Optical tweezers calibration

In order to make calibrated measurements from single molecules two more items are required (1) a four-quadrant photodiode position sensor (4QD) to accurately measure the position of the bead held in the optical tweezer (Figure 12.5) (2) a piezoelectric substage to enable controlled movements to the specimen during the experiments and in order to calibrate the system. Both of these components can be interfaced to the computer using A/D and D/A convertors. 

Figure 12.5 Position calibration. Left a bead is held in the optical tweezers and a 1 Hz squarewave oscillation is applied to the AODs the displacements are (a) 50, (b) 100, (c) 200 and (d) 500 nm. Right a large amplitude triangle wave is applied to the AODs to move the bead held in the optical tweezer over the full active area of the detector. The sensitivity is greatest when the bead is in the centre of the 4QD. Ideally the image of the bead held in the optical tweezers should be approximately half the size of the 4QD. This gives greatest sensitivity and suflident detector range to perform experiments...

Stokes calibration involves applying a known viscous drag force to a bead held in the optical tweezer and recording how far it is displaced from the tweezer centre. Application of a triangle wave oscillation of known size and frequency to the specimen chamber with the piezoelectric substage produces a viscous drag force given by Stoke s law... 

Figure 12.6 Calibration of trap stiffness using Stokes drag. The stiffness of the trap can be determined using Stokes drag force. A triangle wave is applied to the stage which holds the specimen chamber while a bead is held in the optical tweezer. The rapid movement of the stage creates a force, F, on the bead caused by the motion of the surrounding fluid. This causes the bead to be displaced a distance, x, from the trap centre the greater the system stiffness the less the bead is displaced. f/X= stiffness of the tweezers K) (inset)...

Figure 12.7 CaLibration of trap stiffness by thermal noise analysis. A single 1.1 jim bead is held in the optical tweezers and data is collected at 2 kHz. (a) The graph shows the bead position vs time -solid lines denote 1 standard deviation of bead position, (b) The same data plotted as a histogram. The mean displacement is 0 nm and the variance is determined by the vibration due to brownian noise, (c) The trap stiffness can be determined from this information using the equipartition principle lf2Ktrsj, x ) = l/2ksT, where Ktrap trap stiffness, (x ) = variance, /fB= Boltzman constant and T= absolute temperature...

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