Mathematical modelling for correlation between temperature and mechanical strain in long period gratings

Optical fiber sensors based on long period grating (LPG) are effective devices in sensing simultaneously temperature and mechanical strain. It was shown that different shifts in the resonant bands for the transmitted spectrum of an LPG sensor can be correlated with variation in temperature or mechanical strain. This paper presents the effects of non-linearity and cross-sensibility in the LPG resonance condition arising from combined effects of temperature and mechanical strain, proposing an adjustment coefficient in order to compensate these effects in a simple and effective way, reducing uncertainties in simultaneous measurements of temperature and mechanical strain.