Theoretical minimum uncertainty of modulation enhanced spinning disk confocal microscopy

Modulation enhanced single-molecule localization microscopy (meSMLM), where emitters are sparsely activated with patterned illumination, increases the localization precision over SMLM. Furthermore, meSMLM improves the resolution over structured illumination microscopy while reducing the required amount of illumination patterns. These factors motivate enabling meSMLM in existing systems which employ patterned illumination intensity. Here, we introduce SpinFlux: modulation enhanced localization for spinning disk confocal microscopy. SpinFlux uses a spinning disk with pinholes in its illumination and emission paths, to illuminate select regions in the sample during each measurement. The resulting intensity-modulated emission signal is analyzed to localize emitters with improved precision. We derive a statistical image formation model for SpinFlux and we quantify the theoretical minimum uncertainty, in terms of the Cramér-Rao lower bound, for various illumination pattern configurations. We find that SpinFlux requires multiple patterns to improve the localization precision over SMLM, with the maximum improvement being 1.17 when using a single pattern. When using two pinholes on opposing sides of the emitter position, the x -localization precision can locally be improved 2.62-fold over SMLM, whereas the y -precision is improved by maximally a factor 1.12. When using pinholes in a triangular configuration around the emitter position, the localization precision is balanced over the x and y -directions at approximately a twofold local improvement over SMLM, at the cost of suboptimal precision in each individual direction. When doughnut-shaped illumination patterns, created with a phase mask in the illumination and emission paths, are used for SpinFlux, the local precision improvement over SMLM is increased 3.5-fold in the x - and y -directions. While localization on ISM data ideally results in an average global improvement of 1.48 over SMLM, or 2.10 with Fourier reweighting, SpinFlux is the method of choice for local refinements of the localization precision. Why it matters: One of the main objectives of singlemolecule localization microscopy (SMLM) is to improve the precision with which single molecules can be localized. This has been successfully achieved through modulation enhanced SMLM, which uses patterned illumination to increase the information content of signal photons. However, this technique relies on setups with increased technical complexity over SMLM. With SpinFlux, we locally enable a twoto 3.5-fold precision improvement over singlemolecule localization microscopy, which can be achieved with only minor modifications to existing spinning disk confocal microscopy setups (e.g. a phase mask in the illumination and emission paths). In addition, our modeling framework enables evaluation of a wide variety of spinning disk setups and therefore paves the way for optimal spinning disk design. ### Competing Interest Statement The authors have declared no competing interest.