The paper is devoted to a theoretical and numerical study of lacunary
gratings, namely, gratings where some lines are missing. From a rigoro
us electromagnetic theory of scattering by this structure, the limits
of validity of three approximate and simple theories are given. These
approximate theories are used in order to predict some interesting pro
perties of lacunary gratings. Finally, we try to give a quantitative a
nswer to the following question: how to detect the lacunary defect rat
io from intensity measurements?