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An FBG is sensitive to both strain (ε) and temperature (T) changes. In a simplified approximation, one can write:

Wwere λ is the FBG-wavelength; *λ** _{0}* the wavelength at an arbitrary reference strain ε

The above formula holds for *free* FBGs and not for FBGs which are fixed to a structure, like for strain gages. In this case, formula (1) should be modified slightly due to the influence of the thermal expansion of the structure. If the structure has a linear expansion coefficient α* _{t}* , then the thermal expansion of the structure is given by α

It needs to be noticed that a more accurate approximation of the DTG® response is given by the following function:

where λ* * is the DTG® wavelength; λ* _{0}* the nominal wavelength i.e. the wavelength at zero strain and at a fixed reference temperature

This more complex formula is important to use when large temperature variations are expected and is standard implemented for strain gauges in the Illumisense software of FBGS.

Typical values for S1, S2 and k are:

S1 = 6.37E-06

S2 = 7.46E-09

k = 0.772

assuming T expressed in °C and ε expressed in strain.

The thermal expansion coefficient of te fiber α_{f} is typical around 0.5 μstrain/°C

**Notice:** Parameters S1, S2 and α_{f} do not take into account the influence of the coating.