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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 25 — Dec. 15, 2003
  • pp: 3485–3489
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Large capture-range of a single-beam gradient optical trap

Perry G. Schiro, Christopher L. DuBois, and Alfred S. Kwok  »View Author Affiliations


Optics Express, Vol. 11, Issue 25, pp. 3485-3489 (2003)
http://dx.doi.org/10.1364/OE.11.003485


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Abstract

We have observed long-range trapping with a single-beam gradient force optical trap. 6 to 10 µm polystyrene beads that are initially ≈100 µm away from the trap-center can be pulled into the trap-center. Particle-tracking enables us to determine the trajectory of a bead as it moves towards the trap-center and map out a capture zone inside which trapping can occur.

© 2003 Optical Society of America

1. Introduction

The single-beam gradient force optical trap, first observed 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]

], has found many applications in biology, ranging from force measurements on the femtonewton scale [2

2. J.-G. Meiners and S. R. Quake, “Femtonewton force spectroscopy of single extended DNA molecules,” Phy. Rev. Lett. 84, 5014–5017 (2000). [CrossRef]

] to the study of molecular motors [3

3. S. M. Block, C. L. Asbury, J. W. Shaevitz, and M. J. Lang, “Probing the kinesin reaction cycle with a 2D optical force clamp,” Proc. Natl. Acad. Sci. 100, 2351–2356 (2003). [CrossRef] [PubMed]

]. The forces and properties of single-beam gradient traps such as trap stiffness have been studied extensively using micron-sized polystyrene and glass beads. To our knowledge, most of these studies have been limited to a region that is within one bead-diameter of the trap center. Both experimental [4

4. R. W. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (1996). [CrossRef] [PubMed]

] and theoretical [5

5. 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]

] studies have shown that the trap exerts a maximum restoring force on a bead when the bead is displaced from the trap center by about one bead-radius. “The size of the trapping zone in a typical single-beam gradient trap is fixed and rather small, on the order of the light wavelength,” [6

6. K. Svoboda and S. M. Block, “Biological Applications of Optical Forces,” Annu. Rev. Biophys. Biomed. Struct. 23, 247–285 (1994). [CrossRef]

] although the interference of two annular beams has been used to create multiple trap positions and extend the size of the trapping zone [7

7. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arit, W. Sibbett, and K. Dholakia, “Creation and Manipulation of Three-Dimensional Optically Trapped Structures,” Science 296, 1101–1103 (2002). [CrossRef] [PubMed]

]. Trapping has been described as “the free floating balls literally ‘jumping’ into the trap when they pass within a ball diameter or so of the trap position.” [8

8. S. P. Smith, S. R. Bhalotra, A. L. Brody, B. L. Brown, E. K. Boyda, and Mara Prentiss, “Inexpensive optical tweezers for undergraduate laboratories,” Am. J. Phys. 67, 26–35 (1999). [CrossRef]

] However, we have observed that a single-beam gradient force optical trap has a larger capture range: polystyrene beads that are initially ≈100 µm away from the trap-center can be pulled into the trap-center in a few tens of seconds.

2. Optical system

Fig. 1. Experimental Setup

A schematic of our experimental setup is shown in Fig. 1. The source of our optical trap is a diode laser assembly (Melles Griot 56ICS115), which uses an anamorphic prism and a microlens to respectively circularize and collimate the output of an 832 nm laser diode. The laser beam enters an inverted microscope (Leica DMIRB) with bright field illumination. A Plan FLOUTAR 100× 1.3 N.A. oil immersion objective focuses the laser light into a sample chamber to form the optical trap. The 7 mm output of the diode laser assembly is expanded by a telescope consisting of a f=25-cm and a f=35-cm focal length plano-convex lens to overfill the back aperture of the microscope objective to ensure the formation of a strong trap. The sample chamber consists of a #1.5 glass microscope cover slip and a glass microscope slide separated by a layer of paraffin film. The sample chamber is filled with a colloidal suspension of polystyrene beads (Polysciences) and rests inverted on the microscope stage, with the cover slip in the bottom. The microscope objective collects light scattered by polystyrene beads in the sample chamber. After passing through a dichroic mirror and a beam-splitter internal to the microscope, the scattered light is imaged onto a video camera (GBC) and a digital still camera (Nikon Coolpix 995) via two tube lenses. A small fraction of the back-scattered laser diode light is transmitted by the dichroic mirror, which allows us to monitor our laser trap with the video camera. A digital video converter (Canopus ADVC 100) digitizes the analog video output of the still camera. A MacIntosh G4 computer records the motion of a polystyrene sphere as it is being pulled into the optical trap. The optics in the Nikon still camera does not transmit the near-infrared laser diode light, enabling us to observe the polystyrene bead without being overwhelmed by the scattered laser diode light. We calculate the laser power delivered to the sample by multiplying the input power into the back aperture of the microscope objective by the objective's transmission at 832 nm.

3. Trajectories

Figure 2 shows how we observe long-range trapping. The red lines denote the rays entering the microscope objective with the largest convergence angle ϕmax.

Fig. 2. Observation of long-range trapping. The green asterisk marks the position of the bead when the video in Fig. 3 starts.

Fig. 3. (2.1 Mb) Long-range trapping of a 10 µm polystyrene bead with 54 mW of laser power.

We use the image processing software ImageJ [9] to perform a frame-by-frame analysis of our long-range trapping videos. Performing background subtraction and grayscale-thresholding produces a black and white movie with the bead appearing as a black circle. We then use the particle-tracking routine in ImageJ to determine the x and y coordinates of the center of the bead’s image and its area in every frame of the video. The area of the bead’s image increases as the bead gets more and more out of focus. We can thus calibrate the z coordinate of the bead by finding the areas of a bead’s image at known axial positions with respect to the focal plane of the objective. When the bead is within one bead-diameter of the trap-center, diffraction produces Fresnel rings in the bead’s image, which causes the area of the bead to fluctuate as z changes. These fluctuations in the area create large uncertainties in the z coordinate of the bead when it is within one bead-diameter of the trap-center. Since we are focusing on large capture-range in this paper, this region is not particularly important. Finally, we obtain the trapping trajectory of a bead by plotting the position of the bead in each video frame. We use cylindrical coordinates to describe the position of the beads. However, due to circular symmetry around the z-axis, the θ coordinate is omitted. The trapping data we present are for polystyrene beads with diameters 2a=6 µm and 10 µm. Since 2a≫832 nm, the wavelength of the trapping laser, ray optics can be used to describe the interaction between the trapping laser and the beads. Ashkin shows that in the ray optics regime, the force exerted by a ray incident on a bead can be resolved into two components [5

5. 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]

]. The scattering force acts along the direction of the ray while refraction gives rise to the gradient force, which acts perpendicular to the ray.

Fig. 4. Long-range trapping trajectories of two 10 µm beads, with 54 mW and 18 mW laser power. The trajectory at 54 mW corresponds to the positions of the bead in Fig. 3.

4. Capture zone

Fig. 5. Capture zone for long-range trapping with 29 mW laser power. A trapping-trajectory taken at 36 mW laser power is superimposed to show how the edge of the zone corresponds to the position where long-range trapping starts at a particular radial position. The inset (not to scale) illustrates how the capture zone is within a region illuminated by the trapping laser.

These markers form a line that is at an angle of 64° with respect to the z-axis. We have experimentally observed that this line marks the boundary of a “capture zone” (inset in Fig. 5); if we block the trapping beam and position a bead anywhere within the capture zone, trapping will occur when we unblock the trapping beam. Since the largest convergence angle for rays entering our aqueous sample from the N.A.=1.3 microscope objective is ϕmax=78°, the trapping zone falls only within the innermost 19% of the volume of the sample chamber that is illuminated by the trapping laser.

7. Conclusion

We have demonstrated that a single-beam gradient force optical trap has a large capture-range: it can trap a polystyrene bead that is initially ≈100 µm (15 bead-diameters for 6 µm beads) away from the trap-center. However, trapping can only occur if a bead is initially positioned within the capture zone, which corresponds to a region within the conical volume that is illuminated by the trapping-laser. Further analysis of the trajectories will enable us to quantitatively understand the force acting on a bead as long-range trapping occurs.

Acknowledgments

We gratefully acknowledge J. Steven Ross for his help with implementing ImageJ in our lab, Dr. John Crocker for referring us to the Melles-Griot diode laser module, and Dr. Koen Visscher for a helpful discussion. PGS and CLB were supported by the Pomona College Summer Undergraduate Research Program.

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.

J.-G. Meiners and S. R. Quake, “Femtonewton force spectroscopy of single extended DNA molecules,” Phy. Rev. Lett. 84, 5014–5017 (2000). [CrossRef]

3.

S. M. Block, C. L. Asbury, J. W. Shaevitz, and M. J. Lang, “Probing the kinesin reaction cycle with a 2D optical force clamp,” Proc. Natl. Acad. Sci. 100, 2351–2356 (2003). [CrossRef] [PubMed]

4.

R. W. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (1996). [CrossRef] [PubMed]

5.

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]

6.

K. Svoboda and S. M. Block, “Biological Applications of Optical Forces,” Annu. Rev. Biophys. Biomed. Struct. 23, 247–285 (1994). [CrossRef]

7.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arit, W. Sibbett, and K. Dholakia, “Creation and Manipulation of Three-Dimensional Optically Trapped Structures,” Science 296, 1101–1103 (2002). [CrossRef] [PubMed]

8.

S. P. Smith, S. R. Bhalotra, A. L. Brody, B. L. Brown, E. K. Boyda, and Mara Prentiss, “Inexpensive optical tweezers for undergraduate laboratories,” Am. J. Phys. 67, 26–35 (1999). [CrossRef]

9.

http://rsb.info.nih.gov/ij/

OCIS Codes
(140.7010) Lasers and laser optics : Laser trapping
(350.4990) Other areas of optics : Particles

ToC Category:
Research Papers

History
Original Manuscript: November 4, 2003
Revised Manuscript: December 8, 2003
Published: December 15, 2003

Citation
Perry Schiro, Christopher DuBois, and Alfred Kwok, "Large capture-range of a single-beam gradient optical trap," Opt. Express 11, 3485-3489 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-25-3485


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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. J.-G. Meiners and S. R. Quake, �??Femtonewton force spectroscopy of single extended DNA molecules,�?? Phy. Rev. Lett. 84, 5014-5017 (2000). [CrossRef]
  3. S. M. Block, C. L. Asbury, J. W. Shaevitz, and M. J. Lang, �??Probing the kinesin reaction cycle with a 2D optical force clamp,�?? Proc. Natl. Acad. Sci. 100, 2351-2356 (2003). [CrossRef] [PubMed]
  4. R. W. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, �??Quantitative measurements of force and displacement using an optical trap,�?? Biophys. J. 70, 1813-1822 (1996). [CrossRef] [PubMed]
  5. 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]
  6. K. Svoboda and S. M. Block, �??Biological Applications of Optical Forces,�?? Annu. Rev. Biophys. Biomed. Struct. 23, 247-285 (1994). [CrossRef]
  7. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arit, W. Sibbett, and K. Dholakia,, �??Creation and Manipulation of Three-Dimensional Optically Trapped Structures,�?? Science 296, 1101-1103 (2002). [CrossRef] [PubMed]
  8. S. P. Smith, S. R. Bhalotra, A. L. Brody, B. L. Brown, E. K. Boyda and Mara Prentiss, �??Inexpensive optical tweezers for undergraduate laboratories,�?? Am. J. Phys. 67, 26-35 (1999). [CrossRef]
  9. http://rsb.info.nih.gov/ij/

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