On obtaining high spectral resolution in extreme ultraviolet/soft X-ray monochromators operating off-plane diffraction in a divergent incident beam.

When the trajectory of an incident beam is oriented parallel to the grooves of a periodic grating structure the radiation beam is diffracted off-plane orthogonal to the plane of incidence. The diffraction efficiency in this condition is very high and in a grating with a sawtooth profile it can approach the reflection coefficient for a simple mirror, when the diffraction order of interest follows the direction for specular reflection at the flat part of the steps. When this concept is used in a plane grating in a monochromator for synchrotron radiation sources, the incident beam is almost always collimated in order to minimize any deterioration of the beam properties due to aberrations, which will be introduced in the diffraction process when an uncollimated beam is used. These aberrations are very severe when the groove density is constant. It will be shown that the effect of these aberrations can be corrected after the diffraction by the use of astigmatic focusing. The latter can be provided by a crossed mirror pair with different focal lengths in the corresponding orthogonal directions. Then a monochromator based on this concept can provide source size limited spectral resolution in an uncollimated incident beam. This is identical to the spectral resolution that can be provided by the same grating when operated at the same position in a collimated incident beam. The source size limited spectral resolution in this case corresponds to a high spectral resolving power of better than ΔE/E = 10 000 for photon energies around 300 eV in the soft X-ray range.