4.5.2 Practical Grating Issues
The gratings used for X-ray beamline monochromators and analyzers usually consist
of a series of indentations or grooves in a glass or metal substrate, and they are used
in grazing incidence geometry, where each reflecting surface acts as a source. To
maximize monochromator efficiency, the optics designer can work with (1) the
coating material, (2) the geometry of the groove profile, and (3) the shape of the
substrate and the groove spacing.
4.5.2.1 Coatings
As we saw with mirrors, a high Z coating on a grating yields a higher refractive index
decrement δ and better reflectivity. Common coatings include gold, platinum, and
rhodium. It is important to remember that (just as with mirrors) the coating material
will introduce altered reflectivity in the region of its absorption edges. Even higher
efficiencies are now being achieved by adding multilayer coatings (described later in
this chapter) to the grating substrate [96–99]. The shape of the substrate will depend
on whether one uses the grating solely for dispersing the X-ray energies or whether
one also wants the grating to focus the X-rays.
4.5.2.2 Groove Profiles
Although the grating equation tells us where the diffraction peaks occurs, it does not
tell us about the relative intensity of different diffraction orders. When doing a
spectroscopy measurement in say first order, all of the photons going into the second
and higher orders (as well as zeroth order) are wasted. However (as suggested by
Rayleigh in 1874 [100]), by manipulating the shape of the individual grating lines,
one can alter the distribution of order intensity. Below we illustrate three types of
gratings: (a) “amplitude gratings,” (b) “blazed gratings,” and (c) “laminar gratings”
(or “lamellar gratings”) (Fig. 4.12).
The amplitude grating is the simplest type of grating, where only the lands
between the grooves contribute to diffraction (Fig. 4.12). If the land/groove ratio is
1:1, even with 100% reflectivity, the theoretical mth-order efficiency ε m is [102]:
ε 0 ¼ 25% ε m ¼ 100= mπ
ð Þ
2 % m ¼ Æ1, Æ 3, Æ 5, . . .
ð4:24Þ
For such a grating, most of the radiation goes into the zero-order reflection, where
the grating acts like a plane mirror, with no separation of different wavelengths.
A blazed grating has the diffracting lands cut at an angle, the “blaze angle,” with
respect to the mean grating surface. In principle, such a grating can approach 100%
82
4 X-ray Optics and Synchrotron Beamlines
The gratings used for X-ray beamline monochromators and analyzers usually consist
of a series of indentations or grooves in a glass or metal substrate, and they are used
in grazing incidence geometry, where each reflecting surface acts as a source. To
maximize monochromator efficiency, the optics designer can work with (1) the
coating material, (2) the geometry of the groove profile, and (3) the shape of the
substrate and the groove spacing.
4.5.2.1 Coatings
As we saw with mirrors, a high Z coating on a grating yields a higher refractive index
decrement δ and better reflectivity. Common coatings include gold, platinum, and
rhodium. It is important to remember that (just as with mirrors) the coating material
will introduce altered reflectivity in the region of its absorption edges. Even higher
efficiencies are now being achieved by adding multilayer coatings (described later in
this chapter) to the grating substrate [96–99]. The shape of the substrate will depend
on whether one uses the grating solely for dispersing the X-ray energies or whether
one also wants the grating to focus the X-rays.
4.5.2.2 Groove Profiles
Although the grating equation tells us where the diffraction peaks occurs, it does not
tell us about the relative intensity of different diffraction orders. When doing a
spectroscopy measurement in say first order, all of the photons going into the second
and higher orders (as well as zeroth order) are wasted. However (as suggested by
Rayleigh in 1874 [100]), by manipulating the shape of the individual grating lines,
one can alter the distribution of order intensity. Below we illustrate three types of
gratings: (a) “amplitude gratings,” (b) “blazed gratings,” and (c) “laminar gratings”
(or “lamellar gratings”) (Fig. 4.12).
The amplitude grating is the simplest type of grating, where only the lands
between the grooves contribute to diffraction (Fig. 4.12). If the land/groove ratio is
1:1, even with 100% reflectivity, the theoretical mth-order efficiency ε m is [102]:
ε 0 ¼ 25% ε m ¼ 100= mπ
ð Þ
2 % m ¼ Æ1, Æ 3, Æ 5, . . .
ð4:24Þ
For such a grating, most of the radiation goes into the zero-order reflection, where
the grating acts like a plane mirror, with no separation of different wavelengths.
A blazed grating has the diffracting lands cut at an angle, the “blaze angle,” with
respect to the mean grating surface. In principle, such a grating can approach 100%
82
4 X-ray Optics and Synchrotron Beamlines