The height-height correlation function H(r) from a scale-invariant surface is compared with the corresponding power-spectrum function W(q) using a variety of mathematical scaling functions. We show that for a non-self-affine surface with the roughness exponent α≥1, one of the asymptotic scaling relations, either H(r)∼${\mathit{r}}^{2\mathrm{\alpha }}$ or W(q)∼${\mathit{q}}^{\mathrm{-}2\mathrm{\alpha }\mathrm{-}\mathit{d}}$, can be violated. An inconsistency in the values of α also exists between H(r) and W(q) when α>0.9. The impact on the data analysis using different experimental methods is discussed.

• Received 8 September 1994

DOI:https://doi.org/10.1103/PhysRevB.51.2479