A nonlinear approach to tracking single nanometer-scale fluorescent particles

We describe a nonlinear control law for tracking single, sub-diffraction limit fluorescent particles that takes advantage of the geometric properties of the spatial intensity pattern. We present simulation results for tracking a single particle based on confocal measurements to illustrate the approach. The control law converts each intensity measurement into actuator commands directly, and consequently should yield improved temporal response over existing algorithms. We consider both two- and three-dimensional tracking.