Through analysis of digital images, camera-based single-particle tracking enables quantitative determination of transport properties of nanoparticles and molecules and provides nanoscale information about material properties such as viscosity and elasticity. However, it has recently been recognized that finite image resolution and the blurring of a particle's position over camera integration times introduce artifacts into measurement results even for a particle executing simple diffusion. Common data analysis methods based on the mean-square displacement do not properly account for these effects. In this paper, we study the distribution of camera-based single-particle tracking measurements for freely-diffusing particles in the presence of these errors. We derive a computationally convenient and asymptotically optimal maximum likelihood estimator, together with the corresponding Fisher information matrix. Our results not only provide an optimal estimator of diffusion coefficients, but also enable calibration of an instrument's resolution without the need for separate measurements on immobilized particles. The effect of varying the excitation intensity during the camera integration time is analyzed, and it is found that a double-pulse sequence maximizes the information content in some common experimental scenarios. Our results provide a rigorous theoretical framework and practical experimental recipe for achieving optimal performance in camera-based single-particle tracking.
Citation: Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Pub Type: Journals
Single Particle Tracking, Maximum Likelihood, Diffusion