Optical performance prediction of thin-walled Wolter type I mirror shells for x-rays in the 1- to 8-keV energy range

摘要

Abstract: The XMM telescope consists of nested thin Wolter Type-1 mirror shells replicated from superpolished master pieces which are 600 mm long and between 300 and 700 mm in diameter. By using several measuring devices surface deformations ranging from several hundred $mu@m in vertical amplitude down to a few angstroms could be detected. The goal of this study is to predict, on the basis of these surface topology measurements, the optical performance of the mirror shells over the specified energy range of the telescope (0.3 - 8 keV). To analyze the effect of deformations which can be treated by geometrical optics (slope errors), a Monte-Carlo code was developed which uses a three-dimensional model of the telescope to trace individual rays through the telescope. The code allows for the separation of different deformation types and predicts their influence on the optical performance individually. This analysis turned out to be a valuable tool for improving the manufacturing processes of the mirror shells. We found the computed point spread function in excellent agreement with the ones measured in a full-aperture test at 1.5 keV x-ray energy. The half energy widths matched within 15%. At 8 keV, a loss in optical performance was observed. A comparison of the surface data with mirrors that performed well at 8 keV showed deformations with spatial wavelengths below 1 mm to be responsible for the degradation at 8 keV x-ray energy. Even though the rms surface roughness of these deformations is a factor of three below the Rayleigh criterion, the smooth-surface condition is not fulfilled: the microroughness does not show any correlation with the 8-keV performance of the mirrors. On the other hand, we observed a strong correlation of the integral slope error of these deformations with the 8-keV quality of the mirrors. We conclude that in the transition region between Rayleigh limit and smooth surface limit approximate optical predictions can be achieved by applying geometrical optics.!22