Particle tracking stereomicroscopy in optical tweezers: Control of trap shape

Abstract

Abstract:We present an optical system capable of generating stereoscopic images to track trapped particles in three dimensions. Two-dimensional particle tracking on each image yields three dimensional position information. Our approach allows the use of a high numerical aperture (NA= 1.3) objective and large separation angle, such that particles can be tracked axially with resolution of 3 nm at 340 Hz. Spatial Light Modulators (SLMs), the diffractive elements used to steer and split laser beams in Holographic Optical Tweezers, are also capable of more general operations. We use one here to vary the ratio of lateral to axial trap stiffness by changing the shape of the beam at the back aperture of the microscope objective. Beams which concentrate their optical power at the extremes of the back aperture give rise to much more efficient axial trapping. The flexibility of using an SLM allows us to create multiple traps with different shapes.

Holographic aberration correction: optimising the stiffness of an optical trap deep in the sample

“…The experimental system combines a standard holographic tweezers setup with a custom stereoscopic microscope [15] enabling 3D particle tracking (see Fig. 1).…”

“…We expand the laser beam to fill the active region of a spatial light modulator (Boulder Nonlinear Systems, XY Series, 512x512 pixels) which we subsequently image onto the back aperture of the trapping objective (similar to the system described in [16]). With our stereo imaging system [15] we extract 3D position distributions of a trapped particle from its two 2D video images recorded with a single high speed camera (Prosilica GE680C). It has been noted by many works in the field [10,17] that beam aberrations degrade the axial trap stiffness more than the lateral one.…”

Four-directional stereo-microscopy for 3D particle tracking with real-time error evaluation

“…The position of a particle within each image is tracked in two dimensions by finding its centre of symmetry [9]. The particle's apparent position is a projection of its 3D position onto the focal plane from a direction defined by the angle of illumination.…”

“…θ i = 0 • , θ j = 180 • ), and the polar angles of the two illuminators are equal, then Eqs. (1)- (3) give those described in [9]. For accurate tracking using Eqs.…”

“…By illuminating from two distinct directions simultaneously, two views of the sample from different angles can be imaged using a single objective lens [7]. The superimposed images can be separated by channel colour [8], or by redirecting the light in the Fourier plane of the sample with a bi-prism [9]. By performing two dimensional tracking of the position of a particle in each image, its three dimensional coordinates can be reconstructed using parallax.…”