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Shack-Hartmann multiple-beam optical tweezers

Peter John Rodrigo, René Lynge Eriksen, Vincent Ricardo Daria, and Jesper Glückstad

Open Access Open Access

Abstract

We introduce a new method for generating an array of programmable optical tweezers based on the principle of the Shack-Hartmann wave front sensor. In this approach, a lenslet array divides a laser beam into multiple point sources that are subsequently imaged onto the sample plane of an inverted microscope. This results in a matrix of tightly focused beams used for local confinement and manipulation of micron-sized dielectric particles in an aqueous solution. Using a spatial light-modulating device, the phase profile of the laser beam is computer-encoded providing for controlled spatial deflections of the trapping beams.

©2003 Optical Society of America

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Supplementary Material (2)

Media 1: MPG (1738 KB)     
Media 2: MPG (1888 KB)     

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Figures (6)
Fig. 1.
Fig. 1. Block diagram for the proposed Shack-Hartmann-based optical tweezing methodology. The resulting xyz-deflectable beam spots are scaled onto the sample plane of a microscope.

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Fig. 2.
Fig. 2. Shack-Hartmann-type multiple-beam optical tweezers. Spatial Fourier-transforms of programmable phase gratings are imaged onto the tweezer plane for parallel particle trapping with fine positioning modality. In this case, the computer addresses the SLM in four quadrants for independent encoding of grating period and orientation. At the tweezer plane, this corresponds to a control in the magnitude and direction of each trapping beam deflection.

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Fig. 3.
Fig. 3. (MPEG, 1,739KB) Simultaneous trapping of four microspheres (encircled in the first frame) using a 2×2 Shack-Hartmann optical tweezer system. The white cross indicates one microsphere located at the bottom surface. During displacement of the sample stage, the out-of-focus particle moved to the left while the trapped microspheres remained in their respective trapping positions.

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Fig. 4.
Fig. 4. Wrapping of a linear phase function into an equivalent blazed phase grating (Modulo-2π). This blazing technique also applies in two-dimensions where ϕ=ϕ (x, y).

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Fig. 5.
Fig. 5. An example of computer-generated gray level pattern forming a 2×2 array of blazed phase gratings on the SLM. This defines the horizontal and vertical deflections of each of the four optical traps.

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Fig. 6.
Fig. 6. (MPEG, 1,889KB) Parallel trapping of polystyrene microspheres with independent deflection control. Shown at the right is a sequence of magnified images of one trapped particle (encircled in the left frame) illustrating different directions of deflection (magnitude ~ 1.5 µm).

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Equations (3)

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Δ r ij = λ f 1 2 π ( ∂ ϕ ∂ r ) ij
θ ij = tan − 1 [ ( ∂ ϕ ∂ y ) ij ( ∂ ϕ ∂ x ) ij ] ,
Δ r ij = λ f l T ij .
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