  The development of synchrotron radiation light sources has been going on for
decades. Recently, X-ray free-electron lasers as well as the fourth-generation
synchrotron radiation sources based on multiple bend achromat lattices are
commissioned and constructed. These advanced light source facilities result in
beam with superior performance, such as higher brilliance, higher degree of
coherence, smaller achievable focused size. To take full advantage of the
unique properties of the source, the superior benefits of synchrotron radiation
require high standards for the quality of optics used in beamline construction.
In this paper, we took nanoprobe beamline as an example and propose a method to
achieve pre-designed specifications of beamline by imposing restrictions on
certain parameters of the X-ray reflective mirrors. By using this method, one
can clearly illustrate the requirements of optical performance for the surface
accuracy of reflective mirrors and determine which specific requirement is more
stringent, which avoids procuring significantly more expensive mirrors than
necessary, the correspondence between spatial frequencies and statistical
parameters would also be understood. Furthermore, we have studied the problem
that power spectral density (PSD) function cannot guarantee an accurate
judgement of the mirror quality. This method can also be generalized to designs
of other beamlines.

Accelerator Physics;Optics