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 he 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.

Automated summary

In measurement systems, it is crucial to obtain both the calibration curve and its associated uncertainty for the entire operating range. Different methods should be considered based on the characteristics of the measurement and nature of the experiments. This study presents a step-by-step procedure to simultaneously obtain calibration and uncertainty curves, using MLE, WLS, and ISO-28037 recommendations, as demonstrated in the calibration of a U-Bent plastic optical fiber sensor measuring sucrose solution density related to RI.