Height-correlation dependence of coherent reflection
= Height-correlation dependence of coherent reflection
The quadratic coherent correction weights the <power spectrum of surface height> by $\beta(q)$, so equal <root mean square> heights can give different mean fields. Only an additional long-spatial-scale approximation, with spectrum concentrated at $|q|\ll k$, reduces it to $2k^2\sigma^2$. Second-order surface scattering therefore contains information absent from first-order coherent reflection.