densities diffracts this parallel beam, and a cylindrical mirror focuses the radiation
onto the exit slit. The monochromatic beam is then refocused onto the sample. As a
representative performance, with the intermediate resolution (2000 l mm
À1 ) grating,
the beamline delivers ~10
12 photons s
À1 at 750 eV with a E/ΔE resolution of
~15,000 or 50 meV. The ADDRESS analyzer for RIXS experiments [153] will be
discussed in the Photon-In Photon-Out section (Chap. 8).
A variation on the PGM design is to use variable line spacing (VLS) gratings
[154]. This allows for beamlines to operate without slits and to achieve very high
resolution. The line spacing is varied so that the grating itself focuses a particular
wavelength at a given distance. Such a beamline at the APS (Fig. 4.28) provides
~10
10 s
À1 over the 250–1700 eV range with an E/ΔE of 50,000 [155].
A popular alternative approach is based on a spherical grating monochromator
(SGM) with a constant included angle in a variable Rowland circle geometry
(Fig. 4.28). This was first implemented by Chen and Sette at NSLS as the “Dragon”
beamline [103, 156]. In contrast with other beamlines discussed so far, it begins by
focusing instead of collimating in the vertical and in the horizontal (Fig. 4.28). After
passing through a slit, the beam is projected onto a spherical grating. The grating
works not only to monochromate the beam but also to focus it in the vertical onto the
exit slit. However, the focus position changes with the energy selected, so the exit slit
has to move as the energy is scanned. The design has been commercialized by
Horiba and is used at many light sources including the SRRC [157] and the Canadian
Light Source [158] (Fig. 4.28).
4.8 Suggested Exercises
1. Using the small angle approximation for cos θ, derive the expression for the
glancing angle for total external reflection: cos θ cg ¼ n 2 /n 1 .
2. Using tabulated indices of refraction, calculate the focal length and transmission
at 35 Å of a bi-concave carbon lens with a radius of curvature of 81 μm.
3. The EPU beamline at the ALS has a pre-mirror at a glancing angle of 1.9
.
(a) Estimate the reflectivity at 35 Å for a Au mirror at this angle, using δ ¼ 0.01
and β ¼ 0.009.
(b) Using tabulated values, estimate the reflectivity of the same mirror at
2.6 KeV.
(c) Would it be worthwhile to add a crystal mono for S K-edge work (see
Chap. 7)?
4. Suppose you are trying to build a multilayer mirror for capturing emission at the
nitrogen Kα fluorescence line (Appendix I). A Si/Ru multilayer can give a
reflectivity of better than 8% at 20
. Find a combination of materials and spacings
that will give (in principle) a better reflectivity. Why is the reflectivity better?
5. The Pohang Light Source has an undulator beamline with a 700 l/mm plane
grating monochromator. Assuming a glancing angle of 1.7
:
4.8 Suggested Exercises
103
onto the exit slit. The monochromatic beam is then refocused onto the sample. As a
representative performance, with the intermediate resolution (2000 l mm
À1 ) grating,
the beamline delivers ~10
12 photons s
À1 at 750 eV with a E/ΔE resolution of
~15,000 or 50 meV. The ADDRESS analyzer for RIXS experiments [153] will be
discussed in the Photon-In Photon-Out section (Chap. 8).
A variation on the PGM design is to use variable line spacing (VLS) gratings
[154]. This allows for beamlines to operate without slits and to achieve very high
resolution. The line spacing is varied so that the grating itself focuses a particular
wavelength at a given distance. Such a beamline at the APS (Fig. 4.28) provides
~10
10 s
À1 over the 250–1700 eV range with an E/ΔE of 50,000 [155].
A popular alternative approach is based on a spherical grating monochromator
(SGM) with a constant included angle in a variable Rowland circle geometry
(Fig. 4.28). This was first implemented by Chen and Sette at NSLS as the “Dragon”
beamline [103, 156]. In contrast with other beamlines discussed so far, it begins by
focusing instead of collimating in the vertical and in the horizontal (Fig. 4.28). After
passing through a slit, the beam is projected onto a spherical grating. The grating
works not only to monochromate the beam but also to focus it in the vertical onto the
exit slit. However, the focus position changes with the energy selected, so the exit slit
has to move as the energy is scanned. The design has been commercialized by
Horiba and is used at many light sources including the SRRC [157] and the Canadian
Light Source [158] (Fig. 4.28).
4.8 Suggested Exercises
1. Using the small angle approximation for cos θ, derive the expression for the
glancing angle for total external reflection: cos θ cg ¼ n 2 /n 1 .
2. Using tabulated indices of refraction, calculate the focal length and transmission
at 35 Å of a bi-concave carbon lens with a radius of curvature of 81 μm.
3. The EPU beamline at the ALS has a pre-mirror at a glancing angle of 1.9
.
(a) Estimate the reflectivity at 35 Å for a Au mirror at this angle, using δ ¼ 0.01
and β ¼ 0.009.
(b) Using tabulated values, estimate the reflectivity of the same mirror at
2.6 KeV.
(c) Would it be worthwhile to add a crystal mono for S K-edge work (see
Chap. 7)?
4. Suppose you are trying to build a multilayer mirror for capturing emission at the
nitrogen Kα fluorescence line (Appendix I). A Si/Ru multilayer can give a
reflectivity of better than 8% at 20
. Find a combination of materials and spacings
that will give (in principle) a better reflectivity. Why is the reflectivity better?
5. The Pohang Light Source has an undulator beamline with a 700 l/mm plane
grating monochromator. Assuming a glancing angle of 1.7
:
4.8 Suggested Exercises
103