Image Processing for Real-Time Particle Tracking and Control

(left) Typical image of a fluorescent particle (pixel size 123 nm).
The VWCM algorithm truncates the image in successive iterations (dotted lines)
until the position estimate (solid dot) lies at the center.
(right)A particle was translated both in the imaging plane (red circles spaced
by 100 nm) and perpendicular to it. The defocused images are highly distorted,
but the VWCM estimates (blue squares) are unaffected.

A critical component for developing viable nanofabrication technology is a system for inexpensive, fast metrology to facilitate process evaluation and ultimately enable real-time control. One goal of our research program is to develop robust optical measurement tools for tracking nanoparticles with high spatial and temporal resolution and with real-time readout capability.

There are many tracking algorithms in the literature designed to extract the position of a particle from a diffraction-limited image of the type shown in the figure. These algorithms usually exhibit excellent performance within their design conditions, but they are often too slow or simply not suitable for real-time tracking of particles with images of varying shapes, which might arise, for example, from polarization-dependent dipole emission patterns, non-spherical particles, or diffusion into and out of focus. To overcome these obstacles, we recently developed an algorithm that allows fast and accurate single-particle tracking with images of highly variable shapes.

Our algorithm is based on the computationally simple center of mass (CM) estimator, which makes no assumptions about the image shape (for example, that it is Gaussian). Unfortunately, the CM estimator exhibits a severe and well-known bias towards the center of an image. We overcome this statistical bias by an iterative procedure in which we truncate a portion of the image after each CM estimate so that in the next iteration the position estimate will be closer to the center and statistically less biased. The truncation procedure defines a virtual window, hence the algorithm's name: Virtual Window Center-of-Mass (VWCM). Its performance is shown in the figure, where despite severe image distortions the VWCM can locate a particle with 5 nm precision (standard deviation of repeated measurements) using only 5000 photons. The computation time is only a few milliseconds, small enough for implementation in real-time, at the full frame rate of a high speed charge-coupled device (CCD) camera.

Andrew J. Berglund - NIST
Matthew D. McMahon - NIST
Jabez J. McClelland - NIST
J. Alexander Liddle - NIST

Online: June 2009
Last Updated: June 2009

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