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FIGURE 4.31. The optical setup used to implement multiple 3D dynamic trapping and manipulation: PC— Personal Computer, PPM—Programmable Phase Modulator, X100—microscope objective, DM—Dichroic Mirror, CCD—Charged Couple Device sensor [126].

FIGURE 4.32. Three trapped particles moved independently in x-y-z in a 8 x 8 x 8 |jm3 volume: a) the scheme of the trajectories followed by the particles; b) the superposition of 6 images taken during the movement from bottom to the top in 20s [125].

FIGURE 4.32. Three trapped particles moved independently in x-y-z in a 8 x 8 x 8 |jm3 volume: a) the scheme of the trajectories followed by the particles; b) the superposition of 6 images taken during the movement from bottom to the top in 20s [125].

Crystal Spatial Light Modulator) with an electrically-addressed intensity modulator. Its main characteristics are: 1024 x 768 pixels on the LC display, 19 lp/^m maximum display spatial resolution on the PAL-SLM, 20 x 20 mm2 active area, 8 bit addressing, XVGA signal format and provides a phase shift higher than 2n at X = 1064 nm. To generate 3D arrays of traps, we calculate DOEs which includes the lens effect, based on the spherical wave approach described in detail in references [124] and [125]. The desired pattern is thus obtained in a volume centered at a distance equal with the focal length of this lens. This pattern is then transferred by the convergent lens L and the microscope objective (X100,1.4 NA) into the focal plane of the microscope objective, with a scale factor proportional to the ratio of their focal lengths. The sample cell is also positioned in the focus of the microscope objective. The dichroic mirror DM is used to properly fit the beam into the entrance pupil of the microscope objective. We have used an inverted microscope from Nikon (TE2000-E) and a Charged Couple Device (CCD) sensor to monitor the behavior of the particles interacting with the laser beam in the sample cell. One can consider, in practice, two slightly different versions of the setup described above. The first is shown in figure 4.31. The second, easier to align and handle, is obtained by removing the convergent lens L and sending the laser beam directly trough the microscope objective thus allowing an easier alignment. The sample cell is built with two microscope slides separated by sticky tape 120 ^m thick and filled with 2 ^m diameter silica spheres immersed in water (0.2 % concentration). In order to demonstrate the possibility to move trapped particles independently in x-y-z, three micro spheres were first trapped. Once the particles trapped, we could manipulate them independently as indicated in figure 4.32.a, by changing the DOE. The calculation of a new DOE takes about 1 sec (since the DOE is rather big: 1024 x 768 pixels). In figure 4.32.b, shown is the superposition of six images taken during the movement performed in 20 seconds. This movement was obtained with DOEs calculated using the spherical wave approach. The vertical displacement along the optical axis, z, is visible in the figure from different focusing of the micro spheres: spheres located on upper positions have smaller images than the spheres located in the focal plane of the microscope objective. The size of these images was correlated with the sphere vertical positions during a calibration procedure before the experiment. The particles are moved inside a volume of about 8 x 8 x 8 |im3 with a 0.3 |im lateral increment for x-y displacements and 1 |im increment for vertical displacement along z axis. The number of trapped beads could be increased to hundreds for 2D and tens for 3D micromanipulation. The limitation comes from the available laser power (about 1 mW is required for each trapped particle). For 3D micromanipulation an additional limitation comes from the light scattered by the particles trapped in different planes.

4.5.2. 3D Micromanipulation of Cells by Means of Optical Tweezers

Following the technique described in the previous paragraph one can create an array of beads surrounding biological samples like cells. The beads can be used to trap and stress cells in order to understand their behavior under such conditions. In order to perform these investigations we surrounded the cell by beads and performed a preliminary experiment [126]. Nine latex microspheres were trapped and arranged as shown in figure 4.33. Eight of them were kept in a fixed position on a circle of 20 | m diameter. The one bead left has to be trapped and shifted axially for 6 |im. Since the manipulation conditions were known a priori, we calculated ten phases DOEs using the spherical wave approach. Each DOE corresponds to the same position of the beads trapped on the circle but to a different axial position for the axial trapped bead. A detail of such a DOE (512 x 512 pixels) is depicted in figure 4.34.a. The beads, trapped into the same plane are depicted in figure 4.34.b. After 10 sec, the central bead is shifted along the optical axis by 6 |m and the trapped beads in the new configuration are shown in figure 4.34.c and figure 4.34.d. One can notice that the central bead is not perfectly centered. This is due to the small misalignment between the optical axis of the MO and the optical axis defined by DOE implemented on the PPM.

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