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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 19 — Sep. 13, 2010
  • pp: 19941–19950
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Light fields with an axially expanded intensity distribution for stable three-dimensional optical trapping

Susanne Zwick, Christian Schaub, Tobias Haist, and Wolfgang Osten  »View Author Affiliations


Optics Express, Vol. 18, Issue 19, pp. 19941-19950 (2010)
http://dx.doi.org/10.1364/OE.18.019941


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Abstract

We introduce a new kind of light field to improve and simplify the trapping process of axially displaced particles. To this end we employ a light field with an axially expanded intensity distribution, which at the same time enables stable axial trapping. We present simulations of the axial intensity distribution of the novel trapping field and first experimental results, which demonstrate the improvement of the reliability of the axial trapping process. The method can be used to automate trapping of particles that are located outside of the focal plane of the microscope.

© 2010 Optical Society of America

1. Introduction

Optical tweezers enable the trapping and manipulation of microscopic-sized particles by means of light. Using a focused laser beam, particles with the size of nanometers up to several tenths of micrometers can be trapped. Optical tweezers have been introduced in the 1980s by Ashkin et al. [1

1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986). [CrossRef] [PubMed]

] and since then they have been applied in various fields, like e.g. fundamental research in physics, medicine, and biology (e.g. [2

2. S. Chu, “Laser manipulation of atoms and particles,” Science 253, 861–866 (1991). [CrossRef] [PubMed]

, 3

3. A. E. Knight, C. Veigel, C. Chambers, and J. Molloy, “Analysis of single-molecule mechanical recordings: application to acto-myosin interactions,” Prog. Biophys. Mol. Biol. 77, 45–72 (2001). [CrossRef] [PubMed]

]).

Employing spatial light modulators (SLM) as flexible holographic display media to control the traps leads to considerable advantages for optical micro manipulation [4–7

4. Y. Hayasaki, S. Sumi, K. Mutoh, S. Suzuki, M. Itoh, T. Yataga, and N. Nishida., “Optical manipulation of microparticles using diffractive optical elements,” Proc. SPIE 27778, 229 (1996).

]. The modulator is positioned in the Fourier domain of the object (see Fig. 1). By displaying a Fourier phase hologram, a nearly arbitrary number of traps can be generared and moved independently in three-dimensions without any mechanically moving parts. In practice, the number of traps is only limited by the space-bandwidth product of the modulator and the laser power [8

8. S. Zwick, T. Haist, M. Warber, and W. Osten, “Dynamic holography using pixileted light modulators,” Appl. Opt. (to be published). [PubMed]

]. The holographic approach enables to improve the trapping efficiency by generating new trapping fields or new trapping geometries, like expanded spots [9

9. T. Haist, S. Zwick, M. Warber, and W. Osten, “Spatial light modulators—versatile tools for holography,” J. Holography Speckle 3, 125–136 (2006). [CrossRef]

], donut-shaped beams [10–13

10. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophysical Journal 61, 569–582 (1992). [CrossRef] [PubMed]

], twin traps [14

14. S. Zwick, T. Haist, Y. Miyamoto, L. He, M. Warber, A. Hermerschmidt, and W. Osten, “Holographic twin traps,” J. Opt. A, Pure Appl. Opt. 11, 034011 (2009). [CrossRef]

, 15

15. M. Pitzek, R. Steiger, G. Thalhammer, S. Bernet, and M. Ritsch-Marte, “Optical mirror trap with a large field of view,” Opt. Express 17, 19414–19423 (2009). [CrossRef] [PubMed]

] or to correct for aberrations [16–18

16. J. Liesener, M. Reicherter, and H. Tiziani, “Determination and compensation of aberrations using SLMs,” Opt. Commun. 233, 161–166 (2004). [CrossRef]

].

One very interesting application of optical tweezers is the sorting of single particles or cells [19

19. A. Jonás and P. Zemánek, “Light at work: the use of optical forces for particle manipulation, sorting, and analysis,” Electrophoresis 29(24), 4813–4851 (2008). [CrossRef]

]. This can be realized using optical lattices in combination with microfluidic systems [20

20. J. Glückstadt, “Sorting particles with light,” Nat. Mater. 3, 9–10 (2004). [CrossRef]

, 21

21. K. Ladavac, K. Kasza, and D. Grier, “Sorting by periodic potential energy landscapes: optical fractionation,” Phys. Rev. E 70, 010901 (2004). [CrossRef]

]. Such systems only allow passive sorting depending on optical properties, which influence the trapping force. More flexible active sorting has been realized using single or dual-beam traps in combination with image processing [22

22. S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. Grover, “Automated single-cell sorting system based on optical trapping,” J. Biomed. Opt. 6, 14–22 (2001). [CrossRef] [PubMed]

]. Microfluidic systems can be easily applied to separate the sorted particles for further processing [23

23. M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421–424 (2003). [CrossRef] [PubMed]

].

Holographic optical tweezers are very suitable to automate the trapping of microscopic objects, as the three-dimensional control of traps can be completely realized via software. Automated trapping is especially suitable for applications which require a high throughput (as e.g. cell sorting or diagnostics [24

24. F. Schaal, M. Warber, S. Zwick, T. Haist, and W. Osten, “Marker-free cell discrimination by holographic optical tweezers,” J. Europ. Opt. Soc. Rap. Public. 4, 09028 (2009). [CrossRef]

]).

However, in order to achieve stable three-dimensional trapping with optical tweezers, a strong axial intensity gradient has to be generated. This is normally realized using a high numerical aperture microscope objective. A high numerical aperture however leads to strong localization of the trapping region. If an object is not positioned in the trapping plane, it is pushed away by the scattering force. In this way manual trapping in practice is tricky and depends strongly on the experience of the user. Objects are often pushed away during the first try to trap and therefore have to be tracked by adjusting the axial position of the microscopic stage. This considerably complicates the trapping of several objects at the same time and automation is difficult.

Fig. 1. (Color online) Principle setup of holographic optical tweezers. An expanded laser illuminates a spatial light modulator (SLM) located in the Fourier domain of the object. A hologram is displayed by the SLM. The modulated wave front is coupled into a microscope using a Kepler telescope (lenses L2 and L3) and reconstructed in the object plane, which is imaged on a CCD.

In the following we present a new approach to realize automated trapping by simplifying the trapping process. The approach uses a wavefront with an axially expanded intensity distribution based on Bessel beams [25–28

25. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001). [CrossRef]

]. We start with simulations of the characteristics of the chosen light field and present first experimental results achieved with this new configuration.

2. Simulation Results

To realize automated trapping, a simplification of the trapping process should be achieved. Analysing the conventional trapping process, it was found that the monitoring of the trapped objects is simplified considerably if particles can all be brought into the observation plane.

Particles which are positioned beyond the trap are pushed away by the scattering force and cannot be trapped without refocusing the trap. However, particles which are positioned between the microscope objective and the trap (see Fig. 2) can be pushed by the scattering force into the trapping plane, which normally corresponds to the observation plane. However, in conventional single beam traps the guiding of axially displaced particles into the trap only works reliably if the distance between particle and trap is relatively small because the high numerical aperture of single beam traps leads to a strong decrease of the scattering force with increasing distance. Increasing the beam intensity can only compensate for this to a certain extend as it can also damage living biological objects.

Fig. 2. (Color online) Trapping of an object which is positioned outside of the trapping plane. Within the trapping region the object can be pushed into the trapping plane by the help of the scattering force. If the distance d of the particle to the trap is too far or respectively the intensity is too low, the object is not trapped.

To increase the axial region of influence of the scattering force, the intensity distribution along the optical axis has to be expanded. A well-known possibility to do so is the trapping with the so-called Bessel beams [25–28

25. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001). [CrossRef]

].

Bessel beams can be generated with good approximation using an axicon which is inserted into a Gaussian beam with the beam waist ω 0. The resulting intensity distribution on the optical axis shows an axial expansion zmax of [25

25. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001). [CrossRef]

]:

zmax=ω0(n1)γ,
(1)

with the opening angle γ and the relative index of refraction n of the axicon. Within this region, the lateral size of the central maximum is to some extend constant (non-diffractive beam). Therefore, it provides a focal line of light which is laterally very well localized along the optical axis. For this reason, pushing an object along the optical axis (optical guiding [25

25. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001). [CrossRef]

]) is easier with a Bessel beam than with a Gaussian beam.

Therefore, we tried to directly apply an axicon in the Fourier domain. Since an axicon is a pure phase object, the light efficiency is very good. However, this arrangement (see Fig. 3) does not generate a Bessel beam in the object plane.

In order to analyze the light field generated by an axicon in the Fourier domain, simulations have been performed using scalar diffraction theory. A homogeneous plane wave illumination of the axicon has been assumed. The axicon was modeled as a pure phase axicon without taking into account any quantization or pixelation effects or amplitude modulation due to the SLM. The simulations have been performed for a water-immersion microscope objective with 63× magnification and a numerical aperture of 1.2. The axicon is displayed by the SLM as a modulo 2π phase distribution. For the characterization of the axicon, we use the maximum phase shift ϕmax, as this corresponds to the number of rings in the hologram. The relation to a physical axicon with the opening angle γ and the height a is given by

Fig. 3. (Color online) Generation of axially expanded light fields using an axicon in the Fourier plane of the object.
ϕmax=a·n=12tanγ·Daxicon·n,
(2)

In our setup, the SLM is imaged into the pupil of the microscope objective with a magnification of β′. In case of complete illumination of the pupil, the effective diameter of the axicon is given by the aperture of the pupil Dpupil = Daxicon · β′.

Figure 4 represents the amplitude (defined as the absolute value of the complex electromagnetic field) and corresponding intensity distribution (square of the amplitude) of the simulated light field in the object domain, in the cases of conventional trapping without axicon [ϕmax = 0λ in Fig. 4(a)] and with axicons inducing different maximum phase shift [ϕmax = 5λ and 15λ in Fig. 4(b) and Fig. 4(c)], respectively. It shows that increasing the maximum phase shift of the axicon has a positive effect on the expansion of the axial intensity distribution. At the same time, defocus is induced which complicates the monitoring of the trapped particles. Nevertheless, it is possible to cancel it during the experiment by superposing an additional corrective defocus term to the hologram.

Figure 5 depicts the axial intensity distribution of light fields with different ϕmax. The intensity is increasing according to the distance to the microscope objective and dropping off with a high gradient, which enables stable axial trapping. Increasing ϕmax results in a much smoother axial intensity peak (Fig. 5), although small oscillations are induced due to the diffraction at the edge of the axicon. The maximum intensity is reduced (Fig. 6) as the intensity is spread along the axial direction. The extent of the light field along the axial direction, defined as the region where the axial intensity is greater than 10% of the maximum intensity, increases approximately linearly with the maximum phase shift ϕmax (Fig. 7).

Fig. 4. (Color online) Amplitude (left, logarithmic scale) and intensity distribution (right) of the beam profiles generated with different axicons. Propagation direction of the light field is from negative to positive Z. The intensity distribution for ϕmax = 0λ corresponds to a conventional trap using a diffraction limited focus of a homogenous beam. With increasing maximum axicon phase shift ϕmax, the intensity is distributed over a larger axial region. Additionally, defocus is induced, which has to be balanced with a superimposed corrective defocus term on the hologram in order to simplify monitoring.
Fig. 5. (Color online) Axial intensity distribution generated with different maximum axicon phase shifts ϕmax. The maximum intensity decreases with the maximum axicon phase shift, while the intensity is distributed over a large axial region. The defocus generated by the axicon has been balanced.
Fig. 6. Decrease of the maximum axial intensity with maximum axicon phase shift ϕmax.
Fig. 7. Axial extent of the intensity distribution depending on the maximum axicon phase shift ϕmax. The axial extent has been defined as a decay of the intensity to 10% of the maximum intensity.
Fig. 8. Trapping experiments with the novel approach:(a) particles on object slide, (b) particles 20 µm defocused, (c) particles guided along the optical axis and axially and laterally trapped using three axially expanded light fields.

3. Optical Trapping Experiments

The trapping behavior of the axially expanded light fields were characterized experimentally. In our experimental setup (compare Fig. 1), we used a phase-only liquid crystal on silicon display (Holoeye Pluto NIR, 1920 × 1080 pixels, 8 µm pixel pitch, 2π phase shift at 1064 nm). A NIR-laser (IP Group IRE-Polus PYL-20M, 1064nm, up to 20 W output power) is illuminating the SLM displaying a Fourier phase hologram and coupled into a microscope (Zeiss Axiovert 200M) via a telescope, which is imaging the SLM into the pupil of the microscope objective with a magnification of β′ = 1.1. The hologram is reconstructed by a Zeiss C-Apochromat 63×/1.2 water-immersion microscope objective.

Figure 8 demonstrates trapping with the novel light field. Figure 8(a) shows some polystyrene-beads with the diameter of 3 µm and a refraction index of 1.59 being positioned on the object slide. After axially displacing the microscope stage by 20 µm, the particles can be guided into the observation plane using 3 axially expanded light fields, even though they are nearly not visible any more due to the limited depth of focus. As expected, the particles are trapped stable in the observation plane. Since the position of stable axial trapping is independent of the laser power, trapping is not due to radiation pressure but due to an axial gradient force which overcomes the forward acting scattering force. Therefore, in contrary to conventional Bessel beams the novel light fields enable stable three-dimensional trapping.

Fig. 9. Duration of the trapping process of an 3 µm-object being positioned at different distances d from the trap. The duration and the repeatability (given by the error bars) of the trapping process can be improved using an axially expanded light field. The optimal maximum phase shift ϕmax depends on the distance d.

Additionally, it was found during the experiments that the trapping process was faster and more reliable in comparison to the conventional trapping field. Therefore, the axially expanded trapping field is advantageous to automate the trapping of particles which are positioned between the microscope objective and the trap.

To demonstrate this fact, the following experiment has been performed: a trap was generated in a defined axial distance d of a spherical object (compare Fig. 2). Thereby the focal plane is defined to be the plane of stable axial trapping, which is aligned with the observation plane by superimposing a corrective defocus term to the hologram. The trapping plane The time period, during which the object is guided into the stable trap by the expanded scattering force was measured. The output power of the trapping laser was reduced until guiding of the object into the stable trap with a conventional trapping field (ϕmax=0 λ) was not reliable.

Figure 9 shows the guiding period of a polystyren-bead with the diameter of 3 µm for the distances d = 10,15,20, and 30 µm. The experiment was performed for different ϕmax each time with 10–20 measurements. The repeatability of the measurement is given by the variation (standard deviation) of the measured guiding period, which is shown in Fig. 9 as error bars.

The measurements show that the repeatability and speed of the guiding process is improved compared to a conventional trapping field (ϕmax = 0λ), even though the maximum intensity in the stable trap is reduced. Additionally, the optimum guiding period is shifted to higher ϕmax with an increasing axial distance d of the particle to the trap. While for d = 10 µm a maximum phase shift of ϕmax = 4 − 10λ is suitable, a distance of d = 20 µm requires an axicon with a phase shift of around ϕmax = 10 − 17λ. Using a ϕmax larger than the suitable range, the time of the guiding period slightly increases again, due to a trade-off between the axial expansion of the scattering force and the decrease of the maximum intensity. The ideal maximum phase shift ϕmax for a given object therefore depends on the distance d and can be adapted to the application.

4. Conclusion

In this contribution we have presented a new kind of light field which improves and simplifies the trapping of axially displaced particles. We employ a light field with an axially expanded intensity distribution, which extends the scattering force along the optical axis and – in contrary to conventional Bessel beams – enables at the same time stable three-dimensional trapping. By this approach, particles, which are positioned between the microscope objective and the trap, can be guided into the stable trap. This has been demonstrated experimentally for 3 µm-particles up to 30 µm away from the trapping plane despite the reduced maximum intensity of the beam. The trapping speed and reliability can be optimized via the adjustment of the maximum phase shift ϕmax of the axicon according to the trapping distance.

Due to the clear improvement of the trapping of axially displaced particles, these novel trapping fields are very well suited for automated trapping.

Acknowledgement

The authors would like to thank the German Ministry of Education and Research (BMBF) for financial support under the project AZTEK (13N8809).

References and links

1.

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986). [CrossRef] [PubMed]

2.

S. Chu, “Laser manipulation of atoms and particles,” Science 253, 861–866 (1991). [CrossRef] [PubMed]

3.

A. E. Knight, C. Veigel, C. Chambers, and J. Molloy, “Analysis of single-molecule mechanical recordings: application to acto-myosin interactions,” Prog. Biophys. Mol. Biol. 77, 45–72 (2001). [CrossRef] [PubMed]

4.

Y. Hayasaki, S. Sumi, K. Mutoh, S. Suzuki, M. Itoh, T. Yataga, and N. Nishida., “Optical manipulation of microparticles using diffractive optical elements,” Proc. SPIE 27778, 229 (1996).

5.

Y. Hayasaki, M. Itoh, T. Yatagai, and N. Nishida, “Nonmechanical optical manipulation of microparticle using spatial light modulator,” Opt. Rev. 6, 24–27 (1999). [CrossRef]

6.

M. Reicherter, T. Haist, E. Wagemann, and H. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999). [CrossRef]

7.

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

8.

S. Zwick, T. Haist, M. Warber, and W. Osten, “Dynamic holography using pixileted light modulators,” Appl. Opt. (to be published). [PubMed]

9.

T. Haist, S. Zwick, M. Warber, and W. Osten, “Spatial light modulators—versatile tools for holography,” J. Holography Speckle 3, 125–136 (2006). [CrossRef]

10.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophysical Journal 61, 569–582 (1992). [CrossRef] [PubMed]

11.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995). [CrossRef]

12.

N. B. Simpson, L. Allen, and M. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996). [CrossRef]

13.

D. W. Zhang and X.-C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett. 28, 740–742 (2003). [CrossRef] [PubMed]

14.

S. Zwick, T. Haist, Y. Miyamoto, L. He, M. Warber, A. Hermerschmidt, and W. Osten, “Holographic twin traps,” J. Opt. A, Pure Appl. Opt. 11, 034011 (2009). [CrossRef]

15.

M. Pitzek, R. Steiger, G. Thalhammer, S. Bernet, and M. Ritsch-Marte, “Optical mirror trap with a large field of view,” Opt. Express 17, 19414–19423 (2009). [CrossRef] [PubMed]

16.

J. Liesener, M. Reicherter, and H. Tiziani, “Determination and compensation of aberrations using SLMs,” Opt. Commun. 233, 161–166 (2004). [CrossRef]

17.

M. Reicherter, T. Haist, S. Zwick, A. Burla, L. Seifert, and W. Osten, “Fast hologram computation and aberration control for holographic tweezers,” Proc. SPIE 5930 (2005). [CrossRef]

18.

K. D. Wulff, D. G. Cole, R. L. Clark, R. DiLeonardo, J. Leach, J. Cooper, G. Gibson, and M. J. Padgett, “Aberration correction in holographic optical tweezers,” Opt. Express 14, 4169–4174 (2006). [CrossRef] [PubMed]

19.

A. Jonás and P. Zemánek, “Light at work: the use of optical forces for particle manipulation, sorting, and analysis,” Electrophoresis 29(24), 4813–4851 (2008). [CrossRef]

20.

J. Glückstadt, “Sorting particles with light,” Nat. Mater. 3, 9–10 (2004). [CrossRef]

21.

K. Ladavac, K. Kasza, and D. Grier, “Sorting by periodic potential energy landscapes: optical fractionation,” Phys. Rev. E 70, 010901 (2004). [CrossRef]

22.

S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. Grover, “Automated single-cell sorting system based on optical trapping,” J. Biomed. Opt. 6, 14–22 (2001). [CrossRef] [PubMed]

23.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421–424 (2003). [CrossRef] [PubMed]

24.

F. Schaal, M. Warber, S. Zwick, T. Haist, and W. Osten, “Marker-free cell discrimination by holographic optical tweezers,” J. Europ. Opt. Soc. Rap. Public. 4, 09028 (2009). [CrossRef]

25.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001). [CrossRef]

26.

J. Arlt, K. Dholakia, J. Soneson, and E. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001). [CrossRef]

27.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002). [CrossRef] [PubMed]

28.

D. McGloin, V. Garces-Chavez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28, 657–659 (2003). [CrossRef] [PubMed]

29.

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13, 689–694 (2005). [CrossRef] [PubMed]

OCIS Codes
(350.4855) Other areas of optics : Optical tweezers or optical manipulation
(070.6120) Fourier optics and signal processing : Spatial light modulators

ToC Category:
Optical Trapping and Manipulation

History
Original Manuscript: June 28, 2010
Revised Manuscript: August 9, 2010
Manuscript Accepted: August 9, 2010
Published: September 3, 2010

Virtual Issues
Vol. 5, Iss. 13 Virtual Journal for Biomedical Optics

Citation
Susanne Zwick, Christian Schaub, Tobias Haist, and Wolfgang Osten, "Light fields with an axially expanded intensity distribution for stable three-dimensional optical trapping," Opt. Express 18, 19941-19950 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-19941


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References

  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986). [CrossRef] [PubMed]
  2. S. Chu, "Laser manipulation of atoms and particles," Science 253, 861-866 (1991). [CrossRef] [PubMed]
  3. A. E. Knight, C. Veigel, C. Chambers, and J. Molloy, "Analysis of single-molecule mechanical recordings: application to acto-myosin interactions," Prog. Biophys. Mol. Biol. 77, 45-72 (2001). [CrossRef] [PubMed]
  4. Y. Hayasaki, S. Sumi, K. Mutoh, S. Suzuki, M. Itoh, T. Yataga, and N. Nishida, "Optical manipulation of microparticles using diffractive optical elements," Proc. SPIE 27778, 229 (1996).
  5. Y. Hayasaki, M. Itoh, T. Yatagai, and N. Nishida, "Nonmechanical optical manipulation of microparticle using spatial light modulator," Opt. Rev. 6, 24-27 (1999). [CrossRef]
  6. M. Reicherter, T. Haist, E. Wagemann, and H. Tiziani, "Optical particle trapping with computer-generated holograms written on a liquid-crystal display," Opt. Lett. 24, 608-610 (1999). [CrossRef]
  7. J. E. Curtis, B. A. Koss, and D. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002). [CrossRef]
  8. S. Zwick, T. Haist, M. Warber, and W. Osten, "Dynamic holography using pixilated light modulators," Appl. Opt. (to be published). [PubMed]
  9. T. Haist, S. Zwick, M. Warber, and W. Osten, "Spatial light modulators-versatile tools for holography," J. Holography Speckle 3, 125-136 (2006). [CrossRef]
  10. A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992). [CrossRef] [PubMed]
  11. H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms," J. Mod. Opt. 42, 217-223 (1995). [CrossRef]
  12. N. B. Simpson, L. Allen, and M. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. Mod. Opt. 43, 2485-2491 (1996). [CrossRef]
  13. D. W. Zhang, and X.-C. Yuan, "Optical doughnut for optical tweezers," Opt. Lett. 28, 740-742 (2003). [CrossRef] [PubMed]
  14. S. Zwick, T. Haist, Y. Miyamoto, L. He, M. Warber, and A. Hermerschmidt, "andW. Osten, "Holographic twin traps," J. Opt. A, Pure Appl. Opt. 11, 034011 (2009). [CrossRef]
  15. M. Pitzek, R. Steiger, G. Thalhammer, S. Bernet, and M. Ritsch-Marte, "Optical mirror trap with a large field of view," Opt. Express 17, 19414-19423 (2009). [CrossRef] [PubMed]
  16. J. Liesener, M. Reicherter, and H. Tiziani, "Determination and compensation of aberrations using SLMs," Opt. Commun. 233, 161-166 (2004). [CrossRef]
  17. M. Reicherter, T. Haist, S. Zwick, A. Burla, L. Seifert, and W. Osten, "Fast hologram computation and aberration control for holographic tweezers," Proc. SPIE 5930 (2005). [CrossRef]
  18. K. D. Wulff, D. G. Cole, R. L. Clark, R. DiLeonardo, J. Leach, J. Cooper, G. Gibson, and M. J. Padgett, "Aberration correction in holographic optical tweezers," Opt. Express 14, 4169-4174 (2006). [CrossRef] [PubMed]
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