Brownian motion in a nonhomogeneous force field and photonic force microscope

The photonic force microscope (PFM) is an opto-mechanical technique that uses an optically trapped probe to measure forces in the range of pico to femto Newton. For a correct use of the PFM, the force field has to be homogeneous on the scale of the Brownian motion of the trapped probe. This condition implicates that the force field must be conservative, excluding the possibility of a rotational component. However, there are cases where these assumptions are not fulfilled. Here, we show how to expand the PFM technique in order to deal with these cases. We introduce the theory of this enhanced PFM and we propose a concrete analysis workflow to reconstruct the force field from the experimental time series of the probe position. Furthermore, we experimentally verify some particularly important cases, namely, the case of a conservative and of a rotational force field.