Axial accuracy in localization microscopy with 3D point spread function engineering.

Area of Science:

• Super-resolution microscopy
• Biophysics
• Optical imaging

Background:

• Single-molecule localization microscopy (SMLM) achieves nanometer precision in 3D emitter localization.
• 3D encoding often uses engineered point spread functions (PSFs) via cylindrical lenses or phase masks.
• Current SMLM performance assessments prioritize precision over accuracy, neglecting systematic axial errors.

Purpose of the Study:

• To theoretically analyze and quantify systematic axial localization errors in SMLM.
• To investigate the impact of point spread function (PSF) model mismatches on z-localization accuracy.
• To propose methods for mitigating these axial localization errors.

Main Methods:

• Utilized a vector PSF model incorporating super-critical angle fluorescence (SAF) and aplanatic correction.
• Developed theory for focal plane definition under SAF conditions.
• Simulated and analyzed axial errors for astigmatic, double-helix, and saddle-point PSFs.

Main Results:

• Identified significant absolute axial biases up to 140 nm (astigmatic), 250 nm (saddle-point), and 120 nm (double-helix).
• Observed relative axial errors exceeding 50% for tested PSFs.
• Demonstrated that PSF model mismatches are a key source of systematic axial errors.

Conclusions:

• Systematic axial errors in SMLM are substantial and depend on the chosen 3D PSF.
• Accurate z-localization requires addressing PSF model mismatches and validating focal plane definitions.
• Proposed workflow offers a path to experimentally verify findings and mitigate axial biases.