![]() Wherever the underlying physics is the same, the exact quantitative description of its consequences provided here is portable as a qualitative and semi-quantitative understanding of its consequences in general. More important, the trends observed in our exact results when parameter values are varied are valid also for more complex geometries for which no exact analytical solutions exist. These expressions permit determination of diffusion coefficients and domain sizes for given movies for the simple geometries we consider. They apply also in the common case where the exposure time is smaller than the time-lapse due, e.g., to “dead time” caused by the readout process in the camera. Our expressions are valid for all exposure times, irrespective of the size of the confining space and the value of the diffusion coefficient. We give explicit and exact expressions for the variance of measured positions and the mean-squared displacement of a Brownian particle confined in, respectively, a 1D box, a 2D box, a 2D circular disc, and a 3D sphere. This motion blur can compromise estimates of diffusion coefficients and the size of the confining domain if not accounted for correctly. Since particles move during this exposure time, particles image with motion blur. These are recorded with sufficient exposure time per frame to be able to detect and localize particles in each frame. Particle trajectories are typically determined from time-lapse recorded movies. ![]() Environments may be, e.g., a domain in a cell membrane, an interior compartment of a cell, or an engineered nanopit. Mesoscopic environments and particles diffusing in them are often studied by tracking such particles individually while their Brownian motion explores their environment. Department of Health Technology, Technical University of Denmark, Kongens Lyngby, Denmark. ![]() Mortensen*, Henrik Flyvbjerg and Jonas N. ![]()
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