A nonlinear controller for three-dimensional tracking of a fluorescent particle in a confocal microscope

We describe an algorithm for using a confocal microscope for tracking single fluorescent particles diffusing in three dimensions. The algorithm uses a standard confocal setup and directly translates each fluorescence measurement into an actuator command. Through physical simulations, we illustrate 3-D tracking in both stage scanning and beam scanning confocal systems. The simulated stage scanning system achieved tracking of particles diffusing in 3-D with coefficients up to 0.2 μm²/s when the average fluorescence intensities was less than 1.84 counts per measurement cycle (corresponding to less than 18,400 counts per second) in the presence of background fluorescence with a rate of 5,000 counts per second. Increasing the fluorescence intensity to approximately 193 counts per measurement cycle (1,930,000 counts per second) allowed the system to track up to particles diffusing with coefficients as large as 0.7 μm²/s. The beam steering system allowed for faster motion of the focal volume of the microscope and successfully tracked particles diffusing with coefficients up to 0.7 μm²/s with fluorescence measurement intensities of approximately 0.189 counts per measurement cycle (37,570 counts per second) and with coefficients up to 90 μm²/s when the fluorescence intensity was increased to 19 counts per measurement cycle (3,807,500 counts/sec).