Abstract

Phase-hologram patterns that can shape the intensity distribution of a light beam in several planes simultaneously can be calculated with an iterative Gerchberg-Saxton algorithm [T. Haist et al., Opt. Commun. 140, 299 (1997)]. We apply this algorithm in holographic optical tweezers. This allows us to simultaneously trap several objects in individually controllable arbitrary 3-dimensional positions. We demonstrate the interactive use of our approach by trapping microscopic spheres and moving them into an arbitrary 3-dimensional configuration.

© 2004 Optical Society of America

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References

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Appl. Opt. (2)

Appl. Phys. Lett. (1)

V. Bingelyte, J. Leach, J. Courtial, and M. J. Padgett, �??Optically controlled three-dimensional rotation of microscopic objects,�?? Appl. Phys. Lett. 82, 829�??831 (2003).
[CrossRef]

Biophys. J. (1)

J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrick-Jones, and D. C. S. White, �??Single-molecule mechanics of heavy-meromyosin and S1 interacting with rabbit or drosophila actins using optical tweesers,�?? Biophys. J. 68, S298�??S305 (1995).

Contemp. Phys. (1)

J. E. Molloy and M. J. Padgett, �??Lights, action: optical tweezers,�?? Contemp. Phys. 43, 241�??258 (2002).
[CrossRef]

Cytometry (1)

K. Visscher, G. J. Brakenhoff, and J. J. Kroll, �??Micromanipulation by multiple optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope,�?? Cytometry 14, 105�??114 (1993).
[CrossRef] [PubMed]

Nature (2)

D. G. Grier, �??A revolution in optical manipulation,�?? Nature 424, 810�??816 (2003).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, and T. Yamane, �??Optical trapping and manipulation of single cells using infrared-laser beams,�?? Nature 330, 769�??771 (1987).
[CrossRef] [PubMed]

Opt. Commun. (4)

J. E. Curtis, B. A. Koss, and D. G. Grier, �??Dynamic holographic optical tweezers,�?? Opt. Commun. 207, 169�??175 (2002).
[CrossRef]

T. Haist, M. Schönleber, and H. J. Tiziani, �??Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,�?? Opt. Commun. 140, 299�??308 (1997).
[CrossRef]

P. C. Mogensen and J. Glückstad, �??Dynamic array generation and pattern formation for optical tweezers,�?? Opt. Commun. 175, 75�??81 (2000).
[CrossRef]

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, �??Multi-functional optical tweezers using computer-generated holograms,�?? Opt. Commun. 185, 77�??82 (2000).
[CrossRef]

Opt. Lett. (5)

Optik (1)

R. W. Gerchberg and W. O. Saxton, �??A practical algorithm for the determination of the phase from image and diffraction plane pictures,�?? Optik 35, 237�??246 (1972).

Phys. Rev. Lett. (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, �??Direct Observation of Transfer of Angular Momentum to Absorbtive Particles from a Laser Beam with a Phase Singularity,�?? Phys. Rev. Lett. 75, 826�??829 (1995).
[CrossRef] [PubMed]

Rev. Sci. Instr. (1)

E. R. Dufresne and D. G. Grier, �??Optical tweezer arrays and optical substrates created with diffractive optics,�?? Rev. Sci. Instr. 69, 1974�??1977 (1998).
[CrossRef]

Science (1)

A. Terray, J. Oakey, and D. W. M. Marr, �??Microfluidic control using colloidal devices,�?? Science 296, 1841�??1844 (2002).
[CrossRef] [PubMed]

Other (1)

V. Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis Ltd, London, 1997).

Supplementary Material (2)

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Figures (3)

Fig. 1.
Fig. 1.

Flow chart for the GS algorithm for intensity shaping (a) in one plane, Q, and (b) in several planes, shown here for 2 planes, Q 1 and Q 2. The arrows marked PQi and Qi P respectively indicate the mathematical operations that transform the amplitude profile in plane P into that plane Qi and vice versa (usually forward and inverse Fourier transforms). The current amplitude profile is always represented in terms of its intensity, I(x, y), and phase, Φ(x, y); the desired intensity profiles in planes P and Qi are respectively labelled IP and IQi . The circled phase profile (in the plane P) converges to the phase-hologram pattern.

Fig. 2.
Fig. 2.

Beam shaped in three transverse planes. The main series of images shows modelled intensity distributions (over a 7mm×7mm area) in transverse planes at various distances z behind the hologram. The wavelength is λ=633nm. At z=20cm, 50cm and 100cm the intensity takes on the shape of the characters “1”, “2” and “3”, respectively. The phase hologram (calculated with the multi-plane GS algorithm; a grayscale representation is shown) is illuminated by a collimated Gaussian beam. The additional images show experimental results, which were obtained by illuminating a commercial SLM (Boulder Nonlinear Systems 512×512 SLM system), acting as the shown phase hologram, with the widened beam from a HeNe laser.

Fig. 3.
Fig. 3.

[2.1MB], [1.6MB] Interactive (a) and pre-programmed (b) 3-dimensional (3D) rearrangement of optically trapped 2µm-diameter glass spheres. The 3D positions of all the spheres are indicated underneath each video frame of the view through the microscope during different stages of the re-arrangement; all spheres (moving or stationary) were optically trapped at all times. In example a the positions of the individual spheres were changed interactively in the computer program, which then calculated the required hologram patterns in real time. This took about 3 minutes (the movie is speeded-up by a factor of ≈5); the speed was limited by the time it took to enter the new positions into the program. In (b) 100 hologram patterns, which had been pre-calculated with the multiplane-GS algorithm, were displayed on the SLM over a period of 15s (the times at which individual frames were taken are indicated at the top of each frame; the movie runs in real time).

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