2.3.3 Force

As mentioned before, the calibration of force can be performed by different methods that allow to check the process. According to the experimental setup (Fig. 2.10), the instrument detects the change in the light momentum of the laser beams that form the optical trap, which allows us to directly measure the force accurately. There is a linear relation (see Eqs. 2.25 and 2.27) between the PSD reading and the actual force exerted on the bead by the optical trap, which can be written as

$\displaystyle [\mathrm{ForceY}]=[\mathrm{PSDy}]\times M_y + O_y$ (2.32)

where [ForceY] is the actual force on the $ y$ axis in pN, [PSDy] = [TrapAPsdY] + [TrapBPsdY] is the sum of the readings of the PSDs of both traps in the $ y$ direction, $ M_y$ is the calibration factor and $ O_y$ is a force offset, already corrected by the data acquisition board. The offset allows to make the reading of the [PSDy]=0 if the spot of the laser beam does not perfectly hit the center of the PSD detector when no force is applied. The value of $ M_y$ is independent of the trap power and the calibration protocols can be repeated at different laser powers as an extra test. It is important to mention that, unlike the measurement of distance, the force measurements are not normalized by the total power received. It is what makes the difference between a power-dependent magnitude (force) and a power-independent one (distance). Here we only show the method used in force calibration for the $ y$ axis. The same procedure applies to $ x$ and $ z$ axis. Three different methods were used to calibrate the PSD that measures the force.

JM Huguet 2014-02-12