Double-Helix based Real-Time Single Particle Tracking

Abstract

In Real-Time, Feedback-Driven Single Particle Tracking methods, measurements of the emission intensity from a labeled, nanometer-scale particle are used in a feedback loop to track the motion of the particle as it moves inside its native environment, including within living cells. In this work, we take advantage of Point Spread Function (PSF) engineering techniques that encode the axial position of the particle into the shape of the PSF in the focal plane to eliminate the need for out-of-focal-plane measurements, reducing the complexity of implementation and decreasing the overall measurement time of the control loop. Specifically, we used the Double Helix PSF (DH-PSF) in which a single fluorescent source gives rise to two lobes in the image plane with the lobes rotating in the plane as the particle moves along the optical axis. We designed simple estimators of the relative error between the particle and the tracker, and a simple proportional feedback controller to regulate that error to zero. We explored the efficacy of the approach through simulation studies, demonstrating the tracking of fast-moving particles (with diffusion coefficients up to 10 {\mu\text{m}^2/\text{s}}) over long time periods (multiple seconds).