Three-dimensional particle tracking with subnanometer resolution using off-focus images.

A three-dimensional (3D) particle tracking algorithm based on microscope off-focus images is presented in this paper. Subnanometer resolution in all three axes at 400 Hz sampling rate is achieved using a complementary metal-oxide-semiconductor (CMOS) camera. At each sampling, the lateral position of the spherical particle is first estimated by the centroid method. The axial position is then estimated by comparing the radius vector, which is converted from the off-focus two-dimensional image of the particle with no information loss, with an object-specific model, calibrated automatically prior to each experiment. Estimation bias and variance of the 3D tracking algorithm are characterized through analytical analysis. It leads to an analytical model, enabling prediction of the measurement performance based on calibration data. Finally, experimental results are presented to illustrate the performance of the measurement method in terms of precision and range. The validity of the theoretical analysis is also experimentally confirmed.