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

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.

Pulsed laser manipulation of an optically trapped bead: Averaging thermal noise and measuring the pulsed force amplitude

“…The beams originate from a fiber laser (IPG, YLM-20-SC, 20 Watt cw) which is spatially shaped using generalized phase contrast (GPC) optics in combination with a spatial light modulator (SLM), see detailed description in [19]. This produces two individual discshaped intensity profiles that are imaged at the focal planes of two objectives (Olympus LMPlan IR 50x, NA 0.55) positioned opposite to each other.…”

Motion analysis of optically trapped particles and cells using 2D Fourier analysis

“…The frame rate of the cameras was set to 400 Hz with a region of interest (ROI) of 576 × 576 pixels, and the two cameras are synchronized to within 17 nanoseconds. The method used to calibrate the imaging system, as well as more thorough description of the experimental setup, is described in previous work [13]. The motion of the trapped particle is followed for 600 seconds resulting in 240000 frames to be analyzed per camera.…”

“…This gives a Gaussian distribution centered on zero displacement with a standard deviation σ = 8 nm. The accuracy of the reference tracking method is described in more detail in [13] and is limited by the camera resolution, mechanical drift of the setup and the tracking algorithm. This amounts to an accuracy limited to a standard deviation σ = 5 nm.…”

“…In addition, the distribution is multiplied with the sampling time squared. The power spectrum of the displacement can thus be obtained from the well known power spectrum of the position [13,19] ( ) ( ) 2 2 2 2 2 2 2 2 2 .…”

“…The large working distance between the objectives (> 10 mm) enables monitoring of the trapped objects from two orthogonal directions with an end-view camera (along the trapping beam direction) and a side-view camera [13,14] thus obtaining 3D information of the particle motion and the trap stiffness. First, we describe the FTMA method and illustrate its application by measuring the trap stiffness for a 10 µm diameter polystyrene bead under illumination.…”