Abstract

Real-time dynamic holographic optical tweezers suffer from an intrinsic limitation. The diffractive optical element, which is the key to reconstruction, requires time for the calculation and physical constraints to be satisfied. In particular, when working in a volume these requirements become highly expensive. Quadrant kinoform represents an alternative to traditional 3D holograms. A spatial domain multiplexing combined with lens term phase profiles allow the independent addressing and control of different planes in the reconstruction volume. The bidimensional holograms used pose less severe physical constraints and the reduced size leads, at the cost of a lower reconstruction resolution, to a consistent speedup in the computation time thus improving real-time interactions.

© 2007 Optical Society of America

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References

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2007

S. Monneret, F. Belloni, and O. Soppera, "Combining fluidic reservoirs and optical tweezers to control beads/living cells contacts," Microfluidics and Nanofluidics (2007); http://www.springerlink.com/content/1v216l6873485058/?p=665491cc0981482bb0da39d40f2a6651&pi=2.
[CrossRef]

2006

2005

2004

2003

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

G. Shabtay, "Three-dimensional beam forming and Ewald's surfaces," Opt. Commun. 226, 33-37 (2003).
[CrossRef]

2002

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

2001

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

2000

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]

1999

X. Wei, B. J. Tromberg, and M. D. Calahan, "Mapping the sensitivity of T cells with an optical trap: polarity and minimal number of receptors for Ca2+ signaling," Proc. Natl. Acad. Sci. U.S.A. 96, 8471-8476 (1999).
[CrossRef] [PubMed]

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

1998

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

1995

1972

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

1969

L. Lesem, P. Hirsch, and J. Jordan, "The kinoform: a new wavefront reconstruction device," IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Appl. Opt.

IBM J. Res. Dev.

L. Lesem, P. Hirsch, and J. Jordan, "The kinoform: a new wavefront reconstruction device," IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

J. Mod. Opt.

G. Sinclair, P. Jordan, J. Leach, M. J. Padgett, and J. Cooper, "Defining the trapping limits of holographical optical tweezers," J. Mod. Opt. 51, 409-414 (2004).
[CrossRef]

Jpn. J. Appl. Phys., Part 1

D. Cojoc, V. Emiliani, E. Ferrari, R. Malureanu, S. Cabrini, R. Z. Proietti, and E. Di Fabrizio, "Multiple optical trapping by means of diffractive optical elements," Jpn. J. Appl. Phys., Part 1 , 43, 3910-3915 (2004).
[CrossRef]

Microfluidics and Nanofluidics

S. Monneret, F. Belloni, and O. Soppera, "Combining fluidic reservoirs and optical tweezers to control beads/living cells contacts," Microfluidics and Nanofluidics (2007); http://www.springerlink.com/content/1v216l6873485058/?p=665491cc0981482bb0da39d40f2a6651&pi=2.
[CrossRef]

Nature

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

New J. Phys.

G. Whyte and J. Courtial, "Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm," New J. Phys. 7, 117 (2005).
[CrossRef]

Opt. Commun.

G. Shabtay, "Three-dimensional beam forming and Ewald's surfaces," Opt. Commun. 226, 33-37 (2003).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[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. Express

Opt. Lett.

Optik

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

Proc. Natl. Acad. Sci. U.S.A.

X. Wei, B. J. Tromberg, and M. D. Calahan, "Mapping the sensitivity of T cells with an optical trap: polarity and minimal number of receptors for Ca2+ signaling," Proc. Natl. Acad. Sci. U.S.A. 96, 8471-8476 (1999).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, "Computer-generated holographic optical tweezer arrays," Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

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

Supplementary Material (2)

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Figures (7)

Fig. 1
Fig. 1

(Color online) If we consider each point on the SLM as a point source, the system numerical aperture can be defined as N A system = sin α and indicates the restricted set of k vectors in the k space that are recollected by the first optical element after the SLM, and that can be used for the reconstruction. The angle α depends on the distance D of lens L1 and its aperture. It is clear that working in reflection mode imposes a minimum distance D to accommodate the lens L1 in order for it not to obstruct the incoming beam. At the same time, to avoid distortion and lower performances, the angle φ formed by the incident and reflected beam on the SLM must be kept as small as possible. Therefore, a trade-off must be made on the N A system thus limiting the space of k vectors useful for reconstructing the target pattern.

Fig. 2
Fig. 2

Basic principle of QK. A hologram composed of four different subunits is combined with four coaxial lens terms to obtain a 3D reconstruction. Here is reported a simple case with only one trap addressed by each subunit.

Fig. 3
Fig. 3

(Color online) Scheme of the optical bench. The laser beam comes from a near infrared 2W source (IPG Laser, Germany); T1 is a 8 × telescope to overfill the SLM active area in order to have the most possible uniform intensity profile, while T2 is a magnification < 1 × telescope to fit the pupil of a 40 × , N A objective = 1.3 oil immersion Zeiss Plan Neofluar objective in the inverted microscope. The SLM is an an Hamamatsu X8267-15 programmable phase modulator. The λ / 2 plate is used in combination with a polarizing beam splitter (PBS) to finely adjust the laser power. The PBS is used as well to fix the correct polarization for the SLM.

Fig. 4
Fig. 4

( 3.26   MB ) Movie of the first assay of quadrant kinoform reporting nine 2   μm diameter silica beads, which move from a common plane to three different planes and describe a peristaltic movement.

Fig. 5
Fig. 5

( 2 .80   MB ) Movie of the second assay of QK showing four 2   μm diameter silica beads, which rotate one over the other each being on a different plane.

Fig. 6
Fig. 6

For a fixed, measured output laser power, several holograms of different kinds (traditional holograms with commonly used patterns, QKs, lens terms, gratings) have been displayed on the SLM and the collected light at the objective pupil measured. Results are shown on the left of the figure. The laser output has an oscillation of 1% around the nominal output. We also estimated the relative trap power for holographic traps and nonholographic ones, for the same trap position, by evaluating the escape velocity of 2 .3   μm diameter silica beads (at the right of the figure). For holographic traps, blazed gratings are displayed on the SLM to produce traps relatively close to the beam axis, in order to minimize losses due to light collection by the objective pupil finite area. For nonholographic ones, the SLM is turned off and then acts as a mirror that is mechanically tilted to adjust the trap position. In this way, we are sure that any difference in trap strength is given by the diffraction process and not, for example, by a difference in the optical path or in the focusing away from the beam axis.

Fig. 7
Fig. 7

Forces comparison. The values were recovered from a drag-method assay performed at a distance of 10   μm from the bottom slide. In the case of the holographic trapping, we employed a four trap pattern on the corner of a 40   μm side square. In the QK assay, the same pattern was realized addressing each trap with a kinoform subunit. The escape velocities were measured both along the x and y axis for each trap. We here plot the average between the x and y measures for each trap and among each peak for the traditional kinoform and the QK, moreover for holographic traps the final result is also normalized (multiplication by 4 of the escape velocity) for comparison with the single tweezers. The error bars represent the range dispersion of the measures around the mean value. The bigger error bars in the escape velocity values of the traditional kinoform reflects the inhomogeneity on the reconstruction probably due to aberrations in the optical train. It is important to note how QK is less sensitive to this effect and provides a direct way to counterbalance it by simply modifying the size of each subunit. However, during the experiments all subunits were kept equal in size.

Tables (1)

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Table 1 Q Factors and Inhomogeneity Comparison a

Equations (45)

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512 × 512
10 200 K
n med
f obj
ϕ lens ( x , y ) = 2 π n med ( x 2 + y 2 ) z f obj 2 λ .
8 ×
< 1 ×
40 ×
N A objective = 1.3   oil
0.17   mm
600   mW
15   mW / trap
1 min
20 mW / trap
3
70
10   μm
( 0 .9 × 0 .8 = 0.72 )
v escape
2.3   μm
F drag = 6 π η r v escape
40   μm
10   μm
Q = F trap c n P laser ,
F trap
P laser
0.03 0.12
10   μm
( Q kinoform   tweezers / Q single   tweezers = 0.060 / 0.117 = 0.513 )
40   μm
( Q QK / Q single   tweezers = 0.036 / 0.117 = 0.308 )
N A system = sin α
N A system
8 ×
< 1 ×
40 ×
N A objective = 1.3
λ / 2
( 3.26   MB )
2   μm
( 2 .80   MB )
2   μm
2 .3   μm
10   μm
40   μm

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