What is "wavelength-to-physical quantity conversion"?

OFSCN Global Technical Center OFSCN Technical Knowledge Base
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How does the software automatically convert “nanometers” to “degrees Celsius” or “microstrain”?

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Fiber Bragg Grating (FBG) demodulation software converts “wavelength (nanometers \text{nm} or picometers \text{pm} )” in the spectrum to “temperature (^\circ\text{C} )” or “micro-strain ( \mu\varepsilon )”. Its core calculation process is based on optical sensing physical principles and factory calibration polynomial algorithms.

The entire automatic conversion process mainly involves the following steps:

I. Physical Mechanism and Wavelength Shift Extraction

The center reflection wavelength of a Fiber Bragg Grating (Bragg wavelength) 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 Variation: 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 photoelastic 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 reference initial state \lambda_0:

\Delta \lambda = \lambda - \lambda_0

II. Calibration Conversion Formula in Software

The demodulation software does not blindly convert; instead, it substitutes values into formulas based on the characteristic coefficients calibrated for each sensor during factory testing:

1. Strain Conversion (Usually a Linear Formula)

For fiber Bragg grating strain sensors, within the elastic deformation range, the wavelength shift has a very high linearity with strain. The calibration formula is typically expressed as:

\varepsilon = K_{\varepsilon} \cdot \Delta \lambda + \varepsilon_0
  • \varepsilon : Calculated micro-strain value (in \mu\varepsilon).
  • K_{\varepsilon} : Strain sensitivity calibration coefficient (units are usually \mu\varepsilon/\text{pm} or \mu\varepsilon/\text{nm}). The sensitivity of a standard bare single-mode fiber Bragg grating is typically around 1.2\ \text{pm}/\mu\varepsilon (i.e., the coefficient is approximately 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 Bragg gratings is approximately 10\ \text{pm}/^\circ\text{C}. Metal-packaged temperature sensors, due to the thermal expansion strain-sensitizing effect of the packaging material, typically have sensitivities ranging from 30\ \text{pm}/^\circ\text{C} \sim 40\ \text{pm}/^\circ\text{C}.
  • Wide Temperature Range or High-Temperature Range: Since the thermo-optic coefficient and thermal expansion coefficient are not constant values 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 simultaneously affected by 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 employs a temperature compensation module:

  1. Introduce a stress-free reference fiber Bragg grating temperature sensor in the same environment to measure the wavelength shift caused by ambient temperature variations in real-time, \Delta \lambda_T .
  2. The software subtracts the temperature-induced wavelength shift from the total shift: \Delta \lambda_{\varepsilon} = \Delta \lambda_{\text{total}} - \Delta \lambda_T .
  3. Substitute the net strain-induced wavelength shift \Delta \lambda_{\varepsilon} into the strain calibration polynomial to output the true micro-strain (\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 calculate wavelength shift \Delta \lambda \rightarrow call the sensor calibration coefficients and fitting polynomial configured for the corresponding channel \rightarrow output engineering physical quantities ( ^\circ\text{C} , \mu\varepsilon , \text{mm} , etc.) in real-time.