An algorithm to solve the inverse problem of synchrotron radiation adaptive mirrors’ tuning is presented. The influence functions are modeled and calculated for a generic bimorph mirror. An error function minimization method is used to simulate the correction of the surface figure of the mirror in some particular conditions. Possible applications to free-electron-laser mirror simulations are pointed out.
Adaptive x-ray optics are more and more used in synchrotron beamlines, and it is probable that they will be considered
for the future high-power free-electron laser sources, as the European XFEL now under construction in Hamburg, or
similar projects now in discussion. These facilities will deliver a high power x-ray beam, with an expected high heat load
delivered on the optics. For this reason, bendable mirrors are required to actively compensate the resulting wavefront
distortion. On top of that, the mirror could have also intrinsic surface defects, as polishing errors or mounting stresses. In
order to be able to correct the mirror surface with a high precision to maintain its challenging requirements, the mirror
surface is usually characterized with a high accuracy metrology to calculate the actuators pulse functions and to assess its
initial shape. After that, singular value decomposition (SVD) is used to find the signals to be applied into the actuators,
to reach the desired surface deformation or correction. But in some cases this approach could be not robust enough for
the needed performance. We present here a comparison between the classical SVD method and an error function
minimization based on root-mean-square calculation. Some examples are provided, using a simulation of the European
XFEL mirrors design as a case of study, and performances of the algorithms are evaluated in order to reach the ultimate
quality in different scenarios. The approach could be easily generalized to other situations as well.
The European X-Ray Free Electron Laser will deliver high intensity ultrashort pulses of x-rays. The results of
the x-ray interaction with matter in such a regime are not yet fully understood and the energy threshold for surface
modifications remains unknown. The behavior of optical components under irradiation is a major issue for the
European XFEL project. In fact some experiments rely on the coherence and high quality wave front of the beam and
any degradation, even on the nanometer scale, of the x-ray optical components will affect the performance of these
Hence investigation of radiation effects on materials is needed. We will describe the on-going program at the
European XFEL which aims at developing new approaches for beamline design specific to FEL light source. Different
tools are used in order to simulate the beam propagation and interaction with optical elements.