Self-calibrating subpiconewton balance using optically levitated microspheres

The measurement of weak forces at the sub-piconewton scale is essential in a wide range of scientific and engineering applications. However, the performance of existing sensors is often constrained by limited sensitivity and intricate signal processing requirements. Here, we present a sub-piconewton force measurement apparatus with high sensitivity and resolution based on a weakly focused vertical optical levitation system. By employing an active null-balance method to counteract applied weak forces, this apparatus enables direct force measurement without the need to convert the force into intermediate variables. Experimental results demonstrate that this apparatus enables force measurement over a large linear dynamic range from -1000 fN to 1000 fN, with a resolution of 52 fN. This method provides a high-sensitivity platform for sub-piconewton force measurements and provides a potential foundation for future applications in micro-force metrology.