Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light

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Abstract
A quadrant photodiode placed in the back-focal plane of the microscope of a laser trap provides a high-resolution position sensor. We show that in addition to the lateral displacement of a trapped sphere, its axial position can be measured by the ratio of the intensity of scattered laser light to the total amount of the light reaching the detector. The addition of the axial information offers true three-dimensional position detection in solution, creating, together with a position control, a photonic force microscope with nanometer spatial and microsecond temporal resolution. The measured position signals are explained as interference of the unscattered trapping laser beam with the laser light scattered by the trapped bead. Our model explains experimental data for trapped particles in the Rayleigh regime (radius a < 0.2λ) for displacements up to the focal dimensions. The cross-talk between the signals in the three directions is explained and it is shown that this cross-talk can be neglected for lateral displacements smaller than 75 nm and axial displacements below 150 nm. The advantages of three-dimensional single-particle tracking over conventional video-tracking are shown through the example of the diffusion of the GPI-anchored membrane protein Thy1.1 on a neurite. Microsc. Res. Tech. 44:378–386, 1999.