Performance Of Adaptive Optics System Research Articles

Analysis of speckle-beacon size impact on wavefront sensing and closed-loop control in deep turbulence conditions

The impact of the laser beacon size on the performance of an ideal phase-conjugation-type adaptive optics (AO) system is analyzed using wave-optics-based numerical simulation. The analysis includes wavefront aberration sensing and closed-loop control for laser beam propagation both in vacuum and in distributed (volume) atmospheric turbulence with the beacon beam scattering off a flat extended target with Lambertian surface roughness. For mitigation of the impact of target-induced speckle effects on the performance of AO systems, speckle-average wavefront sensing and control approaches are introduced and analyzed. The results demonstrate that proposed speckle-average phase conjugation control algorithms enable partial mitigation of turbulence-induced aberrations in presence of strong speckle modulations.

Implementing a Hybrid Method for Shack–Hartmann Wavefront Spots Labeling on FPGA

This paper presents a real-time implementation of a hybrid connected component labeling method for processing the Shack–Hartmann wavefront sensor’s images for an adaptive optics (AO) system. The output image of a wavefront sensor is an image of spots. During the sensor’s operation, it can happen that highly distorted wavefronts (WF) may cause the spots to shift outside of their sub-aperture, which may lead to the reduction of the AO system performance. This article explains the benefits of high-performance computing and parallel processing of a field programmable gate array (FPGA). The objective is to calculate the centroids of these spots. A hybrid labeling method was investigated to fulfill this purpose. First, this method was implemented using a forward and backward scan with a respective mask for each scan. Additionally, a relabeling process is applied after labeling each line, and it is carried out in both directions. After labeling, several processing units were implemented in parallel to calculate centroids. Each unit is responsible for calculating the centroid of one label. The system runs in real time with a latency of one frame, which means the output image is a fusion of a current frame and the centroids of the previous frame. Forward and backward labeling requires a large amount of memory, which is the reason for limiting the investigation to forward labeling only. The forward labeling was successfully implemented, and the centroids were detected under minimum spot distortion conditions. This forward labeling implementation also runs in real time with significant latency reduction to calculate the centroids, which leads to minimizing the overall AO system latency, enabling faster computation and correction in addition to reducing the memory usage to 1% when compared to the forward and backward labeling usage of 81% as an advantage for the hardware implementation.

Comparative Analysis of Image-shift Measurement Algorithms for Solar Shack–Hartmann Wavefront Sensors

Observations of the Sun provide unique insights into its structure, evolution, and activity, with significant implications for space weather forecasting and solar energy technologies. Ground-based telescopes offer cost-effective and flexible solutions for high-resolution solar observations, but image quality can be affected by atmospheric turbulence. Adaptive optics (AO) systems equipped with Shack–Hartmann wave front sensors (SH-WFS) enable real-time image correction to mitigate these effects. The accuracy of SH-WFS relies on correlation algorithms that measure wave front shifts, but reaching consistent conclusions regarding their accuracy remains challenging. In this study, we conducted an evaluation and comparison of standard correlation algorithms (the Square Difference Function, Normalized Cross-Correlation, Absolute Difference Function, Absolute Difference Function-Squared, and the Covariance Function in the frequency domain (CFF)) using simulated and authentic solar images. We optimized the algorithms through pre-processing techniques and carefully selected the most suitable window function for the CFF algorithm. Additionally, we analyzed the influence of various factors, such as shift ranges, bias, and the size of live images on the accuracy of algorithms. The consistent findings revealed that the CFF algorithm demonstrates superior measurement accuracy and robustness compared to the others. Choosing the CFF algorithm for solar observations can significantly enhance measurement accuracy, AO system performance, and the overall quality of solar research findings, thereby providing crucial support for space weather forecasting and other related scientific fields.

Adaptive Optical Closed-Loop Control on the Basis of Hyperparametric Optimization of Convolutional Neural Networks

In adaptive optics systems, the precision wavefront sensor determines the closed-loop correction effect. The accuracy of the wavefront sensor is severely reduced when light energy is weak, while the real-time performance of wavefront sensorless adaptive optics systems based on iterative algorithms is poor. The wavefront correction algorithm based on deep learning can directly obtain the aberration or correction voltage from the input image light intensity data with better real-time performance. Nevertheless, manually designing deep-learning models requires a multitude of repeated experiments to adjust many hyperparameters and increase the accuracy of the system. A wavefront sensorless system based on convolutional neural networks with automatic hyperparameter optimization was proposed to address the aforementioned issues, and networks known for their superior performance, such as ResNet and DenseNet, were constructed as constructed groups. The accuracy of the model was improved by over 26%, and there were fewer parameters in the proposed method, which was more accurate and efficient according to numerical simulations and experimental validation.

Reducing the impact of adaptive optics lag on optical and quantum communications rates from rapidly moving sources

Wavefront of light passing through the turbulent atmosphere gets distorted. This causes signal loss in free-space optical communication as the light beam spreads and wanders at the receiving end. Frequency and/or time division multiplexing adaptive optics (AO) techniques have been used to conjugate this kind of wavefront distortion. However, if the signal beam moves relative to the atmosphere, the AO system performance degrades due to high temporal anisoplanatism. Here, we solve this problem by adding a pioneering beacon that is spatially separated from the signal beam with time delay between spatially separated pulses. More importantly, our protocol works irrespective of the signal beam intensity and, hence, is also applicable to secret quantum communication. In particular, using semi-empirical atmospheric turbulence calculation, we show that for low earth orbit satellite-to-ground decoy state quantum key distribution with the satellite at zenith angle <30°, our method increases the key rate by at least 215% and 40% for satellite altitudes of 400 and 800 km, respectively. Finally, we propose a modification of the existing wavelength division multiplexing systems as an effective alternative solution to this problem.

Analyzing long-term performance of the Keck-II adaptive optics system

We present an analysis of the long-term performance of the W. M. Keck observatory laser guide star adaptive optics (LGS-AO) system and explore factors that influence the overall AO performance most strongly. Astronomical surveys can take years or decades to finish, so it is worthwhile to characterize the AO performance on such timescales in order to better understand future results. The Keck telescopes have two of the longest-running LGS-AO systems in use today, and as such they represent an excellent test-bed for processing large amounts of AO data. We use a Keck-II near infrared camera 2 (NIRC2) LGSAO surve of the Galactic Center (GC) from 2005 to 2019 for our analysis, combining image metrics with AO telemetry files, multiaperture scintillation sense/differential imaging motion monitor turbulence profiles, seeing information, weather data, and temperature readings in a compiled dataset to highlight areas of potential performance improvement. We find that image quality trends downward over time, despite multiple improvements made to Keck-II and its AO system, resulting in a 9 mas increase in the average full width at half maximum (FWHM) and a 3% decrease in the average Strehl ratio over the course of the survey. Image quality also trends upward with ambient temperature, possibly indicating the presence of uncorrected turbulence in the beam path. Using nine basic features from our dataset, we train a simple machine learning (ML) algorithm to predict the delivered image quality of NIRC2 given current atmospheric conditions, which could eventually be used for real-time observation planning and exposure time adjustments. A random forest algorithm trained on this data can predict the Strehl ratio of an image to within 18% and the FWHM to within 7%, which is a solid baseline for future applications involving more advanced ML techniques. The assembled dataset and coding tools are released to the public as a resource for testing new predictive control and point spread function-reconstruction algorithms.

Analyzing the Effects of a Basin on Atmospheric Environment Relevant to Optical Turbulence

The performance of adaptive optics (AO) systems are highly dependent upon optical turbulence. Thus, it is necessary to have the appropriate knowledge of the spatiotemporal characteristics of optical turbulence strength. In this paper, the spatiotemporal distribution of meteorological parameters (wind and temperature) and optical turbulence parameters (turbulence strength, temperature gradient, and wind shear) derived from pulsed coherent Doppler lidar, a microwave radiometer, and ERA5 reanalysis data are investigated, and the results show that the meteorological parameters in a basin develop independently, while the external influence will increase above the basin. By fitting radiosonde data, an existing parameterized model was improved to be more in line with the evolutionary properties of local optical turbulence. The development of temperature gradient and wind shear is influenced by the basin, which ultimately leads to an optical turbulence vertical profile that is discrepant at different altitude layers. The results indicate that temperature gradient plays a dominant role in turbulence generation below 2 km, and wind shear increases its impact significantly above 2 km. Furthermore, the optical turbulence parameters (outer scale, turbulence diffusion coefficient, and turbulence energy dissipation rate) and optical turbulence strength have good consistency, which might be derived from the combined effect of terrain and complex environment. Finally, the integrated parameters for astronomy and optical telecommunication were derived from optical turbulence strength profiles. An appropriate knowledge of optical turbulence is essential for improving the performance of adaptive optics systems and astronomical site selection.

Cascade adaptive optics: contrast performance analysis of a two-stage controller by numerical simulations

The contrast performance of current extreme adaptive optics (XAO) systems can be improved by adding a second AO correction stage featuring its own wavefront sensor (WFS), deformable mirror (DM), and real-time controller. We develop a dynamical model for such a cascade adaptive optics (CAO) system with two stages each controlled by a standard integrator and study its control properties. We study how such a configuration can improve an existing system without modifying the first stage. We analyze the CAO architecture in general and show how part of the disturbance is transferred from low to high temporal frequencies with a nefarious effect of the second stage integrator overshoot and suggest possible ways to mitigate this. We also carry out numerical simulations of the particular case of a first stage AO using a Shack–Hartmann WFS and a second stage AO with a smaller DM running at a higher framerate to reduce temporal error. In this case, we demonstrate that the second stage improves imaging contrast by one order of magnitude and shortens the decorrelation time of atmospheric turbulence speckles by even a greater factor. The results show that CAO presents a promising and relatively simple way to upgrade some existing XAO systems and achieve improved imaging contrasts fostering a large number of science case including the direct imaging of exoplanets.

Influence of bandwidth error on the performance of adaptive optics systems for uncooperative beacons.

We discuss the capability of adaptive optics to increase the performance of laser systems operating in atmospheric turbulence. Our approach is based on the Zernike filter functions, Taylor's frozen-flow hypothesis, and bandwidth limitations of a realistic servo control system. System performance is analyzed in terms of the Strehl ratio on target. Our results for plane-wave geometry indicate that adaptive optics can be effective even when engaging fast moving targets and that moderate closed-loop bandwidths of ∼100Hz would suffice for most analyzed scenarios. Applications of interest are beam delivery systems and free-space optical communications.

Wavefront prediction using artificial neural networks for open-loop adaptive optics

ABSTRACT Latency in the control loop of adaptive optics (AO) systems can severely limit performance. Under the frozen flow hypothesis linear predictive control techniques can overcome this; however, identification and tracking of relevant turbulent parameters (such as wind speeds) is required for such parametric techniques. This can complicate practical implementations and introduce stability issues when encountering variable conditions. Here, we present a non-linear wavefront predictor using a long short-term memory (LSTM) artificial neural network (ANN) that assumes no prior knowledge of the atmosphere and thus requires no user input. The ANN is designed to predict the open-loop wavefront slope measurements of a Shack–Hartmann wavefront sensor (SH-WFS) one frame in advance to compensate for a single-frame delay in a simulated 7 × 7 single-conjugate adaptive optics system operating at 150 Hz. We describe how the training regime of the LSTM ANN affects prediction performance and show how the performance of the predictor varies under various guide star magnitudes. We show that the prediction remains stable when both wind speed and direction are varying. We then extend our approach to a more realistic two-frame latency system. AO system performance when using the LSTM predictor is enhanced for all simulated conditions with prediction errors within 19.9–40.0 nm RMS of a latency-free system operating under the same conditions compared to a bandwidth error of 78.3 ± 4.4 nm RMS.

Performance of real-time adaptive optics compensation in a turbulent channel with high-dimensional spatial-mode encoding.

The orbital angular momentum (OAM) of photons is a promising degree of freedom for high-dimensional quantum key distribution (QKD). However, effectively mitigating the adverse effects of atmospheric turbulence is a persistent challenge in OAM QKD systems operating over free-space communication channels. In contrast to previous works focusing on correcting static simulated turbulence, we investigate the performance of OAM QKD in real atmospheric turbulence with real-time adaptive optics (AO) correction. We show that even though our AO system provides a limited correction, it is possible to mitigate the errors induced by weak turbulence and establish a secure channel. The crosstalk induced by turbulence and the performance of AO systems is investigated in two configurations: a lab-scale link with controllable turbulence, and a 340 m long cross-campus link with dynamic atmospheric turbulence. Our experimental results suggest that an advanced AO system with fine beam tracking, reliable beam stabilization, precise wavefront sensing, and accurate wavefront correction is necessary to adequately correct turbulence-induced error. We also propose and demonstrate different solutions to improve the performance of OAM QKD with turbulence, which could enable the possibility of OAM encoding in strong turbulence.

Voltages prediction algorithm based on LSTM recurrent neural network

Because of the characteristic of delay of adaptive optics system, the performance of adaptive optics system can be improved effectively by predicting the deformation mirror voltages. This paper presents a nonlinear voltages prediction algorithm based on LSTM recurrent neural network. It is found that the predicted voltages by LSTM neural network are consistent with the actual voltages. By comparing the prediction results of the proposed algorithm with those of other prediction algorithms, the prediction algorithm based on LSTM has higher prediction accuracy. This algorithm has strong applicability and higher accuracy in adaptive optics voltages prediction.

Limitations imposed by optical turbulence profile structure and evolution on tomographic reconstruction for the ELT

ABSTRACT The performance of tomographic adaptive optics (AO) systems is intrinsically linked to the vertical profile of optical turbulence. First, a sufficient number of discrete turbulent layers must be reconstructed to model the true continuous turbulence profile. Secondly over the course of an observation, the profile as seen by the telescope changes and the tomographic reconstructor must be updated. These changes can be due to the unpredictable evolution of turbulent layers on meteorological time-scales as short as minutes. Here, we investigate the effect of changing atmospheric conditions on the quality of tomographic reconstruction by coupling fast analytical AO simulation to a large data base of 10 691 high-resolution turbulence profiles measured over two years by the Stereo-SCIDAR instrument at ESO Paranal, Chile. This work represents the first investigation of these effects with a large, statistically significant sample of turbulence profiles. The statistical nature of the study allows us to assess not only the degradation and variability in tomographic error with a set of system parameters (e.g. number of layers and temporal update period), but also the required parameters to meet some error threshold. In the most challenging conditions where the profile is rapidly changing, these parameters must be far more tightly constrained in order to meet this threshold. By providing estimates of these constraints for a wide range of system geometries as well as the impact of different temporal optimization strategies we may assist the designers of tomographic AO for the extremely large telescope to dimension their systems.

On-sky correction of non-common path aberration with the pyramid wavefront sensor

The paper deals with with the on-sky performance of the pyramid wavefront sensor-based Adaptive Optics (AO) systems. These wavefront sensors are of great importance, being used in all first light AO systems of the ELTs (E-ELT, GMT, and TMT), currently in design phase. In particular, non-common path aberrations (NCPAs) are a critical issue encountered when using an AO system to produce corrected images in an associated astronomical instrument. The AO wavefront sensor (WFS) and the supported scientific instrument typically use a series of different optical elements, thus experiencing different aberrations. The usual way to correct for such NCPAs is to introduce a static offset in the WFS signals. In this way, when the AO loop is closed the sensor offsets are zeroed and the deformable mirror converges to the shape required to null the NCPA. The method assumes that the WFS operation is linear and completely described by some pre-calibrated interaction matrix. This is not the case for some frequently used wavefront sensors like the Pyramid sensor or a quad-cell Shack-Hartmann sensor. Here we present a method to work in closed-loop with a pyramid wavefront sensor, or more generally a non-linear WFS, introducing a wavefront offset that remains stable when AO correction quality changes due to variations in external conditions like star brightness, seeing, and wind speed. The paper details the methods with analytical and numerical considerations. Then we present results of tests executed at the LBT telescope, in daytime and on sky, using the FLAO system and LUCI2 facility instrument. The on-sky results clearly show the successful operation of the method that completely nulls NCPA, recovering diffraction-limited images with about 70% Strehl ratio in H band in variable seeing conditions. The proposed method is suitable for application to the above-mentioned ELT AO systems.

Robustness of prediction for extreme adaptive optics systems under various observing conditions

Context. For high-contrast imaging systems, such as VLT/SPHERE, the performance of the system at small angular separations is contaminated by the wind-driven halo in the science image. This halo is a result of the servo-lag error in the adaptive optics (AO) system due to the finite time between measuring the wavefront phase and applying the phase correction. One approach to mitigating the servo-lag error is predictive control. Aims. We aim to estimate and understand the potential on-sky performance that linear data-driven prediction would provide for VLT/SPHERE under various turbulence conditions. Methods. We used a linear minimum mean square error predictor and applied it to 27 different AO telemetry data sets from VLT/SPHERE taken over many nights under various turbulence conditions. We evaluated the performance of the predictor using residual wavefront phase variance as a performance metric. Results. We show that prediction always results in a reduction in the temporal wavefront phase variance compared to the current VLT/SPHERE AO performance. We find an average improvement factor of 5.1 in phase variance for prediction compared to the VLT/SPHERE residuals. When comparing to an idealised VLT/SPHERE, we find an improvement factor of 2.0. Under our 27 different cases, we find the predictor results in a smaller spread of the residual temporal phase variance. Finally, we show there is no benefit to including spatial information in the predictor in contrast to what might have been expected from the frozen flow hypothesis. A purely temporal predictor is best suited for AO on VLT/SPHERE. Conclusions. Linear prediction leads to a significant reduction in phase variance for VLT/SPHERE under a variety of observing conditions and reduces the servo-lag error. Furthermore, prediction improves the reliability of the AO system performance, making it less sensitive to different conditions.

Measuring line-of-sight sodium density structure using laser guide stars

ABSTRACT The performance of adaptive optics systems employing sodium laser guide stars can be improved by continuously monitoring the vertical density structure of mesospheric sodium along the line of sight. We demonstrate that sodium density profiles can be retrieved by amplitude modulation of continuous wave (CW) lasers. In an experiment conducted at the Large Zenith Telescope (LZT), ESO’s Wendelstein Raman-fibre laser was amplitude-modulated with a pseudo-random binary sequence and profiles were obtained by cross-correlation of the modulation pattern with the observed return signal from the laser guide star. For comparison, high-resolution profiles were obtained simultaneously using the lidar system of the LZT. The profiles obtained by the two techniques show noise contamination, but were found to agree to within the measurement error. As a further check, a comparison was also made between several lidar profiles and those obtained by simultaneous observations using a remote telescope to image the laser plume from the side. The modulated CW lidar technique could be implemented by diverting a small fraction of the returned laser light to a photon counting detector. Theoretical analysis and numerical simulations indicate that, for 50 per cent modulation strength, the sodium centroid altitude could be retrieved every 5 s from a single laser guide star, with an accuracy which would induce a corresponding wavefront error of 50 nm for the Extremely Large Telescope and less than 30 nm for the Thirty Meter Telescope and Giant Magellan Telescope. If multiple laser guide stars are employed, the required modulation amplitude will be smaller.

Improved adaptive-optics performance using polychromatic speckle mitigation.

Adaptive-optics (AO) systems correct the optical distortions of atmospheric turbulence to improve resolution over long paths. In applications such as remote sensing, object tracking, and directed energy, the AO system's beacon is often an extended beacon reflecting off an optically rough surface. This situation produces speckle noise that can corrupt the wavefront measurements of the AO system, degrading its correction of the turbulence. This work studies the benefits of speckle mitigation via polychromatic illumination. To quantify the benefits over a wide range of conditions, this work uses a numerical wave-optics model with the split-step method for turbulence and the spectral-slicing method for polychromatic light. It assumes an AO system based on a Shack-Hartmann wavefront sensor. In addition, it includes realistic values for turbulence strength, turbulence distribution along the path, coherence length, extended-beacon size, and object motion. The results show that polychromatic speckle mitigation significantly improves AO system performance, increasing the Strehl ratio by 180% (from 0.10 to 0.28) in one case.

Adaptive optics in the mouse eye: wavefront sensing based vs. image-guided aberration correction.

Adaptive Optics (AO) is required to achieve diffraction limited resolution in many real-life imaging applications in biology and medicine. AO is essential to guarantee high fidelity visualization of cellular structures for retinal imaging by correcting ocular aberrations. Aberration correction for mouse retinal imaging by direct wavefront measurement has been demonstrated with great success. However, for mouse eyes, the performance of the wavefront sensor (WFS) based AO can be limited by several factors including non-common path errors, wavefront reconstruction errors, and an ill-defined reference plane. Image-based AO can avoid these issues at the cost of algorithmic execution time. Furthermore, image-based approaches can provide improvements to compactness, accessibility, and even the performance of AO systems. Here, we demonstrate the ability of image-based AO to provide comparable aberration correction and image resolution to the conventional Shack-Hartmann WFS-based AO approach. The residual wavefront error of the mouse eye was monitored during a wavefront sensorless optimization to allow comparison with classical AO. This also allowed us to improve the performance of our AO system for small animal retinal imaging.

Representative optical turbulence profiles for ESO Paranal by hierarchical clustering

Knowledge of the optical turbulence profile is important in adaptive optics (AO) systems, particularly tomographic AO systems such as those to be employed by the next generation of 40 m class extremely large telescopes (ELTs). Site characterisation and monitoring campaigns have produced large quantities of turbulence profiling data for sites around the world. However AO system design and performance characterisation is dependent on Monte-Carlo simulations that cannot make use of these large datasets due to long computation times. Here we address the question of how to reduce these large datasets into small sets of profiles that can feasibly be used in such Monte-Carlo simulations, whilst minimising the loss of information inherent in this effective compression of the data. We propose hierarchical clustering to partition the dataset according to the structure of the turbulence profiles and extract a single profile from each cluster. This method is applied to the Stereo-SCIDAR dataset from ESO Paranal containing over 10000 measurements of the turbulence profile from 83 nights. We present two methods of extracting turbulence profiles from the clusters, resulting in two sets of 18 profiles providing subtly different descriptions of the variability across the entire dataset. For generality we choose integrated parameters of the turbulence to measure the representativeness of our profiles and compare to others. Using these criterion we also show that such variability is difficult to capture with small sets of profiles associated with integrated turbulence parameters such as seeing.

Numerical estimation of wavefront error breakdown in adaptive optics

Aims. Adaptive optics (AO) system performance is improved using post-processing techniques, such as point spread function (PSF) deconvolution. The PSF estimation involves characterization of the different wavefront (WF) error sources in the AO system. We propose a numerical error breakdown estimation tool that allows studying AO error source behavior such as their correlations. We also propose a new analytical model for anisoplanatism and bandwidth errors that were validated with the error breakdown estimation tool. This model is the first step for a complete AO residual error model that is expressed in deformable mirror space, leading to practical usage such as PSF reconstruction or turbulent parameters identification. Methods. We have developed in the computing platform for adaptive optics systems (COMPASS) code, which is an end-to-end simulation code using graphics processing units (GPU) acceleration, an estimation tool that provides a comprehensive error breakdown by the outputs of a single simulation run. We derive the various contributors from the end-to-end simulator at each iteration step: this method provides temporal buffers of each contributor. Then, we use this tool to validate a new model of anisoplanatism and bandwidth errors including their correlation. This model is based on a statistical approach that computes the error covariance matrices using structure functions. Results. On a SPHERE-like system, the comparison between a PSF computed from the error breakdown with a PSF obtained from classical end-to-end simulation shows that the statistics convergence limits converge very well, with a sub-percent difference in terms of Strehl ratio and ensquared energy at 5λ/D separation. A correlation analysis shows significant correlations between some contributors, especially WF measurement deviation error and bandwidth error due to centroid gain, and the well-known correlation between bandwidth and anisoplanatism errors is also retrieved. The model we propose for the two latter errors shows an SR and EE difference of about one percent compared to the end-to-end simulation, even if some approximations exist.