A control circuit operably couples to a non-invasive imaging system that utilizes a particular corresponding effective spectrum and receives imaging information as pertains to an object being imaged. The control circuit uses that information to identify the particular corresponding spectrum for the corresponding source of radiation by, at least in part, evaluating candidate spectra as a function, at least in part, of physical likelihood (for example, by identifying a spectrum that is physically unlikely or physically impossible). Evaluating the candidate spectra as a function of physical likelihood can comprise evaluating the candidate spectra with respect to regularization, smoothness, being non-negative, normalization characteristics, monotonic characteristics, envelope limitations, quasi-concave characteristics, and/or consistency with one or more physics models of choice to note but a few options in these regards.