Abstract
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.
Highlights
The vast majority of optical trapping schemes, and applications thereof, rely on the use of a single tightly focused laser beam, known as the optical tweezers
The output of the laser is directed into the laser modulation module (MM) which prepares the beam using a generalized phase contrast (GPC) technique and modulates it using a spatial light modulator (SLM)
The SLM can be addressed by a computer and used to specify the number, the size, the shape, the intensity and the spatial position of the laser beams emerging from the MM
Summary
The vast majority of optical trapping schemes, and applications thereof, rely on the use of a single tightly focused laser beam, known as the optical tweezers. In the case of force measurements involving multiple trapped objects it is necessary to characterize the dependence of the trap stiffness on the spatial location in the trapped volume. The force characterization relies on our ability to watch the trapped particles in both end-view (along the trapping beam axis) and in side-view (perpendicular to the trapping beam axis) at the same time by using two synchronized CMOS cameras. This allows us to obtain the stiffness of the trap(s), along all three orthogonal axes in space, by the standard methods of power spectrum analysis and equipartition. The synchronicity of the cameras allow us Received September 21, 2011; published December 15, 2011
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