462 Principles of Optical Fiber Grating Sensors increases. When using composite thermal compensation (e.g., with the liquid crys- tal polymer coating), the relative tensile strengths of the fiber and polymer must be taken into account [43]. Based on this principle, a loose tube version of this scheme has been implemented in which the tube was made of the oriented liquid crystal polymer [45]. 10.1.9 Fiber Bragg Grating Wavelength Temperature Compensation Techniques Of course, it is important to ensure that the dominant thermal expansion is from the contribution of the compensating scheme. This technique has been used to effectively compensate the sensitivity to the temperature in FBGs and Fig. 10.18 shows the compensation of the grating previously shown in Fig. 10.6. Residual thermal sensitivity is 0.8 pm- C À1 over a À40 to þ70 C range, with complete compensation over a few degrees around þ40 C. What is apparent in Fig. 10.18 is the nonlinear compensation of the grating. This is because the temperature dependence of the FBG is not linear and may be described as l B ¼ l 0 þ ADT þ BDT 2 þ . . . ; ð10:1:21Þ where A and B are constants, DT is the change in the temperature from a reference point, and l 0 is the Bragg wavelength at the reference temperature. It is therefore always possible to achieve absolute temperature compensation at some temperature, depending on the setting point of the compensator. For the Bragg wavelength to be insensitive to temperature, dl ¼ A þ 2BDT ¼ 0: dDT ð10:1:22Þ Wavelength, nm 1540.2 1540.0 ­40 ­20 0 20 40 Temperature, °C 60 80 Figure 10.18 A thermalized packaged FBG. Multiple graphs show the variation in the Bragg wavelength through temperature cycling. Note the nil variation in the wavelength as a function of temperature around þ40 C, which is the design wavelength for this compensator. The total variation in the wavelength is Æ45 pm over the 110 C temperature range.