Recently the possibility of focusing, imaging and spectroscopy with Fr
esnel zones etched on a flat multilayer substrate instead of a curved
substrate has been shown. This is now known as Bragg-Fresnel Multilaye
r lenses (BFML). Lamellar gratings etched in a multilayer (LMG) are th
e basic type of Bragg-Fresnel optics. In this paper we describe import
ant points in the fabrication, computer simulation, and testing of the
LMs. They can be very interesting as a spectroscopic device with a re
latively high dispersion and efficiency. We develop a rigorous theory
of diffraction combined with the layer-by-layer differential integrati
on numerical method. The agreement with experimentals results obtained
for a lamellar grating with several period and various etched depths
in a W/Si multilayer is very good. The main result is an increase of t
he effective extinction depth (t(ext)) in short-period gratings which
gives a possibility to increase the absolute diffraction efficiency of
the LGM practically from 30% to 60% in the first order with a totally
suppressed zero order.