Measurement of probe displacement to the thermal resolution limit in photonic force microscopy using a miniature quadrant photodetector

Abstract

A photonic force microscope comprises of an optically trapped micro-probe and a position detection system to track the motion of the probe. Signal collection for motion detection is often carried out using the backscattered light off the probe-however, this mode has problems of low S/N due to the small backscattering cross sections of the micro-probes typically used. The position sensors often used in these cases are quadrant photodetectors. To ensure maximum sensitivity of such detectors, it would help if the detector size matched with the detection beam radius after the condenser lens (which for backscattered detection would be the trapping objective itself). To suit this condition, we have used a miniature displacement sensor whose dimensions makes it ideal to work with 1:1 images of micrometer-sized trapped probes in the backscattering detection mode. The detector is based on the quadrant photo-integrated chip in the optical pick-up head of a compact disc player. Using this detector, we measured absolute displacements of an optically trapped 1.1 μm probe with a resolution of ∼10 nm for a bandwidth of 10 Hz at 95% significance without any sample or laser stabilization. We characterized our optical trap for different sized probes by measuring the power spectrum for each probe to 1% accuracy, and found that for 1.1 μm diameter probes, the noise in our position measurement matched the thermal resolution limit for averaging times up to 10 ms. We also achieved a linear response range of around 385 nm with cross talk between axes ≃4% for 1.1 μm diameter probes. The detector has extremely high bandwidth (few MHz) and low optical power threshold-other factors that can lead to its widespread use in photonic force microscopy.