Influence of high numerical aperture on depth-of-field enhancing phase mask optimization in localization microscopy

Area of Science:

• Optical microscopy
• Super-resolution imaging

Background:

• Phase masks enhance depth-of-field (DoF) in localization microscopy.
• Standard models for phase mask optimization use a simplified quadratic pupil phase term.
• These models neglect high numerical aperture (NA) and refractive index mismatches common in advanced microscopy.

Purpose of the Study:

• To evaluate the performance of phase masks under realistic high NA conditions.
• To determine if masks optimized with a simplified model are effective in complex microscopy setups.
• To assess the impact of refractive index mismatches on DoF extension.

Main Methods:

• Utilized the Gibson & Lanni (GL) high NA image formation model.
• Compared performance of phase masks optimized with quadratic model versus GL model.
• Analyzed the effect of NA and immersion refractive indices on DoF extension.

Main Results:

• Depth-of-field extension is scaled by a factor dependent on the microscope's NA.
• Phase masks optimized with the simplified quadratic model show near-optimal performance within the GL model framework.
• The findings are robust despite refractive index mismatches.

Conclusions:

• The simplified quadratic model provides a reliable basis for designing phase masks for extended DoF in localization microscopy.
• Optimized phase masks are broadly applicable across various microscopy setups with different NA and immersion indices.
• This work validates the use of generic optimized masks, simplifying experimental design.