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A self-calibrating variable magnification three-dimensional (3D) tracking system for single fluorescent nanoparticles is proposed. The system was based on astigmatic micro-imaging and has a simple configuration incorporating a dual-spot position detection unit ray transfer matrix. By analyzing this matrix and utilizing the beam vector measurement of a dual-spot position detection unit, it was demonstrated that the proposed tracking system had the self-calibration functions of coaxiality and magnification; thus, it could accurately track the adopted fluorescent nanoparticles through zoom microscopical measurements in 3D. The available measurements of the proposed system and accuracy were experimentally validated.

A Three-Dimensional Tracking Method with the Self-Calibration Functions of Coaxiality and Magnification for Single Fluorescent Nanoparticles