A study published in Scientific Reports provides an analytical framework for Optical Fiber Angular Displacement Sensors (OFAS) that can measure tilt angles in multiple directions. This model correlates the detected light intensity with angular displacement and distance, addressing common challenges in fiber optic sensing.
The Role of Fiber Optic Sensing Technology
Industry 5.0 emphasizes human-centric, sustainable, and resilient manufacturing, where advanced sensing technologies play a crucial role in enhancing human-machine interaction. Among these technologies, precise tilt angle measurement is particularly important in industrial automation and structural health monitoring, as misalignment can affect safety and operational performance.
Fiber Optic Sensors (OFS) are particularly suitable for such applications due to their compact size, durability in harsh environments, and resistance to electromagnetic interference. They offer advantages over traditional mechanical or MEMS-based alternatives.
Within this category, intensity-modulated fiber displacement sensors (OFDS) can detect changes in reflected light from tilted surfaces. However, many existing fiber displacement sensor designs rely on trial-and-error calibration, making it difficult to accurately measure tilt in multiple directions without additional hardware.
This highlights the need for a more universal model to predict sensor behavior under different configurations and orientations.
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Development of the Analytical Framework
Researchers developed a model using Gaussian beam optics to describe the propagation of light from the transmitting fiber (TF) to a reflective surface that may tilt in different directions. This model considers mirror tilt, light propagation based on fiber numerical aperture (NA), and fiber positioning. It estimates the light captured by the receiving fiber (RF) by integrating the intensity over the entire RF surface.
To improve computational efficiency, the model employs a simplified formula based on the mean value theorem. This approximation performs well under standard conditions, including tilt angles of ±20°, distances of up to 15 mm, and NA values between 0.09 and 0.45.
Five fiber bundle configurations were evaluated: bifurcated fiber bundle (one TF and one RF), symmetric fiber bundle (one TF, two RFs on opposite sides), differential fiber bundle (two RFs at different distances on one side), trifurcated fiber bundle (one TF surrounded by two ring RFs), and a quasi-random 19-fiber arrangement with multiple TFs and RFs.
For each design, the model assesses the sensor response as a function of fiber size, distance, NA, and tilt angle. Experiments utilized a 660 nm laser, precision moving devices, detectors, and data acquisition tools. To validate the model, tests were conducted on four commercial bifurcated fiber bundles with core sizes of 50 microns, 200 microns, and 600 microns, as well as a custom trifurcated fiber bundle.
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Sensor Response Characteristics
Results indicate that bifurcated bundles respond significantly to tilt, but may produce similar output signals at different distances, complicating interpretation. They also exhibit asymmetric behavior for positive and negative tilts, limiting bidirectional detection. Increasing fiber spacing can enhance sensitivity but reduces range.
Symmetric bifurcated fiber bundles provide a more balanced response. Utilizing the ratio of the photodetector voltage helps reduce common noise and improve measurement consistency. The logarithmic response is approximately linearly related to the tilt angle, aiding calibration. Differential bundles further reduce noise and provide clearer signals, assisting in estimating tilt and distance.
The quasi-random 19-fiber bundle shows highly symmetric responses and a wider measurement range. Using multiple fibers helps reduce alignment errors and improve reliability. Sensitivity analysis indicates that typical variations in fiber size and NA result in only minor changes in output, with angle errors below 0.3°, indicating stable performance.
Applications and Practical Considerations
The OFAS design and model presented are suitable for compact, reliable tilt measurement. They hold potential application value in structural monitoring of infrastructure such as bridges and dams, where early detection of tilt can inform maintenance. Industrial applications include machine calibration and turbine blade monitoring, which require high precision.
Due to their resistance to electromagnetic interference, these sensors are also suitable for harsh environments, making them applicable in aerospace systems, such as aircraft engine monitoring. The trifurcated bundle can measure both tilt and distance while controlling noise, which may be very useful in complex application scenarios.
Conclusion
This study introduces a unified analytical model for intensity-based optical fiber angular displacement sensors, validated through experimental tests with tilt angles of ±20° and distances of up to 15 mm. Symmetric and differential configurations demonstrate advantages in reducing noise and supporting multi-axis tilt detection with minimal calibration.
Future work may extend this model to cover larger tilt angles, non-mirror surfaces, and dynamic working conditions. Combining real-time processing could further enhance resolution and reduce complexity. The agreement between model predictions and experimental results aids in the further development of practical, efficient fiber sensing solutions.
References:Zubia, G., et al. (2025). Exhaustive analysis and simple model of an angular displacement optical fiber sensor. Sci Rep.
DOI: 10.1038/s41598-025-05063-4
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