# What is the "calibration coefficient"?

**URL:** <https://forum.ofscn.net/t/what-is-the-calibration-coefficient/2753>\
**Category:** OFSCN Technical Knowledge Base\
**Tags:** fbg-technology\
**Created:** [September 7, 2026, 3:17pm UTC](https://forum.ofscn.net/t/what-is-the-calibration-coefficient/2753 "2026-09-07T15:17:57Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![VoidWalker](https://forum.ofscn.net/letter_avatar_proxy/v4/letter/v/848f3c/32.png) [@VoidWalker](https://forum.ofscn.net/u/VoidWalker)\
**Post date:** [September 7, 2026, 3:17pm UTC](https://forum.ofscn.net/t/what-is-the-calibration-coefficient/2753/1 "2026-09-07T15:17:57Z")

</div>

Why do I have to enter the number from the sensor certificate into the software?

---

<div class="post-metadata">

**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:** [September 7, 2026, 3:19pm UTC](https://forum.ofscn.net/t/what-is-the-calibration-coefficient/2753/2 "2026-09-07T15:19:54Z")

</div>

The only raw quantity directly measured by Fiber Bragg Grating (FBG) demodulators at the physical layer is the **optical wavelength (Wavelength, typically in nm or pm)**, not the finally required engineering physical quantities like temperature (°C), strain (με), pressure, or stress.

Those numbers on the sensor’s Calibration Certificate are the **Calibration Coefficients (or sensitivity parameters)** for that specific sensor. The reason for inputting them into the core of the demodulation analysis software is as follows:

* * *

### 1. Implementing the Mathematical Conversion from “Wavelength Drift Amount → Physical Engineering Quantity”

According to the principle of Fiber Bragg Grating sensing, the Bragg reflection wavelength \lambda\_B satisfies the formula:

\lambda\_B = 2 n\_{\text{eff}} \Lambda

where n\_{\text{eff}} is the effective refractive index of the fiber core and \Lambda is the grating period. When the sensor is subjected to external temperature or mechanical strain changes, the thermo-optic effect, thermal expansion effect, or photoelastic effect causes a wavelength shift \Delta\lambda.

The demodulator can only recognize the position change of the reflection spectrum peak (\Delta\lambda = \lambda\_t - \lambda\_0). The demodulation software must rely on the functional relationship defined by the calibration coefficients to calculate and display the measured picometer (pm)-level wavelength drift in engineering units.

* * *

### 2. Matching Mathematical Models (Linear and Polynomial) for Different Physical Quantities and Temperature Ranges

Different types of fiber Bragg grating sensors and their operating temperature ranges have distinct physical response characteristics, and the coefficients on the certificate correspond to different conversion mathematical models:

1. **Linear Model (First-order Polynomial):**
  - **Strain Sensors:** OFSCN® metal-tubing or polymer-encapsulated fiber Bragg grating strain sensors typically exhibit excellent linearity at room temperature, with their calibration formula being a first-order polynomial:
\Delta\varepsilon = K \cdot \Delta\lambda
The unit of the calibration coefficient K in the formula is usually \mu\varepsilon/\text{pm}.
  - **Room Temperature/Low-Temperature Sensors:** For temperature sensors with a 100\ ^\circ\text{C} specification, the calibration formula usually employs a first-order polynomial (in units of ^\circ\text{C}/\text{pm}).

2. **Non-linear Correction Model (Second-order Polynomial):**
  - **Mid-to-High Temperature Sensors:** When operating in wider or higher temperature ranges (e.g., 300\ ^\circ\text{C}, 500\ ^\circ\text{C}, 800\ ^\circ\text{C}), the thermal expansion coefficient of the encapsulation metal structure and the thermo-optic coefficient of silica fiber exhibit non-linear changes with increasing temperature. Therefore, the factory calibration formula is typically a second-order polynomial:
T = A \cdot (\Delta\lambda)^2 + B \cdot \Delta\lambda + C
The multiple parameters on the certificate are the coefficients for the quadratic term A, the linear term B, and the constant term C (units are usually fitted based on ^\circ\text{C}/\text{pm}). Inputting these coefficients corrects for non-linear errors at high temperatures, ensuring measurement accuracy across the full range.

* * *

### 3. Eliminating Manufacturing Tolerances and Individual Differences

During the writing, cutting, assembly, and curing of seamless metal tubes or elastomer encapsulation of fiber gratings, there are minor mechanical processing tolerances, slight differences in pre-tension, and variations in interfacial shear strain transfer efficiency.

Therefore, each sensor undergoes multi-point experimental fitting in a metrology-grade reference test environment (such as a high-precision constant temperature bath, oven, or material testing machine) before leaving the factory. The calibration coefficients on the certificate represent the **exclusive and true physical response characteristics** of that specific sensor. Inputting accurate calibration coefficients is a necessary prerequisite for ensuring the traceability and measurement accuracy of the testing system.