From Displacement to Angle: Diamond-Based 3D Rotation Sensing for High-Precision Cellular Force Measurement

Cellular traction forces are conventionally measured by tracking the displacement of beads or micropillars and converting them to force via mechanical models. Although widely used, these displacement-based methods primarily report translational motion and, when based on the linear Euler-Bernoulli beam assumption, can suffer from geometric-nonlinearity errors under non-negligible deformation. Here we introduce an alternative approach: quantifying force by directly measuring pillar rotation angle rather than displacement, using fluorescent nanodiamonds (FNDs) as embedded 3D orientation markers. Specifically, by integrating optically detected magnetic resonance (ODMR) with laser polarization modulation (LPM), we determine the complete three‑dimensional orientation of FNDs attached to polydimethylsiloxane (PDMS) micropillars with sub‑degree precision (∼0.5°). This angle‑based measurement framework enables force reconstruction from pillar rotation and provides a robust analytical readout for stocky beams and large deformations. Finite‑element simulations demonstrate that our method reduces force estimation errors by at least 10% compared to linear displacement‑based approaches. Moreover, we successfully capture three-dimensional pillar deformations, including bending and in-plane rotation, that are inaccessible to the conventional displacement‑only method. Taken together, our work establishes diamond‑based angular force microscopy as a high‑precision platform for mechanobiology.