We demonstrate a technique for obtaining fully dynamic multiple-beam optical tweezers using the generalized phase contrast (GPC) method and a phase-only spatial light modulator (SLM). The GPC method facilitates the direct transformation of an input phase pattern to an array of high-intensity beams, which can function as efficient multiple optical traps. This straightforward process enables an adjustable number of traps and real-time control of the position, size, shape and intensity of each individual tweezer-beam in arbitrary arrays by encoding the appropriate phase pattern on the SLM. Experimental results show trapping and dynamic manipulation of multiple micro-spheres in a liquid solution.
© 2002 Optical Society of America
Single-beam optical tweezers  is useful for a wide range of inter-disciplinary research and is a practical tool for: (1) the measurement of interaction forces and manipulation of cells, sub-cellular structures and individual DNA-molecules; and (2) assembly of microstructures on the micro- and nano-scale [2,3]. When an array of particles has to be trapped simultaneously and manipulated independently, there is a need to generate multiple tweezer-beams where the shape, size, position and intensity of each beam can be controlled individually and preferably manipulated in real-time.
In a recent work, we demonstrated the simultaneous trapping of four particles using a fixed tweezer-beam array based on the generalized phase-contrast (GPC) method and a prefabricated phase mask . Our approach to generate multiple-beam optical tweezers (MOT) is non-mechanical and an alternative to techniques that are based on either refractive optics with multiple beam paths , VCSEL arrays , interference patterns of Laguerre-Gaussian light beams  or raster-type mechanical beam steering , which are either component intensive, has relative low laser power, restricted trapping pattern geometries or is mechanically complex. An approach based on computer-generated holograms (CGH) has also been demonstrated as a non-mechanical alternative for producing MOT [8, 9]. This approach allows for encoding the CGH on to a spatial light modulator (SLM) and facilitates a non-mechanical dynamic MOT system that is capable of independent positioning of individual beams . However, real-time CGH-based manipulation of individual particles in large trapping arrays is limited because of the complex computation process, the high requirements to the space-bandwidth product of the SLM, and the inherent diffraction losses that could affect the trapping efficiency of each beam.
In this work, we demonstrate a fully dynamic MOT system that makes use of the GPC method and a phase-only SLM for generating an array of high-intensity beams, suitable for optical trapping and real-time manipulation of micro-particles. In our approach, a phase-only SLM encodes the desired pattern directly in the phase component of a collimated and expanded laser beam. This phase-encoded information serves as the input for a GPC system [12,13], in which a phase-contrast filter (PCF) generates a high-contrast intensity pattern that directly corresponds to the phase perturbation of the input wavefront. The intensity pattern is focused using a microscope objective lens for trapping of microscopic particles. We use an optically addressed phase-only SLM , which is addressed using the video signal from a computer. Hence, it is possible to control the position of the tweezer-beams by movement of the computer cursor or a pointing device, resulting in a real-time direct manipulation of individual optical traps. The phase-only SLM is not pixelated and this fact combined with the straightforward phase-encoding procedure, results in an efficient, real-time re-distribution of light from the incident laser beam into the individual tweezer-beams. With our method, it is possible to hold certain traps stationary, whilst other traps are moved. Furthermore, it is also possible to adopt an arbitrary beam profile best suited for a given trapping task.
2. Optical setup
Figure 1 shows the schematic diagram for the implementation of the GPC-based MOT system using a phase-only SLM. We have used a 200 mW diode laser operating at a wavelength λ=830 nm. The expanded and collimated laser beam is incident on a reflection-geometry SLM inclined at angle 5 degrees with respect to the optical axis of the system. The SLM is a parallel-aligned nematic liquid crystal type (Hamamatsu Photonics), which can modulate phase of at least 2π at 830nm . The SLM is optically addressed by a VGA-resolution (640×480 pixels) liquid crystal projector element that is controlled from the video output of a computer (PC). A 4 mm-diameter iris (Ir1) is placed in front of the SLM. The diameter of the iris is matched to the diameter of the phase contrast filter (PCF) in order to optimize the contrast of the output intensity distribution . The phase-modulated light is directed into the 4-f filtering system that is composed by lenses L1 (f=200mm) and L2 (f=100mm), and a PCF positioned at the Fourier-plane. The 50 μm-diameter PCF is designed to give a π-phase shift at 830 nm and is fabricated by depositing photo-resist on a glass optical flat. A highcontrast intensity distribution, which is directly related to the phase-pattern on the SLM, is generated in the back focal plane of L2 where an image-plane filtering iris (Ir2) is placed in order to remove any undesired halo-light, which is a well-known effect occurring in phase contrast filtering systems 4]. The lens L3 (f=300 mm) and the microscope objective, MO, (Leica PL-APO, ×100, NA=1.4) form the second 4-f lens system that scales the intensity distribution in the tweezer-plane. The fluorescence port of an inverted microscope (Leica DM-IRB) is used to couple the infrared laser light to the back-focal plane of the MO via a dichroic mirror (DM), which is reflecting at λ =830 nm and transmitting in the visible range. Visible light from the illuminator is scattered by the trapped particles and imaged to a CCD-camera using the same MO and the tube lens, LT. The total de-magnification of the modulation aperture of the SLM is 1/300 and results in an effective 13 μm-diameter working region in the tweezer-plane. The size of one resolution cell (pixel) at the SLM is 41.4 μm  that is estimated to correspond to 0.14 μm in the tweezer plane.
3. Trapping and dynamic manipulation
3.1 Static trap
The functionality of this system is tested using a suspension of 2 μm polystyrene beads in deionized water. A 30-μm-thick sample cell containing the micro-sphere solution is prepared using a microscope slide and a cover slip separated by sticky tape. Figure 2(a) shows a phase pattern addressed on the SLM that generates a 4×4 tweezer-beam array. After appropriate calibration of the SLM, the binary gray levels 1 and 150 correspond to the phase shift values 0 and π, respectively. The diameter of each phase dot at the SLM is 9 pixels corresponding to a diameter of 1.2 μm in the tweezer-plane.
The intensity distribution in the image plane of the first 4-f lens set-up has a top-hat profile. In the tweezer-plane, the intensity distribution approaches the resolution limit of the MO, resulting in a near Gaussian profile. This makes it possible to generate efficient trapping beams using the GPC approach by means of a binary-phase SLM and thus, simpler than other techniques that require a multi-phase level SLM for high light efficiency.
Figure 2(b) shows the simultaneous trapping of 16 micro-spheres in the GPC-generated 4×4 trapping beam array. A scale-bar is placed at the bottom indicating a distance of 5 μm.
This image is recorded under normal visible illumination light with a DM, which is transmitting at the visible range, and a laser-line blocking-filter placed in front of the camera. It is worthwhile to note that the trapping beam array produced by our method does not contain a disturbing zero-order beam in the center as well as noise from higher-order diffracted beams, which are unavoidable occurrences in the holographic approach.
In order to have sufficient trapping strength, the laser power incident on the SLM is set to 60 mW. With an estimated efficiency of the system of 35%, yields a laser power of 1.3 mW for each trap in the tweezer-plane. Identifying the laser power of each trap makes it possible to calibrate the system so that individual trapping forces are controlled in proportion to the laser power .
3.2 Dynamic trapping
A second experiment was carried out in order to demonstrate the dynamic properties of our approach. The limiting factor for the generation and dynamic manipulation of the tweezer-beams is the response time of the liquid crystals in the SLM, which is approximately 40 ms . Figure 3 shows an image sequence that demonstrates the simultaneous trapping of eight polystyrene micro-spheres arranged in six- and two-fold traps, rotating in opposite directions and with different speeds. The time lapse between each image frame is 240 ms, as shown in the upper right corner of each frame. A scale-bar is placed in the first image, indicating a distance of 10 μm. The first frame of the sequence has two dotted circles with an arrow indicating the rotation directions of the particles. The two particles rotating in the inner circle rotates counter clock-wise nearly one full rotation and the outer six particles rotate clock-wise 1/8 of a full rotation. The peripheral speed of the inner two particles is 3.3 μm/s and the outer six particles rotate with a peripheral speed of 1.6 μm/s. As can be seen in the sequence, two particles present to the left and right of each frame are moving freely due to Brownian motions and are clearly not under the influence of radiation pressure effects from the trapping beams. The laser power of each trap was kept at the same level as in the first experiment.
In the current optical setup, the 8 mm diameter input aperture of the objective lens and the long focal lengths of lenses L1 to L3 result to a very broad intensity distribution along the optical axis. This effectively provides a two-dimensional trap compelling the particles to be trapped against the microscope slide. This system can have potential applications for alignment of components in micro-opto-mechanical systems [15,16], assembly of microstructures , or cell sorting , where manipulation along the optical axis is not a prerequisite. However, if the choice of application requires trapping along a single-plane with the particles suspended along the optical axis, lenses L1 to L3 have to be modified in order to have the beam cover the entire area and make-use of the full numerical aperture of the lenses. This effectively harnesses the full functionality of the lenses to its diffraction limit. Moreover, if multiple particles have to be trapped in multiple positions along the optical axis, independent three-dimensional manipulation can be introduced in the system by insertion of an additional phase-only SLM for encoding of dynamic Fresnel lens-functionality for each trapping beam. The modified system, however, would not be easily interfaced to the fluorescence port of the inverted microscope and would require the whole system to be built on a custom designed microscope setup.
Simultaneous trapping of micron-sized particles is demonstrated using the generalized phase contrast approach with a phase-only spatial light modulator to generate multiple-beam optical tweezers. In this approach, the number, position, shape, size and speed of each trap can be dynamically and independently controlled from a simple PC-interface. Our method has a high light efficiency even with a binary-phase SLM and works in real-time using a straightforward computer interface.
This work has been funded as part of an award from the Danish Technical Scientific Research Council and an equipment grant from the Center for Biomedical Optics and New Laser Systems. We express our gratitude to T. Hara and Y. Kobayashi of Hamamatsu Photonics for the useful discussions on the operation of the SLM. We also thank P. C. Mogensen for his indispensable help during this project.
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