The optical tweezers we have built in the previous Chapter can trap and manipulate small objects. However, in order to perform more complex experiments, where, e.g., optical tweezers are used as sensitive force transducers to exert and measure forces ranging from tens of femtonewtons to hundreds of piconewtons, it is necessary to track the motion of the trapped objects and to measure the corresponding optical forces. In this Chapter, we will discuss how to do this using a trapped spherical particle. The position of several Brownian particles can be tracked by digital video microscopy with nanometre and millisecond resolution. It is also possible to employ interferometric techniques for more precise (down to a fraction of a nanometre) and faster (up to several tens of megahertz) measurements on a single Brownian particle. Knowing the trajectory of an optically trapped particle, it is possible to calibrate the optical trap, i.e., to obtain the value of the trap stiffness, using one of various alternative calibration procedures such as the mean square displacement analysis [Fig. 9.1a], the autocorrelation function analysis [Fig. 9.1b] and the power spectrum analysis [Fig. 9.1c], which we will also explore in this Chapter.
* This chapter was written together with Giuseppe Pesce.
9.1 Digital video microscopy
9.1.1 Digital cameras
9.2.2 Acquisition hardware
9.3 Calibration techniques: An overview
9.4 Potential analysis
9.5 Equipartition method
9.6 Mean squared displacement analysis
9.7 Autocorrelation analysis
9.7.1 Crosstalk analysis and reduction
9.8 Power spectrum analysis
9.8.1 Analytical least square fitting
9.8.2 Hydrodynamic corrections
9.8.3 Noise tests
9.9 Drag force method