Exhaustive Analysis and Simple Model of an Angular Displacement Optical Fiber Sensor

Accurate tilt-angle measurement is vital in applications ranging from aerospace to civil infrastructure monitoring, especially under harsh conditions where conventional inclinometers may fail. Here, we present a comprehensive analytical model for multi-axis tilt sensing based on intensity-modulated optical fiber sensors (OFDSs). By capturing how a Gaussian beam, reflected from a tilted target, couples into arrays of receiving fibers, our model bridges geometric fiber parameters, numerical aperture, and target distance to predict the measured power for various tilt angles and axes. We validate its performance experimentally using multiple fiber-bundle configurations—bifurcated, trifurcated, symmetrical, and 19-fiber arrangements—demonstrating robust operation up to ±20º tilt over distances of up to 15 mm. In each case, the theoretical predictions match well with measured data, showing that differential or concentric fiber layouts suppress noise and eliminate ambiguities in tilt-direction detection. Compared to existing fiber-optic and mechanical inclinometers, our approach is simpler to fabricate, can be tailored to specific operational ranges, and remains highly resilient in electromagnetically harsh or space-limited environments. Moreover, we show how multi-fiber geometries enable axis-wise tilt discrimination and improved sensitivity through differential measurements. These findings highlight the potential for cost-effective, real-time, multi-axis tilt sensors that can address Industry 5.0 and advanced physics lab instrumentation needs. Future work will extend the sensor to larger angular spans and complex reflective surfaces, aiming to further broaden its applicability and reach.