A piezoelectric deformable X-ray mirror for phase compensation based on global optimization

Abstract

As a strong tool for the study of nanoscience, the synchrotron hard X‐ray nanoprobe technique enables researchers to investigate complex samples with many advantages, such as in situ setup, high sensitivity and the integration of various experimental methods. In recent years, an important goal has been to push the focusing spot size to the diffraction limit of ∼10 nm. The multilayer‐based Kirkpatrick–Baez (KB) mirror system is one of the most important methods used to achieve this goal. This method was chosen by the nanoprobe beamline of the Phase‐II project at the Shanghai Synchrotron Radiation Facility. To overcome the limitations of current polishing technologies, the use of an additional phase compensator was necessary to decrease the wavefront distortions. In this experiment, a prototype phase compensator has been created to show how to obtain precise wavefront compensation. With the use of finite‐element analysis and Fizeau interferometer measurements, some important factors such as the piezoresponse, different actuator distributions, stability and hysteresis were investigated. A global optimization method based on the measured piezoresponse has also been developed. This method overcame the limitations of the previous local algorithm related to the adjustment of every single actuator for compact piezoelectric layouts. The mirror figure can approach a target figure after several iterations. The figure difference can be reduced to several nanometres, which is far better than the mirror figure errors. The prototype was also used to successfully compensate for the real wavefront errors from upstream and for its own figure errors, measured using the speckle scanning technique. The residual figure error was reduced to a root‐mean‐square value of 0.7 nm.

Data-driven modeling and control of an X-ray bimorph adaptive mirror

“…Comprehensive physical modeling of the mirror (e.g. using finite-element analysis) is possible (Song et al, 2009;Jiang et al, 2019), but it requires highly specific system characterization, which cannot always be achieved in practice. In recent years, similar complex systems such as the storage ring itself are now using techniques derived from machine learning to improve their stability (Leemann et al, 2019).…”

Bimorph mirror processing and fabrication research

“…Referring to the existing piezoelectric BM size design in China [7] , in order to meet the requirement that the length of the reflector on the beamline of the fourth generation synchrotron light source usually reaches more than 200 mm, we design the reflector base size in the numerical simulation at 200 mm × 55 mm × 10 mm, and accordingly, the length and width of the PZT is fixed at 200 mm × 17.5 mm. the PZT, due to the processing capability limitation, the face shape error is large, and also, it is introduced in the bonding, which will transfer the error to the reflective surface and cause the reflective surface to produce submicron face shape error.…”

“…Compared with traditional X-ray mirrors, deformation mirrors have two major advantages: first, the active control of its surface shape, deformation mirrors can actively adjust its surface shape to further improve the surface shape accuracy, reducing the technical difficulty and cost of precision optical processing; second, the dynamic control of deformation mirrors can meet the fourth-generation light source beam line required dynamic aberration correction capabilities, including correction of their own errors. Since the 1990s, some international synchrotron radiation devices have carried out the research and development of bimorph mirror (BM) [3][4][5][6][7] , and have made great progress. In this paper, numerical simulations are used to analyze the effects of the design of the braking unit size and the mirror clamp support on the deformation process.…”

X-ray Phase-Contrast Imaging Using Near-Field Speckles

“…For optics characterisation at the synchrotron, other recently published reports on specklebased metrology apply the scanning approach to the in-situ characterisation of multilayers [Jiang et al, 2017[Jiang et al, , 2019b and the iterative optimisation of a piezoelectric deformable mirror [Jiang et al, 2019a]. The implementation of the setup for the first was similar to the one proposed by using 1D scanning of the diffuser.…”