Characterization of the diffusive dynamics of particles with time-dependent asymmetric microscopy intensity profiles

We put forth an algorithm to track isolated micron-size solid and liquid particles that produce time-dependent asymmetric intensity patterns. This method quantifies the displacement of a particle in the image plane from the peak of a spatial cross-correlation function with a reference image. The peak sharpness results in subpixel resolution. We demonstrate the utility of the method for tracking liquid droplets with changing shapes and micron-size particles producing images with exaggerated asymmetry. We compare the accuracy of diffusivity determination with particles of known size by this method to that by common tracking techniques and demonstrate that our algorithm is superior. We address several open questions on the characterization of diffusive behaviors. We show that for particles, diffusing with a root-mean-square displacement of 0.6 pixel widths in the time between two successive recorded frames, more accurate diffusivity determinations result from mean squared displacement (MSD) for lag times up to 5 time intervals and that MSDs determined from non-overlapping displacements do not yield more accurate diffusivities. We discuss the optimal length of image sequences and demonstrate that lower frame rates do not affect the accuracy of the estimated diffusivity.