On the equivalence of binary phase masks optimized for localization or detection in extended depth-of-field...

Area of Science:

• Microscopy
• Optical Engineering
• Biophysics

Background:

• Single-molecule localization microscopy (SMLM) requires precise emitter localization.
• Extending the depth of field (DoF) in SMLM is crucial for 3D imaging.
• Binary annular masks offer a method to enhance SMLM DoF.

Purpose of the Study:

• To investigate the impact of binary annular masks on both emitter detection and localization accuracy in SMLM.
• To quantify and mitigate the effect of phase masks on the emitter detection step.
• To validate the design strategy of optimizing masks based on Fisher information.

Main Methods:

• Utilizing Fisher information to assess emitter localization accuracy.
• Employing the Bhattacharyya distance as a detection-oriented information-theoretical criterion.
• Analyzing the combined effect of phase masks on the two-step post-processing pipeline (detection and localization).

Main Results:

• Annular binary phase masks designed to maximize Fisher information also maximize emitter detection probability in most practical scenarios.
• The optimization strategy based solely on Fisher information is supported for practical mask design.
• The study provides a rigorous framework for evaluating mask performance across the entire SMLM post-processing pipeline.

Conclusions:

• The common practice of optimizing binary annular masks for SMLM by maximizing Fisher information is validated.
• The chosen mask design strategy effectively balances localization accuracy and detection probability.
• This work contributes to the development of improved DoF extension techniques in SMLM.