High sensitivity fiber optic angular displacement sensor and its application for detection of ultrasound

In this paper, we report the development of an intensity modulated fiber optic sensor for angular displacement measurement. This sensor was designed to present high sensitivity, linear response, wide bandwidth and, furthermore, to be simple and low cost. The sensor comprises two optical fibers, a positive lens, a reflective surface, an optical source, and a photodetector. A mathematical model was developed to determine and simulate the static characteristic curve of the sensor and to compare different sensor configurations regarding the core radii of the optical fibers. The simulation results showed that the sensor configurations tested are highly sensitive to small angle variation (in the range of microradians) with nonlinearity less than or equal to 1\%. The normalized sensitivity ranges from $(0.25\times V_{\rm max})$ to $(2.40\times V_{\rm max})$ mV/$\mu$rad (where $V_{\rm max}$ is the peak voltage of the static characteristic curve) and the linear range, from 194 to 1840 $\mu$rad. The unnormalized sensitivity for a reflective surface with reflectivity of 100\% was measured as 7.7 mV/$\mu$rad. The simulations were compared with experimental results to validate the mathematical model and to define the most suitable configuration for ultrasonic detection. The sensor was tested on the characterization of a piezoelectric transducer and as part of a laser ultrasonics setup. The velocity of the longitudinal, shear, and surface waves were measured on aluminum samples as 6.43 mm/$\mu$s, 3.17 mm/$\mu$s, 2.96 mm/$\mu$s, respectively, with an error smaller than 1.3\%. The sensor proved to be suitable to detect ultrasonic waves and to perform time-of-flight measurements and nondestructive inspection, being an alternative to the piezoelectric or the interferometric detectors.