Estimation of the trajectory from autofocused trajectory using interpolation method

Abstract

We investigated the use of the trajectories of an auto-focused images of a microsphere. The trajectory obtained does not have a uniform time interval because autofocus mechanism is processes images for different axial distances and capture the best image of the sample. From the trajectory, we used cubic spline interpolation to recover a trajectory that has uniform
time interval. Using the interpolated trajectory, the diffusion coefficient was calculated for different time interval and yield a much much greater diffusion coefficient than the theoretical diffusion coefficient.