Three-dimensional imaging and force characterization of multiple trapped particles in low NA counterpropagating optical traps

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/mm per mW at a beam waist separation of 67 mm whereas the longitudinal stiffness is approximately 20 times lower. The experimental findings are in reasonable agreement with a recent physical-geometric optics calculation.