Characterization of nonlinearities in the dose dependence of thermoluminescence

Nonlinearities often occur in the dose dependence of thermoluminescence (TL). These include sublinearity, usually when there is an approach to saturation in the dose dependence, as well as supralinearity, also termed superlinearity in the literature. Different researchers in the field have viewed the effect of supralinearity/superlinearity from two somewhat different points of view. One point of view has to do with the rate of change with dose of the dose dependence function. The other approach is related more to the applications of TL in dosimetry and archaeological and geological dating, and basically has to do with the correction to be made in extrapolation in cases where supra(super) linearity occurs following an initial linear dose range, or prior to such a linear range. In the present work we propose quantitative methods to characterize these nonlinearities. We suggest the use of two different nonlinearity indices, depending upon how one wishes to describe the nonlinearity. We propose use of the term "supra linearity index", f{hook}(D), in cases where the feature of interest is the deviation from linearity, namely, when the correction in extrapolation is the main issue. We propose the term "superlinearity index", g(D), in dose ranges where the growth is "more than linear" and when extrapolation is not the main issue. We mathematically define each of these indices and give examples of their use for different dose dependencies.