Actuator placement for minimum force modal control of continuous faceplate deformable mirrors

In conventional Adaptive optics (AO) system, wavefront aberration is measured by wavefront sensor. However, a point source is usually not available in most imaging systems. Therefore development of deformable mirror control scheme in adaptive optics system based on vision information will extend the application area of AO technique. A focus measure (FM) is a measure of image quality and can be calculated from image data obtained from the image sensor. It can be used to find the optimal shape of the deformable mirror that compensates the wavefront aberration. In this paper, we analyze the performance of focus measures under different types of wavefront aberrations. The relation of FM vs. the aberration strength is analyzed systematically for different aberration modes and different FM functions. The FM performance under combination of aberrations is also investigated. This research supplies a guide for selection of the suitable FM function and strategy for control of deformable mirror in the AO system.

An Adaptive Optic (AO) system is a fundamental requirement of 8m-class telescopes. We know that in order to obtain the maximum possible resolution allowed by these telescopes we need to correct the atmospheric turbulence. Thanks to adaptive optic systems we are able to use all the effective potential of these instruments, drawing all the information from the universe sources as best as possible. In an AO system there are two main components: the wavefront sensor (WFS) that is able to measure the aberrations on the incoming wavefront in the telescope, and the deformable mirror (DM) that is able to assume a shape opposite to the one measured by the sensor. The two subsystem are connected by the reconstructor (REC). In order to do this, the REC requires a “common language" between these two main AO components. It means that it needs a mapping between the sensor-space and the mirror-space, called an interaction matrix (IM). Therefore, in order to operate correctly, an AO system has a main requirement: the measure of an IM in order to obtain a calibration of the whole AO system. The IM measurement is a 'mile stone' for an AO system and must be done regardless of the telescope size or class. Usually, this calibration step is done adding to the telescope system an auxiliary artificial source of light (i.e a fiber) that illuminates both the deformable mirror and the sensor, permitting the calibration of the AO system. For large telescope (more than 8m, like Extremely Large Telescopes, ELTs) the fiber based IM measurement requires challenging optical setups that in some cases are also impractical to build. In these cases, new techniques to measure the IM are needed. In this PhD work we want to check the possibility of a different method of calibration that can be applied directly on sky, at the telescope, without any auxiliary source. Such a technique can be used to calibrate AO system on a telescope of any size. We want to test the new calibration technique, called “sinusoidal modulation technique”, on the Large Binocular Telescope (LBT) AO system, which is already a complete AO system with the two main components: a secondary deformable mirror with by 672 actuators, and a pyramid wavefront sensor. My first phase of PhD work was helping to implement the WFS board (containing the pyramid sensor and all the auxiliary optical components) working both optical alignments and tests of some optical components. Thanks to the “solar tower” facility of the Astrophysical Observatory of Arcetri (Firenze), we have been able to reproduce an environment very similar to the telescope one, testing the main LBT AO components: the pyramid sensor and the secondary deformable mirror. Thanks to this the second phase of my PhD thesis: the measure of IM applying the sinusoidal modulation technique. At first we have measured the IM using a fiber auxiliary source to calibrate the system, without any kind of disturbance injected. After that, we have tried to use this calibration technique in order to measure the IM directly “on sky”, so adding an atmospheric disturbance to the AO system. The results obtained in this PhD work measuring the IM directly in the Arcetri solar tower system are crucial for the future development: the possibility of the acquisition of IM directly on sky means that we are able to calibrate an AO system also for extremely large telescope class where classic IM measurements technique are problematic and, sometimes, impossible. Finally we have not to forget the reason why we need this: the main aim is to observe the universe. Thanks to these new big class of telescopes and only using their full capabilities, we will be able to increase our knowledge of the universe objects observed, because we will be able to resolve more detailed characteristics, discovering, analyzing and understanding the behavior of the universe components.

It is well known that using two or more deformable mirrors (DMs) can improve the compensation ability of an adaptive optics (AO) system. However, to keep the stability of an AO system, the correlation between the multiple DMs must be suppressed during the correction. In this paper, we proposed a slope-based decoupling algorithm to simultaneous control the multiple DMs. In order to examine the validity and practicality of this algorithm, a typical woofer-tweeter (W-T) AO system was set up. For the W-T system, a theory model was simulated and the results indicated in theory that the algorithm we presented can selectively make woofer and tweeter correct different spatial frequency aberration and suppress the cross coupling between the dual DMs. At the same time, the experimental results for the W-T AO system were consistent with the results of the simulation, which demonstrated in practice that this algorithm is practical for the AO system with dual DMs.

Received January 21, 2013; accepted March 5, 2013; posted online July 30, 2013 The hysteresis nonlinearity of piezoelectric actuator is one of the main defects in the control of deformable mirror which is widely used as a key component in adaptive optics system. This letter put forward a modified Prandtl-Ishlinskii (PI) model in order to precisely describe the hysteresis nonlinearity of piezoelectric actuator. With this proposed model, an inverse-model based controller used for trajectory tracking in open-loop operation is designed to compensate the hysteresis nonlinearity effect. Then, some tracking control experiments for the desired triangle trajectory are performed. From the experimental results, we can see that the positioning precision in open loop operation is significantly improved with this inverse-model based controller. © 2013 Chinese Optics Letters.

Some computational problems arising in adaptive optics imaging systems

We discuss the chosen concepts, detailed design, implementation and calibration of the 85-electrode adaptive optics (AO) system of the Swedish 1-meter Solar Telescope (SST), which was installed in 2013. The AO system is unusual in that it uses a combination of a monomorph mirror with a Shack-Hartmann (SH) wavefront sensor (WFS) and a second high-resolution SH microlens array to aid the characterization, calibration, and modal control of the deformable mirror. An Intel PC workstation performs the heavy image processing associated with cross-correlations and real-time control at a 2 kHz update rate with very low latency. The computer and software continue the successful implementation since 1995 of earlier generations of correlation tracker and AO systems at SST and its predecessor, the 50-cm Swedish Vacuum Solar Telescope, by relying entirely on work-station technology and an extremely efficient algorithm for implementing cross-correlations with the large field of view of the WFS. We describe critical aspects of the design, calibrations, software, and functioning of the AO system. The exceptionally high performance is testified through the highest Strehl ratio (inferred from the measured granulation contrast) of existing meter-class solar telescopes, as demonstrated here at wavelengths shorter than 400 nm and discussed in more detail in a previous separate publication We expect that some aspects of this AO system may also be of interest outside the solar community.

This paper describes the development of the tip-tilt mirror control for an adaptive optics system based on the use of FPGA technology instead of using the traditional approach with DSP or microprocessor. The aim of this work is to show that for this kind of application the FPGA technology is not only a viable solution but probably also the best one in some situations, especially when a huge amount of parallel data processing is needed. This will probably be the case of adaptive optics systems for very large telescopes. A brief description of the whole adaptive optics system will be given although the paper will focus especially on the tip-tilt mirror control and its implementation with FPGAs. A new version of the deformable mirror control is also being implemented in FPGAs and will be finished in the near future.

Nearly every new large-scale laser system application at LLNL has requirements for beam control which exceed the current level of available technology. For applications such as inertial confinement fusion, laser isotope separation, laser machining, and laser the ability to transport significant power to a target while maintaining good beam quality is critical. There are many ways that laser wavefront quality can be degraded. Thermal effects due to the interaction of high-power laser or pump light with the internal optical components or with the ambient gas are common causes of wavefront degradation. For many years, adaptive optics based on thing deformable glass mirrors with piezoelectric or electrostrictive actuators have be used to remove the low-order wavefront errors from high-power laser systems. These adaptive optics systems have successfully improved laser beam quality, but have also generally revealed additional high-spatial-frequency errors, both because the low-order errors have been reduced and because deformable mirrors have often introduced some high-spatial-frequency components due to manufacturing errors. Many current and emerging laser applications fall into the high-resolution category where there is an increased need for the correction of high spatial frequency aberrations which requires correctors with thousands of degrees of freedom. The largest Deformable Mirrors currently availablemore » have less than one thousand degrees of freedom at a cost of approximately $1M. A deformable mirror capable of meeting these high spatial resolution requirements would be cost prohibitive. Therefore a new approach using a different wavefront control technology is needed. One new wavefront control approach is the use of liquid-crystal (LC) spatial light modulator (SLM) technology for the controlling the phase of linearly polarized light. Current LC SLM technology provides high-spatial-resolution wavefront control, with hundreds of thousands of degrees of freedom, more than two orders of magnitude greater than the best Deformable Mirrors currently made. Even with the increased spatial resolution, the cost of these devices is nearly two orders of magnitude less than the cost of the largest deformable mirror.« less

We characterize the errors associated with open-loop control of a microelectromechanical system deformable mirror (DM) using an approach that combines sparse calibration of the electrostatic actuator state space with an elastic plate model of the mirror facesheet. We quantify sources of measurement error and modeling error and demonstrate that the DM can be shaped in a single step to a tolerance of ∼8nm of that achievable with iterative feedback-based closed-loop control. Zernike polynomials with up to 2.5μm amplitude were made with this approach and yielded a shape error of <25nm rms in most cases. Residual errors were shown to be due primarily to spatial resolution limits inherent in the DM (e.g., uncontrollable errors).

A general approach is presented for evaluating and optimizing the degree of atmospheric turbulence compensation achieved by an adaptive optics system employed as part of a extended field-of-view astronomical telescope. This method applies to an adaptive optics system incorporating either one or multiple natural and/or laser guide stars sensed by wave-front slope sensors, a wave-front reconstruction algorithm equivalent to a matrix multiply, a servo control law to temporally filter the output of the wave-front reconstructor, and one or several deformable mirrors optically conjugate to different ranges along the telescope’s line-of-sight. The degree of atmospheric turbulence compensation achieved by such a configuration is evaluated in terms of the residual mean-square phase distortion and turbulence-induced optical transfer function at each point in the telescope’s field-of-view. This evaluation accounts for the combined, interacting effects of the atmospheric turbulence C n 2 ( h ) profile and wind velocity profile, wave-front sensor and deformable mirror fitting error, wave-front sensor noise, finite control system bandwidth, and the net anisoplanatism associated with a given constellation of natural and/or laser guide stars. Optimal wave-front reconstruction algorithms are derived which minimize the telescope’s field-of-view-averaged residual mean-square phase distortion. These evaluation and optimization results are first-order in the sense that they neglect diffraction effects and assume that all adaptive optics components are strictly linear. Results for the case of a finite servo bandwidth also require the wave-front reconstruction algorithm coefficients to satisfy a set of linear constraints; the reconstructor must precisely predict the deformable mirror actuator command vector in the absense of sensor noise and atmospheric turbulence. Numerical results are presented for a variety of adaptive optics configurations incorporating either a single guide star, multiple guide stars and a single deformable mirror, or multiple guide stars and two deformable mirrors.

We have created a new adaptive optics system using a holographic modal wavefront sensing method capable of autonomous (computer-free) closed-loop control of a MEMS deformable mirror. A multiplexed hologram is recorded using the maximum and minimum actuator positions on the deformable mirror as the "modes". On reconstruction, an input beam will be diffracted into pairs of focal spots - the ratio of particular pairs determines the absolute wavefront phase at a particular actuator location. The wavefront measurement is made using a fast, sensitive photo-detector array such as a multi-pixel photon counters. This information is then used to directly control each actuator in the MEMS DM without the need for any computer in the loop. We present initial results of a 32-actuator prototype device. We further demonstrate that being an all-optical, parallel processing scheme, the speed is independent of the number of actuators. In fact, the limitations on speed are ultimately determined by the maximum driving speed of the DM actuators themselves. Finally, being modal in nature, the system is largely insensitive to both obscuration and scintillation. This should make it ideal for laser beam transmission or imaging under highly turbulent conditions.

The Adaptive Optics Laboratory at the University of Victoria (Canada) and the Subaru Telescope NAOJ (Hawaii) are collaborating to develop a simple method allowing open-loop control of MEMS deformable mirrors. This method consists of an iterative algorithm based on 3 simple equations and 4 constants. The 4 constants are different for each mirror, therefore a characterization step is necessary to evaluate their values for a given mirror. In this paper we describe the model and the 3 equations it relies on. We also propose a characterization methodology and finally present the preliminary results respectively obtained on Victoria and Subaru test beds.

Since atmosphere turbulence has an effect on laser propagation, it causes wavefront error usually , changes intensity and coherence of laser, disturbs detection of lidar. The adaptive optical system has broad application in the field of laser transmission because it can adjust characters of optical system ,detect and correct the wavefront error at the same time. Adaptive optics technology uses deformable mirrors to perform dynamic phase modulation and endow optical system the ability to decrease the influence of dynamic wavefront errors. In this paper ,a correction method of the micro-miniature adaptive optical system based on Micro Electromechanical System (MEMS) technology is proposed by analyzing the working theory of the adaptive optical system. An experimental system including deformable mirror based on Micro Electromechanical System (MEMS) technology is designed to correct a factitious wavefront error.The influence function and voltage-deflection curve are researched, and the voltage control matrix is educed. By using the voltage control , the static wavefront aberration is corrected. Several important capabilities of deformable mirrors is tested. With the voltage control matrix, the corrected capability of the adaptive optical system is achieved successfully .The experimental results show that the adaptive optical system can preferably correct the wavefront error, that has small volume and steady capability, and greatly improve the capability of lidar detection.

Author Index to volume 202

An adjustable surface shape with a high accuracy attracts a significant interest in the development of X-ray optical elements. However, the optical parameters of the conventional polished mirror are fixed, lacking adaptability and leading to significantly limited application targets. Based on adaptive optics technology, the X-ray deformable mirror can be achieved using the bending principle of a piezoelectric bimorph. In this study, we developed an X-ray lead-zirconate-titanate-(PZT) deformable mirror with an adjustable surface shape. The X-ray deformable mirror was simulated and optimized using the ANSYS software to ensure the feasibility of the design scheme. An X-ray deformable mirror prototype was manufactured based on the simulation results. It had a simple structure consisting of a 400-μmthick D263 glass substrate and 500-μm-thick PZT thin sheet. The PZT thin sheet consisted of 11 element electrode actuators. We used a ZYGO interferometer for an on-line surface shape feedback of the X-ray deformable mirror. By changing the voltage loads of the actuators, the glass substrate surface shape could be adjusted, and a target cylinder with a radius of curvature of 30 m was obtained. The curvature radius of the target cylinder could be changed, from 5 m to infinity.