Optomechanical Modeling and Validation of a Distributed Bragg Reflector Force Sensor With Drift and Temperature Compensation

Distributed Bragg reflector fiber laser with the dual-polarization mode is commonly used as a sensing element in optical sensors. Lateral force on such a fiber induces birefringence and results in beating frequency generation in it. Also, the change in the magnitude of the lateral force is correlated to the shift in the beating frequency. This article presents a multi-physics optomechanical model for a fiber laser force sensor based on the birefringence phenomenon. To this end, a theoretical model for the sensing principle was developed through employing the elastic beam theory, Hertzian contact mechanics, and optical birefringence principle. Based on the linearity of the developed optomechanical model to the lateral force and ambient temperature variation, a multi-linear regression calibration for the force sensor was proposed and experimentally validated. Also, the temperature-induced drift in the beating frequency was compensated through exponential adjustment. Moreover, the calibration results showed a relatively small sensitivity for temperature sensing with respect to the external force (cross-talk). This phenomenon was predicted with the theoretical model. Verification of the calibration revealed a root-mean-square error of 0.12°C and 0.04 N for temperature and force sensing, respectively. Furthermore, the validation study showed a root-mean-square error of 0.04± 0.03 N and zero hysteresis for the developed sensor. Moreover, the theoretical sensitivity to external force was similar to the experimental results. For future applications, the compliance of the sensor specifications with the requirements of three surgical procedures was confirmed through comparison with the available literature.