Applied Physics B

, Volume 83, Issue 1, pp 127–133 | Cite as

Performance bounds on single-particle tracking by fluorescence modulation

  • A.J. BerglundEmail author
  • H. Mabuchi


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.


Tracking Error Linear Regime Noise Density Noise Spectral Density Feedback Bandwidth 
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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Physical Measurement and Control 266-33California Institute of TechnologyPasadenaUSA

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