Application of a Multiple Regression Model for the Simultaneous Measurement of Refractive Index and Temperature Based on an Interferometric Optical System

Abstract

Interferometric optical systems have been proposed for implementing dual-parameter optical sensors. For this type of sensors, the sensitivity matrix equation is generally used to determine the parameters to be measured based on the sensitivity of each parameter to one particular feature of the output reflective spectrum of the interferometric system. One of the disadvantages of this method is that the measurement ranges will be very short if the sensitivities are not linear or if these present cross-sensitivity. In this work, a multiple regression model for the simultaneous detection of refractive index and temperature based on an interferometric optical sensor is proposed. Here, the mathematical model is a weighted sum of features used to estimate the values of two response variables. These features are functions of an initial set of 27 explanatory variables whose values were extracted of the output reflective spectrum of the interferometric system. Besides, in order to sustenance the model application, the sensor was modeled and experimentally carried out. Three cases were studied: the estimation of temperature at different refractive indices, the estimation of temperature when refractive index is equal to one, and the estimation of refractive index at different temperatures. For each one of these cases, an optimal basis of functions was founded with the algorithm proposed and used to estimate the values of the response variables. Besides, a technique to reduce the initial set of variables was implemented. Finally, for the experimental data, For each one of these cases, an optimal basis of functions was founded with the algorithm 1 proposed and used to estimate the values of the response variables.