Co-designed annular binary phase masks for depth-of-field extension in single-molecule localization microscopy.

Area of Science:

• Optical microscopy
• Nanotechnology
• Biophysics

Background:

• Single-molecule localization microscopy (SMLM) enables super-resolution imaging of nanoscale structures.
• High numerical aperture objectives improve localization precision but limit depth-of-field (DoF).
• Limited DoF restricts 3D imaging and analysis of dynamic molecular processes.

Purpose of the Study:

• To develop a framework for optimizing phase masks to extend the DoF in SMLM.
• To benchmark phase mask performance using the Cramér-Rao bound (CRB) for localization accuracy.
• To enable quantitative comparison and design of DoF-enhancing elements for microscopy.

Main Methods:

• Optical co-design principles were applied to optimize phase masks.
• Annular binary phase masks were designed and evaluated using the CRB.
• Performance was compared against Incoherently Partitioned Pupil masks.
• A maximum likelihood-based localization algorithm was used to validate accuracy.

Main Results:

• Optimized phase masks, including a two-ring binary design, significantly extend the DoF in SMLM.
• The proposed masks achieve localization accuracy close to the theoretical CRB limit.
• The framework provides a quantitative basis for evaluating DoF-enhancing phase masks.

Conclusions:

• Phase masks offer an effective strategy to overcome DoF limitations in SMLM.
• The developed framework serves as a valuable engineering tool for optimizing super-resolution microscopy.
• This work facilitates improved 3D imaging and dynamic studies of biological nanostructures.