# What is "shape sensing packaging"? **URL:** \ **Category:** OFSCN Technical Knowledge Base\ **Tags:** fbg-technology\ **Created:** [August 4, 2026, 2:10pm UTC](https://forum.ofscn.net/t/what-is-shape-sensing-packaging/2482 "2026-08-04T14:10:45Z")\ **Posts on this page:** 2\ **Page:** 1
**Author:** ![VoidWalker](https://forum.ofscn.net/letter_avatar_proxy/v4/letter/v/848f3c/32.png) [@VoidWalker](https://forum.ofscn.net/u/VoidWalker)\ **Post date:** [August 4, 2026, 2:10pm UTC](https://forum.ofscn.net/t/what-is-shape-sensing-packaging/2482/1 "2026-08-04T14:10:45Z")
How to encapsulate three optical fibers together so that it can sense how it is bent? ---
**Author:** ![OFSCN\_Tech\_Expert](https://forum.ofscn.net/user_avatar/forum.ofscn.net/ofscn_tech_expert/32/199_2.png) [@OFSCN\_Tech\_Expert](https://forum.ofscn.net/u/OFSCN_Tech_Expert)\ **Post date:** [August 4, 2026, 2:11pm UTC](https://forum.ofscn.net/t/what-is-shape-sensing-packaging/2482/2 "2026-08-04T14:11:59Z")
Encapsulating three (or more) optical fibers together to perceive the bending morphology of three-dimensional space falls within the **core technical domain of Fiber Optic Shape Sensing**. Its underlying physical mechanism utilizes the **non-axial strain gradient** generated during material bending. * * * ### I. Physical Sensing Principle When a flexible structure undergoes bending: 1. **Neutral Axis** : Located at the center of the cross-section, its length remains unchanged, and the strain is zero. 2. **Tension on Outer Side & Compression on Inner Side** : Eccentric positions on the outer side of the bend experience tensile stress, resulting in positive strain (tension +\varepsilon); eccentric positions on the inner side of the bend experience compressive stress, resulting in negative strain (compression -\varepsilon). A single optical fiber can only measure one-dimensional axial strain (tension/compression), making it impossible to determine the physical direction of bending. To fully determine the **curvature (\\kappa)** and **bending angle (\\theta)** in a two-dimensional plane or three-dimensional space, it is necessary to place **at least 3 optical fibers** non-collinearly and off the neutral axis within the same cross-section (or use a multicore fiber with more than 3 eccentric cores). * * * ### II. Core Process Elements of Three-Fiber Shape Sensing Encapsulation To perfectly encapsulate three optical fibers together and accurately sense bending, engineering encapsulation needs to address the following four key issues: #### 1. Symmetrical Cross-Sectional Geometric Configuration (120^\circ Spatial Angle) The three optical fibers must be attached or embedded parallel to the periphery of a central substrate (e.g., flexible alloy filament, polymer core rod, etc.) at symmetrical 120^\circ intervals. This geometric symmetry ensures the orthogonal mathematical solvability for directional decoupling during the three-axis strain calculation. #### 2. No Slip Shear Strain Transfer (Rigid Curing Layer) High shear modulus special adhesives or continuous polymer composite encapsulation processes with high shear modulus must be used for close curing between the optical fiber and the substrate structure. **Relative slippage between the optical fiber and the substrate must be strictly prohibited**. If even minor relative displacement occurs at the interface, the micro-strain generated by bending will not be transmitted losslessly to the photosensitive units (e.g., Fiber Bragg Gratings, FBG) inside the optical fiber. #### 3. Precise Alignment of Longitudinal Measurement Points (FBG Arrays) On the three optical fibers, the positions of the etched Fiber Bragg Grating (FBG) measurement segments along the longitudinal axis (z-axis) must be strictly aligned. When calculating the bending parameters for a specific cross-section, the algorithm must extract the wavelength shift data from each of the three optical fibers at the same longitudinal position z\_i. #### 4. Temperature and Strain Decoupling (Common Mode Rejection) Environmental temperature changes cause isotropic thermal expansion of the optical fiber material, generating equivalent thermal strains (common-mode signals) on all three fibers. Bending deformation, however, produces differential strains that are opposite in direction (tension on the outer side, compression on the inner side). By performing differential calculations on the strains of the three optical fibers at the same cross-section, the interference from environmental temperature drift can be naturally eliminated, achieving pure bending measurement without temperature cross-sensitivity. * * * ### III. 3D Shape Reconstruction Mathematical Model At the same cross-sectional position z along the coordinate axis, the axial strains measured by the three optical fibers are denoted as \varepsilon\_1(z), \varepsilon\_2(z), and \varepsilon\_3(z), respectively. According to the geometric relationships in material mechanics, the bending curvature \kappa(z) at that position can be calculated: \kappa(z) = \frac{2}{3r} \sqrt{\varepsilon\_1^2 + \varepsilon\_2^2 + \varepsilon\_3^2 - \varepsilon\_1\varepsilon\_2 - \varepsilon\_2\varepsilon\_3 - \varepsilon\_3\varepsilon\_1} _(where r is the eccentricity radius of the optical fiber from the neutral axis of the cross-section)_ Simultaneously, the bending direction angle \theta(z) can be solved: \theta(z) = \arctan\left( \frac{\sqrt{3}(\varepsilon\_3 - \varepsilon\_2)}{2\varepsilon\_1 - \varepsilon\_2 - \varepsilon\_3} \right) By integrating the curvature \kappa(z) and angle \theta(z) at continuous measurement points along the fiber’s axial length using differential geometry (such as derived from Frenet-Serret frames or the transfer matrix method), the true bending posture and geometric trajectory of the entire fiber optic sensor in three-dimensional space can be fully reconstructed. * * * ### IV. Related OFSCN® Products and Solutions Beijing Dacheng Yongsheng Technology Co., Ltd. (OFSCN®), based on fiber Bragg grating encapsulation technology, offers standardized and customized products for shape sensing and multi-axis strain measurement: #### 1. Fiber Optic Shape Sensors Utilizing polymer and elastic alloy composite encapsulation processes, multiple FBG sensors are precisely encapsulated to achieve bending and posture monitoring of flexible structures. [OFSCN® Fiber Optic Shape Sensor](https://www.ofscn.net/fbg-products/shape.html) ![OFSCN® Fiber Optic Shape Sensor](https://forum.ofscn.net/uploads/default/original/1X/a8b8ae1c1af75ba21c051fd0c7cecc0f6e308c08.jpeg) ![OFSCN® Fiber Optic Shape Sensor](https://forum.ofscn.net/uploads/default/original/1X/a51b765e0437709fa6c14e5d3eabc60c147dc5e6.jpeg) #### 2. Multicore Fiber Gratings Employing single multicore optical fibers (MCF) with fiber grating arrays etched on different cores significantly reduces the outer diameter of the multi-axis strain sensing unit and the bending neutral axis deviation. [OFSCN® Bare Fiber Multicore Fiber Grating / FBG String](https://www.ofscn.net/fbg-products/multicore-fbg.html) #### 3. Fiber Optic Grating 3D Force Sensors 3 FBG measurement segments are longitudinally arranged at 120^\circ intervals around the circumference of a hard alloy substrate, used for precise measurement of multi-directional forces and bending vectors. [OFSCN® Fiber Optic Grating 3D Force Sensor](https://www.ofscn.net/fbg-products/pressure-sensor.html) ![OFSCN® Fiber Optic Grating 3D Force Sensor](https://forum.ofscn.net/uploads/default/original/1X/d0310a0ad3f2e375dd33aeba0ffee613a584add0.jpeg) ![OFSCN® Fiber Optic Grating 3D Force Sensor](https://forum.ofscn.net/uploads/default/original/1X/50d132976337ffe1806d5915eb0fd9a447e487d9.jpeg)