Measuring 01-nm motion in 1 ms in an optical microscope with differential back-focal-plane detection

Back-focal-plane detection of micrometer-sized beads offers subnanometer resolution for single-molecule, optical trapping experiments. However, laser beam-pointing instability and mechanical drift of the microscope limit the resolution of optical-trapping experiments. By combining two infrared lasers with improved differential beam-pointing stability $\left(<0.05 \mathit{\mu }\mathrm{rad}\right)$, we simultaneously measure and subtract the motion of the microscope stage, leading to a resolution of $<0.1 \mathrm{nm}$ in 1 ms and stability of 0.5 nm over 60 s. Repeated steps of 0.4 nm at 1 Hz are resolved with a signal-to-noise ratio of 25.