Piezoelectric Deformable Mirror Research Articles

Investigation of PZT Materials for Reliable Piezostack Deformable Mirror with Modular Design.

This article presents a study of the electrophysical properties of a piezoceramic material for use in adaptive optics. The key characteristics that may be important for the manufacturing of piezoelectric deformable mirrors are the following: piezoelectric constants (d31, d33, d15), capacitance, elastic compliance values s for different crystal directions, and the dielectric loss tangent (tgδ). Based on PZT ceramics, the PKP-12 material was developed with high values of the dielectric constant, piezoelectric modulus, and electromechanical coupling coefficients. The deformable mirror control elements are made from the resulting material-piezoceramic combs with five individual actuators in a row. In this case, the stroke of the actuator is in the range of 4.1-4.3 microns and the capacitance of the actuator is about 12 nF.

Fixed-time observer-based tracking controller for a hysteretic piezoelectric deformable mirror of an adaptive optic system.

Piezoelectric deformable mirrors (DM) are benefited from the high accuracy and swift dynamics. The hysteresis phenomenon, which inherently exists in piezoelectric materials, degrades the capability and precision of the adaptive optics (AO) systems. Also, the dynamics of piezoelectric DMs make the controller design more complicated. This research aims to design a fixed-time observer-based tracking controller (FTOTC), which estimates the dynamics, compensates the hysteresis, and ensures tracking to the actuator displacement reference, in the fixed time. Unlike the existing inverse hysteresis operator-based methods, the proposed observer-based controller overcomes the computational burdens and estimates the hysteresis in real-time. The proposed controller tracks the reference displacements, while the tracking error converges in the fixed time. The stability proof is presented by two consecutive theorems. Numerical simulations demonstrate superior tracking and hysteresis compensation by the presented method, from a comparison viewpoint.

Piezoelectric deformable mirror driven by unimorph actuator arrays on multi-spatial layers.

In order to reduce the cost of the piezo actuator array deformable mirror (DM), a piezoelectric DM driven by unimorph actuator arrays on multi-spatial layers is proposed. The actuator density can be multiplied by increasing the spatial layers of the actuator arrays. A low-cost DM prototype with 19 unimorph actuators located on three spatial layers is developed. The unimorph actuator can generate a wavefront deformation up to 11 µm at an operating voltage of 50 V. The DM can reconstruct typical low-order Zernike polynomial shapes accurately. The mirror can be flattened to 0.058 µm in RMS. Furthermore, a focal spot close to Airy spot is obtained in the far field after the aberrations of the adaptive optics testing system being corrected.

High-resolution visible imaging with piezoelectric deformable secondary mirror: experimental results at the 1.8-m adaptive telescope

High-resolution visible imaging with piezoelectric deformable secondary mirror: experimental results at the 1.8-m adaptive telescope

Bimorph mirrors at synchrotron beamlines: from walking to flying

With brighter synchrotron sources, automated sample changers, and faster detectors, there is a strong scientific need for rapid and precise variation of the X-ray beam profile, rather than the “set and forget” operation of years past. Piezoelectric bimorph deformable mirrors already allow quick beam profile changes without the heat generation and wear of mechanical devices. Now, their early technological limitations – excessively constraining holders, progressive “junction effect” distortion, and communication bottlenecks with power supplies – are being overcome by a collaboration of scientists and engineers both in industry and at Diamond Light Source. A new generation of bimorph mirrors maintains a stable figure over extended periods of operation. Improved holders and flexible electrical connectors are greatly reducing the mechanical strain imparted to bimorphs, thereby improving their speed, accuracy, and stability. A more sophisticated high voltage power supply has on-board signal processing capacity, allowing large focusing changes within seconds and providing programmable time-varying voltage profiles to counteract piezoelectric creep. The communication between beamline systems and power supplies is being freed of bottlenecks and now runs stably up to 1 Hz. Early tests have already shown that bimorph mirrors can repeatedly switch the size of an X-ray beam in well under 10 seconds. Bimorph mirrors at synchrotron beamlines are now growing beyond the largely static operation of the past and gaining a new dynamism through development projects that are now well advanced. We report on how these endeavours will make it easier for beamlines to utilise the full potential of bimorph mirrors.

Calculation of the modified control matrix for a selected unimorph deformable mirror to compensate the piezoelectric hysteresis effect using the inverse Bouc-Wen model.

The hysteresis behavior of piezoelectric actuators degrades the positioning accuracy and bandwidth of nano-positioning systems. Therefore, considering the hysteresis of piezoelectric deformable mirrors is completely essential and also improves the modeling accuracy of adaptive optics layouts. Because of the unique adaptability and mathematical flexibility of the Bouc-Wen model it has gained popularity, and as a result, in many scientific applications, it is one of the most conventional models typically employed to describe nonlinear hysteretic systems. Among different deformable mirrors, a unimorph piezoelectric deformable mirror is a suitable choice to be used in adaptive optics systems because of its relative convenience and cost-effective production. This paper proposes a new, to the best of our knowledge, approach to determine the influence function and the voltage control matrix of a specific unimorph mirror by considering a simplified inverse Bouc-Wen hysteresis model as a frequency function. Then the results for two selected standard Zernike modes, defocus and astigmatism-x, have been simulated using Comsol Multiphysics and MATLAB at a range of 5 to 100 Hz. For a more comprehensive comparison, the root-mean-square error and the coefficients of the Zernike terms have been applied as two criteria. According to the simulation results, the hysteresis effect of piezoelectric actuators has been significantly compensated by applying the inverse Bouc-Wen model at different frequencies, especially for higher frequencies. The effectiveness of the inverse Bouc-Wen model to compensate the hysteresis has been observed in astigmatism-x mode slightly more than in the defocus mode.

Shape control of thin deformable mirror with distributed piezoelectric sensors and actuators

This paper presents shape control of a thin piezoelectric deformable mirror in order to compensate the form errors caused by disturbances. The finite element model describing the dynamics of the mirror was obtained by Hamilton’s principle and discretization was performed by nine nodes thin shell element according to the Kirchhoff-Love theory. The state space approach was used to generate matrices for control procedure. Because of the multivariable nature of the control problem involved in such structures and noise, the adaptive LQG-Kalman controller with multiple input-multiple output design was implemented to control the shape of the mirror. The proposed approach and related perspectives were finally discussed.

Development of a 36-element piezoelectric deformable mirror for synchrotron radiation and its surface control ability

The predecessor of China Optics was China Optics and Applied Optics Digest, which was founded in 1985. At that time, it was the only retrieval journal in the field of optics in China. At the end of 2008, China Optics and Applied Optics Digest was renamed

Simulation and experimental investigation on the temperature-induced distortion characteristics of the hybrid connection structure deformable mirror.

The stacked array piezoelectric deformable mirror (DM) used in adaptive optics (AO) systems usually has actuator-corresponding high-frequency temperature-induced distortion (TID) on its mirror surface when the working temperature is different from the design temperature, which is harmful to beam quality. To effectively eliminate the actuator-corresponding high-frequency TID, we introduce a hybrid connection structure deformable mirror (H-DM), which adopts a magnetic connection structure besides the conventional adhesive connection structure. The TID characteristics of the H-DM are analyzed using the finite element method, and the wavefront compensation capability of the novel H-DM is also investigated in simulation. In the experiment, the initial surface shape and the TID characteristics of a lab-manufactured H-DM are measured. The experimental results show that the H-DM has a good initial surface shape, and no actuator-corresponding high-frequency distortion exists in the surface shape of the H-DM when the environment temperature changes. Thus it can be seen the TID could be well corrected by the H-DM itself, and thereby the environmental adaptability of the DM could be improved substantially.

Thermal Balance and Active Damping of a Piezoelectric Deformable Mirror for Adaptive Optics

Piezoelectric unimorph deformable mirrors offer a cheap solution to adaptive optics, with mass production capability. However, standard solutions have significant drawbacks: (i) the static shape is sensitive to the temperature, and (ii) the low structural damping limits the control bandwidth, because of the interaction between the shape control and the vibration modes of the mirror. This paper discusses how these two problems may be alleviated by using a mirror covered with an array of actuators working in d31 mode on the back side and a ring of transducers (actuators and sensors) on the front side, outside the pupil of the mirror.

Damping of piezoelectric space instruments: application to an active optics deformable mirror

This paper presents the shunt damping of a unimorph piezoelectric mirror intended to be used as an active secondary corrector in future space telescopes. We propose to take advantage of the actuation capability of the piezoelectric mirror, to increase its natural damping during the critical launch phase of the spacecraft. The piezoelectric actuators, intended to be used for active optics, are shunted on a passive resistive and inductive RL circuit during the launch operation. The proposed concept is verified numerically and experimentally on a piezoelectric deformable mirror prototype, developed on behalf of the European Space Agency. We show that the shunt damping significantly reduces the response of the most critical mode of the mirror (− 23 dB) as well as the stress in the mirror when subjected to a typical vibro-acoustic launch load. This reduces the risk of damaging the mirror during the delicate launch phase, without increasing the complexity of the design.

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

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.

Research on elastic modes of circular deformable mirror for adaptive optics and active optics corrections.

In this paper, an elastic mode method of deformable mirror is proposed to decompose arbitrary wave-front errors of adaptive optics system. The elastic modes are derived with an analytical method of linear piezoelectricity based on a bimorph piezoelectric deformable mirror (BPDM), and the three-dimensional formulas of elastic modes are presented. Here a BPDM with an aperture of 165 mm as an example is numerically studied. Two different kinds of dynamic boundary conditions are considered, and the dependence of the elastic modes aberrations upon the orders and rotational symmetries is evaluated. Besides, a comparative study for elastic mode and Zernike polynomials is presented in the numerical analysis. The results have demonstrated that the elastic mode method can be not only used instead of Zernike polynomials, but also more effective to decompose arbitrary wave-front errors of a deformable mirror. Furthermore, finite element analysis method is used to validate the analytic method. The conclusions have shown reasonably consistent results between the two methods.

Dynamic adaptive X-ray optics. Part II. High-speed piezoelectric bimorph deformable Kirkpatrick-Baez mirrors for rapid variation of the 2D size and shape of X-ray beams.

The tangential curvature of actively bent X-ray mirrors at synchrotron radiation and X-ray free-electron laser (XFEL) facilities is typically only changed every few hours or even days. This operation can take tens of minutes for active optics with multiple bending actuators and often requires expert guidance using in situ monitoring devices. Hence, the dynamic performance of active X-ray optics for synchrotron beamlines has historically not been exploited. This is in stark contrast to many other scientific fields. However, many areas of synchrotron radiation and XFEL science, including macromolecular crystallography, could greatly benefit from the ability to change the size and shape of the X-ray beam rapidly and continuously. The advantages of this innovative approach are twofold: a large reduction in the dead time required to change the size of the X-ray beam for different-sized samples and the possibility of making multiple changes to the beam during the measurement of a single sample. In the preceding paper [Part I; Alcock, Nistea, Signorato & Sawhney (2019), J.Synchrotron Rad. 26, 36-44], which accompanies this article, high-speed visible-light Fizeau interferometry was used to identify the factors which influence the dynamic bending behaviour of piezoelectric bimorph deformable X-ray mirrors. Building upon this ex situ metrology study, provided here is the first synchrotron radiation beamline implementation of high-speed adaptive X-ray optics using two bimorphs operating as a Kirkpatrick-Baez pair. With optimized substrates, novel opto-mechanical holders and a next-generation high-voltage power supply, the size of an X-ray beam was rapidly and repeatedly switched in <10 s. Of equal importance, it is also shown that compensation of piezoelectric creep ensures that the X-ray beam size remains stable for more than 1 h after making a major change. The era of high-speed adaptive X-ray optics for synchrotron radiation and XFEL beamlines has begun.

Dynamic adaptive X-ray optics. Part I. Time-resolved optical metrology investigation of the bending behaviour of piezoelectric bimorph deformable X-ray mirrors.

Piezoelectric bimorph deformable mirrors (`bimorphs') are routinely used on many synchrotron and free-electron laser beamlines to provide active variation in the size and shape of the X-ray beam. However, the time-domain potential of such optics has never been fully exploited. For the first time, the fast dynamic bending response of bimorphs is investigated here using Fizeau interferometry. Automated scripts for acquisition and analysis were developed to collect Fizeau data at a rate of 0.1 Hz to record dynamic changes in the optical surface as voltages were applied to the electrodes of the piezoelectric actuators. It is demonstrated that residual drift in the tangential radius of curvature of a bimorph can be significantly reduced using enhanced opto-mechanical holders and a fast programmable high-voltage power supply. Further improvements are achieved by applying small opposing voltages to compensate for piezoelectric creep. The present study shows that bimorphs can truly be used as high-speed adaptive optics for the X-ray domain, even without closed-loop feedback correction. This opens the possibility for relatively simple real-time tuning of the profile of X-ray bimorphs. Part II of this study [Alcock, Nistea, Signorato, Owen, Axford, Sutter, Foster & Sawhney (2019), J. Synchrotron Rad. 26, 45-51] builds upon these results and demonstrates how bimorphs can rapidly provide customisable sizes and shapes of synchrotron X-ray beams, specifically tailored to suit the experimental samples being investigated.

Analysis on fitting capability to human aberrations of bimorph deformable mirrors

This study adapted simulations to analyze the fitting capabilities to human aberration of three kinds of Bimorph Deformable Mirrors (DMs) with different spatial resolutions, especially the capability to fit to 3~ 35th orders of Zernike static aberrations and the human aberrations, including the eye of diseases. It's shown that Bimorph DM is well suitable for fitting to low-order aberrations with the error less than 0.15. As the spatial resolution increased, the capability of fitting aberrations enhanced totally. Compared with traditional discrete piezoelectric DM, 35-element Bimorph DM had smaller fitting error on the first 20th Zernike aberration. This simulated analysis provided an analytical method for the selection of Bimorph DMs for high-resolution human eye imaging systems. In addition, it provided a research foundation of further improvement of the Bimorph DM in fitting aberrations capability.

Simulational and experimental investigation on the actuator-corresponding high-frequency aberration of the piezoelectric stacked array deformable mirror

The high-frequency aberrations (HIFAs) that are corresponding to the actuator array have been reported to exist on the initial surface shape of many deformable mirrors (DMs), such as the bimorph DM, the unimorph DM, the monomorph DM, and the membrane DM. This actuator-corresponding high-frequency aberration (AC-HIFA) could not be corrected effectively by the DM and would limit the correction ability of the DM. In this paper, we presented the AC-HIFA in a stacked array piezoelectric (PZT) DM, which may result in ghost damage that is dangerous in the high power laser system. More importantly, we investigated a solution through simulation and experiment that by using a mirror plate and a long thin post array, which were machined integrally from a piece of BK7 glass, the AC-HIFA could be eliminated completely. In addition, the structural parameters' influences on the AC-HIFA were investigated in the simulation, which could help other researchers to determine appropriate parameters of the mirror and the posts and to make a fine surface shape in their own DMs.

Analysis of a discrete-layout bimorph disk elements piezoelectric deformable mirror

We introduce a discrete-layout bimorph disk elements piezoelectric deformable mirror (DBDEPDM), driven by the circular flexural-mode piezoelectric actuators. We formulated an electromechanical model for analyzing the performance of the new deformable mirror. As a numerical example, a 21-actuators DBDEPDM with an aperture of 165 mm was modeled. The presented results demonstrate that the DBDEPDM has a stroke larger than 10 μm and the resonance frequency is 4.456 kHz. Compared with the conventional piezoelectric deformable mirrors, the DBDEPDM has a larger stroke, higher resonance frequency, and provides higher spatial resolution due to the circular shape of its actuators. Moreover, numerical simulations of influence functions on the model are provided.

Hysteresis compensation of piezoelectric deformable mirror based on Prandtl–Ishlinskii model

Hysteresis of piezoelectric deformable mirror (DM) reduces the closed-loop bandwidth and the open-loop correction accuracy of adaptive optics (AO) systems. In this work, a classical Prandtl–Ishlinskii (PI) model is employed to model the hysteresis behavior of a unimorph DM with 20 actuators. A modified control algorithm combined with the inverse PI model is developed for piezoelectric DMs. With the help of PI model, the hysteresis of the DM was reduced effectively from about 9% to 1%. Furthermore, open-loop regenerations of low-order aberrations with or without hysteresis compensation were carried out. The experimental results demonstrate that the regeneration accuracy with PI model compensation is significantly improved.

Super-resolution pupil filtering for visual performance enhancement using adaptive optics

Ocular aberration correction can significantly improve visual function of the human eye. However, even under ideal aberration correction conditions, pupil diffraction restricts the resolution of retinal images. Pupil filtering is a simple super-resolution (SR) method that can overcome this diffraction barrier. In this study, a 145-element piezoelectric deformable mirror was used as a pupil phase filter because of its programmability and high fitting accuracy. Continuous phase-only filters were designed based on Zernike polynomial series and fitted through closed-loop adaptive optics. SR results were validated using double-pass point spread function images. Contrast sensitivity was further assessed to verify the SR effect on visual function. An F-test was conducted for nested models to statistically compare different CSFs. These results indicated CSFs for the proposed SR filter were significantly higher than the diffraction correction (p < 0.05). As such, the proposed filter design could provide useful guidance for supernormal vision optical correction of the human eye.