Piezoelectric ceramic actuators have the advantages of fast response speed and high positioning accuracy and are widely used in micro-machinery, aerospace, precision machining machinery, and other precision positioning fields. However, hysteretic nonlinearity has a great influence on the positioning accuracy of piezoelectric ceramic actuators, so it is necessary to establish a hysteretic model to solve this problem. In this paper, the principles of the Preisach model, the Prandtl Ishilinskii (PI) model, the Maxwell model, the Duhem model, the Bouc–Wen model, and the Hammerstein model and their application and development in piezoelectric hysteresis modeling are described in detail. At the same time, the classical model, the asymmetric model and the rate-dependent model of these models are described in detail, and the application of the inverse model corresponding to these models in the feedforward compensation is explained in detail. At the end of the paper, the methods of inverse model acquisition and control frequency of these models are compared. In addition, the future research trend of the hysteresis model is also prospected. The ideas and suggestions highlighted in this paper will guide the development of piezoelectric hysteresis models.

In the cophasing of the segmented optical mirrors, the Shack–Hartmann wavefront sensor is not sensitive to the submirror piston error and the large range piston errors beyond the cophasing detection range of phase diversity algorithm. It is necessary to introduce specific sensors (e.g., microlenses or prisms), but they greatly increase the complexity and manufacturing cost of the optical system. In this Letter, we introduce the convolutional neural network (CNN) to distinguish the piston error range of each submirror. To get rid of the dependence of the CNN dataset on the imaging target, we construct the feature vector by the in-focal and defocused images. The method surpasses the fundamental limit of the detection range by using different wavelengths. Finally, the results of the simulation experiment indicate that the method is effective.

The phase diversity (PD) algorithm will eventually be converted into a large-scale nonlinear numerical optimization problem, so the selection of numerical optimization algorithm will directly determine the accuracy and speed of the algorithm settlement. In this paper, we introduce the cuckoo search optimization algorithm, which has the advantages of simple model, few parameters, and easy implementation, to the phase diversity algorithm. By improving the step size control factor in the original cuckoo search algorithm, we can make it have faster optimization speed for PD. In the simulation experiments, we further proved and gave a simple explanation in theory that in the case of large-scale wavefront sensing, compared to the traditional particle swarm algorithm, this improved algorithm has higher accuracy and faster convergence speed. Finally, we set up a simple experimental system and proved the effectiveness of the improved cuckoo search algorithm for PD.

The wave-front phase expanded on the Zernike polynomials is estimated from a pair of images by the use of a maximum-likelihood approach, the in-focus image and the defocus image, which contaminated by noise, will greatly reduce the solution accuracy of the phase diversity (PD) algorithm. In the study, we introduce the deep denoising convolutional neural networks (DnCNNs) into the image preprocessing of PD to denoise the in-focus image and defocus the image containing gaussian white noise to improve the robustness of PD to noise. The simulation results show that the composite PD algorithm with DnCNNs is better than the traditional PD algorithm in both RMSE of phase estimation and SSIM, and the mean of the RMSE of the phase estimation of the improved PD algorithm is reduced by 78.48%, 82.35%, 71.09% and 73.67% compared with the mean of the RMSE of the phase estimation of the traditional PD algorithm. The well-trained DnCNNs runs fast, which does not increase the running time of traditional PD algorithms, and the compound approach may be widely used in various domains, such as the measurements of intrinsic aberrations in optical systems and compensations for atmospheric turbulence. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Tilt vibrations inevitably have negative effects on some precise engineering even after applying horizontal and vertical vibration isolations. It is difficult to adopt a traditional passive vibration isolation (PVI) scheme to realize tilt vibration isolation. In this paper, we present and develop a tilt active vibration isolation (AVI) device using a vertical pendulum (VP) tiltmeter and a piezoelectric transducer (PZT). The potential resolution of the VP is dependent on the mechanical thermal noise in the frequency bandwidth of about $0.0265 \mathrm{nrad}$, which need not be considered because it is far below the ground tilt of the laboratory. The tilt sensitivity of the device in an open-loop mode, investigated experimentally using a voltage controller, is found to be $\left(1.63\pm 0.11\right)\times {10}^5 \mathrm{V}/\mathrm{rad}$. To compensate for the hysteresis nonlinearity of the PZT, we experimentally established the multi-loop mathematical model of hysteresis, and designed a parallel controller consisting of both a hysteresis inverse model predictor and a digital proportional–integral–differential (PID) adjuster. Finally, the response of the device working in close-loop mode to the tilt vibration was tested experimentally, and the tilt AVI device showed a good vibration isolation performance, which can remarkably reduce the tilt vibration, for example, from 6.0131 μrad to below 0.0103 μrad.

The emergence of segmented mirrors is expected to solve the design, processing, manufacturing, testing, and launching of space telescopes of large apertures. However, with the increase in the number of sub-mirrors, the sensing and correction of co-phase errors in segmented mirrors will be very difficult. In this paper, an independent three-dimensional method for sub-mirror co-phase error sensing and correction method is proposed. The method is based on a wide spectral modulation transfer function (MTF), mask, population optimization algorithm, and online model-free correction. In this method, the sensing and correction process of each sub-mirror co-phase error is independent of each other, so the increase in the number of sub-mirrors will not increase the difficulty of the method. This method can sense and correct the co-phase errors of three dimensions of the sub-mirror, including piston, tip, and tilt, even without modeling the optical system, and has a wide detection range and high precision. And the efficiency is high because the sub-mirrors can be corrected simultaneously in parallel. Simulation results show that the proposed method can effectively sense and correct the co-phase errors of the sub-mirrors in the range [−50λ, 50λ] in three dimensions with high precision. The average RMSE value in 100 experiments of the true co-phase error values and the experimental co-phase error values of one of the six sub-mirrors is 2.358 × 10⁻⁷λ.