X-ray optical systems: from metrology to Point Spread Function

摘要

One of the problems often encountered in X-ray mirror manufacturing issetting proper manufacturing tolerances to guarantee an angular resolution -often expressed in terms of Point Spread Function (PSF) - as needed by thespecific science goal. To do this, we need an accurate metrological apparatus,covering a very broad range of spatial frequencies, and an affordable method tocompute the PSF from the metrology dataset. [...] However, the separationbetween these spectral ranges is difficult do define exactly, and it is alsounclear how to affordably combine the PSFs, computed with different methods indifferent spectral ranges, into a PSF expectation at a given X-ray energy. Forthis reason, we have proposed a method entirely based on the Huygens-Fresnelprinciple to compute the diffracted field of real Wolter-I optics, includingmeasured defects over a wide range of spatial frequencies. Owing to the shallowangles at play, the computation can be simplified limiting the computation tothe longitudinal profiles, neglecting completely the effect of roundnesserrors. Other authors had already proposed similar approaches in the past, butonly in far-field approximation, therefore they could not be applied to thecase of Wolter-I optics, in which two reflections occur in sequence within ashort range. The method we suggest is versatile, as it can be applied tomultiple reflection systems, at any X-ray energy, and regardless of the nominalshape of the mirrors in the optical system. The method has been implemented inthe WISE code, successfully used to explain the measured PSFs ofmultilayer-coated optics for astronomic use, and of a K-B optical system in useat the FERMI free electron laser.