Mirrors For Adaptive Optics Research Articles

On the effects of spider-arms vignetting on interferometric measurements of deformable mirrors

The interferometric calibration and measurement of deformable mirrors for adaptive optics are often performed on complex optical system with spider arms. The spider shadows may divide the mirror surface into separate islands on the detector, so the interferometer fails in reconnecting them to a common phase value. The calibration measurements then suffer from such artificial differential pistons across islands, which is converted into a wrong actuator command and in general into a poor calibration. We review the effects of spider arms shadowing as experienced during the optical calibration of large format adaptive mirrors, such as the Large Binocular Telescope and Very Large Telescope ones; we describe the procedures that we tested to cope with these issues and their effectiveness; and we present a laboratory assessment of the effect of such a shadowing with a dedicated test setup. Our work is part of a preparatory activity for the optical test of the European Extremely Large Telescope adaptive mirror M4.

Active Damping, Vibration Isolation, and Shape Control of Space Structures: A Tutorial

This tutorial reviews the author’s contributions to the active control of precision space structures over the past 35 years. It is based on the Santini lecture presented at the IAC-2022 Astronautical Congress in Paris in September 2022. The first part is devoted to the active damping of space trusses with an emphasis on robustness. Guaranteed stability is achieved by using decentralized collocated actuator–sensor pairs. The so-called integral force feedback (IFF) is simple, robust, and effective, and the performances can be predicted easily with simple formulae based on modal analyses. These predictions have been confirmed by numerous experiments. The damping strategy for trusses has been extended to cable structures, and also confirmed experimentally. The second part addresses the problem of vibration isolation: isolating a sensitive payload from the vibration induced by the spacecraft (i.e., the unbalanced mass of attitude control reaction wheels and gyros). A six-axis isolator based on a Gough–Stewart platform is discussed; once again, the approach emphasizes robustness. Two different solutions are presented: The first one (active isolation) uses a decentralized controller with collocated pairs of the actuator and force sensor, with IFF control. It is demonstrated that this special implementation of the skyhook, unlike the classical one, has guaranteed stability, even if the two substructures it connects are flexible (typical of large space structures). A second approach (passive) discusses an electromagnetic implementation of the relaxation isolator where the classical dash-pot of the linear damper is substituted by a Maxwell unit, leading to an asymptotic decay rate of −40 dB/decade, similar to the skyhook (although much simpler in terms of electronics). The third part of the lecture summarizes more recent work done on the control of flexible mirrors: (i) flat mirrors for adaptive optics (AO) controlled by an array of piezoelectric ceramic (PZT) actuators and (ii) spherical thin shell polymer reflectors controlled by an array of piezoelectric polymer actuators (PVDF-TrFE) aimed at being deployed in space.

Laboratory demonstration of the prediction of wind-blown turbulence by adaptive optics at 8 kHz with use of LQG control.

The low-latency adaptive optical mirror system (LLAMAS) is designed to push the limits on achievable latencies and frame rates. It has 21 subapertures across its pupil. A reformulated version of the linear quadratic Gaussian (LQG) method predictive Fourier control is implemented in LLAMAS; for all modes, it takes just 30µs to compute. In the testbed, a turbulator mixes hot and ambient air to produce wind-blown turbulence. Wind prediction clearly improves correction when compared to an integral controller. Closed-loop telemetry shows that wind-predictive LQG removes the characteristic "butterfly" and reduces temporal error power by up to a factor of three for mid-spatial frequency modes. Strehl changes seen in focal plane images are consistent with telemetry and the system error budget.

Eigenmode Wavefront Decoupling Algorithm for LC–DM Adaptive Optics Systems

To realize the decoupling control of the dual corrector of liquid crystal (LC)–deformable mirror (DM) adaptive optics (AO) systems and prevent the loss of correction ability induced by coupling aberrations, a wavefront decoupling method based on DM eigenmodes was proposed. The coupling relationship of two correctors was studied, and the distribution of aberrations corrected using the DM and LC was investigated. First, a DM eigenmode matrix was derived according to the DM influence function. Then, aberrations were decomposed according to the Strehl ratio, and the projection of the LC response matrix on the DM eigenmode matrix, that is, the coupling term, was derived. Before using the LC corrector, the coupling item was eliminated for the decoupling of the two correctors, and the decoupling effect was verified through simulations. Finally, a 2 m telescope LC–DM AO system was developed to validate the proposed method. The simulation and experimental results showed that the root mean square of the DM-corrected residual after 55 eigenmodes’ correction was 0.09 μm. After decoupling correction, the resolution of the 700–1700 nm wide band improved from 1.1 to 1 times the diffraction limit, which is 1.2 times better than that obtained using the traditional Zernike mode correction.

Distortion Correction In Particle Image Velocimetry For Measurements Through Fluctuating Interfaces Using A Deep Neural Network And Wavefront Sensing

Imaging-based flow measurements like Particle Image or Particle Tracking Velocimetry re-quire an undistorted optical access to the measurement location. Changes of the refractive index in the light path can cause image deterioration and lead to severe measurement errors. While static aberration as e.g. from curved walls can be corrected by of means static correction optics or dedicated light ray models, this is hardly possible if the aberration change with time at high bandwidth. Many cases of this kind exists in fluid mechanics as e.g. free liquid jets, bubbles, droplets or film flows. These interfaces are related to several open research questions that concern the interaction between the media on both sides of the interface. Hardware-based corrections adapted from astronomy that employs a deformable membrane mirror, a wavefront sensor and a fast control electronics are a viable approach for solving this measurement problem. However, these closed-loop control schemes require extensive and dedicated hardware and are limited by the technical specifications of the adaptive optical mirror in terms of correction bandwidth, stroke and spatial resolution. Here we present an approach based on Multiple-Input deep convolutional neural network that works with a wavefront sensor only and spares the adaptive optical component. Based on a model experiment and a PIV measurement, we demonstrate that this system is able to correct for the errors that are induced by an oscillating water surface by 82 %. The technique can be an alternative to classical closed-loop adaptive optical systems where the performance of the actuators is not sufficient. This can open a perspective towards measurement of interface-related flows that were not accessible before.

An Atmospheric Turbulence Compensation Algorithm Based on FSM-DM Cascaded AO Architecture for FSO Communications

Free-space optics (FSO) communication enjoys desirable modulation rates at unexploited frequency bands, however, its application is hindered by atmospheric turbulence which causes phase shifting in laser links. Although a single deformable mirror (DM) adaptive optics (AO) system is a good solution, its performance remains unsatisfactory as the proportion of tilts aberrations becomes relatively high. This condition happens when the incident angle of the laser beam for the optical receiver dynamically shifts. To tackle this problem, we introduce a fast steering mirror (FSM), DM cascaded AO architecture, based upon which we also propose an atmospheric turbulence compensation algorithm. In this paper, we compare the compensation ability of FSM and DM towards tilts aberrations. Furthermore, we gain model matrices for FSM and DM from testbed and simulatively verify the effectiveness of our work. For a Kolmogorov theory-based atmospheric turbulence disturbed incident laser beam where the tilt components take up 80% of the total proportion of wavefront aberrations, our proposed architecture compensates the input wavefront to a residual wavefront root mean square (RMS) of 116 wavelength, compared to 16 wavelength for single DM architecture. The study intends to overcome atmospheric turbulence and has the potential to guide the development of future FSO communications.

Performance evaluation of phase plate and deformable mirror for adaptive optics (AO) system

Performance evaluation of phase plate and deformable mirror for adaptive optics (AO) system

Scintillation effects and the optimal sequence of deformable mirrors in multi-conjugate adaptive optics

Multi-conjugate adaptive optics (MCAO) uses two or more deformable mirrors (DMs) at conjugate altitudes approximately matched to the atmospheric turbulence layers to increase the corrected field of view. An important unresolved problem for MCAO is determining the optimal sequence of the DMs. Theoretical considerations and numerical studies suggest that ordering the DMs from lowest to highest altitude reduces the effects of scintillation, whereas on-sky experiments report that the best performance is attained with the ground-layer DM placed last. Using analytical calculations and numerical experiments with Fresnel propagation of Kolmogorov turbulence, we demonstrate that the scintillation results from spatial frequencies higher than the spatial sampling of high-altitude DMs are able to correct. Hence, the effect of scintillation is not impacted by MCAO correction regardless of the sequence of the DMs. Using end-to-end numerical simulations, we find that the dynamic misregistration between the DMs and the wavefront sensors is minimized by placing the ground-layer DM last, leading to increased loop stability and lower wavefront errors. Contrary to conventional wisdom, we recommend that the DMs be sequenced from highest to lowest altitude.

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.

A low voltage and large stroke Lorentz force continuous deformable polymer mirror for wavefront control

This paper presents a low voltage, and large stroke Lorentz-force actuated continuous deformable polymer mirror for adaptive optics. A 5 × 5 actuator array clamped on the rigid mounting rail are formed from single crystal silicon flexible serpentine springs on either side of a rigid crossbar containing a narrow contact pillar. For the mirror, an epoxy-based SU-8 photoresist is used, which enables low voltage operation combined with Lorentz actuator. The Lorentz DM were tested and demonstrated a large 40 μm deformation at 9 mA actuation current, and needing <1 V operation. This Lorentz DM would operate 2 kHz frequency with 40 μm stroke, which can be suitable for large deformation adaptive optics application.

Control-structure interaction in piezoelectric deformable mirrors for adaptive optics

This paper discusses the shape control of deformable mirrors for Adaptive Optics in the dynamic range. The phenomenon of control-structure interaction appears when the mirror becomes large, lowering the natural frequencies fi, and the control bandwidth fc increases to improve the performance, so that the condition fc < fi is no longer satisfied. In this case, the control system tends to amplify the response of the flexible modes and the system may become unstable. The main parameters controlling the phenomenon are the frequency ratio fc / fi and the structural damping s. Robustness tests are developed which allow to evaluate a lower bound of the stability margin. Various passive and active strategies for damping augmentation are proposed and tested in simulation.

Unimorph mirror for adaptive optics in space telescopes.

This paper presents a unimorph deformable mirror intended to be used as secondary corrector in space telescopes. The deformable mirror consists of a single-crystal silicon wafer (76.2mm diameter, 500μm thickness) covered with an optical coating on the front side and an array of 25 independent piezoelectric transducer (PZT) actuators acting in d31 mode on the back side. The mirror is mounted on an isostatic support with three position linear actuators controlling the rigid-body motion. The first part of the paper presents the experimental results obtained with the manufactured prototype. The mirror was tested in terms of root mean square (RMS) wavefront error, open-loop long-term stability, voltage budget for active control, rigid-body actuation, reflectivity, and dynamic response. The prototype is fully compliant with the requirements set by the European Space Agency (ESA). The second part of the paper, purely based on numerical simulations, presents a robust way to face thermal distortion, inherent to unimorph architecture.

CVD SiC deformable mirror with monolithic cooling channels.

We propose a novel deformable mirror (DM) for adaptive optics in high power laser applications. The mirror is made of a Silicon carbide (SiC) faceplate, and cooling channels are embedded monolithically inside the faceplate with the chemical vapor desposition (CVD) method. The faceplate is 200 mm in diameter and 3 mm in thickness, and is actuated by 137 stack-type piezoelectric transducers arranged in a square grid. We also propose a new actuator influence function optimized for modelling our DM, which has a relatively stiffer faceplate and a higher coupling ratio compared with other DMs having thin faceplates. The cooling capability and optical performance of the DM are verified by simulations and actual experiments with a heat source. The DM is proved to operate at 1 kHz without the coolant flow and 100 Hz with the coolant flow, and the residual errors after compensation are less than 30 nm rms (root-mean-square). This paper presents the design, fabrication, and optical performance of the CVD SiC DM.

Aluminum‐coated elastomer thin films for the fabrication of a ferrofluidic deformable mirror

ABSTRACTA procedure for the fabrication of aluminum‐coated reflective PDMS thin films having a low surface roughness and high reflectance is presented. Elastomer films are prepared by spin‐coating on a sacrificial layer that permits subsequent release from the substrate. Appropriate surface treatments are established for the deposition of a thin, highly reflective metal coating. The composite membranes are deposited on an ethylene glycol based ferrofluid to fabricate a new ferrofluidic deformable mirror. Surface deformations of a few micrometers can be produced with low strength magnetic fields. The reflective elastomer membranes do not alter the rheological behavior of the ferrofluid in magnetic fields and thus offer new perspectives for the use of ferrofluidic mirrors in adaptive optics. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017, 134, 44542.

Zonal decoupling algorithm for dual deformable mirror adaptive optics system

A zonal decoupling algorithm used to control a dual deformable mirror (DM) is proposed. One of the two DMs is characterized with a large stroke (woofer), while the other one is characterized by a high spatial frequency (tweeter). A numerical model is used to compare the zonal decoupling algorithm with some traditional zonal decoupling algorithms. The simulation results indicate that the algorithm presented in this Letter improves the performance in suppressing the coupling error. An experimental system is built to prove the effectiveness of this algorithm. The experiments demonstrate that the phase aberrations could be effectively compensated and that the coupling error could also be suppressed.

Segmented bimorph mirrors for adaptive optics: segment design and experiment.

We discuss the concept of lightweight segmented bimorph mirrors for adaptive optics. The segment consists of a monocrystal silicon substrate actuated by an array of in-plane piezoceramic (PZT) actuators with honeycomb electrodes. We focus on technological aspects of the segment design that are critical for space applications and describe a single segment demonstrator. The morphing capability of the segment is evaluated experimentally. We also discuss the local deformations (dimples) associated with the shape of the electrodes acting on the PZT array.

Segmented bimorph mirrors for adaptive optics: morphing strategy.

This paper discusses the concept of a light weight segmented bimorph mirror for adaptive optics. It focuses on the morphing strategy and addresses the ill-conditioning of the Jacobian of the segments, which are partly outside the optical pupil. Two options are discussed, one based on truncating the singular values and one called damped least squares, which minimizes a combined measure of the sensor error and the voltage vector. A comparison of various configurations of segmented mirrors was conducted; it is shown that segmentation sharply increases the natural frequency of the system with limited deterioration of the image quality.

用于自适应光学视网膜成像系统的双压电片变形反射镜

用于自适应光学视网膜成像系统的双压电片变形反射镜

Suppressing low-order eigenmodes with local control for deformable mirrors

To improve the mechanical characteristics of actively controlled continuous faceplate deformable mirrors in adaptive optics, a strategy for reducing crosstalk between adjacent actuators and for suppressing low-order eigenmodes is proposed. The strategy can be seen as extending Saint-Venant’s principle beyond the static case, for small local families of actuators. An analytic model is presented, from which we show the feasibility of the local control. Also, we demonstrate how eigenmodes and eigenfrequencies are affected by mirror parameters, such as thickness, diameter, Young’s modulus, Poisson’s ratio, and density. This analysis is used to evaluate the design strategy for a large deformable mirror, and how many actuators are needed within a family.

Concept, modeling, and performance prediction of a low-cost, large deformable mirror

While it is attractive to integrate a deformable mirror (DM) for adaptive optics (AO) into the telescope itself rather than using relay optics within an instrument, the resulting large DM can be expensive, particularly for extremely large telescopes. A low-cost approach for building a large DM is to use voice-coil actuators connected to the back of the DM through suction cups. Use of such inexpensive voice-coil actuators leads to a poorly damped system with many structural modes within the desired bandwidth. Control of the mirror dynamics using electro-mechanical sensors is thus required for integration within an AO system. We introduce a distributed control approach, and we show that the "inner" back sensor control loop does not need to function at low frequencies, leading to significant cost reduction for the sensors. Incorporating realistic models of low-cost actuators and sensors together with an atmospheric seeing model, we demonstrate that the low-cost mirror strategy is feasible within a closed-loop AO system.