Application of the generalized linear model to enable refractive index measurement with thermal sensitive interferometric sensors

In this work, the use of the generalized linear model (GLM) for refractive index detection, without dependence on temperature based on thermal sensitive interferometric arrangements is proposed. Here, the GLM was evaluated with four different link functions and the linear predictor was composed with a set of explanatory variables that represent different features of the interference pattern of the thermal sensitive interferometric arrangement. Besides, the refractive index sensor was modeled and experimentally implemented in order to support the technique. It is shown that the two models in which the sigmoidal and hyperbolic tangent link functions were used provided the best results. Moreover, it is shown that by using the stepwise regression technique, the number of explanatory variables can be reduced. Finally, for the experimental data, it is shown that by using the GLM with a sigmoidal function as a link function and a reduced set of 20 explanatory variables, the reached root mean square error and the determination coefficient were 0.0012 RIU and 0.9999, respectively for the refractive index range from 1.00 to 1.49 RIU.