Optical Design
The RIXS branch covers an energy range from 400 to 1200 eV. In particular, the performance is optimized for energies in between the Cu L-edge (930 eV) and the O K-edge (532 eV). The resolving power of the RIXS branch is required to be better than 40,000 when the entrance and the exit slits are both set to 1 μm. Because the RIXS signal is very weak, the beamline needs to provide a high photon flux to improve the signal to noise ratio. However, the beamline resolving power is an inverse function of the beamline flux. One has to fi nd an optimization to balance the resolving power and the photon flux. Another important specifi cation is that the beam size at the sample is required to be smaller than 10 μm in the horizontal direction.
AGM-AGS optical design
The design of the AGM-AGS con figuration was fi rst reported in the 2003 SRI meeting held in San Francisco. The AGM-AGS con figuration is based on the energy compensation principle of grating dispersion; Figure 2 illustrates the optical arrangement in which two gratings with an identical central groove density and the same distance to the sample are employed. After passing through the entrance slit, X-rays are dispersed and focused by an active grating AG1 onto the sample. According to the reverse principle of light, the dispersed X-rays on the sample surface can in principle return to the entrance slit through the input light path. If there is a second active grating AG2 located at a position which has an identical central groove density and is at a distance to the sample as that of AG1, the scattered X-rays from the sample can be dispersed and focused similarly by the second active grating AG2 onto a position which corresponds to the entrance slit. For an incidence angle α and a dispersion angle β , the grating dispersion equation is
(sin α - sin β ) + k‧n0‧λ= 0; (eq. 1)
where k and n0 are, respectively, the diffaction order and the groove density at the grating center; λ is the wavelength of the dispersed light. For given k, n0, and α, the change in the dispersion of X-rays by AG1 along the direction perpendicular to the light propagation can be described as follows,
Δy = r2‧Δβ(λ); (eq. 2)
where Δβ is the angle between two principal dispersion lines. For example, as shown in Figure 2, Δβ = β (λ) - β (λ0). From the grating dispersion equation, it is straightforward to obtain that the dispersion change Δy due to the variation in wavelength Δλ is
Δy = ((r2‧k‧n0 )/cos β ) Δλ; (eq. 3)
If we consider the light starting from the AG2 side, i.e., the AG2 disperses and focuses the light onto the sample, the dispersion change at the sample can be described by Δy' = r'‧Δβ'. Hence Eq. 3 indicates that, if n0 = n0', α = α' and r2 = r2', X-rays of an identical energy but originated from the entrance slit and the CCD position can have an identical dispersion change at the sample, i.e., Δy = Δy'. In other words, the dispersion changes from AG1 and AG2 are identical if both gratings have the same optical parameters.
Figure 2 Principle of the energy compensation