A study published in Scientific Reports presents an analytical framework for optical fiber angular displacement sensors (OFAS) that measures tilt angles in multiple directions. This model links detected light intensity with angular displacement and distance, addressing common challenges in fiber-optic sensing.
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Role of Optical Fiber Sensing Technology
Industry 5.0 emphasizes human-centered, sustainable, and resilient manufacturing, where advanced sensing technologies play a key role in enhancing interaction between humans and machines. Among these technologies, accurate tilt angle measurement is especially important in industrial automation and structural health monitoring, as misalignments can compromise safety and operational performance.
Optical fiber sensors (OFSs) 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 optical fiber displacement sensors (OFDS) detect changes in light reflected from tilted surfaces. However, many existing OFDS designs rely on trial-and-error calibration and struggle to measure tilt accurately in multiple directions without additional hardware.
This highlights the need for a more generalized model that can predict sensor behavior across different configurations and orientations.
Development of the Analytical Framework
Researchers developed a model using Gaussian beam optics to describe light propagation from a transmitting fiber (TF) to a reflective surface that may tilt in various directions. The model accounts for mirror tilt, light propagation based on the fiber’s numerical aperture (NA), and fiber positioning. It estimates the light captured by the receiving fiber (RF) by integrating the intensity across the RF surface.
To improve computational efficiency, the model uses a simplified formula based on the mean value theorem. This approximation performs well under standard conditions, including tilt angles up to ±20 °, distances up to 15 mm, and NA values between 0.09 and 0.45.
Five fiber bundle configurations were evaluated: bifurcated bundles (one TF and one RF), symmetric bundles (one TF with two RFs on opposite sides), differential bundles (two RFs at different distances on one side), trifurcated bundles (one TF surrounded by two rings of RFs), and a quasi-random 19-fiber arrangement with multiple TFs and RFs.
For each design, the model assesses sensor response as a function of fiber size, distance, NA, and tilt angle. Experiments used 660 nm laser light, precision movement equipment, detectors, and data acquisition tools. Four commercial bifurcated bundles with core sizes of 50 µm, 200 µm, and 600 µm, along with a custom trifurcated bundle, were tested to validate the model.
Sensor Response Characteristics
The results showed that bifurcated bundles respond clearly to tilt but may produce similar output signals at different distances, complicating interpretation. They also exhibited asymmetric behavior for positive and negative tilts, limiting bidirectional detection. Increasing fiber separation improved sensitivity but reduced range.
Symmetric bifurcated bundles provided more balanced responses. Taking the ratio of photodetector voltages helped reduce common noise, improving measurement consistency. The logarithmic response showed a near-linear relationship with tilt angle, aiding calibration. Differential bundles further reduced noise and provided more distinct signals, aiding in estimating both tilt and distance.
The quasi-random 19-fiber bundle exhibited highly symmetric responses and a wider measurement range. Using multiple fibers helped reduce alignment errors, improving reliability. Sensitivity analysis indicated that typical variations in fiber size and NA caused only small changes in output, with angular errors under 0.3 °, suggesting stable performance.
Applications and Practical Considerations
The OFAS designs and models presented are suited for compact and reliable tilt measurements. They have potential applications in structural monitoring of infrastructure such as bridges and dams, where early detection of tilt can inform maintenance. Industrial uses include machine alignment and turbine blade monitoring, where precision is important.
Due to their resistance to electromagnetic interference and suitability for demanding environments, these sensors are also applicable in aerospace systems, such as engine monitoring in aircraft. The trifurcated bundle’s ability to measure both tilt and distance while managing noise may be useful in complex scenarios.
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Conclusion
The study introduces a unified analytical model for intensity-based optical fiber angular displacement sensors, validated through experimental testing for tilt angles up to ±20 ° and distances up to 15 mm. Symmetric and differential configurations showed advantages in reducing noise and supporting multi-axis tilt detection with minimal calibration.
Future work may extend the model to cover larger tilt angles, non-specular surfaces, and dynamic operating conditions. Incorporating real-time processing could further improve resolution and reduce complexity. The alignment between model predictions and experimental results supports further development of practical, efficient optical fiber sensing solutions.
Journal Reference
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, https://www.nature.com/articles/s41598-025-05063-4
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