Two-laser optical tweezers with a blinking beam

Optics and Lasers in Engineering 94 (2017) 82–89

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Two-laser optical tweezers with a blinking beam a,⁎

a

a

Weronika Lamperska , Jan Masajada , Sławomir Drobczyński , Paweł Gusin

b

MARK

a Department of Optics and Photonics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, PL50-370 Wrocław, Poland b Faculty of Technology and Computer Science, Wrocław University of Science and Technology, 27 Piastowski sq., PL58-560 Jelenia Góra, Poland

A R T I C L E I N F O

A B S T R A C T

Keywords: Optical tweezers Viscosity Trap stiffness Optical trapping Microrheology

We report on a two-laser holographic optical tweezers setup and present its two major advantages over singlelaser one. First, the trap stiffness of a weak trapping beam can be measured with a considerable accuracy. Second, a novel method of examining local viscosity of fluid is proposed. Both measurements are performed based on forcing the oscillations of a microscopic polystyrene bead placed between two optical traps. The two beams are generated by separate laser sources and therefore their trapping power can vary. Moreover, a stronger trap ‘blinks’, modulated by an electronic shutter. The blinking frequency can be precisely adjusted to the experimental conditions, which results in high accuracy of the measurements.

1. Introduction

and report on two kinds of experiments performed with it.

Optical tweezers are being more and more widely used for examination and precise manipulation of micro- and nano-sized objects. Once the object is trapped in the tightly focused laser beam, it can be displaced or rotated by the use of optical forces. The holographic optical tweezers (HOT) [1–3] use computer generated holograms (CGH) in order to form and steer trapping beams. The holograms are generated by the use of spatial light modulators (SLM) [4,5]. The dynamic holography provides a very flexible way of forming and driving tens of various optical traps simultaneously. Optical tweezers have become useful in biotechnology and chemistry as they allow studying piconewton forces acting on a specimen. Such research often requires examining fluid properties in a narrow sample region, i.e. in the range of tens of micrometers. Several reports on measuring local viscosity with optical tweezers can be found [6–10]. The HOT development goes into various directions. The most important is overcoming the limitations imposed on trap quality due to SLM. Although the manufactures improve the performance of the SLM, the HOT is still of lower quality comparing to more classical solutions (for example galvanic mirror optical tweezers). The main problems are the trap optical quality, low switching frequency (typically 60 Hz), laser power losses (especially at infrared range), diffraction artefacts (like zero order beam). There are many ways to solve the above problems. All of them are of limited value and can be applied to a specific measurement problem. The two-laser HOT opens a new possibility for experiments and allows avoiding some problems specific for the single-laser system. In this paper we present our two-laser HOT

2. Preliminary observations

⁎

We have noted several intriguing phenomena while studying the microbead motion affected by the proximity of two optical traps. In our first experiment the single-laser HOT (solid line, Fig. 1) was used. A Nd:YAG laser beam is collimated and illuminates a SLM matrix. SLM (Spatial Light Modulator, Holoeye-Pluto) enables multiple traps generation, both light and dark. Dark traps carry non-zero angular momentum (vortex beams [11,12]). Such vortex traps (also known as doughnut traps) have an annular intensity distribution with a dark region in the trap center. Particles tend to be either trapped inside a bright ring or circulate along it as a result of angular momentum transfer from the beam to the particle. A dimensionless quantity describing an optical vortex and closely related to the ring diameter is called topological charge (m) [13]. The higher the charge, the wider the focused vortex beam. The beam reflected from the SLM surface is tightly focused by the oil-immersion microscope objective (1.3NA, 100x, Olympus UPlanFL N). An adjustable z-position (along the beam axis) of this objective combined with a x-y positioning microscope stage allows examining the entire sample area. Additionally, a heating stage keeps the constant temperature of a sample. Polystyrene microbeads of two sizes (4.5 and 10 µm in diameter) were used in our experiments. A 20 µl volume of beads in aqueous solution was put into the chamber between a microscope slide and a cover slip. The chamber was approximately 0.8 mm deep and the focal point of the trapping beam was located at

Corresponding author. E-mail address: [email protected] (W. Lamperska).

http://dx.doi.org/10.1016/j.optlaseng.2017.03.006 Received 12 December 2016; Received in revised form 27 February 2017; Accepted 17 March 2017 0143-8166/ © 2017 Elsevier Ltd. All rights reserved.

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presents a trajectory of bead center in a x-y plane within 1 s. The bead tends to go back and forth along the line connecting the traps. The oscillations are strictly periodic, with a period of about 0.0082 s (giving a frequency of ~120 Hz). In the second experiment, the Gaussian trap was replaced with a vortex beam (m=30) and thereby the ZOD trap was encircled with a bright ring (Fig. 3a). The bead situated in the inner dark region was set into rotations as a result of an angular momentum transfer from the optical vortex. A retraced trajectory reveals, however, the existence of an additional radial component of this movement. The angular frequency of the revolution depends on the dark beam intensity. In contrast, the angular frequency of minor oscillations does not. A cycle performed by the bead (in 0.125 s) can be seen in Fig. 3b. Approx. 15 radial oscillations occurred within a full rotation, resulting in the angular frequency of ~120 Hz. Indeed, a 120 Hz frequency peak was present in a Fourier spectrum of bead's movement. To sum up, certain periodic driving force (f=120 Hz) was present in our system. A fast-cam recording in the sample plane was performed. As expected, the beams pulsate (‘blink’) as a result of SLM refresh rate (f=60 Hz). More surprisingly, the zero-order diffraction trap and the first-order one are in antiphase, hence the doubled frequency. Indeed, it is a result of the SLM design. During the transition between two subsequent patterns displayed on SLM matrix, pixels take random values. For this short time, ZOD beam increases in intensity while another one decreases significantly. More detailed analysis of this phenomenon can be found in [14]. The bead is attracted to the light ring of the dark trap when the dark trap's intensity increases. When the intensity decreases, the bead moves towards ZOD center. This is the reason for minor oscillations observed in our system. In order to verify the above assumptions, a subtle change to the trap configuration was introduced. The ZOD beam was no longer used. It was substituted by a standard non-vortex trap placed in the center of a doughnut trap. The intensity distribution in the sample plane did not change (as in Fig. 3a). It appears that circulation of the particle may now be treated as purely azimuthal (Fig. 4). Switching trap intensities still occurs, although both first-order diffraction beams blink in a synchronized way. Concluding, the relative pulsation of traps acts as a driving force. A bead would get trapped in a stable position between two beams but their periodical changes in intensity made the particle oscillate. In our work, we expand this idea and propose a novel realization of microscopic harmonic oscillator. To better investigate the behavior of the bead between the two traps, the two-laser HOT is necessary. Its main advantage is avoiding the interference phenomenon between two closely located optical traps. The second is that the trap intensity modulation with a well-controlled frequency is possible.

Fig. 1. The scheme of standard (solid line only) and two-laser (solid + dashed line) holographic optical tweezers.

least 100 µm away from the surface. Therefore, the influence of the glass-water interfaces can be neglected. The image of the sample was recorded with a high-precision fast video camera (5000 fps). In viscosity measurements (Section 5.2) the frame rate was reduced to 500fps due to thermal effects.

2.1. Experiment In the first experiment two traps were used - a zero-order diffraction (ZOD) beam and a holographically generated conventional Gaussian trap. The traps were separated by the distance of 4–5 µm and a 10 µm bead was placed between them. Since the bead experienced a peculiar tremor, a fast video camera was used to observe bead trajectory. Fig. 2

3. Two-laser tweezers The modified experimental setup is presented in Fig. 1 (including dashed line). Two major modifications to our standard optical tweezers were applied: (1) a laser of a different wavelength was introduced and (2) the first laser was connected to a waveform generator. As stated before, the two traps need to be separated by about a bead's radius distance. When they are closer, an interference pattern affects the bead's motion. The bead is either stuck within the central fringe or moves in an irregular way. However, the second laser of different wavelength abolishes the proximity limitation. A 1064 nm cw Nd:YAG laser (Laser Quantum Ventus, 4 W) is now driven by the electronic waveform generator. A signal of a desired shape and frequency is applied. In our experiment, a square-wave function of 50% duty cycle was chosen in order to achieve a ‘blinking’ character of the trap. Hence, the generator acts as an electronic shutter. The other cw solid-state laser diode (980 nm, 0.5 W) is introduced in the system to provide an additional constant (i.e. unmodulated) trap. With both beams on, the bead is held stably by the stronger trap.

Fig. 2. Bead center position in x-y plane within 1 s. The bead was moving between ZOD and conventional trap.

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Fig. 3. a) ZOD trap inside a vortex trap (m=30), imaged in the sample plane; b) trajectory of the bead center within 0.125 s (one period) in trap configuration shown in a). The bead was located in an annular dark region between two traps.

Fig. 4. Trajectory of the bead center within 0.125 s (one period). The bead was located in an annular dark region between the two traps (both holographically generated).

Fig. 5. The measured oscillations of the bead within 1.3 s. The movement was divided into 4 intervals: I – bead in the weaker trap, II – bead pulled towards the stronger trap, III – bead kept in a stronger trap, IV – bead returns to the weaker trap. The pattern is repeated periodically.

However, turning the strong beam off makes the particle settle in this secondary weaker trap. Thus, the bead is set into oscillations by periodically switching one of two generated traps. Both beams pass through the beamsplitter with 3:7 split ratio. This asymmetrical splitting is due to low power of the 980 nm laser. Its actual power in the sample plane was about 40 mW. The Nd:YAG beam power was reduced to 300 mW due to polarization attenuator and losses on the beamsplitter, SLM and objective.

amplitude of oscillations decreased. Hence, the bead moves within a limited path, shorter than the trap separation. The higher the frequency, the more significant drop of the oscillation amplitude. Eventually, it reaches the Brownian motion level. For f=100 Hz (Fig. 6c), a tremor-like plot was obtained. The bead has no time to reach the center of the stronger trap before it is switched off. Nevertheless, its Fourier transform (Fig. 7) reveals the driving frequency peak and its harmonics. The experiment was repeated for a larger bead (10 µm). The trajectory for 3 different modulation frequencies (1 Hz, 10 Hz, 100 Hz) was presented in Fig. 8a–c. Trap separation was about 5.8 µm. Due to the bigger size of the particle, there is a greater drag force acting upon it. Therefore, the bead moves slower and is pulled towards the stronger trap before it can reach the center of the weaker trap. As a result, the maximum distance made by the bead equals ~3.5 µm which is only about 60% of the trap separation. Also, increasing modulation frequency has a bigger influence on the amplitude drop. Changing frequency from 1 Hz to 10 Hz resulted in reducing the amplitude three times, whereas for the 4.5 µm bead the amplitude was only halved.

3.1. Experiment In our primary test, two Gaussian traps and a 4.5 µm bead were used. Traps were located away from each other within a distance providing maximum amplitude of oscillations. For low frequencies this amplitude was almost equal to trap separation (about 2.4 µm). The blinking frequency (i.e. the frequency of rectangular signal from the generator) was set to f=1 Hz. The bead was moving from one trap to another. This motion was stable in time and highly repeatable in a number of trials. The trajectory of bead's center was presented in Fig. 5 and Fig. 6a. Four characteristic intervals were observed. The particle starts from the position of the weaker trap (I), then gets attracted to the stronger beam (II), stays there for a half-period (III) and returns to its initial position (IV) after the blinking trap goes off. There is also a noise component due to the Brownian motion. After increasing the blinking frequency to f=10 Hz (Fig. 6b), the

4. Theoretical explanation In a typical experiment a polystyrene bead is trapped by a focused 84

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Fig. 6. The measured oscillations of 4.5 µm bead within 3 s corresponding to 3 different modulation frequencies; a) black line, f=1 Hz, b) blue line, f =10 Hz, c) green line, f=100 Hz. Trap separation: ~2.4 µm. One can notice that curves in Fig. 6 and Fig. 8 refer to the strong trap located at y=0 and the weak trap at y≈2.4 µm. This way the drop of the amplitude is more legible. Figs. 5, 9, 10, 13 refer to the opposite trap configuration (with the weak trap at y=0) and that is why they seem ‘inverted’. The inverted configuration is more comfortable for curve fitting and the theoretical formulas are more concise.

Fig. 7. Fourier transform of the bead's movement shown in Fig. 6c (green line). Multiple peaks are visible, corresponding to the modulation frequency (100 Hz) and its harmonics.

Fig. 8. The measured oscillations of 10 µm bead within 3 s corresponding to 3 different modulation frequencies; a) black line, f =1 Hz, b) blue line, f =10 Hz, c) green line, f=100 Hz. Trap separation: ~5.8 µm.

regime; L is separation between traps; k1, k2 – stiffness of the first (constant) and second (blinking) trap; m – mass of the bead; µ – dynamic viscosity of fluid; rb – radius of the bead; g(t) – periodic (e.g. square) function. The Reynolds number (R) is defined as the ratio of inertial forces to viscous forces and enables determination of different flow patterns. Due to the microscopic dimensions of the bead, small mass and relatively large fluid viscosity, very low (R«1) Reynolds number regime holds. Thus, the inertial term in the Eq. (1) is dominated by the drag term and can be neglected. This is a common procedure for analysing the bead

laser beam. Despite the trap is stable, the bead jumps randomly due to thermal forces [15]. The forces generated by a trap can be considered proportional to the bead displacement from the trap center (as in the case of a mass on a spring). In our experiment the bead jumps between the two traps. The thermal effects can be neglected when the jump distance is much larger than the amplitude of thermal oscillations. Thus, an equation of motion can be written:

m x ̈ + γ x ̇ + k1 x + k2 g (t ) x = k2 g (t ) L

(1)

where: γ = 6πµrb is the drag constant in the low Reynolds number 85

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dynamics in optical trap [16–18]. Applying the above, Eq. (1) may be rewritten in the form of:

⎧ γx ̇ + k1 x = 0 for ⎨ ⎩ γx ̇ + (k1 + k2 ) x = k2 L for

0 ≤ t < T /2 T /2 ≤ t < T

(2)

where T – is the period of the square signal (50% duty). For t=[0, T/2) the main beam is off; for t=[T/2, T) it is on. The solution to Eq. (2) may be written as: kw t ⎧ C1 e− γ ⎪ x (t ) = ⎨ (k + k ) t ⎪C2 e− w γ s + ⎩

ks L kw + ks

for

0≤t≤

for

T 2

T 2

≤t≤T

(3)

where C1, C2 are constants. The above solution was plotted in Fig. 9. According to Eq. (3) the oscillations of the bead consist of two parts. The first part, referring to the first half-period of movement, describes the particle attracted by the weaker trap while the stronger one is off. We use the term “relaxation curve” to emphasize the weakness of the force acting on the particle resulting in its slower motion in the first half-period. The second part, referring to the second half-period, corresponds to turning the stronger beam on. As a result, the bead is rapidly pulled out of its previous location and trapped by the main beam. It quickly reaches the center of the strong trap and stays there as long as the beam is on. The calculated bead behavior is in agreement with the observed one for the low modulation frequency.

Fig. 10. An example of fitting an exponential function to the relaxation curve.

laser setup, the source of relative motion is the bead itself as it oscillates between the two traps. The “relaxation” part of such movement ~ exp(k w t / γ ) = exp (−Dt ) does not depend on the strong trap stiffness. For known viscosity of fluid, therefore, the stiffness of the weaker trap can be calculated: (4)

k w = γ D = 6πμ rb D

The parameter D can be obtained by fitting an exponential function to the relaxation curve (Fig. 10). Exemplary results for a bead (rb =2.25 µm) in water are presented (Table 1). The blinking frequency was f=1 Hz and the distance between traps was L ≈2.8 µm. Dynamic viscosity of water in 27 °C according to [21] equals 0.853×10−3 Pa s. In order to improve accuracy, the measurements were repeated multiple times and the mean value and standard deviation were calculated. Stiffness of the weaker trap was estimated according to Eq. (4). The constant (i.e. not blinking) beam used in our experiment was so weak that it could hardly trap the bead and stabilize it in one position. In such a case, measuring trap stiffness with conventional methods would be difficult or even impossible. For instance, power spectrum method gives reliable results for stronger traps but it tends to fail in a weak trap regime, where the signal is dominated by substantial thermal fluctuations. Other passive techniques (e.g. equipartition method) are susceptible to the displacement noise [19] and, therefore, suffer from insufficient accuracy in low stiffness region. Nevertheless, we used equipartition method to estimate the trap stiffness. The bead was kept in a weak trap and the mean square displacement was measured. For a temperature T=27 °C we got kw=0.711pN/µm. It roughly coincides with the value obtained previously (kw=0.647pN/µm). To sum up, our variation of drag force method can be a solution for weak traps measurements. It can also be used to measure the stiffness of strong traps. The major advantage of the proposed technique is considerable accuracy and increased resistance to thermal motion. The resistance to noise was verified by conducting two series of measurements. In the first one, an external disturbance was introduced to the sample. It was achieved by placing a cooling system (two independently rotating fans) next to our optical tweezers setup on the same table. In the second one, fans were turned off and the sample was isolated from major external noises. In each series, weak trap stiffness was measured with our variation of drag force method. Subsequently, strong trap stiffness was examined with the standard method of fitting Lorentzian curve to power spectrum of Brownian motion of the trapped bead. Again, two series of measurements were performed: with and without the presence of additional noise compo-

5. Applications In this section the two different experiments are presented. Both are of practical value for the optical tweezers users. In the first experiment we measure the weak trap stiffness, which is a hard task due to thermal noise. In the second experiment the local viscosity measurements are discussed. 5.1. Weak trap stiffness measurements Several techniques of measuring optical trap stiffness have been known so far. They can be divided [19] into passive and active ones. In general, passive methods base on thermal motion of a trapped particle. Various approaches are used to determine trap stiffness, e.g. power spectral analysis [20], equipartition theorem or Boltzmann statistics. Active techniques are referred to as ‘drag force methods’ since the results strongly depend on fluid density and viscosity. They require a relative motion between a bead and surrounding medium, usually achieved by controllable movement of piezo-stage or trap focus displacement. We propose a new variation of the drag force method. In the two-

Table 1 Weak trap stiffness measurements for beads in water.

Fig. 9. Numerical simulation of Eq. (3) for parameters: µ=0.8·10−3 Pa s; rb=2.25 µm; L=2.5 µm; k1=8 pN/µm; k2 =0.5 pN/µm.

86

Dmean

kw [pN/µm] (for µwater =0.853 mPa s)

17.08 ± 0.34

0.647 ± 0.013

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Fig. 11. Power spectrum density with (a) and without (b) additional noise components caused by two rotating cooler fans. Induced frequency peaks in (a) are the reason of reduced accuracy for Lorentzian-fitting method.

Fig. 12. Mean stiffness (a) for strong trap (measured with conventional power spectrum method) and (b) for weak trap (measured with proposed drag force method). Percentage error was marked and its approximate value was presented. One can see that induced noise led to increased error for strong beam while in weak trap case the error did not change much.

Table 2 Refractive indices for different media (according to [28]) with simulated and measured (equipartition method) trapping efficiencies for 4.5 µm polystyrene (n=1.58) beads. Medium

Refractive index (20 °C)

Simulated trapping efficiency (compared to water)

Measured trapping efficiency (compared to water)

Water 20% glycerol solution (v/v) (≈ 24% (w/w)) 30% glycerol solution (v/v) (≈ 35% (w/w))

1.33303 1.36272

100% 96%

100% 96%

1.37740

93%

87%

“isolated” ones. Moreover, power spectrum method for the strong trap suffered from decreased accuracy caused by additional frequency peaks (Fig. 11a). For the weak trap, the presence of external disturbance had almost no influence on the accuracy, proving our drag force method resistant to noise. It should be noted here that no repeatable weak trap stiffness measurements can be done with power spectrum method. However, with our method such measurements can be performed even in noisy conditions.

Fig. 13. Comparison of bead trajectory for two media; a) water, b) 30% glycerol solution. Differences in viscosity of fluids are indicated by D parameter describing the shape of the relaxation curves (dotted red line).

nent. Power spectra for both cases were presented in Fig. 11. Trap stiffness measurements were repeated several times and the mean value, standard deviation and percentage error were calculated. The results are presented in Fig. 12. With the external noise, trap stiffness for both (strong and weak) beams was lower compared to the

5.2. Viscosity measurements A two-laser setup can be a tool for measuring local viscosity of a 87

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Table 3 Dynamic viscosity measurements for aqueous glycerol solution of two different concentrations (20%, 30%). Calculations made for a trap stiffness with and without the correction arising from refractive indices change. Experimental results were compared with literature values (based on formula described in [21]).

20% glycerol solution (v/v) 30% glycerol solution (v/v)

Dmean

µ [mPa s] (for kw =0.647 pN/µm)

µ [mPa s] (for corrected kw)

µ [mPa s] (from [23], 27 °C)

9.56 ± 0.23 6.0 ± 0.2

1.60 ± 0.04 2.56 ± 0.08

(for kw=0.621 pN/µm) 1.53 ± 0.04 (for kw=0.602 pN/µm) 2.37 ± 0.08

1.64 2.43

fluid. The idea of optical tweezers acting as microrheometer was developed by Ziemann, Bausch et al. [22–24]. In their work, magnetic beads were set into oscillations with a coil. As a result, magnetic tweezers were used for measuring viscoelastic moduli of various organic specimens. In a different report, linear viscoelastic shear moduli of complex fluids were extracted from laser deflection particle tracking (LDPT) [8]. Another approach describes local viscosity probed by the analysis of Brownian motion [6]. Our technique of probing dynamic viscosity of fluid is analogous to the method described in Section 5.1. The bead moves between a strong and a weak trap. Its trajectory exposes the differences in properties of surrounding media (Fig. 13). Assuming the stiffness of the weaker trap is known, Eq. (4) may be rewritten as:

μ=

kw 6π rb D

was set to lower value and heat transfer was decreased. The improvement in accuracy was observed but the heat influence was not entirely eliminated. The results show that the method works correctly. However, to get better results the halogen light should be replaced by non-thermal source (e.g. LED illumination) or a shortpass filter should be added to the setup. It can be seen from Table 3. that local viscosity was measured with the uncertainty of about 3–4%. Other papers report on uncertainty ranging from ~12–15% [6,7] to 10% [10]. Thus, proposed method brings an improvement in accuracy of local viscosity measurements. The size of the bead is of great importance and should be carefully chosen depending on the expected viscosity values. In general, sensitivity of measurement is higher for bigger particles. Nevertheless, the drag force acting upon a bead also increases, which may result in overdamping its oscillatory movement. Therefore, for relatively high viscosities, small beads should be applied.

(5)

Several experiments were performed concerning media of various viscosities. The results for 20% and 30% aqueous glycerol solutions were shown in Table 3. Firstly, we put kw=0.647 pN/µm which is the trap stiffness calculated in Section 5.1 for beads in water. However, replacing water with glycerol solution leads to change in a refractive index (Table 2.). As the refractive index increases, trapping efficiency lowers. It has been shown [25] that trap stiffness is proportional to trapping efficiency. As a result, the stiffness also gets reduced. Drop in trapping efficiency was estimated based on formulas described in [26,27]. Additionally, trapping efficiency was calculated with the equipartition theorem basing on a mean square displacement (MDS) of the bead in a given temperature. Here, in the extreme case (water vs. 30% glyc. sol.) the refractive indices difference is ~3% and trapping efficiency is ~7% lower for glycerol. We corrected the trap stiffness reducing it by 4% and 7% and recalculated viscosity (Table 2.). It can be seen that new results do not show a significant improvement in accuracy. Therefore, the correction procedure can be neglected for considerably small difference in refractive indices. The experimental results presented in Table 3. are in general agreement with literature values. However, a slight mismatch can be noticed. Due to nonzero light absorption by water in the near infrared region, the trapping laser beams affect the local temperature of the medium. Laser-induced heating (for 1064 nm) in optical traps was discussed in [29]. The estimated value at the strongly focused beam center was about 0.8 K/100 mW (for 500 nm silica bead). Thus, our beam should increase the temperature by ~2.5 K. In fact, this heating effect is lower. Our measurements are performed when the strong beam is off. The estimated thermal equilibrium time is lower than 10 ms. In contrast, the bead travels from the strong trap to the weak one within ∼0.5 s, i.e. 50 times longer. Moreover, the contribution to heating arising from the trapped particles is negligible (compared to the light absorption by solvent). In our measurements 4.5 µm beads were used providing that most of beam power enters the bead and only minor part traverses the medium, which lowers the heating effect. Since intensive external illumination is required for recording bead position with a CMOS camera in a fast-cam mode, a halogen lamp and a condenser were used in our system. The heat produced by the halogen lamp can locally increase the temperature of a sample. To minimize this effect, frame rate was reduced from 5000 fps to 500 fps, hence extending detector's exposure time. In this mode the lamp brightness

6. Conclusions We have demonstrated a two-laser optical tweezers with a periodically switched trap. The laser intensities and wavelengths were different. In fact, two different wavelengths are not necessary as long as they emerge from two separate sources (i.e. no interference occurs). The strong beam was driven by an electronic modulator, so the corresponding trap was blinking with the well-defined frequency. The weaker trap worked continuously. When the blinking frequency is low, the polystyrene bead returns to the center of the weak trap (when the strong trap is switched off). In this case a reliable trap stiffness measurement of the weak trap can be performed, even in the noisy environment. Measuring the stiffness of such a weak trap is impossible with conventional methods, even when the system is mechanically stable. Of course, the stiffness of much stronger trap can be measured in the same way. The blinking frequency and the distance between traps can be easily changed to find the best conditions for any particular situation. By applying two independent laser sources, harmful interference effects can be avoided. The local fluid viscosity can be measured in the same way (if trap stiffness is known). If the refractive indices of reference and investigated fluid are close, the resultant trap stiffness variation can be neglected. Otherwise, the trap stiffness must be recomputed using the formulas discussed in the literature. As we have noticed, the heat transfer from the lamp to the sample has detectable influence on the measurements. For this reason we have lowered the camera speed to 500fps. It is obvious that in the future experiments the cool light source should be used to improve the measurements accuracy. We have shown that two-laser optical tweezers system has important advantages. Introducing a second laser source to the setup of holographic optical tweezers is not complicated technically, so this modification can be done for any user working with a system with an open optical part. Moreover, the two-laser setup can be easily adopted for many other applications such as parametric oscillations modelling [30] or stochastic resonance studies [31]. References [1] Curtis JE, Koss BA, Grier DG. Dynamic holographic optical tweezers. Opt Commun 2002;207:169–75. [2] Jones PH, Volpe G. Optical tweezers: principles and applications. Cambridge

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