  We compare theoretical, experimental, and computational approaches to random
rough surfaces. The aim is to produce rough surfaces with desirable
correlations and to analyze the correlation functions extracted from the
surface profiles. Physical applications include ultracold neutrons in a rough
waveguide, lateral electronic transport, and scattering of longwave particles
and waves. Results provide guidance on how to deal with experimental and
computational data on rough surfaces. A supplemental goal is to optimize the
neutron waveguide for GRANIT experiments. The measured correlators are
identified by fitting functions or by direct spectral analysis. The results are
used to compare the calculated observables with theoretical values. Because of
fluctuations, the fitting procedures lead to inaccurate physical results even
if the quality of the fit is very good unless one guesses the right shape of
the fitting function. Reliable extraction of the correlation function from the
measured surface profile seems virtually impossible without independent
information on the structure of the correlation function. Direct spectral
analysis of raw data rarely works better than the use of a "wrong" fitting
function. Analysis of surfaces with a large correlation radius is hindered by
the presence of domains and interdomain correlations.
