  One of the problems often encountered in X-ray mirror manufacturing is
setting proper manufacturing tolerances to guarantee an angular resolution -
often expressed in terms of Point Spread Function (PSF) - as needed by the
specific science goal. To do this, we need an accurate metrological apparatus,
covering a very broad range of spatial frequencies, and an affordable method to
compute the PSF from the metrology dataset. [...] However, the separation
between these spectral ranges is difficult do define exactly, and it is also
unclear how to affordably combine the PSFs, computed with different methods in
different spectral ranges, into a PSF expectation at a given X-ray energy. For
this reason, we have proposed a method entirely based on the Huygens-Fresnel
principle to compute the diffracted field of real Wolter-I optics, including
measured defects over a wide range of spatial frequencies. Owing to the shallow
angles at play, the computation can be simplified limiting the computation to
the longitudinal profiles, neglecting completely the effect of roundness
errors. Other authors had already proposed similar approaches in the past, but
only in far-field approximation, therefore they could not be applied to the
case of Wolter-I optics, in which two reflections occur in sequence within a
short range. The method we suggest is versatile, as it can be applied to
multiple reflection systems, at any X-ray energy, and regardless of the nominal
shape of the mirrors in the optical system. The method has been implemented in
the WISE code, successfully used to explain the measured PSFs of
multilayer-coated optics for astronomic use, and of a K-B optical system in use
at the FERMI free electron laser.
