An optically trapped particle works as an extremely sensitive probe for the measurement of pico- and femto-Newton forces in microscopic systems (Photonic Force Microscopy, PFM). A typical set-up (Fig. 1) comprises an optical trap to hold the probe particle and a position sensing system [1]. The latter uses either the forward-scattered (FS) or back-scattered (BS) field projected on a Quadrant Photon Detector (QPD) or a Position Sensitive Detector (PSD) to monitor the position of the particle. In the most common setup, the three-dimensional position is accurately determined by measuring the deflection of the FS-light transmitted through the bead (Fig. 1(a)). However, geometrical constraints may prevent access to this side of the trap, forcing one to make use of the BS-light instead. This happens, for example, when PFM is combined with other techniques, such as atomic force microscopy, which require access to one side of the chamber. In the literature, the use of the BS-light as a signal for position and force detection is mentioned, but not discussed extensively [2]. However, the detector response to the bead position may change significantly in this configuration (Fig. 1(b) and Fig. 1(c)). We, therefore, examine the situation theoretically using a Mie-Debye approach. We then compute the total (incident plus scattered) field and follow its evolution as it is collected by the condenser lenses and projected onto the position detectors in both the forward and backward configurations, comparing the responses of a PSD and a QPD to the displacement of the probe in the optical trap.
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