Centroid precision and orientation precision of planar localization microscopy

Abstract

The concept of localization precision, which is essential to localization microscopy, is formally extended from optical point sources to microscopic rigid bodies. Measurement functions are presented to calculate the planar pose and motion of microscopic rigid bodies from localization microscopy data. Physical lower bounds on the associated uncertainties - termed centroid precision and orientation precision - are derived analytically in terms of the characteristics of the optical measurement system and validated numerically by Monte Carlo simulations. The practical utility of these expressions is demonstrated experimentally by an analysis of the motion of a microelectromechanical goniometer indicated by a sparse constellation of fluorescent nanoparticles. Centroid precision and orientation precision, as developed here, are useful concepts due to the generality of the expressions and the widespread interest in localization microscopy for super-resolution imaging and particle tracking.

Particle Tracking of Microelectromechanical System Performance and Reliability

“…We measure planar motion by particle tracking [4], [9], [10]. Briefly, we deposit fluorescent particles onto the torsion frame and synchronize imaging with a square wave of variable V in to drive the quasistatic motion of the torsion frame between off and on states ( Fig.…”

Transfer of motion through a microelectromechanical linkage at nanometer and microradian scales

“…To characterize the repeatability of the rotational output of the linkage, we deposit a microscale constellation of fluorescent nanoparticles on the rotating link, image the nanoparticles by fluorescence microscopy and track the positions of the nanoparticles during actuation 35–37 . The rotation of the constellation of fluorescent nanoparticles indicates θ.…”

“…Similarly, the number of fluorescent nanoparticles is largely independent of the design of the microsystem, being limited primarily by its surface area and in our experiment exceeding the number of etch holes by a factor of two. Importantly, this tracking method builds on the firm theoretical foundation of localizing point sources 37–40 , enabling novel evaluations of uncertainty and guiding future work. Experimental uncertainties are larger than the theoretical minimum uncertainties, which the number of detected photons and constellation size determine 37–39 , by a factor of only 1.3 to 1.6, indicating a nearly ideal measurement.…”

“…Importantly, this tracking method builds on the firm theoretical foundation of localizing point sources 37–40 , enabling novel evaluations of uncertainty and guiding future work. Experimental uncertainties are larger than the theoretical minimum uncertainties, which the number of detected photons and constellation size determine 37–39 , by a factor of only 1.3 to 1.6, indicating a nearly ideal measurement. Analysis of Allan deviations 41 shows the absence of drift in measurements of θ, demonstrating an approach towards reducing uncertainty below 1 µrad by temporal averaging.…”

Optical tracking of nanoscale particles in microscale environments

“…172 Particle tracking of rigid microstructures complements edge tracking 173 and introduces new capabilities, enabling simultaneous measurement of multiple degrees of freedom, improving centroid precision and orientation precision by scaling up constellation size, and building on the existing theoretical foundation of localization microscopy for rigorous evaluation of measurement uncertainty. 174 …”