We show how to control the relative radiation pressure and thereby the stable trap position of an optically trapped bead by variation of the mean incident axial photon momentum. The thermal position fluctuations of a trapped bead are recorded by a three-dimensional back-focal-plane interferometry. The interferometric detection signals are in agreement with predictions based on an extended Mie theory. Depending on the application, the unique and linear range of such a detection system can be optimized by controlling the trap position of the bead. We use this method to investigate in three dimensions the binding of beads to membranes of living cells during phagocytosis. We found that independent of the bead coating (IgG, complement, LPS, avidin) the most frequent initial mechanical response of the cell was a downward pulling of the bead into the cell. The time delay between binding and response was on average 2 s.