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Atmospheric turbulence causes refractive index fluctuations, which in turn introduce extra distortions to the wavefront of the propagated radiation. It ultimately degrades telescope resolution (in imaging applications) and reduces radiation power density (in focusing applications). One of the possible ways of researching the impact of turbulence is to numerically simulate the spectrum of refractive index fluctuations, to reproduce it using a wavefront corrector and to measure the resultant wavefront using, for example, a Shack–Hartmann sensor. In this paper, we developed turbulence simulator software that generates phase screens with Kolmogorov spectra. We reconstructed the generated set of phase screens using a stacked-actuator deformable mirror and then compensated for the introduced wavefront distortions using a bimorph deformable mirror. The residual amplitude of the wavefront reconstructed by the 19-channel stacked-actuator mirror was 0.26 λ, while the residual amplitude of the wavefront compensated for by the 32-channel bimorph mirror was 0.08 λ.

Free-electron laser (FEL) facilities operating at MHz repetition rates can emit lasers with average powers reaching hundreds of watts. Partial absorption of this power induces thermal deformation of a few micrometres on the mirror surface. Such deformation degrades the characteristics of the reflected photon beam, leading to focal spot aberrations and wavefront distortions that fail to meet experimental requirements. A robust method is necessary to correct the mirror surface shape to meet the Maréchal criterion. This paper proposes a thermal deformation compensation scheme for offset mirrors operating at MHz repetition rates using a piezoelectric deformable mirror. The mirror is side-mounted with slots filled with an indium–gallium alloy, which house copper tubes for water cooling. Eighteen groups of piezo actuators are symmetrically attached to the top and bottom surfaces. The scheme incorporates finite-element analysis for simulation and post-processing verification, utilizing a differential evolution (DE) algorithm for global optimization. The DE algorithm effectively addresses the voltage constraints that the traditional singular value decomposition algorithm cannot handle. Under an X-ray wavelength of 1 nm, the peak-to-valley (PV) height error of the mirror was reduced from 1340.8 nm to 1.1 nm, and the root-mean-square (RMS) height error decreased from 859.1 nm to 0.18 nm. The slope error was corrected to 154 nrad PV and 24 nrad RMS. Significant results were also achieved at an X-ray wavelength of 3 nm. Wave-optics simulations verified the reliability of this approach, and effects on key mirror parameters and conditions were systematically analysed.

X‐ray mirrors for synchrotron radiation are often bent into a curved figure and work under grazing‐incidence conditions due to the strong penetrating nature of X‐rays to most materials. Mirrors of different cross sections have been recommended to reduce the mirror's slope inaccuracy and clamping difficulty in order to overcome mechanical tolerances. With the development of hard X‐ray focusing, it is difficult to meet the needs of focusing mirrors with small slope error with the existing mirror processing technology. Deformable mirrors are adaptive optics that can produce a flexible surface figure. A method of using a deformable mirror as a phase compensator is described to enhance the focusing performance of an X‐ray mirror. This paper presents an active piezoelectric plane X‐ray focusing mirror with a linearly changing thickness that has the ability of phase compensation while focusing X‐rays. Benefiting from its special structural design, the mirror can realize flexible focusing at different focusing geometries using a single input driving voltage. A prototype was used to measure its performance under one‐dimension and two‐dimension conditions. The results prove that, even at a bending magnet beamline, the mirror can easily achieve a single‐micrometre focusing without a complicated bending mechanism or high‐precision surface processing. It is hoped that this kind of deformable mirror will have a wide and flexible application in the synchrotron radiation field. An active piezoelectric plane X‐ray focusing mirror with a linearly changing thickness is presented. Focusing performances of the prototype are measured and a single‐micrometre focusing result is achieved.

Atmospheric turbulence introduces distortions to the wavefront of propagating optical radiation. It causes image resolution degradation in astronomical telescopes and significantly reduces the power density of radiation on the target in focusing applications. The impact of turbulence fluctuations on the wavefront can be investigated under laboratory conditions using either a fan heater (roughly tuned), a phase plate, or a deformable mirror (finely tuned) as a turbulence-generation device and a wavefront sensor as a wavefront-distortion measurement device. We designed and developed a software simulator and an experimental setup for the reconstruction of atmospheric turbulence-phase fluctuations as well as an adaptive optical system for the compensation of induced aberrations. Both systems use two 60 mm, 92-channel, bimorph deformable mirrors and two tip-tilt correctors. The wavefront is measured using a high-speed Shack–Hartmann wavefront sensor based on an industrial CMOS camera. The system was able to achieve a 500 Hz correction frame rate, and the amplitude of aberrations decreased from 2.6 μm to 0.3 μm during the correction procedure. The use of the tip-tilt corrector allowed a decrease in the focal spot centroid jitter range of 2–3 times from ±26.5 μm and ±24 μm up to ±11.5 μm and ±5.5 μm.

We provide a technical description and experimental results of the practical development and offline testing of an innovative, closed-loop, adaptive mirror system capable of making rapid, precise and ultra-stable changes in the size and shape of reflected X-ray beams generated at synchrotron light and free-electron laser facilities. The optical surface of a piezoelectric bimorph deformable mirror is continuously monitored at 20 kHz by an array of interferometric sensors. This matrix of height data is autonomously converted into voltage commands that are sent at 1 Hz to the piezo actuators to modify the shape of the mirror optical surface. Hence, users can rapidly switch in closed-loop between pre-calibrated X-ray wavefronts by selecting the corresponding freeform optical profile. This closed-loop monitoring is shown to repeatably bend and stabilize the low- and mid-spatial frequency components of the mirror surface to any given profile with an error <200 pm peak-to-valley, regardless of the recent history of bending and hysteresis. Without closed-loop stabilization after bending, the mirror height profile is shown to drift by hundreds of nanometres, which will slowly distort the X-ray wavefront. The metrology frame that holds the interferometric sensors is designed to be largely insensitive to temperature changes, providing an ultra-stable reference datum to enhance repeatability. We demonstrate an unprecedented level of fast and precise optical control in the X-ray domain: the profile of a macroscopic X-ray mirror of over 0.5 m in length was freely adjusted and stabilized to atomic level height resolution. Aside from demonstrating the extreme sensitivity of the interferometer sensors, this study also highlights the voltage repeatability and stability of the programmable high-voltage power supply, the accuracy of the correction-calculation algorithms and the almost instantaneous response of the bimorph mirror to command voltage pulses. Finally, we demonstrate the robustness of the system by showing that the bimorph mirror's optical surface was not damaged by more than 1 million voltage cycles, including no occurrence of the `junction effect' or weakening of piezoelectric actuator strength. Hence, this hardware combination provides a real time, hyper-precise, temperature-insensitive, closed-loop system which could benefit many optical communities, including EUV lithography, who require sub-nanometre bending control of the mirror form.

In this work, the complete development of a line module type silicon carbide (SiC) deformable mirror (DM) for adaptive optics (AO) is described. To eliminate the risk of fracture and misalignment during the simultaneous assembly of all actuators and the base plate of a DM, the line module concept is introduced. This line module is a pre-assembled set consisting of a line-shaped base plate to which actuators and flexures are glued in a row. This concept helps reduce the risk of actuator breakage during the assembly process while also providing flexibility by enabling the easy exchange of the line module if defective actuators are found. Flexible stand mounts are used to minimize mirror surface distortion caused by mounting. Distortions of the mirror faceplate in the complete assembly of the DM, caused by assembly tolerances, gravity, and temperature variations, are assessed through simulations. Considering the flattening of the mirror faceplate to its initial state, the distortions are found to be sufficiently low. Finally, the mirror surface stroke is checked with an interferometer, and the dynamic responses and coupling ratios are measured using a laser displacement sensor. The results show that the line module type SiC DM fulfils the design goals.

To capture images of Earth-like planets orbiting distant stars, advanced instruments with exceptional contrast ratios are imperative. While coronagraphs play a crucial role, they often lack the capability to achieve the requisite contrast levels independently. Hence, supplementary apodization techniques are indispensable for augmenting their rejection capabilities. In this context, we introduce an innovative apodization method that harnesses interferometry, seamlessly integrating a deformable mirror into the Michelson interferometer setup. This sophisticated approach entails splitting the incident Point Spread Function (PSF) into two components, introducing an additional inhomgenious phase φ ( x , y ) to one of them via a deformable mirror, and subsequently recombining them to yield an apodized PSF. We illustrate, in particular, the influence of several parameters of the deformable mirror on the optimization of the additional phase profile.

This paper focuses on the change of morphing capabilities for a unimorph deformable mirror impacted by environmental factors, which works in space for active optics applications. Various aspects of disturbing sources are considered, including complex thermal and mechanical conditions on ferroelectric behaviours of strain actuation, and influences of preconfigured initial shapes and stress-induced geometric stiffness on the structural rigidity of the mirror; changes on both the perturbed shape and the Jacobian matrix are discussed. Those variations are regarded as uncertainties in the design of control methods with both open-loop and iterative control strategies tested in the quasi-static range.

Adaptive optics (AO) systems are capable of correcting wavefront aberrations caused by transmission media or defects in optical systems. The deformable mirror (DM) plays a crucial role as a component of the adaptive optics system. In this study, our focus is on analyzing the ability of a 97-element MEMS (Micro-Electro-Mechanical System) DM to correct blurred images of extended sources affected by atmospheric turbulence. The RUN optimizer is employed as the control method to evaluate the correction capability of the DM through simulations and physical experiments. Simulation results demonstrate that within 100 iterations, both the normalized gray variance and Strehl Ratio can converge, leading to an improvement in image quality by approximately 30%. In physics experiments, we observe an increase in normalized gray variance (NGV) from 0.53 to 0.97 and the natural image quality evaluation (NIQE) from 15.35 to 19.73, representing an overall improvement in image quality of about 28%. These findings can offer theoretical and technical support for applying MEMS DMs in correcting imaging issues related to extended sources degraded by wavefront aberrations.

This study presents a numerical simulation-based investigation of a MEMS (micro-electromechanical systems)technology-based deformable mirror employing a piezoelectric film for fundus examination in adaptive optics. Compared to the classical equal-area electrode arrangement model, we optimize the electrode array for higher-order aberrations. The optimized model centralizes electrodes around the mirror center, which realizes low-voltage driving with high-accuracy correction. The optimized models exhibited commendable correction abilities, achieving a unidirectional displacement of 5.74 μm with a driven voltage of 15 V. The voltage–displacement relationship demonstrated high linearity at 0.99. Furthermore, the deformable mirror’s influence matrix was computed, aligning with the Zernike standard surface shape of the order 1–3. To quantify aberration correction capabilities, fitting residuals for both models were calculated. The results indicate an average removal of 96.8% of aberrations to the human eye. This underscores that the optimized model outperforms the classical model in correcting high-order aberrations.