Yazılım ″nanometre″leri ″santigrat ″ye veya ″mikro-gerilme″ye nasıl otomatik olarak dönüştürür?
Fiber Bragg Grating (FBG) demodulation software converts “wavelength (nanometers \text{nm} or picometers \text{pm} )” in the spectrum to “temperature (^\circ\text{C} )” or “microstrain (\mu\varepsilon )”. Its core calculation process is based on optical sensing physical principles and factory calibration polynomial algorithms.
The entire automatic conversion process is mainly divided into the following steps:
I. Physical Mechanism and Wavelength Shift Extraction
The center reflection wavelength (Bragg wavelength) of an FBG satisfies the Bragg condition:
\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 external physical quantities change:
- Temperature change: Due to the thermo-optic effect (n_{\text{eff}} changes with temperature) and thermal expansion effect (\Lambda expands with temperature), the reflection wavelength shifts.
- Strain/Deformation: Due to the photo-elastic effect (n_{\text{eff}} changes with strain) and mechanical stretching/compression (\Lambda changes), the reflection wavelength shifts.
The demodulator first identifies the current grating’s peak wavelength \lambda in real-time using peak-finding algorithms (such as Gaussian fitting, centroid method) and calculates the wavelength shift relative to the baseline initial state \lambda_0:
\Delta \lambda = \lambda - \lambda_0
II. Calibration Conversion Formulas in Software
The demodulation software does not blindly convert; instead, it substitutes values into formulas based on the characteristic coefficients calibrated for each sensor at the factory:
1. Strain Conversion (Usually a Linear Formula)
For fiber grating strain sensors, within the elastic deformation range, the wavelength shift is highly linear with strain. The calibration formula is usually expressed as:
\varepsilon = K_{\varepsilon} \cdot \Delta \lambda + \varepsilon_0
- \varepsilon: Calculated microstrain value (\mu\varepsilon).
- K_{\varepsilon}: Strain sensitivity calibration coefficient (unit is often \mu\varepsilon/\text{pm} or \mu\varepsilon/\text{nm}). The sensitivity of a standard bare single-mode fiber grating is typically around 1.2\ \text{pm}/\mu\varepsilon (i.e., the coefficient is about 0.833\ \mu\varepsilon/\text{pm}). Different packaging structures (such as steel tube packaging, strain gauge packaging) will have different specific coefficients.
2. Temperature Conversion (Linear or Quadratic Polynomial Formula)
- Narrow Temperature Range/Normal Temperature Range: A first-order linear formula can be used:T = K_T \cdot \Delta \lambda + T_0
The temperature sensitivity of bare fiber gratings is approximately 10\ \text{pm}/^\circ\text{C}; temperature sensors with metal packaging typically have a sensitivity of 30\ \text{pm}/^\circ\text{C} \sim 40\ \text{pm}/^\circ\text{C} due to the thermal expansion sensitization effect of the packaging materials.
- Wide or High Temperature Range: Since the thermo-optic coefficient and thermal expansion coefficient are not constant over a wide temperature range, a quadratic polynomial (binomial calibration formula) is usually used to ensure measurement accuracy:T = C_2 \cdot (\Delta \lambda)^2 + C_1 \cdot \Delta \lambda + C_0
The software directly calculates the temperature value in real-time by substituting the C_2, C_1, and C_0 coefficients provided by factory calibration.
III. Cross-Sensitivity and Temperature Compensation Algorithm
In actual strain measurements, the grating is affected by both strain and temperature (cross-sensitivity):
\Delta \lambda_{\text{total}} = \Delta \lambda_{\varepsilon} + \Delta \lambda_{T}
To automatically calculate the true “pure strain,” advanced demodulation software uses a temperature compensation module:
- Introduce a stress-free reference fiber grating temperature sensor in the same environment to measure the wavelength shift caused by ambient temperature changes, \Delta \lambda_T, in real-time.
- The software subtracts the temperature-induced wavelength shift from the total shift: \Delta \lambda_{\varepsilon} = \Delta \lambda_{\text{total}} - \Delta \lambda_T.
- Substitute the net strain-induced wavelength shift, \Delta \lambda_{\varepsilon}, into the strain calibration polynomial to output the true microstrain (\mu\varepsilon) after eliminating temperature interference.
Summary
The essence of automatic conversion by the software is: real-time spectral peak finding to obtain wavelength \rightarrow calculating wavelength shift \Delta \lambda \rightarrow calling the sensor calibration coefficients and fitting polynomial configured for the corresponding channel \rightarrow real-time output of engineering physical quantities (^\circ\text{C}, \mu\varepsilon, \text{mm}, etc.).