Performance bounds on single-particle tracking by fluorescence modulation |
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Authors: | AJ Berglund H Mabuchi |
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Institution: | (1) Physical Measurement and Control 266-33, California Institute of Technology, Pasadena, CA 91125, USA |
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Abstract: | We consider fundamental bounds on the performance of single-particle tracking schemes based on non-imaging, fluorescence modulation
methods. We calculate the noise density of a linearized position estimate arising from photon-counting statistics and find
the optimal estimate of a freely diffusing particle’s position in the presence of this noise. For the experimentally relevant
case of a Gaussian laser rapidly translated in a circular pattern, explicit expressions are derived for the noise density.
Tracking performance limits are obtained by considering the variance in the estimated position of a Brownian particle with
diffusion coefficient D in the presence of a noise density nm, which we find scales generically as (Dnm
2)1/2. For reasonable experimental parameters, a particle with diffusion coefficient D=1 μm2/s cannot be tracked with accuracy better than approximately 100 nm in three dimensions or 80 nm in two dimensions. Using
a combination of exact results and numerical simulation, we construct a ‘phase diagram’ for determining parameter regimes
in which a particle can be tracked in the presence of measurement noise.
PACS 87.64.Tt; 87.64.Ni; 87.15.Vv |
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