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Summary: Appl Phys B (2009) 94: 403409
DOI 10.1007/s00340-008-3352-4
Linear optimal control for tracking a single fluorescent particle
in a confocal microscope
S.B. Andersson · T. Sun
Received: 13 September 2008 / Revised version: 6 December 2008 / Published online: 23 December 2008
© Springer-Verlag 2008
Abstract 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 measure-
ments 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 simula-
tions. 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.
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