Information-Efficient, Off-Center Sampling Results in Improved Precision in 3D Single-Particle Tracking Microscopy

Abstract

In this work, we present a 3D single-particle tracking system that can apply tailored sampling patterns to selectively extract photons that yield the most information for particle localization. We demonstrate that off-center sampling at locations predicted by Fisher information utilizes photons most efficiently. When performing localization in a single dimension, optimized off-center sampling patterns gave doubled precision compared to uniform sampling. A ~20% increase in precision compared to uniform sampling can be achieved when a similar off-center pattern is used in 3D localization. Here, we systematically investigated the photon efficiency of different emission patterns in a diffraction-limited system and achieved higher precision than uniform sampling. The ability to maximize information from the limited number of photons demonstrated here is critical for particle tracking applications in biological samples, where photons may be limited.

Real-Time Feedback-Driven Single-Particle Tracking: A Survey and Perspective

“…An alternative to a fine-grained scan like the orbital or local raster scan methods is to scan the beam through a constellation of a small number of points [16,17,18]. This also requires fast scanning hardware, but has the advantage that the measurement locations can be chosen so as to maximize the position information gained from the observed photons [18]. The same approach is taken with the superresolution technique MINFLUX [19].…”

“…Using ideas from optimal estimation theory, particularly the Fisher Information Matrix and the corresponding Cramér-Rao lower bound, one can ensure the photons that are collected are useful with respect to the localization task [122]. This idea has been shown to improve precision by approximately 20% in 3-D localization relative to uniform sampling [18] and used to design control algorithms for steering the excitation source [22].…”

“…The coverslip is then moved in a known and controlled way using, e.g., a nanopositioning stage. Typical patterns include steps [14,10,128,129,5,18] ((Figure 7d), circles [36], sinusoids [14,4,45,6,19], and helices [36,5,27] (Figure 7e). Because the ground truth of the motion is known, this approach can be used to characterize response time and tracking error.…”

“…For precision, various theoretical metrics have been used. The Fisher information and Cramér-Rao lower bound (CRLB) provide an indicator of the precision with which a static particle can be localized, typically as a function of the number of detected photons [122,19,15,22,18]. This is useful since ideally the feedback is fast enough that the particle can be considered to be approximately static during one cycle.…”

“…The CRLB is of course influenced strongly by the number of detected photons and the signal-to-background ratio, but also by the way in which the position is measured. Optimal measurement can have a significant impact on the precision [122,19,15,18]. Also, in general, a decrease in the detection volume size corresponds to a lower CRLB (and thus increased precision).…”