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

Linjie Ma, Bicong Wang+4 more|arXiv (Cornell University)|Mar 6, 2026

Cellular Mechanics and Interactions0 citations

TL;DR

The paper introduces diamond-based angular force microscopy that measures 3D nanodiamond orientations via ODMR with laser polarization modulation to infer pillar forces, improving accuracy and capturing multi-dimensional deformations beyond displacement tracking.

ABSTRACT

Cellular traction forces are conventionally measured by tracking the displacement of beads or micropillars, an approach fundamentally limited by optical diffraction and the classical Euler-Bernoulli beam assumption, which is accurate only when the traction-induced deformation is relatively small while the aspect ratio of micropillars is large. Here we introduce an alternative approach: quantifying force through direct measurement of rotational angle, in addition of displacement of the micropillar, using fluorescent nanodiamonds 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 nanodiamonds attached to PDMS micropillars with sub-degree precision ($\sim$0.5$^\circ$). This angle-based measurement framework bypasses the resolution constraints of displacement tracking and remains valid for stocky beams or when large deformations occur. Finite-element simulations demonstrate that our method reduces force estimation errors by at least 10% compared to conventional displacement-based approaches. Moreover, we successfully capture multidimensional pillar deformations -- including bending and twisting -- that are inaccessible to conventional displacement-only method. Taken together, our work establishes diamond-based angular force microscopy as a high-precision platform for mechanobiology.

Motivation & Objective

• Motivate and enable high-precision cellular force measurements beyond displacement-based methods.
• Develop a framework to quantify force from rotational angles of embedded nanodiamonds on PDMS micropillars.
• Overcome diffraction and Euler-Bernoulli limitations for large deformations and stocky beam geometries.

Proposed method

• Embed fluorescent nanodiamonds in PDMS micropillars.
• Use optically detected magnetic resonance (ODMR) with laser polarization modulation (LPM) to determine full 3D nanodiamond orientation.
• Combine angle measurements with displacement data to compute forces.
• Validate with finite-element simulations comparing angular vs displacement-based force estimation.
• Demonstrate multi-dimensional pillar deformations including bending and twisting.

Experimental results

Research questions

• RQ1 Can 3D angular orientation of nanodiamonds be measured with sub-degree precision in a cellular-force context?
• RQ2 Does angular (rotation) data improve force estimation accuracy compared with traditional displacement-based methods?
• RQ3 What deformation modes (bending, twisting) become accessible with angle-based sensing?
• RQ4 How does the angular approach perform under large deformations or stocky pillar geometries?

Key findings

• Angular orientation of embedded nanodiamonds can be determined with approximately 0.5 degree precision.
• Finite-element simulations show at least a 10% reduction in force estimation error relative to displacement-based methods.
• The method enables capturing multidimensional pillar deformations (bending and twisting) not accessible by displacement-only approaches.