  It has been known for years how random height variations of a repeated
nano-scale structure can give rise to smooth angular color variations instead
of the well-known diffraction pattern experienced if no randomization is
present. However, until now there has not been published any papers giving an
in-depth mathematical explanation on the mechanisms behind and how to design
the randomness for a given application. This paper presents a mathematical
framework for analyzing these random variations -- rigorously as well as
intuitively.
