and classical Fisher information.
• A scheme to saturate quantum Fisher information was shown to be salvageable with appropriate filtering.

Conclusions:

• The vectorial nature of dipole emission must be considered for accurate super-resolution imaging.
• Azimuthal-radial polarization filtering can preserve the effectiveness of super-resolution techniques.
• This work provides a more rigorous framework for super-resolution microscopy of closely spaced emitters.