  This paper presents the first-principle design approach for X-ray active
optics, using the simulation-modulation cycle in place of the
measurement-modulation feedback loops used in traditional active optics. Hence,
the new active optics have the potential to outperform the accuracy of
surface-shape metrology instruments. We apply an X-ray mirror with localized
thermal elastic deformation to validate the idea. Both the finite element
simulations and surface shape measurements have demonstrated that the active
optics modulation accuracy limit can be achieved at the atomic layer level. It
is believed that the implementation of the first-principle design strategy has
the capacity to revolutionize both the manufacturing processes of X-ray mirrors
and the beamline engineering of synchrotron radiation.
