Determining equivalent dose for optically stimulated luminescence (OSL) dating with physically meaningful dose response curves

Non-linear dose–response curves are common in many thermoluminescence (TL) and optically stimulated luminescence (OSL) dosimetric applications, especially in TL and OSL dating. In most cases, these calibration curves are characterized by saturating exponential expressions; consequently, the accuracy of equivalent dose $D_e$ is highly dependent on the specific position along the saturating exponential curve. In the present work, accuracy is estimated through numerical simulations using novel analytical dose–response expressions based on the Lambert $W$ function. These simulations are subsequently extrapolated to experimental OSL dose–response curves obtained from dating experiments. The $D_e$ was estimated by solving the new dose–response expressions and the error ${\sigma }_{D_e}$, arising from the uncertainty of the natural signal, was evaluated through analytical expressions derived using error propagation theory. Finally, an analytical expression was derived for the derivative of the dose–response function, and the accuracy of $D_e$ correlated with the derivative at the point corresponding to the unknown dose. The newly derived analytical expressions, based on physical models, enable the determination of $D_e$ in both linear and non-linear regions of the dose response curves (DRC). This model offers a significant advantage over other existing empirical expressions, whose results lack theoretical justification. The present study offers a general and objective method to identify samples potentially affected by $D_e$ saturation, through direct evaluation of the derivative of the DRC.