1. Introduction

In 1986 optical trapping of dielectric particles by means of a focused laser beam was demonstrated by Ashkin et al. [1]. Since then, the optical tweezers technique gained a continuous increasing interest especially in view of its application in biological research [2]. This technique allows non invasive manipulation of biological samples like viruses, bacteria, and living cells [3, 4, 5]. Precise measurement of elasticity, forces, torsion and surface tension are also possible with a sub-pN accuracy [6, 7, 8]. In cellular biology, it enables to investigate cell reaction to external cues via the controlled application of localized mechanical and chemical stimuli on cell cortex [9, 10, 11]. A basic optical tweezers set up requires a strongly focused laser beam, a coarse positioning system to center the sample and an imaging system to monitor the experiment [12]. However, the increasing use of this technique in biological research has required the conception of more and more tricky experimental apparatus. Improvements are required both in the imaging part and in the “tweezing” technique. For imaging, sensitive fluorescence techniques combined with optical manipulation is desired in most applications. For manipulation, it is advantageous in some cases to produce multiple optical traps.

 

Fig. 1. Schematic of the multi trap optical tweezers set up.

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Fig. 2. Polystyrene latex beads, 2 µm in diameter, trapped by a circle of laser spot(a); deformed in an ellipse (b); deformed by leaving one part of the circle fixed (c); same beads trapped in a squared array (d); deformed along the x direction (e); traps can be moved independently (f).

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One possibility to realize multi trap systems consists in rapidly scanning a single laser beam using fast beam deflectors. In this way, different traps can be generated by time sharing the laser beam between several positions. A multi-spot pattern is then obtained and its geometry controlled via the deflector system. The use of fast beam deflectors is of crucial importance as the time the trap is ‘off’, servicing another position, has to be shorter than the time the particle needs to diffuse away from its trapping position. Fast beam deflection is very well achieved by the use of acousto-optic deflectors (AOD)[14, 13, 15]. In this case the rise time to produce different deflection angles is of the order of µs, thus allowing the synthesis of multi traps of high stability. An alternative way to generate multi traps makes use of diffractive optical elements (DOEs) [16, 17]. In this case, multi traps are simultaneously generated by focusing the laser beam on a suitable patterned optical element. As a result, the laser is diffracted in a desired arrangement of multi spots. The advantage in respect to the AOD based system is the possibility to generate traps distributed in 3D volumes [18]. Moreover, when the DOEs are implemented on a spatial light modulator (SLM), the optical traps can be independently moved by changing the relative phase of the diffracted pattern [19, 20, 21].

One interesting extension of the multi trap optical tweezers system is to tune separately the trapping force of each spot.

This opportunity can enable promising applications, for example several objects can be manipulated at the same time with a force independently adjusted on the single object. Cell reactions, as adhesion reinforcement, cytoskeleton organization or gene expression, to external gradient of forces can be monitored.

Tuning of the trap stiffness has been already proposed in single trap optical tweezers set up to generate an efficient system of feedback control [22]. In that case modulation of the trap strength has been achieved by an acousto optical modulator.

In this paper, we propose to create a multi trap pattern where the trapping strength of each spot can be tuned in such a way that 2D gradient of force can be generated. In this case, we propose to achieve force-tuning by controlling the number of time the laser beam passes on the same spot. This is achieved by the use of a dual axis AOD system. Examples of possible spot distributions and the corresponding gradient of force one can realize with this method are presented.

 

Fig. 3. Intensity distribution of the spots reflected on the coverslip and imaged onto a CCD camera, for a 4×4 array and a circular distribution.

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Figure 1 shows the multi trap optical tweezers system. The trapping source is a 15W Nd:Yag laser (Spectra Physics, J40) with an emission wavelength of 1064 nm. After a first beam expansion the laser is sent into two orthogonally mounted AODs (AA opto-electronique), the outgoing steered beam is further expanded in order to match the entrance of the objective. A variable intensity attenuator obtained with a combination of a λ/2 plate and a linear polarizer allows us to vary the laser intensity. After the second beam expander the laser beam is sent into an inverted microscope (Zeiss AxioVert 135) and finally, by a dichroic mirror, to the focusing objective (Zeiss Neofluor 100x oil, NA=1.3). The dichroic is positioned above the fluorescence filter block. In this way excitation light from a Mercury lamp mounted on the rear port of the microscope can be focused to the sample with the same objective used for trapping. Fluorescence from the sample is sent to a high sensistive CCD camera (cool Snap HQ, Roper) placed at the left port of the microscope. This configuration allows us to perform at the same time optical trapping and fluorescence imaging. Finally, the transmitted light from an arc lamp is sent to a second CCD camera to image the bead positions. The AODs work with a center drive frequency of 76 MHz, a bandwith of 15 MHz and an access time of 1 µsec.

Examples of dynamic geometries of beads that is possible to realize with a typical AOD based system are shown in Fig. 2(a)–(f). As described in the introduction, by varying the successive pattern of the laser beam, the shape of the array can be varied in a symmetric way or along a preferential axis (Fig. 2 (a)–(e)). Each trap can be moved separately from the rest of the pattern (Fig. 2 (f)).

In the distributions of beads shown in Fig. 2, the trapping force is constant over the entire pattern. By further modifying the sequence of laser beam pattern we can select the number of time the laser passes on each spot in one cycle. In this way, we control the force at each trap independently from the others.

Examples of this, are shown in Fig. 3(a)–(b) for two geometries. Here in order to highlight the intensity distribution, we image on the CCD camera the laser spots (without beads) reflected on the glass of a coverslip. The two figures show the intensity distribution in a 4×4 array and in a circular distribution of spots.

 

Fig. 4. (a) Intensity profile along the arrow of Fig. 3, the row number is indicated in the figure. (b) Force calibration corresponding to the different rows of the array.

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Figure 4(a) shows the intensity profile along the white arrow in Fig. 3(a). In this case we generate a 4×4 pattern of laser spots with an intensity profile which can be described by I(n)=I ₁×n ^1.5, n being the row index and I ₁ the laser intensity along the first row of the array. In this case the laser intensity at the entrance of the AOD was 3 W, corresponding to about 1 W at the entrance of the objective (considering the losses due to the passive optics and the AODs). Considering the further losses due to the objective (about 50%) we estimate I ₁=5 mW.

The forces corresponding to different rows of the array have been derived by measuring the escape velocity of the beads as the arrays are translated horizontally at increasing speed. For each row we derived the escape velocity, v_e(n). From the values of v_e(n), we derived the laser forces F(n) by using the Stokes’s law, F(n)=6πηRv_e(n), (η being the viscosity of the water, R the bead radius). The results are reported in Fig. 4(b). In this case, a trapping force ranging from 0.4 pN in the first row to 3 pN in the last one has been obtained. The 15W laser power allow for this geometry to have a gradient I(n)=I ₁×n ^α, with a value for α up to 3.

In conclusion we have presented a multi force optical tweezers system where pattern of multi spots with a force independently regulated at each spot can be generated. This characteristic opens interesting prospectives as the possibility to investigate cell reaction to external cues via the controlled application of mechanical gradient on cell cortex or the simultaneous manipulation of several objects with forces calibrated independently on each object.

We thank the staff of the platform ‘Imaging of Dynamical Processes in Cellular and Developmental Biology’ of the IJM for helpful advices in the realization of the system. This work was supported by the CNRS (DRAB) by the ARC (Association pour la Reserche sur Cancer) and by the GEFLUC grant. D. Sanvitto was supported by a Marie Curie fellowship, V. Emiliani from CNRS and ARC.