Adaptive Optics System Research Articles

Into nonlinearity and beyond for Zernike-like wavefront sensors

Context. Telescopes like the Extremely Large Telescope (ELT) and the Giant Magellan Telescope (GMT) will be used together with extreme adaptive optics (AO) instruments to directly image Earth-like planets. The AO systems will need to perform at the fundamental limit in order to image Earth twins. A crucial component is the wavefront sensor. Interferometric wavefront sensors, such as the Zernike wavefront sensor (ZWFS), have been shown to perform close to the fundamental sensitivity limit. However, sensitivity comes at the cost of linearity; the ZWFS has strong nonlinear behavior. Aims. The aim of this work is to increase the dynamic range of Zernike-like wavefront sensors by using nonlinear reconstruction algorithms combined with phase sorting interferometry (PSI) and multi-wavelength measurements. Methods. The response of the ZWFS is explored analytically and numerically. Results. The proposed iterative (non)linear reconstructors reach the machine precision for small aberrations (<0.25 rad rms). Coupling the nonlinear reconstruction algorithm with PSI increases the dynamic range of the ZWFS by a factor of three to about 0.75 rad rms. Adding multiple wavebands doubles the dynamic range again, to 1.4 radians rms. Conclusions. The ZWFS is one of the most sensitive wavefront sensors, but has a limited dynamic range. The ZWFS will be an ideal second-stage wavefront sensor if it is combined with the proposed nonlinear reconstruction algorithm.

Ground-layer Adaptive Optics for the 2.5 m Wide-field and High-resolution Solar Telescope

The 2.5 m wide-field and high-resolution solar telescope (WeHoST) is currently under developing for solar observations. WeHoST aims to achieve high-resolution observations over a super-wide field of view (FOV) of 5′ × 5′, and a desired resolution of 0.3″. To meet the scientific requirements of WeHoST, the ground-layer adaptive optics (GLAO) with a specially designed wave front sensing system is as the primary consideration. We introduce the GLAO configuration, particularly the wave front sensing scheme. Utilizing analytic method, we simulate the performance of both classical AO and GLAO systems, optimize the wave front sensing system, and evaluate GLAO performance in terms of PSF uniformity and correction improvement across whole FOV. The results indicate that, the classical AO will achieve diffraction-limited resolution; the suggested GLAO configuration will uniformly improve the seeing across the full 5′ × 5′ FOV, reducing the FWHM across the axis FOV to less than 0.3″ (λ ≥ 705 nm, r 0 ≥ 11 cm), which is more than two times improvement. The specially designed wave front sensor schedule offers new potential for WeHoST’s GLAO, particularly the multi-FOV GLAO and the flexibility to select the detected area. These capabilities will significantly enhance the scientific output of the telescope.

Wavefront reconstruction based on ASH-Net with less lenslets SHWFS

Generally, the number of lenslets in Shack–Hartman wavefront sensor (SHWFS) determines its spatial sampling frequency. However, increasing the number of lenslets is limited by the data processing delay time and low sensitivity in the adaptive optics system. In this paper, a wavefront reconstruction method based on ASH-Net for SHWFS is presented to recover the distorted wavefront from the light spots array with high accuracy with a spatial sampling frequency than traditionally required. The results show that the maximum number of Zernike modes recovered by the method is 36, 54, and 70 for 4 × 4, 6 × 6, and 8 × 8 lenslets arrays, respectively. Residual wavefront root mean square values are as low as about 0.02 μm, corresponding to a Strehl Ratio of 0.99. This method breaks the limitation that the number of reconstructed Zernike modes in the traditional wavefront reconstruction algorithm must be less than the number of effective lenslets. Experiments in lab are used to validate the method. Additionally, fewer lenslets is valuable to improve the detection capability of SHWFS for faint targets. This is important for applications of adaptive optics in areas such as astronomy and retinal imaging.

Performance analysis and optimization of solar multiconjugate adaptive optics systems

ABSTRACT Multiconjugate adaptive optics (MCAO) stands as an essential technology for the development of future large-aperture solar telescopes. Its primary objective is to empower telescopes to achieve nearly diffraction-limited performance while substantially extending the correction field of view (FoV). Conventional solar MCAO relies on the combination of adaptive optics and high-altitude correction (AO + HAC) modules for multiconjugate correction. However, this architectural approach excels in correction performance primarily at the central position, with performance deteriorating as one moves farther from the centre. Consequently, it results in poor consistency of FoV correction performance. To address these limitations, a new architectural approach was introduced, which combines ground layer AO with HAC (GLAO + HAC). Preliminary results have shown that, compared to AO + HAC, this approach significantly enhances FoV correction uniformity. Building upon these initial findings, this paper undertakes a more extensive research of the GLAO + HAC system. Its objective is to compare various solar MCAO system architectures, including AO + HAC, GLAO + HAC, and general MCAO, to finally propose optimization tailored to GLAO + HAC. Through this analysis, the paper conducts the performance comparison between GLAO + HAC and general MCAO. It underscores that, under equivalent configuration parameters, the differences between these two systems are marginal. However, due to the advantage of the independent control of dual correction modules in GLAO + HAC, it can introduce an optimization strategy by increasing the number of subapertures at the cost of reducing the GLAO guide star sensing FoV. Finally, the results of this strategy demonstrate an obvious enhancement in performance and FoV correction consistency within the GLAO + HAC system.

Searching for low-mass companions at small separations in transition disks with aperture masking interferometry

Context. Transition disks have large central cavities that have been resolved by imaging surveys during recent years. Cavities and other substructures in circumstellar disks are often interpreted as signposts to massive companions. Detecting companions at small angular separations is challenging with coronagraphic imaging observations. Aims. We aim to search for stellar and substellar companions in the central regions of transition disks. Such companions could be responsible for the large dust-depleted cavities. We want to determine if these disks might be circumbinary in their nature, similar to the HD 142527 system. Methods. We observed four systems, HD 100453, HD 100546, HD 135344 B, and PDS 70, with the sparse aperture masking mode of VLT/SPHERE, also leveraging the star-hopping method with the adaptive optics system. We extracted the complex visibilities and bispectra from the H2 and H3 imaging data. A binary model was fit to the closure phases to search for companions and estimate detection limits. For validation, we also analyzed four archival datasets of HD 142527 and inferred the orbital elements and atmospheric parameters of its low-mass stellar companion. Results. We have not detected any significant point sources in the four observed systems. With a contrast sensitivity of ≈0.004, we can rule out stellar companions down to ≈2 au and partially explore the substellar regime at separations ≳3–5 au. The analysis of HD 142527 B revealed that its projected orbit is aligned with dust features in the extended inner disk and that the mutual inclination with the outer disk is close to coplanar for one of the two solutions. Atmospheric modeling confirms the low-gravity and slightly reddened spectral appearance (Teff ≈ 3300 K, log 𝑔 ≈ 3.7, and AV ≈ 0.7). The inferred and derived bulk parameters (log L*/L0 ≈ −0.65, M* ≈ 0.4 M⊙, and R* ≈ 1.46 R⊙) are in agreement with dynamical constraints and evolutionary tracks. Conclusions. In contrast to HD 142527, we find no evidence that a close-in stellar companion is responsible for the resolved disk features of HD 100453, HD 100546, HD 135344 B, and PDS 70. Instead of a dynamical effect by a stellar companion, the formation of giant planets or even low-mass brown dwarfs could be shaping the innermost environment (≲20 au) of these circumstellar disks, as is the case with the planetary system of PDS 70.

Overview of modern technologies for measuring, predicting and correcting turbulent distortions in optical waves

This work is an analytical review of the components of modern technology for creating adaptive optics systems for correcting the distortion of optical waves propagating in a turbulent atmosphere. The work consists of the following parts: description of a technique for measuring fluctuations of optical waves in an atmospheric path, theoretical calculations of fluctuations by analytical analysis and mathematical modeling methods, technology for predicting turbulent air movement by the numerical solution of the Navier–Stokes equations and, finally, constructing adaptive optics systems that compensate for the turbulent distortions in optoelectronic image construction systems. Attention is focused on the peculiarities of fluctuations of specially created Laguerre–Gaussian and Bessel–Gaussian beams. Features of the propagation of vortex Laguerre–Gaussian and vortex Bessel–Gaussian beams for the transfer of orbital angular momentum through a turbulent medium are shown. Effects of the relative attenuation of phase and intensity fluctuations of the vortex-free Bessel–Gaussian beams in comparison with similar characteristics of the Gaussian beams are found. The integral scale of the coherence degree of the vortex Bessel–Gaussian beams and vortex conic waves is revealed to be highly sensitive to the influence of atmospheric turbulence, in contrast to the coherence radius of these beams and waves. Arguments are given in favor of the feasibility of constructing adaptive optical systems for a wide-aperture solar telescope operating under a strong atmospheric turbulence.

The Bi–O edge wavefront sensor

Context. Direct detection of exoplanets around nearby stars requires advanced adaptive optics (AO) systems. High-order systems are needed to reach a high Strehl ratio (SR) in near-infrared and optical wavelengths on future giant segmented-mirror telescopes (GSMTs). Direct detection of faint exoplanets with the European Southern Observatory (ESO) Extremely Large Telescope (ELT) will require some tens of thousands of correction modes. The resolution and sensitivity of the wavefront sensor (WFS) are key requirements for this science case. We present a new class of WFSs, the bi-orthogonal Foucault knife-edge sensors (or Bi–O edge), that is directly inspired by the Foucault knife-edge test. The idea consists of using a beam-splitter producing two foci, each of which is sensed by an edge with a direction orthogonal to the other focus. Aims. We describe two implementation concepts: The Bi–O edge sensor can be realised with a sharp edge and a tip-tilt modulation device (sharp Bi–O edge) or with a smooth gradual transmission over a grey edge (grey Bi–O edge). A comparison of the Bi–O edge concepts and the four-sided classical pyramid wavefront sensor (PWS) gives some important insights into the nature of the measurements. Methods. We analytically computed the photon noise error propagation, and we compared the results to end-to-end simulations of a closed-loop AO system. Results. Our analysis shows that the sensitivity gain of the Bi–O edge with respect to the PWS depends on the system configuration. The gain is a function of the number of control modes and the modulation angle. We found that for the sharp Bi–O edge, the gain in reduction of propagated photon noise variance approaches a theoretical factor of 2 for a large number of control modes and small modulation angle, meaning that the sharp Bi–O edge only needs half of the photons of the PWS to reach similar measurement accuracy. In contrast, the PWS is twice more sensitive than the Bi–O edge in the case of very low order correction and/or large modulation angles. Preliminary end-to-end simulations illustrate some of the results. The grey version of the Bi–O edge opens the door to advanced amplitude filtering, which replaces the need for a tip-tilt modulator while keeping the same dynamic range. We show that an additional factor of 2 in reduction of propagated photon noise variance can be obtained for high orders, such that the theoretical maximum gain of a factor of 4 in photon efficiency can be obtained. A diffractive Fourier model that accurately includes the effect of modulation and control modes shows that for the extreme AO (XAO) system configuration of the ELT, the overall gain will well exceed one magnitude in guide-star brightness when compared to the modulated PWS. Conclusions. We conclude that the Bi–O edge is an excellent candidate sensor for future very high order Adaptive Optics systems, in particular on GSMTs.

Using Diffraction Deep Neural Networks for Indirect Phase Recovery Based on Zernike Polynomials.

The phase recovery module is dedicated to acquiring phase distribution information within imaging systems, enabling the monitoring and adjustment of a system's performance. Traditional phase inversion techniques exhibit limitations, such as the speed of the sensor and complexity of the system. Therefore, we propose an indirect phase retrieval approach based on a diffraction neural network. By utilizing non-source diffraction through multiple layers of diffraction units, this approach reconstructs coefficients based on Zernike polynomials from incident beams with distorted phases, thereby indirectly synthesizing interference phases. Through network training and simulation testing, we validate the effectiveness of this approach, showcasing the trained network's capacity for single-order phase recognition and multi-order composite phase inversion. We conduct an analysis of the network's generalization and evaluate the impact of the network depth on the restoration accuracy. The test results reveal an average root mean square error of 0.086λ for phase inversion. This research provides new insights and methodologies for the development of the phase recovery component in adaptive optics systems.

High-bandwidth tilt-tip mirror with octagonal prism flexible mechanism.

The adaptive optical system requires a tilt-tip mirror (TTM) with high bandwidth to compensate for optical beam jitter caused by atmospheric turbulence in real time. This paper introduces a novel, to the best of our knowledge, design of a voice coil TTM using an octagonal flexible mechanism and optimizes its parameters through theoretical analysis and finite element simulations. The results show that its resonance frequency in the non-working direction is up to 1005.2Hz, representing a 19.4% improvement in theoretical calculations and a 13.8% improvement in simulations compared to traditional cylindrical flexible mechanisms. Additionally, the non-working direction stiffness of the flexible support structure has been optimized, enhancing the third-order and higher resonance frequencies of the system to meet the high bandwidth requirements. A prototype of the TTM was developed based on this design, and its deflection angles and responses were measured in the laboratory, confirming the design's reliability. This low-cost, high-bandwidth TTM design facilitates miniaturization of adaptive optical systems, making it beneficial for applications in astronomical observations, laser communication, laser weapons, laser processing, and more.

A deep-learning approach for turbulence correction in free space optical communication with Laguerre–Gaussian modes

Free space optical communication has become increasingly popular in the past decade due to its terahertz bandwidth, unlicensed spectrum, and enhanced security features. This technology has been attracting significant interest from the network community due to its broad applications in future military and civilian protocols. Recently, the use of orthogonal spatial states of the light field, including those with nonzero orbital angular momentum, has increased communication system capacities and bit-transfer rates per photon. However, atmospheric turbulence disrupts the orthogonal spatial modes over propagation. We present a novel deep learning architecture, cGULnet, to mitigate the effects of atmospheric turbulence on spatial multiplexing of Laguerre–Gaussian structured light modes. The model predicts the phase correction patterns required for an adaptive optical system. It is a U-shaped architecture trained adversarially to a patch discriminator similar to conditional generative adversarial neural-networks. The network is trained for exact phase recovery systems without approximating Zernike polynomials, enabling its use in highly phase-sensitive but high-speed spatial multiplexed communication systems. The proposed architecture can predict the successive three frames in a single shot using the previous ten frames. The method was evaluated for a wide range of beam waist sizes in a simulated Laguerre–Gaussian spatial mode multiplexed 1 km free space optical communication link. We have considered 20 dB optical signal-to-noise ratio, with turbulence conditions parameterized by the refractive index structure parameter of Cn2≤5×10−15m−23. It was found to reduce the bit error rate to the International Telecommunication Union recommended forward error correction limit of 3.8×10−3 under high turbulence conditions.

Single-mode waveguides for GRAVITY

The second generation Very Large Telescope Interferometer (VLTI) instrument GRAVITY is a two-field infrared interferometer operating in the K band between 1.97 and 2.43 µm with either the four 8 m or the four 1.8 m telescopes of the Very Large Telescope (VLT). Beams collected by the telescopes are corrected with adaptive optics systems and the fringes are stabilized with a fringe-tracking system. A metrology system allows the measurement of internal path lengths in order to achieve high-accuracy astrometry. High sensitivity and high interferometric accuracy are achieved thanks to (i) correction of the turbulent phase, (ii) the use of low-noise detectors, and (iii) the optimization of photometric and coherence throughput. Beam combination and most of the beam transport are performed with single-mode waveguides in vacuum and at low temperature. In this paper, we present the functions and performance achieved with weakly birefringent standard single-mode fiber systems in GRAVITY. Fibered differential delay lines (FDDLs) are used to dynamically compensate for up to 6 mm of delay between the science and reference targets. Fibered polarization rotators allow us to align polarizations in the instrument and make the single-mode beam combiner close to polarization neutral. The single-mode fiber system exhibits very low birefringence (less than 23°), very low attenuation (3.6–7 dB km−1 across the K band), and optimized differential dispersion (less than 2.04 µrad cm2 at zero extension of the FDDLs). As a consequence, the typical fringe contrast losses due to the single-mode fibers are 6% to 10% in the lowest-resolution mode and 5% in the medium- and high-resolution modes of the instrument for a photometric throughput of the fiber chain of the order of 90%. There is no equivalent of this fiber system to route and modally filter beams with delay and polarization control in any other K-band beamcombiner.

Design and experimental validation of a model-free controller for beam stabilization in adaptive optics systems

Design and experimental validation of a model-free controller for beam stabilization in adaptive optics systems

Enhancing the Capability of Future Medium-size Telescopes: First Light of the SALTO Demonstrator

The adaptive optics (AO) technology is crucial to achieve the full potential of ground-based telescopes. Over the last three decades, the world has witnessed the successful advent and operation of AO systems on large ground-based telescopes. The complexity and cost of AO systems have largely gone down in the last decade thanks to advances in deformable mirror, wavefront sensor, and real-time computing technologies. Here, we present a robust Rayleigh scattered laser-guided single conjugated adaptive optics system called SALTO, which was designed, built, and tested in the Belgian countryside on a 1-meter class telescope. This project aims to demonstrate the possibility of rejuvenating the scientific goals of medium-class telescopes (1-3 m) with AO technology, as well as to enable optical telecommunication from relatively poor observing sites. This paper discusses the overview of the design, integration and calibration of SALTO. It concludes with the presentation of successful on-sky results at 1.55 μm under 2-3" seeing.

Hyper-parameter optimization of iterative control algorithms for adaptive optical systems

Hyper-parameter optimization of iterative control algorithms for adaptive optical systems

Probing Disk Ice Content and Polycyclic Aromatic Hydrocarbon Emission through Multiband MagAO+Clio Images of HD 141569

We present resolved images of the inner disk component around HD 141569A using the Magellan adaptive optics system with the Clio2 1–5 μm camera, offering a glimpse of a complex system thought to be in a short evolutionary phase between protoplanetary and debris disk stages. We use a reference star along with the Karhunen–Loéve image projection (KLIP) algorithm for point-spread function subtraction to detect the disk inward to about 0.″24 (∼25 au assuming a distance of 111 pc) at high signal-to-noise ratios at L′ (3.8 μm), Ls (3.3 μm), and narrowband Ice (3.1 μm). We identify an arc or spiral arm structure at the southeast extremity, consistent with previous studies. We implement forward modeling with a simple disk model within the framework of a Markov Chain Monte Carlo sampler to better constrain the geometrical attributes and photometry using our KLIP-reduced disk images. We then leverage these modeling results to facilitate a comparison of the measured brightness in each passband to find a reduction in scattered light from the disk in the Ice filter, implying significant absorption due to water ice in the dust. Additionally, our best-fit disk models exhibit peak brightness in the southwestern, back-scattering region of the disk, which we suggest to be possible evidence of 3.3 μm polycyclic aromatic hydrocarbon emission. However, we point out the need for additional observations with bluer filters and more complex modeling to confirm these hypotheses.

Solar adaptive optics systems for the New Vacuum Solar Telescope at the Fuxian Lake Solar Observatory

Solar adaptive optics systems for the New Vacuum Solar Telescope at the Fuxian Lake Solar Observatory

Accuracy Analysis for Shack–Hartmann Wave Front Sensing with Extended Sources

Correlating the Shack–Hartmann wave front sensor (SH-WFS) with extended targets is widely used in solar adaptive optics systems. This paper aims to introduce a theoretical analysis that evaluates the accuracy of the SH-WFS on extended sources, with a specific focus on the implementation of the Normalized Cross-correlation (NCC) algorithm. To obtain an accurate error description, we utilized the calculation formula of the NCC algorithm to directly express the coordinates of the maximum value in the correlation function matrix. Furthermore, we determined the variance of the centroid position through the error transfer function, which quantifies the measurement error. In comparison with the previous findings of Michau et al., our result exhibits a coefficient disparity, specifically obtaining results 1.5 times higher than their work. The extensive solar granulation simulation and experimental results validate the theoretical error formulas. These error formulas can effectively estimate the accuracy of the SH-WFS, providing a theoretical foundation for the design of optical systems.

An Efficient Method for Wavefront Aberration Correction Based on the RUN Optimizer

The correction of wavefront aberrations in wavefront sensorless (WFS-less) adaptive optical (AO) systems requires control algorithms that can ensure rapid convergence while maintaining effective correction capabilities. This paper proposes a novel control algorithm based on the RUNge Kutta optimizer (RUN) for WFS-less AO systems that enables the quick and efficient correction of small aberrations, as well as larger aberrations. To evaluate the convergence speed and correction capabilities of a WFS-less AO system based on the RUN control algorithm, we constructed a simulated AO system and an experimental setup with a 97-element deformable mirror (DM), respectively. Additionally, the results obtained with the Particle Swarm Optimization (PSO) algorithm, Differential Evolution Algorithm (DEA), and Genetic Algorithm (GA) are also provided for comparison and analysis. Both the simulated and experimental results consistently demonstrated that our proposed method outperformed several competing algorithms in terms of correction performance and convergence speed. Furthermore, the experimental results further validate the effectiveness of our control algorithm in scenarios involving significant aberrations.

Fractional loop delays in adaptive optics modeling and control.

This paper revisits the problem of optimal (minimum variance) control for adaptive optics (AO) systems when measurement and command applications are asynchronous, resulting in a non-integer servo loop delay. When not properly accounted for, such fractional delays may severely degrade the AO performance, especially in the presence of high-frequency vibrations. We present evidence of this performance degradation thanks to in-lab experimental measurements on the Gran Telescopio Canarias Adaptive Optics (GTCAO) system controlled with standard suboptimal linear quadratic Gaussian (LQG) controllers. A constructive, easy to implement LQG control design is then proposed and validated in a simulation for vibrations affecting the tip-tilt modes. Our methodology is very interesting because it allows a performance assessment for any linear controller in terms of variance, rejection transfer functions, power spectral densities, and stability margins. We also show how the continuous-time disturbance model can be derived from standard discrete-time disturbance data-based modeling.

Reinforcement Learning Environment for Wavefront Sensorless Adaptive Optics in Single-Mode Fiber Coupled Optical Satellite Communications Downlinks

Optical satellite communications (OSC) downlinks can support much higher bandwidths than radio-frequency channels. However, atmospheric turbulence degrades the optical beam wavefront, leading to reduced data transfer rates. In this study, we propose using reinforcement learning (RL) as a lower-cost alternative to standard wavefront sensor-based solutions. We estimate that RL has the potential to reduce system latency, while lowering system costs by omitting the wavefront sensor and low-latency wavefront processing electronics. This is achieved by adopting a control policy learned through interactions with a cost-effective and ultra-fast readout of a low-dimensional photodetector array, rather than relying on a wavefront phase profiling camera. However, RL-based wavefront sensorless adaptive optics (AO) for OSC downlinks faces challenges relating to prediction latency, sample efficiency, and adaptability. To gain a deeper insight into these challenges, we have developed and shared the first OSC downlink RL environment and evaluated a diverse set of deep RL algorithms in the environment. Our results indicate that the Proximal Policy Optimization (PPO) algorithm outperforms the Soft Actor–Critic (SAC) and Deep Deterministic Policy Gradient (DDPG) algorithms. Moreover, PPO converges to within 86% of the maximum performance achievable by the predominant Shack–Hartmann wavefront sensor-based AO system. Our findings indicate the potential of RL in replacing wavefront sensor-based AO while reducing the cost of OSC downlinks.