Adaptive Mirror Research Articles

High fidelity adaptive mirror simulations with reduced order models

In the design process of large adaptive mirrors numerical simulations represent the first step to evaluate the system design compliance in terms of performance, stability and robustness. For the next generation of Extremely Large Telescopes increased system dimensions and bandwidths lead to the need of modeling not only the deformable mirror alone, but also all the system supporting structure or even the full telescope. The capability to perform the simulations with an acceptable amount of time and computational resources is highly dependent on finding appropriate methods to reduce the size of the resulting dynamic models. In this paper we present a framework developed together with the company Microgate to create a reduced order structural model of a large adaptive mirror as a preprocessing step to the control system simulations. The reduced dynamic model is then combined with the remaining system components allowing to simulate the full adaptive mirror in a computationally efficient way. We analyze the feasibility of our reduced models for Microgate’s prototype of the adaptive mirror of the Giant Magellan Telescope.

Controlling cantilevered adaptive X-ray mirrors.

Modeling the behavior of a prototype cantilevered X-ray adaptive mirror (held from one end) demonstrates its potential for use on high-performance X-ray beamlines. Similar adaptive mirrors are used on X-ray beamlines to compensate optical aberrations, control wavefronts and tune mirror focal distances at will. Controlled by 1D arrays of piezoceramic actuators, these glancing-incidence mirrors can provide nanometre-scale surface shape adjustment capabilities. However, significant engineering challenges remain for mounting them with low distortion and low environmental sensitivity. Finite-element analysis is used to predict the micron-scale full actuation surface shape from each channel and then linear modeling is applied to investigate the mirrors' ability to reach target profiles. Using either uniform or arbitrary spatial weighting, actuator voltages are optimized using a Moore-Penrose matrix inverse, or pseudoinverse, revealing a spatial dependence on the shape fitting with increasing fidelity farther from the mount.

Real-time adaptive optics for high-power laser beam correction in the strong turbulence

A combined adaptive optical system designed to correct the wavefront of light radiation distorted by the influence of strong atmospheric turbulence is presented. The system consists of a beam position stabilizer and a fast adaptive optical system operating in real time. Stabilization of the beam position is carried out by two electronically controlled tilt mirrors. The control loop includes two quadrant sensors and an FPGA (field-programmable gate array) that closes the feedback loop. Using information received from Shack-Hartmann wavefront sensor, a bimorph-based adaptive mirror, controlled by another FPGA, is able to compensate for wavefront aberrations for up to 23-th Zernike polynomial in real time. The system was tested under the laboratory turbulence conditions created by a fan heater. The bandwidth of the artificial turbulence in the experiments did not exceed 100 Hz, which corresponds to the average statistical state of the real atmosphere. Results of the correction of the wave front distorted by the artificial turbulence are presented. It is shown that when only a bimorph corrector is used, the value of wavefront tilt angles increases. This presents a certain problem, since a significant part of the turbulence energy falls on the wave front tilts. To address this problem, it is proposed additionally using a system for stabilizing the position of the light beam.

Monolithic deformable mirror based on lithium niobate single crystal for high-resolution X-ray adaptive microscopy

X-ray microscopy is very promising not only for nondestructive and high-spatial-resolution observation of the internal structure of a sample but also for elemental distribution and chemical state analysis. However, the spatial resolution of microscopes remains unsatisfactory owing to the fabrication error in the objective lens. To realize an ultra-high-resolution, we propose and develop a monolithic deformable mirror based on a lithium niobite single crystal and a novel adaptive imaging system based on it. An X-ray interferometer confirmed that shape modification is possible with an accuracy of 0.67 nm in peak to valley under high stability (0.17 nm over 7 h) and hysteresis-free deformation control. Introducing this adaptive mirror into an X-ray microscope based on advanced Kirkpatrick-Baez mirror optics and correcting the wavefront aberration demonstrated that the X-ray image quality could be significantly improved.

Fuzzy Proportional Integral Derivative control of a voice coil actuator system for adaptive deformable mirrors

Fuzzy Proportional Integral Derivative control of a voice coil actuator system for adaptive deformable mirrors

Real-time machine-learning-driven control system of a deformable mirror for achieving aberration-free X-ray wavefronts.

A neural-network machine learning model is developed to control a bimorph adaptive mirror to achieve and preserve aberration-free coherent X-ray wavefronts at synchrotron radiation and free electron laser beamlines. The controller is trained on a mirror actuator response directly measured at a beamline with a real-time single-shot wavefront sensor, which uses a coded mask and wavelet-transform analysis. The system has been successfully tested on a bimorph deformable mirror at the 28-ID IDEA beamline of the Advanced Photon Source at Argonne National Laboratory. It achieved a response time of a few seconds and maintained desired wavefront shapes (e.g., a spherical wavefront) with sub-wavelength accuracy at 20 keV of X-ray energy. This result is significantly better than what can be obtained using a linear model of the mirror's response. The developed system has not been tailored to a specific mirror and can be applied, in principle, to different kinds of bending mechanisms and actuators.

Refractive plasma optics for relativistic laser beams

The high intensities reached today by powerful lasers enable us to explore the interaction with matter in the relativistic regime, unveiling a fertile domain of modern science that is pushing far away the frontiers of plasma physics. In this context, refractive-plasma optics are being utilized in well established wave guiding schemes in laser plasma accelerators. However, their use for spatial phase control of the laser beam has never been successfully implemented, partly due to the complication in manufacturing such optics. We here demonstrate this concept which enables phase manipulation near the focus position, where the intensity is already relativistic. Offering such flexible control, high-intensity high-density interaction is becoming accessible, allowing for example, to produce multiple energetic electron beams with high pointing stability and reproducibility. Cancelling the refractive effect with adaptive mirrors at the far field confirms this concept and furthermore improves the coupling of the laser to the plasma in comparison to the null test case, with potential benefits in dense-target applications.

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.

Adaptive parabolic membrane mirrors for large deployable space telescopes.

A key element for the development of extremely large telescopes in space or balloon-borne observatories will be a reduction in the areal weight of the primary mirror. Large membrane mirrors offer a very low areal weight but are difficult to manufacture with the optical quality needed for astronomical telescopes. This paper demonstrates a practical method to overcome this limitation. In a test chamber we have successfully grown optical quality parabolic membrane mirrors on a rotating liquid in a test chamber. These polymer mirror prototypes of up to 30cm in diameter show a sufficiently low surface roughness and can be coated with reflective layers. By manipulating the parabolic shape locally using radiative adaptive optics methods, it is shown that imperfections or changes in the shape can be corrected. With only tiny local temperature changes induced by the radiation, many micrometers of stroke have been achieved. Scaling the method investigated to produce mirrors with diameters of many meters is possible using available technology. This approach opens the possibility to produce affordable extremely large primary mirrors for space telescopes. With the flexibility of the membrane material, this type of mirror can be compactly rolled up when stored in the launch vehicle, and then be deployed in space.

Simulation of the Human Myopic Eye Cornea Compensation Based on the Analysis of Aberrometric Data.

Various diffractive, refractive and holographic optical elements, such as diffraction gratings; microlens raster; phase plates; multi-order diffractive optical elements; adaptive mirrors; diffractive and refractive axicons; holographic multiplexes and many others are used to analyze wavefront aberrations. We shortly discuss the features (advantages and disadvantages) of various wavefront aberration sensors in the Introduction. The main part of the paper is devoted to the analysis of the weight coefficients of Zernike polynomials obtained during medical examinations of the cornea in the human eye. Using data obtained by aberrometers, the average values of the Zernike polynomial coefficients for the anterior and posterior surfaces of the healthy eye cornea and a myopic one were calculated. The original wavefront for the anterior and posterior surfaces of the cornea was restored separately, as well as the total wave aberration. For an objective assessment of the quality of vision, the corresponding point spread functions (PSFs) were calculated. We propose to compensate for the aberrations of the myopic eye, taking into account the physical features of the corneal surface. The results of numerical simulation showed that in order to improve the quality of the patient's vision, it is necessary to take into account high-order aberrations of the anterior surface of the cornea in the form of a coma of the third order and aberrations of the fourth order.

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.

Development and Commercial Application of Glue-Free Adaptive High Precision X-Ray Mirror

Development and Commercial Application of Glue-Free Adaptive High Precision X-Ray Mirror

Fast shaping control of x ray beams using a closed-loop adaptive bimorph deformable mirror

High-speed adaptive correction of optics, based on real-time metrology feedback, has benefitted numerous scientific communities for several decades. However, it remains a major technological challenge to extend this concept into the hard x ray regime due to the necessity for active mirrors with single-digit nanometer height errors relative to a range of aspheric forms. We have developed a high-resolution, real-time, closed-loop “adaptive” optical system for synchrotron and x ray free electron laser (XFEL) applications. After calibration of the wavefront using x ray speckle scanning, the wavefront diagnostic was removed from the x ray beam path. Non-invasive control of the size and shape of the reflected x ray beam was then demonstrated by driving a piezoelectric deformable bimorph mirror at ∼ 1 H z . Continuous feedback was provided by a 20 kHz direct measurement of the optical surface with picometer sensitivity using an array of interferometric sensors. This enabled a non-specialist operator to reproduce a series of pre-defined x ray wavefronts, including focused or non-Gaussian profiles, such as flattop intensity or multiple split peaks with controllable separation and relative amplitude. Such changes can be applied in any order and in rapid succession without the need for invasive wavefront diagnostic sensors that block the x ray beam for scientific usage. These innovations have the potential to profoundly change how x ray focusing elements are utilized at synchrotron radiation and XFEL sources and provide unprecedented dynamic control of photon beams to aid scientific discoveries in a wide range of disciplines.

Data-driven modeling and control of an X-ray bimorph adaptive mirror.

Adaptive X-ray mirrors are being adopted on high-coherent-flux synchrotron and X-ray free-electron laser beamlines where dynamic phase control and aberration compensation are necessary to preserve wavefront quality from source to sample, yet challenging to achieve. Additional difficulties arise from the inability to continuously probe the wavefront in this context, which demands methods of control that require little to no feedback. In this work, a data-driven approach to the control of adaptive X-ray optics with piezo-bimorph actuators is demonstrated. This approach approximates the non-linear system dynamics with a discrete-time model using random mirror shapes and interferometric measurements as training data. For mirrors of this type, prior states and voltage inputs affect the shape-change trajectory, and therefore must be included in the model. Without the need for assumed physical models of the mirror's behavior, the generality of the neural network structure accommodates drift, creep and hysteresis, and enables a control algorithm that achieves shape control and stability below 2 nm RMS. Using a prototype mirror and ex situ metrology, it is shown that the accuracy of our trained model enables open-loop shape control across a diverse set of states and that the control algorithm achieves shape error magnitudes that fall within diffraction-limited performance.

The European Solar Telescope

The European Solar Telescope (EST) is a project aimed at studying the magnetic connectivity of the solar atmosphere, from the deep photosphere to the upper chromosphere. Its design combines the knowledge and expertise gathered by the European solar physics community during the construction and operation of state-of-the-art solar telescopes operating in visible and near-infrared wavelengths: the Swedish 1m Solar Telescope, the German Vacuum Tower Telescope and GREGOR, the French Télescope Héliographique pour l’Étude du Magnétisme et des Instabilités Solaires, and the Dutch Open Telescope. With its 4.2 m primary mirror and an open configuration, EST will become the most powerful European ground-based facility to study the Sun in the coming decades in the visible and near-infrared bands. EST uses the most innovative technological advances: the first adaptive secondary mirror ever used in a solar telescope, a complex multi-conjugate adaptive optics with deformable mirrors that form part of the optical design in a natural way, a polarimetrically compensated telescope design that eliminates the complex temporal variation and wavelength dependence of the telescope Mueller matrix, and an instrument suite containing several (etalon-based) tunable imaging spectropolarimeters and several integral field unit spectropolarimeters. This publication summarises some fundamental science questions that can be addressed with the telescope, together with a complete description of its major subsystems.

Variance reduction on general adaptive stochastic mirror descent

In this work, we investigate the idea of variance reduction by studying its properties with general adaptive mirror descent algorithms in nonsmooth nonconvex finite-sum optimization problems. We propose a simple yet generalized framework for variance reduced adaptive mirror descent algorithms named SVRAMD and provide its convergence analysis in both the nonsmooth nonconvex problem and the P-L conditioned problem. We prove that variance reduction reduces the SFO complexity of adaptive mirror descent algorithms and thus accelerates their convergence. In particular, our general theory implies that variance reduction can be applied to algorithms using time-varying step sizes and self-adaptive algorithms such as AdaGrad and RMSProp. Moreover, the convergence rates of SVRAMD recover the best existing rates of non-adaptive variance reduced mirror descent algorithms without complicated algorithmic components. Extensive experiments in deep learning validate our theoretical findings.

Resonant Adaptive MEMS Mirror

A novel MEMS continuous deformable mirror (DM) is presented. The mirror can be integrated into optical systems to compensate for monochromatic and chromatic aberrations. It is comprised of a 1.6 mm circular plate supported by eight evenly spaced flexural springs. Unlike traditional bias actuated DMs, it uses resonant electrostatic actuation (REA) to realize low- and high-order Zernike modes with a single drive signal. Instead of the hundreds or thousands of electrodes deployed by traditional DMs, the proposed DM employs only 49 electrodes and eliminates the need for spatial control algorithms and associated hardware, thereby providing a compact low-cost alternative. It also exploits dynamic amplification to reduce power requirements and increase the stroke by driving the DM at resonance. The DM was fabricated using a commercial silicon-on-insulator (SOI) MEMS process. Experimental modal analysis was carried out using laser Doppler vibrometry (LDV) to identify mode shapes of the DM and their natural frequencies. We are able to observe all of the lowest eight Zernike modes.

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.

Improvement of the focusability of petawatt laser pulses after nonlinear post-compression

The nonlinear nature of laser pulse post-compression inevitably leads to wavefront distortions. These distortions are nonstationary, i.e., they vary during the pulse, which significantly complicates the use of adaptive optics. We propose four approaches to compensation of wavefront distortions by means of standard adaptive mirrors, three of which can be implemented experimentally. Numerical simulations show that these approaches allow achieving a focal spot intensity close to the case of a perfectly flat wavefront.

Lab tests of segment/petal phasing with a pyramid wavefront sensor and a holographic dispersed fringe sensor in turbulence with the Giant Magellan Telescope high contrast adaptive optics phasing testbed

The Giant Magellan Telescope (GMT) design consists of seven circular 8.4-m diameter mirrors, together forming a single 25.4-m diameter primary mirror. This large aperture and collecting area can help extreme adaptive optics (ExAO) systems such as GMT’s GMagAO-X achieve the small angular resolutions and contrasts required to image habitable zone earth-like planets around late type stars and possibly lead to the discovery of life outside of our solar system. However, the GMT primary mirror segments are separated by large >30 cm gaps, creating the possibility of fluctuations in optical path differences (piston) due to flexure, segment vibrations, wind buffeting, temperature effects, and atmospheric seeing. To utilize the full diffraction-limited aperture of the GMT for high-contrast, natural guide star-adaptive optics science, the seven mirror segments must be co-phased to well within a fraction of a wavelength. The current design of the GMT involves seven adaptive secondary mirrors, a slow (∼0.03 Hz) off-axis dispersed fringe sensor (part of the acquisition guiding and wavefront sensing system’s active optics off-axis guider), and a pyramid wavefront sensor [PyWFS; part of the natural guide star wavefront sensor (NGWS) adaptive optics] to measure and correct the total path length between segment pairs, but these methods have yet to be tested “end-to-end” in a lab environment. We present the design and working prototype of a “GMT high contrast adaptive optics phasing testbed” that leverages the existing MagAO-X ExAO instrument to demonstrate segment phase sensing and simultaneous AO-control for high-contrast GMT natural guide star science [i.e., testing the NGWS wavefront sensor (WFS) architecture]. We present the first test results of closed-loop piston control with one GMT segment using MagAO-X’s PyWFS with and without simulated atmospheric turbulence. We show that the PyWFS was able to successfully control segment piston without turbulence within 12- to 33-nm RMS for 0 λ / D to 5 λ / D modulation, but was unsuccessful at controlling segment piston with generated ∼0.6 arcsec (median seeing conditions at the GMT site) and ∼1.2 arcsec seeing turbulence due to nonlinear modal cross-talk and poor pixel sampling of the segment gaps on the PyWFS detector. These results suggest that a PyWFS alone is not an ideal piston sensor for the GMT (and likely the TMT and ELT). Hence, a dedicated “second channel” piston sensor is required. We report the success of an alternate solution to control piston using a holographic dispersed fringe sensor (HDFS) while controlling all other modes with the PyWFS purely as a slope sensor (piston mode removed). This “second channel” WFS method worked well to control segment piston to within 50 nm RMS and ±10 μm dynamic range under simulated 0.6 arcsec atmospheric seeing (median seeing conditions at the GMT site). These results led to the inclusion of the HDFS as the official second channel piston sensor for the GMT NGWS WFS. This HDFS + PyWFS architecture should also work well to control piston petal modes on the ELT and TMT telescopes.