Robust evaluation of diffusion coefficient against displacement threshold parameter of single particle tracking algorithm

Single particle/molecule tracking is widely used for the evaluation of diffusion coefficients using diverse tracking algorithms. Many of them require the subtle decision of displacement threshold parameter to enable the appropriate tracking, though it depends on both of the diffusion coefficient itself and the measurement system. A simple and highly transferable technique is proposed to overcome this difficulty based on the evaluation of diffusion coefficient from the peak position of the distribution of squared displacements in the logarithmic scale. In combination with its linear dependence on time, this protocol is remarkably robust against the too large value of the displacement threshold including that covers the whole image. Furthermore, the proposed technique is compatible with many of the existing algorithms by construction.