The central wavelength value that must be filled during the sensor edition corresponds to the wavelength (λ0 in nm) value from which the wavelength variation (x=Δλ, in nm) is calculated. This means that the result for the wavelength variation of a sensor in an instant t (xt, Δλt) is:
Where λt is the wavelength of the sensor measured at the instant t.
If the user’s purpose is to “zero” the measurements from an instant, the value to insert on the CWL field should be the value measured at that particular instant. On the other hand, if the user needs absolute measurements (as, for instance, on temperature sensors) the CWL to use should be the one defined on the Calibration Sheet that is provided with the sensor.
Using the temperature sensor example
On the Calibration Sheet of an HBM FiberSensing temperature sensor, the temperature is described
as a second order polynomial of the wavelength variation:
S2 is the second order sensitivity,
S1 is the first order sensitivity,
S0 is the temperature offset.
The S0 value corresponds to the reference temperature at the calibration procedure, so to get absolute temperature values the x has to be calculated using the same central wavelength from the calibration: the used CWL in the measurements has to be the same as the stated on the calibration sheet of the sensor.
Using the strain sensor example
The FBG based strain sensors dependence to deformation is:
Where k is the k factor of the strain sensor, and S is the strain sensitivity indicated on the calibration sheet.
This deformation will always be registered from an instant that is defined as “zero” meaning that the x value will always be calculated relatively to the wavelength that the sensor was exhibiting at the “zero” moment after the sensor installation.