Deformable Mirror Research Articles

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.

Multilevel synergically controlling wavefront correction of a high-power slab laser system.

We present a multilevel synergically controlling wavefront correction method that can apply in a slab laser system. To fully utilize the response frequency and the stroke of actuators of the single deformable mirror (DM), we design a set of multilevel wavefront correction devices to reduce the root-mean square of wavefront aberration before the DM. As the wavefront of slab geometry solid-state lasers mainly consists of fourth and longitudinally distributed aberration, such as 5th, 9th, and 14th orders of Legendre polynomials. We design a precompensating level of the aberration with a slow-drift mirror, fast-steer mirror, one-dimensional adjustable slab-aberration compensator, and beam-shaping system to reduce these orders of wavefront aberration with low spatial resolution and large stroke. As the controlling bandwidth of different devices is diverse, the coupling oscillation between the precompensating level and adaptive optics (AO) level occurs, then we develop the multilevel synergically control to address the coupling. With the precompensating level, the experimental result shows the residual wavefront aberration of the slab laser is compensated well by the AO level effectively within the compensating capability. We clean up a 9.8kW slab laser system with the beam quality β of far-field focus spots improved from 17.71 to 2.24 times the diffraction limit.

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.

Analytical modelling of adaptive optics systems: Role of the influence function

Context. Adaptive optics (AO) is now a tool commonly deployed in astronomy. The real time correction of the atmospheric turbulence that AO enables allows telescopes to perform close to the diffraction limit at the core of their point spread function (PSF). Among other factors, AO-corrected PSFs depend on the ability of the wavefront corrector (WFC), generally a deformable mirror, to fit the incident wavefront corrugations. Aims. In this work, we focus on this error introduced by the WFC, the so-called fitting error. To date, analytical models only depend on the WFC cut-off frequency, and Monte Carlo simulations are the only solution for studying the impact of the WFC influence function shape on the AO-corrected PSF. We aim to develop an analytical model accounting for the influence function shape. Methods. We first obtain a general analytical model of the fitting error structure function. With additional hypotheses, we then derive an analytical model of the AO-corrected power spectral density. These two analytical solutions are compared with Monte Carlo simulations on different ideal profiles (piston, pyramid, Gaussian) as well as with real hardware (DM192 from ALPAO). Results. Our analytical predictions show a very good agreement with the Monte Carlo simulations. We show that in the image plane, the depth of the correction as well as the transition profile between the AO-corrected area and the remaining turbulent halo depend on the influence functions of the WFC. We also show that the generally assumed hypothesis of stationarity of the AO correction is actually not met. Conclusions. As the fitting error is the intrinsic optimal limit of an AO system, our analytical model allows for the assessment of the theoretical limits of extreme AO systems limited by the WFC in high-contrast imaging through a context where other errors become comparable.

Deep learning-based adaptive optics for light sheet fluorescence microscopy.

Light sheet fluorescence microscopy (LSFM) is a high-speed imaging technique that is often used to image intact tissue-cleared specimens with cellular or subcellular resolution. Like other optical imaging systems, LSFM suffers from sample-induced optical aberrations that decrement imaging quality. Optical aberrations become more severe when imaging a few millimeters deep into tissue-cleared specimens, complicating subsequent analyses. Adaptive optics are commonly used to correct sample-induced aberrations using a deformable mirror. However, routinely used sensorless adaptive optics techniques are slow, as they require multiple images of the same region of interest to iteratively estimate the aberrations. In addition to the fading of fluorescent signal, this is a major limitation as thousands of images are required to image a single intact organ even without adaptive optics. Thus, a fast and accurate aberration estimation method is needed. Here, we used deep-learning techniques to estimate sample-induced aberrations from only two images of the same region of interest in cleared tissues. We show that the application of correction using a deformable mirror greatly improves image quality. We also introduce a sampling technique that requires a minimum number of images to train the network. Two conceptually different network architectures are compared; one that shares convolutional features and another that estimates each aberration independently. Overall, we have presented an efficient way to correct aberrations in LSFM and to improve image quality.

Random vibration testing of microelectromechanical deformable mirrors for space-based high-contrast imaging

Space-based stellar coronagraph instruments aim to directly image exoplanets that are a fraction of an arcsecond separated from and 10 billion times fainter than their host star. To achieve this, one or more deformable mirrors (DMs) are used in concert with coronagraph masks to control the wavefront and minimize diffracted starlight in a region of the image known as the “dark zone” or “dark hole (DH).” The DMs must have a high number of actuators (50 to 96 across) to allow for DHs that are large enough to image a range of desired exoplanet separations. In addition, the surfaces of the DMs must be controlled at the picometer level to enable the required contrast. Any defect in the mechanical structure of the DMs or electronic system could significantly impact the scientific potential of the mission. Thus NASA’s Exoplanet Exploration Program procured two 50 × 50 microelectromechanical DMs manufactured by Boston Micromachines Corporation to test their robustness to the vibrational environment that the DMs will be exposed to during launch. The DMs were subjected to a battery of functional and high-contrast imaging tests before and after exposure to flight-like random vibrations. The DMs did not show any significant functional nor performance degradation at 10 − 8 contrast levels.

Helicity and topological charge tunable optical vortex based on a Hermite-Gaussian beam dynamically controlled folded-cavity resonator

Helicity and topological charge are two important characteristic parameters for vortex beam applications, including optical communications, optical manipulation and material processing, etc. In this work, a helicity and topological charge tunable vortex laser based on a folded resonant cavity is presented. In the resonant cavity, a Z-shaped structure is adopted and two deformable mirrors (DMs) are cascaded into the cavity as intro-cavity modulation elements. By applying different voltage combinations to the DMs, the Hermite-Gaussian (HG) beam with different indices and distribution orientations θ could be generated from the Z-shaped folded-cavity resonator. An extra-cavity astigmatic mode converter is adopted to convert the generated HG beam to the corresponding vortex beam with tunable helicity and topological charge, and the simulation results verified the feasibility of the presented vortex laser. In the experiment, the HGm,0θ beam (m = 1 to 10 and θ = −90 ° to 90 °]) and the vortex beam (topological charge l from ±1 to ±10 and left/right helicity) were flexibly achieved by simply adjusting the driving voltage combinations of the intra-cavity cascaded DMs.

Improving the telescope guiding with field stabilization on the Very Large Telescope/Unit Telescopes

Acquisition and guiding services have been provided at major telescopes in order to improve the quality and efficiency of scientific observations. Field stabilization (FS) is an essential component of the telescope control system. With the arrival of new-generation instruments, the stabilization requirements have increased. Higher correction frequency is required to minimize the residuals. A major re-engineering of the CCD acquisition software now enables an increase of the operational frequency from 25 to 87 Hz. We analyze and discuss the performances of FS at various frequencies on the Very Large Telescope with its 8-m telescopes including the Adaptive 8-m telescope equipped with a deformable secondary mirror. We will report on the analysis of the residuals in function of several operational key parameters, e.g., the loop frequency, the magnitude of the selected telescope guide star, etc. We will also discuss the possible automatization of the FS during night operations.

Electro‐optical performance of the large visible adaptive optics sensor module

AbstractIn order to achieve the best possible atmospheric corrections using its deformable mirrors, the Extremely Large Telescope (ELT) and its instruments will depend on several different wavefront sensor cameras as part of its adaptive optics systems. LISA, one of three wavefront sensor cameras that have been developed in‐house at ESO, will utilize a custom‐designed, large‐format CMOS detector developed by ESO and Teledyne‐e2v: the Large Visible adaptive optics Sensor Module, LVSM, an pixel sensor capable of operation at speeds in excess of 700 frames per second. We present the results of the electro‐optical characterization of this detector.

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.

Characterization of thick and contact lenses using an adaptive Shack–Hartmann wavefront sensor: Limitations and solutions

Lens characterization is a key challenge for reliable optical and imaging techniques. Shack–Hartmann wavefront sensor (SHWFS) is frequently used as an efficient tool for characterizing optical elements. However, the aberrations arising from the incident wavefront, utilized for the characterization process, cause imprecision in the spherical power measurement. Accordingly, the aim of the present study is to construct an experimental configuration that consists of SHWFS incorporated with a deformable mirror (DM) to provide a correction for the incident wavefront aberrations which yields an ideal plane wave. Different types of thick lenses with a wide range of focal lengths and three single-vision contact lenses were tested before and after aberrations compensation and compared to the reference-based method. The comparison was based on measuring the spherical powers for the tested lenses. The results indicate that the accuracy of measurements is influenced by the incident wavefront aberrations, which has been improved by the proposed compensation system. Finally, the limitations are investigated and it was concluded that the system in its current configuration failed to accurately measure some thick lenses. This issue was solved by suggesting a compound lens correction methodology that extended the measurement range of spherical powers beyond the designated measurable range of the system.

Maximizing atmospheric-disturbed fiber coupling efficiency with speckle-based phase retrieval and a single-pixel camera.

An approach to adaptive optics utilizing a single-pixel camera (SPC) is proposed to maximize fiber coupling efficiency at the receiver side of an optical satellite-to-ground link perturbed by atmospheric turbulence. Using a single-pixel wavefront sensor enables operation at longer optical wavelengths, such as near and far infrared, which have advantageous propagation characteristics for free space optical communication. In this approach, a focal plane intensity image of the atmospheric-disturbed wavefront is taken via an SPC using a compressed sensing technique. An iterative speckle-based phase retrieval algorithm is then applied to infer the phase distortion corrected by a deformable mirror in a feedback loop. This computational approach to inferring the phase of the wavefront overcomes the limitations of traditional Shack-Hartman-based approaches, which are difficult to implement at high speed and at the long infrared wavelengths proposed for future optical satellite communication downlinks. It has been shown that fiber coupling efficiency is increased from less than 5% to 40%-50% in medium-to-strong turbulence scenarios with the phase retrieval algorithm proposed in this work.

Adaptive Optical Closed-Loop Control Based on the Single-Dimensional Perturbation Descent Algorithm.

Modal-free optimization algorithms do not require specific mathematical models, and they, along with their other benefits, have great application potential in adaptive optics. In this study, two different algorithms, the single-dimensional perturbation descent algorithm (SDPD) and the second-order stochastic parallel gradient descent algorithm (2SPGD), are proposed for wavefront sensorless adaptive optics, and a theoretical analysis of the algorithms' convergence rates is presented. The results demonstrate that the single-dimensional perturbation descent algorithm outperforms the stochastic parallel gradient descent (SPGD) and 2SPGD algorithms in terms of convergence speed. Then, a 32-unit deformable mirror is constructed as the wavefront corrector, and the SPGD, single-dimensional perturbation descent, and 2SPSA algorithms are used in an adaptive optics numerical simulation model of the wavefront controller. Similarly, a 39-unit deformable mirror is constructed as the wavefront controller, and the SPGD and single-dimensional perturbation descent algorithms are used in an adaptive optics experimental verification device of the wavefront controller. The outcomes demonstrate that the convergence speed of the algorithm developed in this paper is more than twice as fast as that of the SPGD and 2SPGD algorithms, and the convergence accuracy of the algorithm is 4% better than that of the SPGD algorithm.

Combining EFC with spatial LDFC for high-contrast imaging on Subaru/SCExAO

Context.Exoplanet direct imaging is a key science goal of current ground-based telescopes as well as of future ground-based extremely large telescopes and space-based telescopes. Several high-contrast imaging (HCI) systems for direct exoplanet imaging have been developed and are implemented on current telescopes. Despite recent developments in HCI systems, the contrast they deliver is limited by non-common path aberrations (NCPAs) and residual wavefront errors of the adaptive optics (AO) system. To overcome this limitation and reach higher contrast, HCI systems need focal plane wavefront-sensing and control (FPWFS&C) techniques.Aims.We propose a method that provides both deep contrast and a 100% duty cycle by combining two complementary FPWFS&C methods: electric field conjugation (EFC), and spatial linear dark field control (LDFC). The ultimate goal of this work is to generate the high contrast zone, which is called the dark hole, in the focal plane by using EFC and to maintain the contrast within the high-contrast zone by using spatial LDFC without interrupting science observations. We describe the practical implementation, quantify the linearity range over which LDFC can operate, and derive its photon-noise-limited dynamical performance.Methods.We implemented EFC+LDFC on the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) instrument using its internal light source (off-sky). We first deployed the implicit EFC (iEFC) algorithm to generate the dark hole with a classical Lyot coronagraph (CLC) with a 114 mas diameter focal-plane mask at 1550 nm wavelength. This iEFC algorithm was deployed with pair-wise probes. Using iEFC with pair-wise probes, we directly measured the response matrix of the deformable mirror (DM) modes and built the control matrix by inverting the response matrix. After the calibration process, we generated the dark hole by closing the iEFC loop. When the dark hole was generated, we implemented spatial LDFC to restore and maintain the contrast of the dark hole. In the tests shown here, we introduced static and quasi-static speckles, and then we operated spatial LDFC in closed loop to verify its performance. We used numerical simulations to derive linearity range and photon-noise-limited dynamical performance.Results.Using iEFC, we generated the dark hole with a ~2×10−7contrast in a narrow-band filter (λ= 1550 ± 25 nm). We reached a contrast floor limited by the camera noise. Comparison between pre- and post-iEFC images shows that with iEFC in closed-loop operation, an improvement in contrast of a factor ≈ 100–500× was reached across the dark hole. In the spatial LDFC experiments, we were able to nearly fully remove the speckles generated by the DM perturbation and maintain the contrast of the dark hole.Conclusions.This work presents the first laboratory demonstration of combining two FPWFS&C methods, iEFC and spatial LDFC. Linear range and photon-noise-limited sensitivity are provided to derive close-loop performance for on-sky systems. Our results provide a promising approach for taking advantages of both high contrast and a 100% science duty cycle for HCI systems.

Performance of the adaptive optics system for Laser Communications Relay Demonstration's Ground Station 1.

The Laser Communications Relay Demonstration is NASA's multi-year demonstration of laser communication from the Earth to a geosynchronous satellite. The mission currently has two optical ground stations (OGSs), with one in California (OGS1) and one in Hawaii (OGS2). Each ground terminal optical system consists of a high-order adaptive optics (AO) system, a laser transmit system, and a camera for target acquisition. The OGS1 AO system is responsible for compensating for the downlink beam for atmospheric turbulence and coupling it into the modem's single mode fiber. The mission requires a coupling efficiency of 50%, which necessitates a high-order AO system. To achieve this performance, the AO system uses two deformable mirrors with one mirror correcting for low-spatial-frequency aberrations with large amplitude and a second deformable mirror correcting for high-spatial-frequency aberrations with small amplitude. Turbulence is sensed with a Shack-Hartmann wavefront sensor. To meet its performance requirements in the most stressing conditions, the system can operate at frame rates of 20kHz. This high frame rate is enabled by the design of the real-time control system. We present an overview of both the hardware and software design of the system, and describe the control system and methods of reducing non-common path aberrations. Finally, we show measured system performance.

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.

Two-stage control algorithm for magnetic fluid deformation mirror with dual-layer actuators

To increase the correction effectiveness of full-order aberration, a control system based on a magnetic fluid flexible mirror with dual-layer actuators is presented. The combined magnetic field created by the Maxwell coil and the double-layer driving coils controls the geometry of the magnetic fluid surface. A model-based optical sensorless control approach for lower layer coils is developed and aimed to enable high magnitude restoration of lower-order aberrations. An adaptive important factor that causes on Youla parameterization, on the other hand, is developed for the upper coils to rectify higher-order residual aberrations. Matlab is used to simulate the algorithm in order to test its performance in full-order aberration correction, and the results reveal that the approach has good correction performance.

Optical Design of a Slitless Astronomical Spectrograph with a Composite Holographic Grism

In the present work, we consider an optical design of a slitless spectrograph for an existing 0.5 m-class telescope. This design concept has a number of advantages such as compact size, simplicity, and simultaneous coverage of a large field of view. A challenge with this design is correcting aberrations caused by placing a dispersing element in a converging beam. To overcome this issue, we propose to use a composite grism, which represents a combination of a prism and a volume-phase holographic grating, the latter which is split into zones with independently optimized parameters. We demonstrate two designs of such a grism. In both designs, the spectrograph operates in the range of 450–950 nm in an F/6.8 beam and covers a field of view of 35.6′ × 7.2′. Through advanced modeling, it is shown that a composite grism having four rectangular zones with different thickness and index modulation depth of the hologram and recorded with an auxiliary deformable mirror decreases the astigmatic elongation by a factor of 85, increases the spectral resolving power by 4.4 times, and reaches R1389 while increasing the average diffraction efficiency by a factor of 1.31. If we reduce the number of zones to only two, replace the deformable mirror with two static corrector plates, and fix the hologram thickness, the corresponding performance gains still remain high: the astigmatism is reduced by a factor of 61, the spectral resolving power is up to 1.7 times higher, reaching R1067, and the efficiency is increased by a factor of 1.27. This shows that the proposed design allows the construction of a simple and compact instrument, providing high performance over the entire field of view and spectral range.

Low-order wavefront control using a Zernike sensor through Lyot coronagraphs for exoplanet imaging

Context. Wavefront sensing and control (WFSC) will play a key role in improving the stability of future large segmented space telescopes while relaxing the thermo-mechanical constraints on the observatory structure. Coupled with a coronagraph to reject the light of an observed bright star, WFSC enables the generation and stabilisation of a dark hole (DH) in the star image to perform planet observations. Aims. While WFSC traditionally relies on a single wavefront sensor (WFS) input to measure wavefront errors, the next generation of instruments will require several WFSs to address aberrations with different sets of spatial and temporal frequency contents. The multiple measurements produced in such a way will then have to be combined and converted to commands for deformable mirrors to modify the wavefront subsequently. Methods. We asynchronously operate a loop controlling the high-order modes digging a DH and a control loop that uses the rejected light by a Lyot coronagraph with a Zernike wavefront sensor to stabilize the low-order aberrations. Using the HiCAT testbed with a segmented telescope aperture, we implement concurrent operations and quantify the expected cross-talk between the two controllers. We then present experiments that alternate high-order and low-order control loops to identify and estimate their respective contributions. Results. We show an efficient combination of the high-order and low-order control loops, keeping a DH contrast better than 5 × 10−8 over a 30 min experiment and stability improvement by a factor of 1.5. In particular, we show a contrast gain of 1.5 at separations close to the DH inner working angle, thanks to the low-order controller contribution. Conclusions. Concurrently digging a DH and using the light rejected by a Lyot coronagraph to stabilize the wavefront is a promising path towards exoplanet imaging and spectroscopy with future large space observatories.

Compensation for aberrant wavefront in UOWC based on adaptive optics technique employing genetic algorithm

Underwater optical wireless communication (UOWC) has attracted extensive attention due to its merits in transmission latency, bandwidth, and security. However, its performance is usually significantly limited by the scattering, absorption, and turbulence effects. Thus, many schemes have been proposed to enhance its performance via various optimizations at the transmitter, but most of them neglected the wavefront optimization at the receiver. Although traditional adaptive optics based on wavefront detection (AOWD) technology employing wavefront phase sensor (e.g. Shack-Hartmann sensors) and compensator (e.g. deformable mirror) was proposed to alleviate wavefront distortion, it introduced extra challenges in miniaturizing receivers for UOWC. Additionally, traditional AOWD technologies usually employed costly and large computing systems,which reduced their feasibility in reality. In this paper, a novel compensation technology is proposed to optimize the distorted wavefront at the receiver based on the wavefront sensorless adaptive optics (WSAO) technique using improved genetic algorithm (GA). Instead of using the wavefront phase-detector, the proposed technology measures the light intensity via a small photo-detector (PD) and outputs voltage signals though the employed GA to manipulate the deformable mirror (DM) for wavefront compensation. The simulation results indicate that the proposed technology effectively improves the intensity distribution and the Strehl Ratio (SR) of the transmission light in UOWC.