3D spatial trajectories from wavelet correlation

Abstract

We used wavelet correlation to track the three-dimensional Brownian motion of a polystyrene sphere of radius 0.6265 μm suspended in nanopure water solution (25 deg-C). The possible displacement directions are determined by correlation a two-dimensional Mexican Hat wavelet with the detected image of the microsphere. The correlation value is maximum when the sphere is located within the focus plane of the imaging system. The location of the sphere along the z axis is determined via a calibration curve that is established using correlation values yielded by defocused images. The track in the transverse direction shows a good correspondence with commercial software (Applied Precision) with correlation coefficient of 0.96.