Quantitative measurements of force and displacement using an optical trap.

We combined a single-beam gradient optical trap with a high-resolution photodiode position detector to show that an optical trap can be used to make quantitative measurements of nanometer displacements and piconewton forces with millisecond resolution. When an external force is applied to a micron-sized bead held by an optical trap, the bead is displaced from the center of the trap by an amount proportional to the applied force. When the applied force is changed rapidly, the rise time of the displacement is on the millisecond time scale, and thus a trapped bead can be used as a force transducer. The performance can be enhanced by a feedback circuit so that the position of the trap moves by means of acousto-optic modulators to exert a force equal and opposite to the external force applied to the bead. In this case the position of the trap can be used to measure the applied force. We consider parameters of the trapped bead such as stiffness and response time as a function of bead diameter and laser beam power and compare the results with recent ray-optic calculations.