Conceptual framework for self-consistent extinction correction and plasma diagnostics. (a) The observed emission lines are combined into diagnostic line ratios. The ratios are combined pairwise to define c(Hβ) surfaces in the ﹩\mathrm{log}\,{n}_{{\rm{e}}}﹩–﹩\mathrm{log}\,{T}_{{\rm{e}}}﹩ plane (Equation (7)). (b) Multiple surfaces of this kind intersect at a common point, whose intersection identifies the optimized solution that is simultaneously consistent with the extinction and plasma conditions (Equations (8) and (9)).