Why does each sensor come with a dedicated mathematical formula from the factory? OFSCN®
In Fiber Bragg Grating (FBG) sensing technology, the Calibration Formula serves as the mathematical bridge connecting the ‘optical reflection signal’ to the ‘actual engineering physical quantity’.
Simply put, when an FBG sensor is subjected to changes in physical quantities like temperature, strain, displacement, or pressure, its internal reflected center wavelength experiences a drift (measured in picometers, \text{pm}). While an FBG demodulator can only measure this reflected wavelength drift (typically denoted as \Delta \lambda), it cannot directly ascertain the current temperature or tensile force. To accurately convert the wavelength drift \Delta \lambda into the physical parameters required by the user (e.g., temperature \text{°C}, strain \mu\varepsilon), it is essential to rely on a unique calibration formula customized for the specific sensor at the factory.
The reason each sensor must be supplied with a unique mathematical formula upon leaving the factory is determined by its microscopic physical characteristics and complex packaging processes:
1. Microscopic Manufacturing and Fiber Substrate Individual Differences
Although Beijing Dacheng Yongsheng Technology Co., Ltd. (OFSCN®) utilizes high-precision UV lasers and phase masks for grating inscription, at the microscopic level, minute physical tolerances exist in the core doping concentration, geometric roundness, and grating period (\Lambda) of each fiber. This leads to variations in the initial center wavelength (\lambda_0) for each sensor under no-stress/normal temperature conditions. Since the starting point (baseline wavelength) differs, subsequent conversion calculations must be based on the specific initial value of that sensor.
2. Sensor Packaging Process and Material Mechanical Influence
Bare FBGs are extremely fragile and cannot be used directly in practical engineering environments, necessitating physical packaging. Beijing Dacheng Yongsheng Technology Co., Ltd. designs a variety of sensors for different applications:
- For example, the OFSCN® Alloy Tube Packaged Fiber Bragg Grating strain sensor uses an elastic alloy tube for packaging.
- The OFSCN® Polymer-encapsulated Fiber Bragg Grating Strain Sensor (1.5mm/2.3mm diameter) employs a composite packaging structure with polymer materials and steel tubes.
- The OFSCN® 300°C Fiber Bragg Grating Temperature Sensor is packaged in a seamless single-layer steel tube.
During the packaging process, factors such as the curing shrinkage rate of adhesives (like epoxy resin), minor variations in the wall thickness of metal tubes, and the pre-tension applied during production directly impact the sensor’s ‘strain transfer efficiency’ or thermal conductivity characteristics. This results in minor physical differences in sensitivity (i.e., sensitivity coefficient) to external physical changes, even between two sensors from the same batch with identical specifications. To eliminate this systematic error introduced by packaging, each sensor must undergo individual physical calibration.
3. Linear and Non-linear Grading of Physical Response
The relationship between external physical quantities and wavelength drift is not absolutely linear across all ranges:
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Linear Response (One-term Formula): For common temperature strain sensors, such as the OFSCN® Polymer-encapsulated Fiber Bragg Grating Strain Sensor (1.5mm/2.3mm diameter) or the OFSCN® Fiber Bragg Grating Displacement Sensor, the wavelength change exhibits a highly linear relationship with strain/displacement within their working range. Therefore, the factory calibration formula is typically one-term:
\text{Strain} = k \cdot \Delta \lambdawhere the sensitivity coefficient k is usually in units of \mu\varepsilon / \text{pm}.
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Non-linear Response (Two-term Formula): For temperature sensors across a wide temperature range, the temperature coefficients of fiber and metal packaging materials (thermo-optic and thermal expansion coefficients) vary non-linearly with temperature. Using a single linear coefficient would introduce significant errors. Consequently, sensors like the OFSCN® 300°C Fiber Bragg Grating Temperature Sensor or the OFSCN® 500°C Fiber Bragg Grating Temperature Sensor default to using a two-term (quadratic polynomial) calibration formula upon factory dispatch:
T = a \cdot ( \Delta \lambda )^2 + b \cdot ( \Delta \lambda ) + cHere, the calibration parameters include not only the linear term coefficient b but also the quadratic correction coefficient a. The calculation units for the two-term formula are \text{°C} / \text{pm}. For conventional temperature ranges, the OFSCN® 100°C Fiber Bragg Grating Temperature Sensor uses a linear one-term formula, which is sufficient to meet accuracy requirements.
4. Traceability Assurance for High-Precision Measurements
FBG sensing is often employed in high-precision applications such as aerospace, structural health monitoring of bridges and dams, and industrial high-voltage temperature monitoring. To guarantee the absolute accuracy of measurement values, each sensor shipped by Beijing Dacheng Yongsheng Technology Co., Ltd. is tested in high-precision calibration equipment (e.g., constant temperature calibration baths, precision universal material tensile testers). This involves collecting reflected wavelength data under a series of known standard conditions (e.g., actual reflected wavelengths measured at multiple calibration temperature points such as 0\text{°C}, 50\text{°C}, 100\text{°C}, etc.).
Through mathematical curve fitting using methods like least squares, the specific calibration parameters for each sensor (such as coefficient k in the one-term formula or coefficients a, b in the two-term formula) are derived in reverse. This ensures the accuracy and traceability of data measurements.
Summary
During actual deployment, users only need to input the exclusive calibration coefficients from the sensor’s certificate into the relevant channel of the FBG demodulator (or its accompanying data acquisition software). The demodulator will then automatically and in real-time convert the measured wavelength signals into high-precision physical parameters. This ‘one-object-one-formula’ design is the technical cornerstone that enables FBG sensors to achieve high scientific research accuracy and industrial reliability.