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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 26 — Dec. 25, 2006
  • pp: 13107–13112
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GPC-based optical micromanipulation in 3D real-time using a single spatial light modulator

Peter John Rodrigo, Ivan R. Perch-Nielsen, Carlo Amadeo Alonzo, and Jesper Glückstad  »View Author Affiliations


Optics Express, Vol. 14, Issue 26, pp. 13107-13112 (2006)
http://dx.doi.org/10.1364/OE.14.013107


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Abstract

Using a novel dual-beam readout with the generalized phase contrast (GPC) method, a multiple-beam 3D real-time micromanipulation system requiring only one spatial light modulator (SLM) has been realized. A theoretical framework for the new GPC scheme with two parallel illumination beams is presented and corroborated with an experimental demonstration. Three-dimensional arrays of polystyrene microbeads were assembled in the newly described system. The use of air immersion objective lenses with GPC-based optical trapping allowed the simultaneous viewing of the assemblies in two orthogonal bright-field imaging perspectives.

© 2006 Optical Society of America

1. Introduction

For objects with dimensions of a few nanometers up to micrometers, minute forces due to light-matter interaction are normally strong enough to influence the motion of the particles. It was first experimentally demonstrated by Ashkin that optical forces could be used to accelerate and even trap tiny objects [1

1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970). [CrossRef]

]. Since then a great deal of progress has been achieved in optical trapping, both in its applications and technique development [2

2. D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003). [CrossRef] [PubMed]

, 3

3. K. Dholakia and P. Reece, “Optical micromanipulation takes hold,” Nano Today 1, 18–27 (2006). [CrossRef]

]. For example, optical trapping and manipulation of ensembles of microparticles, which opens for promising themes of studies within colloid science and microbiology, are now viable using reconfigurable patterns of optical fields [4–7

4. P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Real-time three-dimensional optical micromanipulation of multiple particles and living cells,” Opt. Lett. 29, 2270–2272 (2004). [CrossRef] [PubMed]

]. Reconfigurability of the confining optical potential landscapes is made feasible and of great ease with the use of computer-programmable spatial light modulators (SLM).

In this paper we demonstrate a GPC-trapping system that utilizes just one SLM to generate CB traps with adjustable power ratios. We employ a single GPC imaging setup for transforming phase into intensity patterns while the SLM provides two off-axis phaseencoding regions illuminated by two equally sized circular beams. Reconfigurable intensity patterns corresponding to the two independently addressable circular regions are relayed to the sample volume and form a dynamic array of CB traps.

The succeeding section outlines theoretical and experimental considerations exploring GPC with a dual-beam illumination. In section 3, we describe the schematic diagram of the proposed single-SLM, GPC-based micromanipulation system and show multiple-particle 3D trapping experiments achieved with it. Finally, we give our summary and some potential extensions of this work.

2. GPC system with two parallel input beams

In order to appreciate the optical engineering aspects of the single-SLM GPC-trapping system that we propose in this work, we first elaborate on the system’s core component, which is the implementation of the GPC scheme with two parallel input beams. Consider a GPC 4f imaging setup with an object, e(x, y), and a phase contrast filter (PCF), H(f x, f y), amplitude transmission functions defined by

e(x,y)=circ((x+x0)2+y2Δr)exp(jϕ1(x+x0,y))
+circ((xx0)2+y2Δr)exp(jϕ2(xx0,y)),
(1)
H(fx,fy)=A[1+(BA1exp(jθ)1)circ(fx2+fy2Δfr)],
(2)

where the two circ-functions in Eq. (1) represent two laterally shifted tophat beams (of identical radii Δr) reading out input phase patterns ϕ 1 and ϕ 2 written on regions R 1 and R 2 of the SLM, respectively, as shown in Fig. 1. The filter parameters A and B are the amplitude transmission coefficients outside and inside, respectively, of an on-axis circular region of radius Δfr in the frequency space. A constant phase shift of θ is introduced to the on-axis focused light within the Δfr radius.

Fig. 1. 4f setup for implementing the GPC method with dual-beam illumination onto circular regions R 1 and R 2 of the spatial light modulator (SLM; Hamamatsu www.hamamatsu.com); PCF, phase contrast filter; L1 and L2, lenses (focal length=300 mm).

Assuming that a non-absorbing phase filter is used such that A=B=1 and θ=π, the field at the image plane of the 4f setup (neglecting space-inversion of the xy′-coordinate system) is given by

{H(fx,fy){e(x,y)}}=circ((x+x0)2+y2Δr)exp(jϕ1(x+x0,y))
2α¯1{circ(fx2+fy2Δfr){circ(x2+y2Δr)}exp(j2πfxx0)}
+circ((xx0)2+y2Δr)exp(jϕ2(xx0,y))
2α¯2{circ(fx2+fy2Δfr){circ(x2+y2Δr)}exp(j2πfxx0)}
(3)

where

α¯i=[π(Δr)2]1Riexp(jϕi)dxdy;fori=1,2.
(4)

g(r)={circ(frΔfr){circ(rΔr)}}
=2πΔr0ΔfrJ1(2πΔrfr)J0(2πrfr)dfr,
(5)

where r=x2+y2 and fr=fx2+fy2 . The similar Fourier transforms found in the second and the fourth terms on the right-hand side of Eq. (3), by the Shift Theorem [9

9. J. W. Goodman, Introduction to Fourier Optics, Second Edition (McGraw-Hill, New York, 1996).

], simply result in laterally displaced versions of the SRW. Thus from Eq. (3), the output intensity I(x′, y′) at the image plane of the 4f setup is described by

I(x,y)=e1(x,y)+e2(x,y)2,
(6)

where

e1(x,y)=circ((x+x0)2+y2Δr)exp(jϕ1(x+x0,y))2α¯1g((x+x0)2+y2)
(7)

and

e2(x,y)=circ((xx0)2+y2Δr)exp(jϕ2(xx0,y))2α¯2g((xx0)2+y2).
(8)

The terms in the squared modulus of Eq. (6), strictly, combine coherently but if the chosen shift value x 0 is sufficiently large, the contributions of cross-product terms in the resultant intensity pattern become less significant. Therefore, the operation in Fig. 1 can be interpreted as two parallel GPC-based phase-to-intensity mappings that utilize the same PCF for their respective Fourier filtering processes.

Our above model of the two-beam input GPC exhibits good agreement with experimental results as shown in Fig. 2. We captured output intensity patterns by placing a CCD camera at the image plane depicted in Fig. 1. In the case of Fig. 2(a), the PCF is removed and we consequently obtain the profile of the two circular illumination beams (modeled as tophat beams). In the presence of an aligned PCF, made from glass optical flat with a tiny cylindrical pit (pit’s depth corresponds to ~π phase shift and radius is ~7.5 µm [8

8. J. Glückstad and P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. 40, 268–282 (2001). [CrossRef]

]), phase-to-intensity conversion is achieved with good contrast as shown in Figs. 2(b) and 2(c). The encoded phase patterns on the SLM are arrays of dots with relative phase depths that may be selected on the fly between zero and π – corresponding to minimum and maximum intensity levels at the image plane. As quantified by the intensity line-scans of Fig. 2, we emphasize the approximately four-fold maximum intensity gain (ratio of intensity mapping of a π phase dot to incident intensity) due to the GPC method. In Fig. 2(b), a binary pattern consisting of π phase dots is used, resulting in duplicated intensity beam arrays, which may be used to form counterpropagating-beam traps with commensurate power ratios. CB traps with different power ratios can be synthesized from intensity patterns in Fig. 2(c) that uses multiple phase-levels on the SLM.

Fig. 2. Comparison of theoretically (solid curve in the line-scan) and experimentally obtained intensity patterns at the image plane of a GPC 4f setup with two adjacent input beams (modeled with tophat intensity profiles) (a) in the absence of the PCF, (b) with an aligned PCF and a binary phase-dot array input, and (c) with an aligned PCF and a multilevel phase-dot array input. Line-scans are taken along the green lines.

3. Single-SLM GPC-based optical trapping system

Fig. 3. Schematic diagram of the proposed optical micromanipulation system. SLM, spatial light modulator; PCF, phase contrast filter; M, mirror; L1 and L2, achromats (focal length=300 mm); L3 and L4, achromats (focal length=400 mm); L5 and L6, singlets (focal length=300 mm and 200 mm, respectively); BS, beam splitter, DM, dicrhoic mirror; O1 and O2, trapping objective lenses (x50, NA=0.55); O3, yz-view objective lens (x50, NA=0.55); CCD1, xy-view camera; CCD2, yz-view camera.

Polystyrene microspheres have higher refractive index than the surrounding medium (i.e. water), and are attracted to regions of maximum lateral trap intensity. Thus, xy-plane manipulation of the particles is easily performed by repositioning the phase dots (and hence the CB traps) using the GUI. Meanwhile, the power ratio of the constituent beams of each CB trap is adjusted until the captured particle moves to a desired stable axial position.

In Fig. 4(a), three microspheres are stably trapped in distinct positions with a distance of ~30 µm axially separating the lowermost position from the topmost one. The xy coordinates of two particles are changed making the three beads appear diagonally arranged on both views as shown in Fig. 4(b). Finally, with eight CB traps, an array of microspheres is interactively assembled into a rhomboid structure.

Trapping of more than one particle along the axial direction can be done with GPC-system, as the user can axially stack up particles in a counterpropagating-beam trap if required. The so-called optical binding effect (particle interaction due to light-scattering) shows a possible means of controlling interparticle spacings axially. Alternatively, two or three beads may be axially positioned by holographic optical tweezers, but with limited interparticle spacings due to constraints of particle shadowing and spherical aberrations in a high-NA focusing objective with short confocal range [6

6. 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]

, 7

7. G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, “Assembly of 3-dimensional structures using programmable holographic optical tweezers,” Opt. Express 12, 5475–5480 (2004). [CrossRef] [PubMed]

].

Fig. 4. Optically assembled arrays of 3-µm diameter polystyrene spheres in 3D simultaneously viewed in xy (top frame) and yz planes (bottom frame). (a)–(b) Two of three spheres are translated in the xy-plane. (c) Eight spheres optically positioned and stably kept in the corners of a virtual parallelepiped.

4. Conclusion

We have verified both theoretically and experimentally the viability of the GPC method with two parallel read-lights for 3D real-time micromanipulation. This implementation of the GPC setup enables the creation of a plurality of independently controllable counterpropagating-beam micromanipulators with the use of only a single SLM. We have also demonstrated two orthogonal bright-field image captures in the trapping system to allow more direct particleposition measurements through a genuine visual inspection of optically assembled microparticles in 3D.

Due to its use of counterpropagating-beam trapping geometry, the GPC-based micromanipulation system’s field of manipulation can be scaled to user-defined extents using a wide selection of objectives with different NA’s. Note that for other trapping systems relying on tightly focused beam gradient-traps (e.g. holographic trapping [2

2. D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003). [CrossRef] [PubMed]

, 3

3. K. Dholakia and P. Reece, “Optical micromanipulation takes hold,” Nano Today 1, 18–27 (2006). [CrossRef]

, 6

6. 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]

, 7

7. G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, “Assembly of 3-dimensional structures using programmable holographic optical tweezers,” Opt. Express 12, 5475–5480 (2004). [CrossRef] [PubMed]

]), the manipulation range is limited due to the necessary use of oil or water immersion high-NA objectives.

Acknowledgments

We would like to thank the support from the EU-FP6-NEST program (ATOM3D), the ESF-Eurocores-SONS program (SPANAS) and the Danish Technical Scientific Research Council (FTP).

References

1.

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970). [CrossRef]

2.

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

3.

K. Dholakia and P. Reece, “Optical micromanipulation takes hold,” Nano Today 1, 18–27 (2006). [CrossRef]

4.

P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Real-time three-dimensional optical micromanipulation of multiple particles and living cells,” Opt. Lett. 29, 2270–2272 (2004). [CrossRef] [PubMed]

5.

P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Four-dimensional optical manipulation of colloidal particles,” Appl. Phys. Lett. 86, 074103 (2005). [CrossRef]

6.

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]

7.

G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, “Assembly of 3-dimensional structures using programmable holographic optical tweezers,” Opt. Express 12, 5475–5480 (2004). [CrossRef] [PubMed]

8.

J. Glückstad and P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. 40, 268–282 (2001). [CrossRef]

9.

J. W. Goodman, Introduction to Fourier Optics, Second Edition (McGraw-Hill, New York, 1996).

10.

I. R. Perch-Nielsen, P. J. Rodrigo, and J. Glückstad, “Real-time interactive 3D manipulation of particles viewed in two orthogonal observation planes,” Opt. Express 18, 2852–2857 (2005). [CrossRef]

OCIS Codes
(140.7010) Lasers and laser optics : Laser trapping
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation
(230.6120) Optical devices : Spatial light modulators

ToC Category:
Trapping

History
Original Manuscript: October 12, 2006
Revised Manuscript: December 5, 2006
Manuscript Accepted: December 8, 2006
Published: December 22, 2006

Virtual Issues
Vol. 2, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Peter John Rodrigo, Ivan R. Perch-Nielsen, Carlo Amadeo Alonzo, and Jesper Glückstad, "GPC-based optical micromanipulation in 3D real-time using a single spatial light modulator," Opt. Express 14, 13107-13112 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-26-13107


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References

  1. A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970). [CrossRef]
  2. D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003). [CrossRef] [PubMed]
  3. K. Dholakia and P. Reece, "Optical micromanipulation takes hold," Nano Today 1, 18-27 (2006). [CrossRef]
  4. P. J. Rodrigo, V. R. Daria, and J. Glückstad, "Real-time three-dimensional optical micromanipulation of multiple particles and living cells," Opt. Lett. 29, 2270-2272 (2004). [CrossRef] [PubMed]
  5. P. J. Rodrigo, V. R. Daria, and J. Glückstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86, 074103 (2005). [CrossRef]
  6. 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]
  7. G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, "Assembly of 3-dimensional structures using programmable holographic optical tweezers," Opt. Express 12,5475-5480 (2004). [CrossRef] [PubMed]
  8. J. Glückstad and P. C. Mogensen, "Optimal phase contrast in common-path interferometry," Appl. Opt. 40, 268-282 (2001). [CrossRef]
  9. J. W. Goodman, Introduction to Fourier Optics, Second Edition (McGraw-Hill, New York, 1996).
  10. I. R. Perch-Nielsen, P. J. Rodrigo, and J. Glückstad, "Real-time interactive 3D manipulation of particles viewed in two orthogonal observation planes," Opt. Express 18,2852-2857 (2005). [CrossRef]

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