Measurement of small forces using an optical trap

A simple and sensitive method for detecting small forces applied to an optically trapped microsphere utilizes the transmitted beam of the trapping laser to monitor microsphere deflections within the potential well of the trap. The rms dynamic displacement detection sensitivity measured in the frequency range from 1 Hz to 10 kHz is ∼1 nm in the radial direction and ∼10 nm along the z (optic) axis. Radiation trapping force constants were calibrated against viscous drag on microspheres in the range between the Rayleigh (r≪0.2λ) and Mie (r≫λ) size regimes. For a 1‐μm‐diam polystyrene sphere trapped with a 60 mW beam the rms spontaneous thermal motion limits the force sensitivity to better than 10^-12 N and lateral spatial resolution to ∼10 nm in a frequency range from 1 Hz to the viscous rolloff frequency ∼1 kHz. The measured maximum trapping efficiencies are compared with the theoretical predictions of the ray‐optics approximation.