Calibration and Uncertainty Evaluation of a Measurement System Using MLE: Application to a U-Bent RI POF-Sensor

In measurement systems, it is essential to have a procedure to obtain not only the calibration curve but also its associated uncertainty for the entire operating range. To achieve it, different alternatives should be taken into account according to the characteristics of the measurement, the way they are taken, the repeatability and reproducibility of the experiments or the nature of the measurement itself. This work presents a step-by-step procedure, to obtain simultaneously the calibration and uncertainty curves of a measurement system, which takes advantage of the maximum likelihood estimation (MLE), the weighted least squares (WLS) method, and the ISO-28037 recommendations. As an application, a U-Bent plastic optical fiber (POF) sensor measuring the sucrose solution density related to the refractive index (RI) is implemented and calibrated according to the proposed procedure.