Pupil function design for multifocal confocal, STED, and isoSTED microscopy

Point scanning super-resolution microscopy techniques such as stimulated emission depletion (STED) microscopy are powerful tools to observe biological samples at sub-diffraction limited resolution in three dimensions. However, scanning the sample with only a single beam limits the imaging speed in these microscopes. Here, we propose a concept to increase this speed by introducing highly flexible multifocal illumination and detection. We introduce phase patterns in the objectives' pupil planes to create arrays of foci in the sample plane with negligible loss of laser power. High uniformity of these foci's intensities is achieved by iteratively applying a weighted Gerchberg-Saxton phase retrieval algorithm. We characterize the performance of this iterative approach numerically and present simulation results that demonstrate the high quality of the focus arrays for future implementations in laser-scanning STED and isoSTED microscopes. The same approach can also be applied in diffraction-limited confocal laser scanning microscopy.