An experimental characterization of the three-dimensional (3D) position and force constants, acting on one or multiple trapped polystyrene beads in a weak counterpropagating beams geometry is reported. The 3D position of the trapped particles is tracked by imaging with two synchronized CMOS cameras from two orthogonal views and used to determine the stiffness along all three spatial directions through power spectrum analysis and the equipartition method. For the case of three trapped beads we measure the dependence of the force constants on the counterpropagating beams waist separation. The maximal transverse stiffnesses, is about 0.1 pN/µm per mW at a beam waist separation of 67 µm whereas the longitudinal stiffness is approximately 20 times lower. The experimental findings are in reasonable agreement with a recent physical-geometric optics calculation.

Motion analysis of optically trapped objects is demonstrated using a simple 2D Fourier transform technique. The displacements of trapped objects are determined directly from the phase shift between the Fourier transform of subsequent images. Using end-and side-view imaging, the stiffness of the trap is determined in three dimensions. The Fourier transform method is simple to implement and applicable in cases where the trapped object changes shape or where the lighting conditions change. This is illustrated by tracking a fluorescent particle and a myoblast cell, with subsequent determination of diffusion coefficients and the trapping forces.

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