4.5.2.3 Grating Shapes and Groove Spacings
The idea of combining a grating with a spherical surface was known in the nineteenth century. Even today, spherical gratings are commonly used (Fig. 4.13).
Spherical gratings are a component of popular “Dragon” beamline designs
[103–105] which continue to be built, as well as constant focal length designs [106].
Focusing can also be achieved with a variable line spacing (VLS) grating
(Fig. 4.13). In these designs, the groove density along the grating surface follows
a polynomial formula, σ( y) ¼ σ 0 + σ 1 y + σ 2 y
2 + σ 3 y
3 , where the polynomial
coefficients are adjusted to minimize optical aberrations at a given wavelength
[107, 108].
It seems that there is still no perfect solution, as beamlines continue to be built
with blazed or laminar gratings, flat and spherical and VLS gratings. Combinations
of curved gratings with variable line spacing are also being explored [109]. For a
spectroscopist, the most important points are to know the (a) resolution and
(b) spectral purity of the radiation being delivered.
4.5.3 Zone Plates
Zone plates (another invention in Lord Rayleigh’s notebooks) are essentially circular, variable line space diffraction gratings (Fig. 4.14). They consist of a set of
circular, concentric rings that become narrower and closer together as they go from
the middle out to the edge. Their focusing properties are like a lens and are
approximately described by the thin lens formula 1/p + 1/q ¼ 1/f, where p and
q are the object and image distances and f is the focal length. Unlike a lens, a zone
plate has different diffraction orders and therefore multiple focal spots.
As shown in Fig. 4.14, the equation describing the required zone plate spacing is:
r n
2
¼ nf λ þ n
2
λ
2
=4
ð4:26Þ
Fig. 4.13 Left: the Rowland circle geometry, where the grating lies on the circle and the slits are
moved to collect different energies. Right: a VLS grating focuses different wavelengths from a
diverging source [108]
84
4 X-ray Optics and Synchrotron Beamlines
The idea of combining a grating with a spherical surface was known in the nineteenth century. Even today, spherical gratings are commonly used (Fig. 4.13).
Spherical gratings are a component of popular “Dragon” beamline designs
[103–105] which continue to be built, as well as constant focal length designs [106].
Focusing can also be achieved with a variable line spacing (VLS) grating
(Fig. 4.13). In these designs, the groove density along the grating surface follows
a polynomial formula, σ( y) ¼ σ 0 + σ 1 y + σ 2 y
2 + σ 3 y
3 , where the polynomial
coefficients are adjusted to minimize optical aberrations at a given wavelength
[107, 108].
It seems that there is still no perfect solution, as beamlines continue to be built
with blazed or laminar gratings, flat and spherical and VLS gratings. Combinations
of curved gratings with variable line spacing are also being explored [109]. For a
spectroscopist, the most important points are to know the (a) resolution and
(b) spectral purity of the radiation being delivered.
4.5.3 Zone Plates
Zone plates (another invention in Lord Rayleigh’s notebooks) are essentially circular, variable line space diffraction gratings (Fig. 4.14). They consist of a set of
circular, concentric rings that become narrower and closer together as they go from
the middle out to the edge. Their focusing properties are like a lens and are
approximately described by the thin lens formula 1/p + 1/q ¼ 1/f, where p and
q are the object and image distances and f is the focal length. Unlike a lens, a zone
plate has different diffraction orders and therefore multiple focal spots.
As shown in Fig. 4.14, the equation describing the required zone plate spacing is:
r n
2
¼ nf λ þ n
2
λ
2
=4
ð4:26Þ
Fig. 4.13 Left: the Rowland circle geometry, where the grating lies on the circle and the slits are
moved to collect different energies. Right: a VLS grating focuses different wavelengths from a
diverging source [108]
84
4 X-ray Optics and Synchrotron Beamlines