Panels (a–c): extinction–distance profiles for three PNe, with names labelled at the lower right. Sources and lines are colour-coded, as in Figure 2. Panel (d): residuals ΔD = D − D_Rfit, where D_Rfit is the distance predicted by the R_PN–distance fit for each PN. PN names are listed along the x-axis, with the adopted literature value of R_PN indicated below each PN. The data points adopt the colours from panels (a) to (c), with our determinations highlighted as black diamonds. All residuals are labelled above their respective points.