Fiber Bragg Grating (FBG) sensors enable precise 2D and 3D shape reconstruction by measuring strain-induced wavelength shifts along multi-core optical fibers.

Principles of FBG Shape Sensing

FBG sensors are short segments of optical fiber with periodic refractive index variations that reflect specific wavelengths of light. When the fiber bends or twists, strain alters the reflected Bragg wavelength, allowing the measurement of curvature and torsion along the fiber. By arranging multiple FBGs along a fiber or in multi-core configurations, the spatial distribution of strain can be used to reconstruct the shape of the fiber or the instrument it is embedded in .

Multi-Core Fiber Approaches

Modern shape sensing often uses multi-core fibers, such as 7-core fibers, where one central core is surrounded by six outer cores. By comparing wavelength shifts from different cores, both bending magnitude and orientation can be determined. This enables 2D and 3D shape reconstruction with high resolution and repeatability. For example, curvature resolution can reach 0.1 m⁻¹ in 2D, and angular errors in 3D reconstruction can be as low as 1.89° .

Computational Methods

Shape reconstruction can be performed using polynomial approximations or analytic geometry. Some methods fit polynomial coefficients to known bend configurations and model curvature as a function of these coefficients, allowing real-time tip position estimation without iterative numerical solutions. This approach achieves sub-millimeter accuracy (<0.1 mm) and is suitable for embedded or edge-computing applications .

Applications

FBG shape sensing is widely applied in:

• Medical robotics: Tracking the shape of catheters, needles, or continuum manipulators for minimally invasive surgery, with curvature detection sensitivity up to 5.50 nm/mm and shape reconstruction errors below 0.5 mm .
• Structural health monitoring: Detecting deformations in buildings, aircraft, and intelligent materials.
• Robotics and navigation: Enabling posture monitoring and closed-loop control in confined or complex environments .

Advantages

• High spatial resolution due to multiple FBG nodes along the fiber.
• Compact and flexible design suitable for confined spaces.
• Real-time monitoring with low computational requirements.
• Robustness against electromagnetic interference, making it ideal for medical and industrial applications . FBG-based shape sensing continues to evolve, with ongoing research improving accuracy, sensitivity, and integration into complex systems for both medical and industrial applications.