We investigated four different approximation models for describing the poly
chromatic reflectance and transmittance of a slab with a randomly rough bou
ndary while taking into account the coherent and the incoherent scattering
of the rough boundary. Comparisons with experiments (an etched-silicon wafe
r) show that approximation models that apply a two-scale roughness to the r
andomly rough boundary and that take into account the coherent and the inco
herent scattering yield better agreement and extend the range of validity o
f the approximation to shorter wavelengths. (C) 1999 Optical Society of Ame
rica.