A far-field interferometry is presented to track the 3D positions of an optically trapped particle. This method can resolve the displacement within nanometers by measuring the intensity shift in the back-focal-plane of the lens which is introduced by the interference between the outgoing laser beam and scattered light from the trapped particle. Factors that affect its characteristics are elaborately analyzed using approximate formula and FDTD stimulation. Also, we propose a valid method to minimize the thermal noise that introduced by Brownian motion of the trapped particle.
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