Localization precision in chromatic multifocal imaging

Abstract

Multifocal microscopy affords fast acquisition of microscopic 3D images. This is made possible using a multifocal grating optic; however, this induces chromatic dispersion effects in the point spread function, impacting image quality and single-molecule localization precision. To minimize this effect, researchers use narrow-band emission filters. However, the choice of optimal emission filter bandwidth in such systems is, thus far, unclear. This work presents a theoretical framework to investigate how the localization precision of a point emitter is affected by the emission filter bandwidth. We calculate the Cramér–Rao lower bound for the 3D position of a single emitter imaged using a chromatic multifocal microscope. Simulation results for a range of emission bandwidth systems show that in the absence of background photons and detector noise localization improves for broader emission filter bandwidth due to increased photon throughput despite a larger chromatic dispersion. When realistic background and measurement noise sources are considered in the imaging process being simulated, there is an optimal bandwidth (not the broadest emission filter bandwidth) which provides the highest localization precision. This study provides a framework for optimally designing chromatic multifocal optics and serves as a theoretical foundation for interpretting results.