The uncertainty of experimental derivatives: application to strain measurement

A procedure is presented to evaluate the uncertainty of derivatives computed from polynomial curves or surfaces fitted to experimental data. The procedure takes into account the uncertainties in the dependent and independent variables and agrees with international recommendations. It is valid independent of the experimental technique from which data are obtained. The application of the procedure is demonstrated by evaluating the uncertainty of strains calculated by differentiation of whole-field displacement data obtained by moiré interferometry.