X-ray echelles: account of groove profile deformations for diffraction efficiency in electromagnetic calculus

A possibility of achieving high efficiencies of high number diffraction orders is considered for blaze gratings working in the X-ray range. The diffraction efficiency depends on the flatness of the reflecting facet of grooves, characterized by the average blaze angle and camber. A phenomenological formula was obtained for the relationship between these groove parameters and the modulus of the maximum order number, at which the grating efficiency is still maximum. Using the PCGrate™ code, this formula is confirmed by the results of numerical simulation of the diffraction efficiency of unique X-ray echelles. The obtained theoretical estimate makes it possible to classify a manufactured grating according to its maximum achievable diffraction efficiency, i.e., before efficiency measurements or calculus.