Optimal two-point static calibration of measurement systems with quadratic response

Two-point static calibration can be easily performed by any system having a minimal computation capability. Often, the reference inputs for that calibration are the end values of the measurement range. However, they are not the optimal selection because the resulting error is minimal only for those reference inputs, which are not necessarily those with most interest. This paper proposes two optimization criteria for the selection of calibration points that need reference inputs whose values do not depend on the nonlinearity of the actual response, provided this is quadratic. Both criteria give parallel calibration lines and can also be applied to other nonlinear responses if the measurement range is divided into convenient intervals. A numerical example shows the performance of each criterion, and their application to thermocouple linearization illustrates their advantage with respect to simple end-point linearization.