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X-ray single-grating interferometry was applied to conduct accurate wavefront corrections for hard X-ray nanofocusing mirrors. Systematic errors in the interferometer, originating from a grating, a detector, and alignment errors of the components, were carefully examined. Based on the measured wavefront errors, the mirror shapes were directly corrected using a differential deposition technique. The corrected X-ray focusing mirrors with a numerical aperture of 0.01 attained two-dimensionally diffraction-limited performance. The results of the correction indicate that the uncertainty of the wavefront measurement was less than λ/72 in root-mean-square value.

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.

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.

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.

The common aperture optical system enhances light utilization efficiency during the imaging process by utilizing a single shared aperture. This approach not only facilitates independent synchronous multi-band imaging across various applications but also reduces the complexity, size, and cost of optical systems. However, conventional common aperture optical systems typically employ inclined plates or prisms for spectral splitting, which can introduce wavefront distortion in the transmission light path, an issue that is particularly problematic in imaging systems with a large field of view. In this work, we propose employing a freeform lens to correct wavefront distortion arising from imperfections within an optical system. We present a design methodology for the freeform lens based on ray tracing techniques. The application of this freeform lens effectively mitigates wavefront distortion in an infrared dual-band composite detection system, resulting in commendable optical performance across both mid-infrared and far-infrared bands.

Wavefront distortion caused by atmospheric turbulence can be described as different types of aberrations, such as piston, tilt, defocusing, astigmatism, coma and so on. The operation of dual deformable mirrors can have mutual coupling effects, which affect the correction effect of wavefront distortion. This study combines a fast-steering mirror (FSM) and a deformable mirror (DM) to form a dual-deformable-mirrors wavefront correction system, and proposes a decoupling algorithm that can correct any specified aberration. In this decoupling algorithm, both the FSM and the DM are controlled using the mode method, and the specific corrected aberrations are obtained based on a limited matrix. The compensation ability of the DM is directly characterized by the mode coefficients of the aberrations, which can achieve independent correction of any order of aberrations and effectively reduce the coupling effect of the dual-deformable-mirrors wavefront correction system. An adaptive optical dual-deformable-mirrors wavefront correction system experiment was built to verify the decoupling algorithm. When the DM corrects the 3rd-, 10th-, and 25th-order aberrations, and the FSM only corrects the 1st- and 2nd-order aberrations, the coupling coefficients are approximately 1.17×10−3, 1.814×10−2 and 7.81×10−3, respectively, and their magnitude reaches 10−2 and below 10−2, respectively. The experimental results show that the decoupling algorithm can effectively suppress the coupling effect between the FSM and the DM.

We demonstrate real-time wavefront correction in a high-energy high-average-power DiPOLE100/Bivoj laser using adaptive optics. A bimorph deformable mirror and a Shack–Hartmann wavefront sensor reduced wavefront error 10-fold and improved the Strehl ratio 11-fold. Design aspects such as the deformable mirror actuator geometry, optimal placement and loop frequency are discussed for integration into next-generation high-energy high-average-power lasers.

Atmospheric and oceanic turbulence can severely degrade the orbital angular momentum (OAM) mode purity of vortex beams in cross-media optical links. Here, we propose a hybrid correction framework that fuses multiscale phase-screen modeling with a lightweight U-Net predictor for phase-distortion—driven solely by measured optical intensity—and augments it with a feed-forward, Gaussian-reference subtraction scheme for iterative compensation. In our experiments, this approach boosts the l = 3 mode purity from 38.4% to 98.1%. Compared to the Gerchberg–Saxton algorithm, the Gaussian-reference feed-forward method achieves far lower computational complexity and greater robustness, making real-time phase recovery feasible for OAM-based communications over heterogeneous channels.

Wavefront distortion occurs when vortex beams are transmitted in the atmosphere. The turbulence effect greatly affects the transmission of information, so it is necessary to use adaptive optical correction technology to correct the wavefront distortion of the vortex beam at the receiving end. In this paper, a method of vortex wavefront distortion correction based on the deep deterministic policy gradient algorithm is proposed; this is a new correction method that can effectively handle high-dimensional state and action spaces and is especially suitable for correction problems in continuous action spaces. The entire system uses adaptive wavefront correction technology without a wavefront sensor. The simulation results show that the deep deterministic policy gradient algorithm can effectively correct the distorted vortex beams and improve the mode purity, and the intensity correlation coefficient of single-mode vortex light can be increased to about 0.88 and 0.69, respectively, under weak turbulence and strong turbulence, and the intensity coefficient of weak-turbulence multi-mode vortex light can be increased to about 0.96. The experimental results also show that the adaptive correction technology based on the deep deterministic policy gradient algorithm can effectively correct the wavefront distortion of vortex light.

The correction of wavefront aberrations in wavefront sensorless (WFS-less) adaptive optical (AO) systems requires control algorithms that can ensure rapid convergence while maintaining effective correction capabilities. This paper proposes a novel control algorithm based on the RUNge Kutta optimizer (RUN) for WFS-less AO systems that enables the quick and efficient correction of small aberrations, as well as larger aberrations. To evaluate the convergence speed and correction capabilities of a WFS-less AO system based on the RUN control algorithm, we constructed a simulated AO system and an experimental setup with a 97-element deformable mirror (DM), respectively. Additionally, the results obtained with the Particle Swarm Optimization (PSO) algorithm, Differential Evolution Algorithm (DEA), and Genetic Algorithm (GA) are also provided for comparison and analysis. Both the simulated and experimental results consistently demonstrated that our proposed method outperformed several competing algorithms in terms of correction performance and convergence speed. Furthermore, the experimental results further validate the effectiveness of our control algorithm in scenarios involving significant aberrations.