The generalized phase contrast (GPC) method has been applied to transform a single TEM00 beam into a manifold of counterpropagating-beam traps capable of real-time interactive manipulation of multiple microparticles in three dimensions (3D). This paper reports on the use of low numerical aperture (NA), non-immersion, objective lenses in an implementation of the GPC-based 3D trapping system. Contrary to high-NA based optical tweezers, the GPC trapping system demonstrated here operates with long working distance (>10 mm), and offers a wider manipulation region and a larger field of view for imaging through each of the two opposing objective lenses. As a consequence of the large working distance, simultaneous monitoring of the trapped particles in a second orthogonal observation plane is demonstrated.
©2005 Optical Society of America
The Generalized Phase Contrast (GPC) method [1,2], which performs photon-efficient synthesis of arbitrary two-dimensional (2D) intensity patterns, enables real-time interactive manipulation of a plurality of colloidal particles [3–6]. The use of the GPC method to create reconfigurable arrays of counterpropagating-beam traps has extended the approach to volume manipulation of particles. Previously, we demonstrated the ability to control an arbitrary amount of traps dynamically for real-time interactive multiple-particle manipulation in all three dimensions (3D) [7,8]. Due to the large dynamic range for axial positioning of particles achievable by the GPC-synthesized counterpropagating-beam traps, particles can be moved well outside the focal plane of the microscope. A particle out of focus becomes hardly visible and measurements of particle position and velocity vectors become unattainable.
The GPC-based trapping system achieves particle trapping in the x-y (transverse) plane due to gradient forces and z (axial) trapping due to equilibrium between the scattering forces caused by a set of counterpropagating beams [9,10]. The counterpropagating beams are highly collimated in the trapping region. A beam with a cross-section appropriate for trapping a micrometer-sized particle may be projected with different values of numerical aperture (NA) of the microscope objective. This is achieved either by changing the lens before the objective (i.e., magnification adjustment) or by changing the size of SLM phase patterns. This leaves the choice of microscope objectives open, and those best suited to the particular experiment can be chosen.
In this work, the ability to choose from several NA values was utilized to solve the imaging problem posed by defocused particles, as mentioned above. Here we employ two low-NA objectives with long working distances (WD). These objectives increase the WD by more than one order of magnitude, i.e., from less than 0.5 mm in our previous implementation [7,8] to 10.6 mm, thereby giving a previously unseen distance from objective lens to the trapping region. This effectively removes constraints on the sample chamber dimensions and enables us to explore new solutions. A design for an easily assembled disposable sample chamber containing a window for side view is devised. This chamber makes it possible to attain volumetric particle information by observing simultaneously in two orthogonal planes; x-y top view and x-z side view. The extra information makes it realizable to monitor the particle dynamics in the whole trapping volume by direct observation.
A schematic view showing the setup and the workflow associated with optical trapping is illustrated in Fig. 1. The computer collects data from cameras looking from the top and side, thereby showing video data from two orthogonal projections of the sample volume. Via a developed computer user-interface, the operator can take advantage of this set of information either on a hardware level by manipulating the light pattern directly, or oriented towards an experiment by choosing groups of particles and assigning 3D positions and movement paths. User interaction is divided into two matrices, one for each spatial light modulator (SLM; Hamamatsu PPM). The first matrix – the “image” – governs the x-y positioning of the particles and is a one-to-one mapping of the desired intensity distribution to be projected into the sample volume. The second matrix contains the “height” information for use in a polarization-encoding scheme and is assigning a z-position to each trap .
The optical setup shown in Fig. 1 starts with an expanded TEM00 mode from a near-infrared cw Titanium:Sapphire laser illuminating SLM-1; a computer controlled phase-only SLM that encodes the image (the first matrix) into a 2D phase distribution. This phase is converted into a 2D intensity distribution using the GPC method described in detail elsewhere [1,2]. The resulting intensity pattern is imaged onto SLM-2; a spatially addressable polarization modulator that controls the polarization of the individual pixels and is addressed by the second matrix. After the polarization encoding, the light is relayed into the “microscope triangle”. At the first vertex of this triangle, a polarizing beam-splitter (PBS) separates the encoded beam into two orthogonally polarized beams that are relayed, by respective dichroic beam splitters (BS filter) at the two other triangle vertices, into the sample to form counterpropagating-beam traps. By selecting an appropriate focal length for the lenses in the relay, the scaling between pixels on the SLM and in the sample plane can be chosen.
It is worth noting that the phase encoding in SLM-1 is binary only (phase levels 0 and π), which greatly simplifies the requirements to the first spatial light modulator. This also means that SLM-1 can take advantage of the faster refresh-rate of alternative SLM-technology based on either ferroelectric liquid crystals or deformable mirrors. The polarization encoding by SLM-2 can be separated into a coarse DC plus a fine-tuning AC encoding. This means that SLM-2 can be implemented with a fast and low-cost LCOS or LCD-type display unit. Using this scheme, the DC rotation is induced by a half-wave plate, used to perform the coarse adjustment of the relative intensities between top and bottom beams. Final AC corrections are then applied to the individual pixels, and will only require minor corrections for fine adjustment of the particle heights in the sample chamber.
A relatively large distance from objective-barrel tip to the focal plane (working distance) is achieved by using two Olympus LMPLFL 50x objectives, each with 10.6 mm WD and NA=0.55. A Mitutoyo MPlanApo 20x objective (20.0 mm WD, NA=0.42) is mounted horizontally, i.e. orthogonal to the common axis of the two identical 50x objectives. The 20x objective, together with a lens of f=150 mm, is used for imaging onto a CCD camera. This setup gives a view from the side into the sample volume, while also providing a frame of reference by showing a perspective view of the sample bottom surface.
3. Experiments and results
A straightforward design for a disposable sample chamber containing a channel with windows at the top, bottom and the side was assembled using UV adhesive and microscope cover glass of varying sizes glued together. The sample chamber was filled with a dilute aqueous solution of 3.0 µm polystyrene beads (PolySciences) using capillary forces. The ends of the channel were sealed with UV adhesive. The laser was adjusted to provide a power in each counterpropagating beam trap in the order of 5 mW at 830 nm wavelength. The cross-section of each trap approximately matches the size of the beads. To demonstrate the functionality of the setup, and to avoid obscuring the images, simple bead configurations were formed. The optically trapped and dynamically manipulated particles can be seen from side and top views as shown in Figs. 2 and 3.
The trap positions are updated at 20 Hz, constrained only by the effective refresh rate of the applied spatial light modulators. As successive traps are overlapping the update rate gives a smooth transition between intermediate steps. Because the force imposed by an individual trap decreases with particle distance from trap center, a smoothly updated trap ensures stability of the particle confinement in the corresponding optical potential well.
By measuring the time it takes to move a particle 20 µm, we found that in the x-y plane, the gradient forces are able to move the particles with a velocity of up to 10 µm/s. However, in the z-direction, the scattering forces are capable of driving particles even faster at 15–25 µm/s. The rapid z-movements are achieved with a very low risk of losing the particles since the particles are displaced along directions parallel with the columns of light.
4. Discussion and conclusion
The freedom to customize the microscope objectives specifically to the requirements in a given experiment is not only valuable when characterizing the optical traps, but can also have profound implications in many areas where such features associated with high-NA immersion objective lenses are considered drawbacks. In particular, deteriorating spherical aberrations of the trapping beams for large depth displacements inherently associated with the use of both expensive and cumbersome high-NA immersion objective lenses can be totally avoided. Another important property of the GPC method is the true real-time relation between the observed, desired and resulting dynamic 3D particle arrangement; there is a direct relation between the desired particle arrangement to the light intensity distribution in the sample volume. This one-to-one relation requires no intermediate calculations or time-consuming iterative algorithms. The response of the system as a whole is therefore only limited by hardware constraints i.e. the update rate of the optical components and how rapidly the particles move when manipulated by a given light intensity.
The GPC-based counterpropagating-beam traps enable true real-time 3D manipulation of a plurality of particles, without enforcing constraints on the optics. This gives the GPC-based system several strong features. True real-time without intermediate calculations leaves the computer free to support the user, which eases and speeds up data acquisition and subsequent automation of the experiments. The counterpropagating beams are collimated and therefore mainly use counteracting scattering forces in the z-direction which gives stable axial trapping while reducing the maximum light intensity the particles have to withstand as compared to standard optical tweezers. Furthermore, the GPC method does not constrain the numerical aperture of the microscope objectives, which in turn permits the use of long working distance objective lenses and/or permit a large field of view and volume of manipulation when required in an experiment.
By utilizing low-NA objectives in a GPC trapping architecture, we have achieved a previously unseen working distance that has enabled us to observe simultaneously from top and side. The obtained visual data is an alternative to those gained from confocal microscopy , but differs in that the images from the two orthogonal planes are captured simultaneously and in real-time. The information gives us full volumetric particle position control in the sample which in turn enables us to calibrate and fine-tune the counterpropagating beams and observe dynamics of particles that lie outside the focal plane of an ordinary top view microscope. As future extension, two or more particles may be placed in the same column to investigate axial optical binding  in more than one pair of counterpropagating beams. The controllability offered by our system also enables one to study the interparticle interaction in pairs of counterpropagating fields with variable relative strengths. These extensions may lead to interesting schemes for the construction of denser colloidal crystals in 3D. Finally, the large working distance gives a freedom to observe and manipulate particles in devices (e.g. microfluidics and lab-on-a-chip systems) that are too cumbersome to fit into a microscope with high-NA oil/water immersion objectives.
This work has been funded by the European Science Foundation through the Eurocores-SONS program and through the European-FP6-NEST project, ATOM3D, and partially by an internal grant awarded by Risø National Laboratory.
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