Linear optimal control for tracking a single fluorescent particle in a confocal microscope
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We study the problem of localizing and tracking in a confocal laser scanning microscope a single fluorescent particle diffusing in three dimensions. The position of the particle is estimated from a collection of intensity measurements using a novel analytical algorithm. This estimator is then combined with a tracking algorithm based on a linear quadratic Gaussian controller to steer the detection volume of the microscope and follow the molecule. The feasibility of the approach is demonstrated through numerical simulations. These results indicate that, in such a system, tracking in three dimensions of a particle moving with a diffusion constant larger than 1 μm2/s is possible without the need for additional sensors or lasers.