Localization precision in chromatic multifocal imaging

TL;DR

This paper develops a theoretical framework to analyze how emission filter bandwidth affects localization precision in chromatic multifocal microscopy, balancing photon throughput and chromatic dispersion for optimal imaging accuracy.

Contribution

It introduces a method to calculate the Cramér-Rao lower bound for 3D localization in chromatic multifocal systems, guiding optimal filter bandwidth selection.

Findings

Broader emission filters improve localization precision despite increased chromatic dispersion.

Theoretical results guide the design of chromatic multifocal microscopes.

Photon throughput positively impacts localization accuracy.

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 into 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 Cram\'er-Rao lower bound for the 3D position of a single emitter imaged using a chromatic multifocal microscope. Results show that the localization precision improves with broader emission filter bandwidth due to increased photon throughput, despite a larger chromatic dispersion. This study provides a framework for optimally designing chromatic multifocal optics and serves as a theoretical foundation for interpretting results.