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Force detection in optical tweezers using backscattered light

J. H. G. Huisstede, K. O. van der Werf, M. L. Bennink, and V. Subramaniam

Open Access Open Access

Abstract

In force-measuring optical tweezers applications the position of a trapped bead in the direction perpendicular to the laser beam is usually accurately determined by measuring the deflection of the light transmitted through the bead. In this paper we demonstrate that this position and thus the force exerted on the bead can be determined using the backscattered light. Measuring the deflection for a 2.50µm polystyrene bead with both a position sensitive detector (PSD) and a quadrant detector (QD) we found that the linear detection range for the PSD is approximately twice that for the QD. In a transmission-based setup no difference was found between both detector types. Using a PSD in both setups the linear detection range for 2.50µm beads was found to be approximately 0.50µm in both cases. Finally, for the reflection-based setup, parameters such as deflection sensitivity and linear detection range were considered as a function of bead diameter (in the range of 0.5–2.5µm). 140pN was the largest force obtained using 2.50µm beads.

©2005 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. Schematic overview of the optical trap in which the detection in transmission and reflection is indicated. For the transmission detection a condenser lens collects a part of the light transmitted by a trapped bead and directs it onto a position detector, which is positioned slightly behind the conjugate back focal plane of the condenser lens. In reflection the backscattered light is directed on a position detector using a beam splitter.

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Fig. 2.
Fig. 2. Schematic representation of the reflection-based optical tweezers setup. A beam expander provides overfilling of the back-aperture of a high NA objective. The laser power at this aperture is controlled by combining a half-wave plate and a polarizing beam splitter cube. A quarter-wave plate just in front of the objective provides circularly polarized light for the trap. A beam splitter directs the backscattered light onto a position sensitive detector where a second beam splitter in the detection path (indicated with the dotted line) enables visualizing the reflection pattern on a CCD camera (CCD1). A halogen lamp provides white light illumination for imaging the trapped bead via a dichroic mirror (DM) on a second CCD camera (CCD2).

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Fig. 3.
Fig. 3. Comparison between a PSD (black curve) and a QD (red curve) for a reflection-based OT setup. The bead size was 2.50µm. Three images of the reflection pattern are shown, recorded at a bead position of -0.6, 0.0 and +0.6µm. These positions are also indicated in the deflection curves with the numbers 1, 2 and 3, respectively. The lower error graph indicates the difference between the experimental data and a linear line (also shown), having a slope similar to the slope of the deflection curve around the center position of the bead. The error was calculated as the difference between these two lines, divided by the value of the linear line at 1.0µm, and expressed as a percentage. The dotted line in the error graph indicates an error of 5% used to determine the linear detection range of both the PSD and the QD. As a result the linear range, expressed relatively to the center position of the trapped bead, for the PSD is 0.57µm and for the QD 0.25µm.

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Fig. 4.
Fig. 4. Comparison between a PSD (black curve) and a QD (red curve) for a transmission-based OT setup. The bead size was 2.50µm. Three images of the reflection pattern are shown, recorded at a bead position of -0.6, 0.0 and +0.6µm. These positions are also indicated in the deflection curves with the numbers 1, 2 and 3, respectively. The lower error graph indicates the difference between the experimental data and a linear line (also shown), having a slope similar to the slope of the deflection curve around the center position of the bead. The error is calculated in a similar way as done for the reflection-based results shown in Fig. 3. The dotted line in the error graph indicates an error of 5% used to determine the linear detection range of both the PSD and the QD. As a result the linear range for both the PSD and the QD is 0.45µm.

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Fig. 5.
Fig. 5. Spectra for a 2.50µm bead at 170mW laser power acquired in a transmission-based and reflection-based OT setup. Furthermore the noise spectra without a trapped bead is plotted for both setups to pinpoint they are thermal noise limited. When no bead is trapped, for the transmission-based setup there is still a laser signal, but for the reflection-based setup it is not. Therefore the shot-noise limitation visible at higher frequencies, is higher for the reflection-based setup. The transmission-based setup, on the other hand, is still sensitive for mechanical and acoustical noise when no bead is trapped, appearing as 1/f-noise and several peaks for frequencies lower than 1kHz. The bandwidth of the detection system is 9.7kHz.

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Fig. 6.
Fig. 6. Position sensitive detector signal as a function of the bead position for different bead sizes, all acquired at 225mW laser trap power. For the 1.44 and 2.50µm bead the linear range is determined by the shape of the reflection pattern. The linear range for the 0.45 and 1.07µm bead is determined by the escape force, the maximum force that can be applied on the bead before it is pushed out of the trap.

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Tables (1)

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Table 1. Experimental Results for different bead sizes

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Equations (3)

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F → drag = γ v → = 6 π η r v →
S x ( f ) = k b T γ π 2 ( f c 2 + f 2 )
f ≪ f c ⇒ S x ( 0 ) ≈ k b T γ π 2 f c 2 = 4 γ k b T k tr 2
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