Development of a distributed three-dimensional inclinometer based on OFDR technology and the Frenet-Serret equations

The inclinometer is a vital tool for monitoring internal displacement in slopes. However, existing fiber-optic inclinometers lack the ability to monitor three-dimensional deformation. To overcome this limitation, this study introduces a novel distributed inclinometer based on Optical Frequency Domain Reflectometer (OFDR) technology. The inclinometer uses Frenet-Serret equations to achieve three-dimensional displacement calculation. To validate the proposed method and the feasibility of the OFDR inclinometer, finite element analysis and experimental testing are conducted. A comparison is made between the proposed method and the conjugate beam and finite difference algorithm. The results demonstrate the reliability of the displacement calculation. The distributed inclinometer developed based on the Frenet-Serret equations and OFDR technology can achieve three-dimensional deformation measurement in space. The measurement results are satisfactory, with the maximum errors in the OFDR inclinometer's measurements per unit length being within 0.45%. This capability enables effective measurement of internal displacement within slopes.