Kα₁–Kα₂ characteristic of a parabolic graded multilayer

Line shapes of the Kα₁–Kα₂ doublet beam reflected from a parabolic graded multilayer (PGM) were analysed by ray tracing and rocking-curve measurements using an Si(400) flat single crystal. The integrated intensity and the intensity ratio of Kα₂ to Kα₁ of the reflected beam vary with the angle of incidence at the PGM. The rates of these variations are considered to increase with increasing spectral resolution of the PGM. The Kα₁ and Kα₂ beams are reflected from the PGM in slightly different directions. Therefore, the angular separation between the Kα₁ and Kα₂ peaks of the observed diffraction profile of a sample becomes smaller than that calculated from the two wavelengths for Kα₁ and Kα₂ when the PGM and the sample are arranged in the (+−) setting, and vice versa when they are in the (++) setting. The magnitude of the shift of the angular separation is close to the experimental uncertainty in the determination of the peak positions when the PGM consists of W/Si bilayers, whereas it is estimated to be three times as large when a PGM of high spectral resolution is used.