Single Conjugate Adaptive Optics Research Articles

Point spread function reconstruction for single-conjugate adaptive optics on extremely large telescopes

Modern ground-based telescopes like the planned extremely large telescope (ELT) depend heavily on adaptive optics (AO) systems to correct for atmospheric turbulence. Even though AO correction is used, the quality of astronomical images still is degraded due to the time delay stemming from the wavefront sensor integration time and temporal response of the deformable mirror(s) (DM). This results in a blur, which can be mathematically described by a convolution of the true image with the point spread function (PSF). We present an algorithm for single-conjugate adaptive optics PSF reconstruction adapted to the needs of ELTs in a storage efficient way. In particular, the classical PSF reconstruction algorithm is changed in several points to give a more accurate estimate for the post-AO PSF. Bilinear splines are used as basis functions to minimize the computational effort. Results obtained in an end-to-end simulation tool show qualitatively good reconstruction of the PSF compared with the PSF calculated directly from the simulated incoming wavefront. Furthermore, the used algorithm has a reasonable runtime and memory consumption.

Focal-plane Cn2(h) profiling based on single-conjugate adaptive optics compensated images

Knowledge of the atmospheric turbulence in the telescope line-of-sight is crucial for wide-field observations assisted by adaptive optics (AO), for which the Point Spread Function (PSF) becomes strongly elongated due to the anisoplanatism effect. This one must be modelled accurately to extrapolate the PSF anywhere across the Field of view (FOV) and improve the science exploitation. However, anisoplanatism is a function of the Cn2(h) profile, that is not directly accessible from single conjugate AO telemetry. One may rely on external profilers, but recent studies have highlighted more than 10% of discrepancies with AO internal measurements, while we aim better than 1% of accuracy for PSF modelling. To tackle this existing limitation, we present the Focal plane profiling (FPP), as a $C_n^2(h)$ profiling method that relies on post-AO focal plane images. We demonstrate such an approach complies with a 1%-level of accuracy on the $C_n^2(h)$ estimation and establish how this accuracy varies regarding the calibration stars magnitudes and positions in the field. We highlight that photometry and astrometry errors due to PSF mis-modelling reaches respectively 1% and 50{\mu}as using FPP on a Keck baseline, with a preliminary calibration using a star of magnitude H=14 at 20". We also validate this concept using Canadas NRC-Herzberg HENOS testbed images in comparing FPP retrieval with alternative $C_n^2(h)$ measurements on HeNOS. The FPP approach allows to profile the $C_n^2(h)$ using the SCAO systems and improve significantly the PSF characterisation. Such a methodology is also ELT-size compliant and will be extrapolated to tomographic systems in a near future.

Tensor-based predictive control for extremely large-scale single conjugate adaptive optics.

In this paper we propose a data-driven predictive control algorithm for large-scale single conjugate adaptive optics systems. At each time sample, the Shack-Hartmann wavefront sensor signal sampled on a spatial grid of size N×N is reshuffled into a d-dimensional tensor. Its spatial-temporal dynamics are modeled with a d-dimensional autoregressive model of temporal order p, where each tensor storing past data undergoes a multilinear transformation by factor matrices of small sizes. Equivalently, the vector form of this autoregressive model features coefficient matrices parametrized with a sum of Kronecker products between d-factor matrices. We propose an Alternating Least Squares algorithm for identifying the factor matrices from open-loop sensor data. When modeling each coefficient matrix with a sum of r terms, the computational complexity for updating the sensor prediction online reduces from O(pN4) in the unstructured matrix case to O(prd N2(d+1)d). Most importantly, this model structure breaks away from assuming any prior spatial-temporal coupling as it is discovered from the data. The algorithm is validated on a laboratory testbed that demonstrates the ability to accurately decompose the coefficient matrices of large-scale autoregressive models with a tensor-based representation, hence achieving high data compression rates and reducing the temporal error especially for a large Greenwood per sample frequency ratio.

Off-axis point spread function characterization in laser guide star adaptive optics systems

Adaptive optics (AO) restore the angular resolution of ground-based telescopes, but at the cost of delivering a time-and space-varying point spread function (PSF) with a complex shape. PSF knowledge is crucial for breaking existing limits on the measured accuracy of photometry and astrometry in science observations. In this paper, we concentrate our analyses on anisoplanatism signature only onto PSF: for large-field observations (20) with single-conjugated AO, PSFs are strongly elongated due to anisoplanatism that manifests itself as three different terms for Laser-guide star (LGS) systems: angular, focal and tilt. We propose a generalized model that relies on a point-wise decomposition of the phase and encompasses the non-stationarity of LGS systems. We demonstrate it is more accurate and less computationally demanding than existing models: it agrees with end-to-end physical-optics simulations to within 0.1% of PSF measurables, such as Strehl-ratio, FWHM and fraction of variance unexplained. Secondly, we study off-axis PSF modelling is with respect to C 2 n (h) profile (heights and fractional weights). For 10 m class telescope, PSF morphology is estimated at 1%-level as long as we model the atmosphere with at least 7 layers whose heights and weights are known respectively with 200m and 10%-precision. As a verification test we used the Canada's NRC-Herzberg HeNOS testbed data, featuring four lasers. We highlight capability of retrieving off-axis PSF characteristics within 10% of fraction of variance unexplained, which complies with the expected range from the sensitivity analysis. Our new off-axis PSF modelling method lays the groundwork for testing on-sky in the near future.

ELT-scale adaptive optics real-time control with the Intel Xeon Phi Many Integrated Core Architecture

We propose a solution to the increased computational demands of Extremely Large Telescope (ELT) scale adaptive optics (AO) real-time control with the Intel Xeon Phi Knights Landing (KNL) Many Integrated Core (MIC) Architecture. The computational demands of an AO real-time controller (RTC) scale with the fourth power of telescope diameter and so the next generation ELTs require orders of magnitude more processing power for the RTC pipeline than existing systems. The Xeon Phi contains a large number (> 64) of low power x86 CPU cores and high bandwidth memory integrated into a single socketed server CPU package. The increased parallelism and memory bandwidth are crucial to providing the performance for reconstructing wavefronts with the required precision for ELT scale AO. Here, we demonstrate that the Xeon Phi KNL is capable of performing ELT scale single conjugate AO real-time control computation at over 1.0 kHz with less than 20 {\mu}s RMS jitter. We have also shown that with a wavefront sensor camera attached the KNL can process the real-time control loop at up to 966 Hz, the maximum frame-rate of the camera, with jitter remaining below 20 {\mu}s RMS. Future studies will involve exploring the use of a cluster of Xeon Phis for the real-time control of the MCAO and MOAO regimes of AO. We find that the Xeon Phi is highly suitable for ELT AO real time control.

Wave-front error breakdown in laser guide star multi-object adaptive optics validated on-sky by Canary

Context. Canary is the multi-object adaptive optics (MOAO) on-sky pathfinder developed in the perspective of multi-object spectrograph on extremely large telescopes (ELTs). In 2013, Canary was operated on-sky at the William Herschel telescope (WHT), using three off-axis natural guide stars (NGS) and four off-axis Rayleigh laser guide stars (LGS), in open-loop, with the on-axis compensated turbulence observed with a H-band imaging camera and a Truth wave-front sensor (TS) for diagnostic purposes. Aims. Our purpose is to establish a reliable and accurate wave-front error breakdown for LGS MOAO. This will enable a comprehensive analysis of Canary on-sky results and provide tools for validating simulations of MOAO systems for ELTs. Methods. To evaluate the MOAO performance, we compared the Canary on-sky results running in MOAO, in single conjugated adaptive optics (SCAO) and in ground layer adaptive optics (GLAO) modes, over a large set of data acquired in 2013. We provide a statistical study of the seeing. We also evaluated the wave-front error breakdown from both analytic computations, one based on a MOAO system modelling and the other on the measurements from the Canary TS. We have focussed especially on the tomographic error and we detail its vertical error decomposition. Results. We show that Canary obtained 30.1%, 21.4% and 17.1% H-band Strehl ratios in SCAO, MOAO and GLAO respectively, for median seeing conditions with 0.66′′ of total seeing including 0.59′′ at the ground. Moreover, we get 99% of correlation over 4500 samples, for any AO modes, between two analytic computations of residual phase variance. Based on these variances, we obtain a reasonable Strehl-ratio (SR) estimation when compared to the measured IR image SR. We evaluate the gain in compensation for the altitude turbulence brought by MOAO when compared to GLAO.

层向多层共轭自适应光学系统的模拟

The adaptive optics (AO) system in which one turbulence layer is corrected has a good compensation performance only over small field of view. The technology of multi-conjugate adaptive optics (MCAO) can overcome the limitation. The elementary structure and working principle of layer oriented multi-conjugate adaptive optics (LOMCAO) system was presented. Simulation method of LOMCAO system was investigated, including how to generate dynamic turbulence wavefront data, wavefront reconstruction algorithm of pyramid wavefront sensor and close-loop modal control procedure of deformable mirror. Simulations for single layer-conjugate and two layer-conjugate AO systems were carried out. The simulation results show that LOMCAO system has better correction performance over a larger field of view than single-conjugate AO system due to the face that much more guide stars are used and two layer turbulence are compensated in LOMCAO system.

Anisoplanatism effect on the E-ELT SCAO point spread function. A preserved coherent core across the field

Context. The science case studies and the optimized designing of the future adaptive optics-fed extremely large telescope instruments require the precise simulation of their adaptive optics system, potentially over their whole field of view, whatever the adaptive optics flavor the instruments will be equipped with.Aims. We simulate the anisoplanatism effect on the extremely large telescope single conjugate adaptive optics point spread function. Our interest in this expected degradation of the correction performance with respect to the off-axis distance is in terms of the point spread function Strehl ratio and profile.Methods. Adaptive optics simulations at the scale of extremely large telescopes are challenging given the large parameter space to explore for the adaptive optics dimensioning and the large number of degrees of freedom at play for a given set of simulation parameters. To address this problem, we have used three different simulation tools with increasing degree of fidelity compared to a real adaptive optics system. The first is based on analytical formulae and allowed us to derive the Strehl ratio degradation with the off-axis distance. The second is a Fourier-based code and provided us with both the Strehl ratio and the point spread function profile in the field. The last is an end-to-end code based on the graphical processing unit technology and also provided us with the Strehl ratio and the point spread function profile in the field.Results. The three tools we used demonstrated a fast execution time even at the extremely large telescope scale. Cross-checks between the different codes were performed and demonstrated the coherency of the results. In addition to the expected degradation of the adaptive optics performance with the field angle, we demonstrated that in the simulation conditions applicable to the E-ELT, the single conjugate adaptive optics point spread function remains topped with a coherent core even at off-axis distances as large as 60 arcsec and consequently very low Strehl ratios. We also studied the impact of the outer scale on the point spread function profile, demonstrating that the aforementioned Airy-like pattern is observable even when the outer scale is larger than the telescope diameter.Conclusions. These results could push for the preservation over a large field of the optical quality of any common path optics between the telescope and the instruments in single conjugate adaptive optics mode. This could offer some astrometric capabilities to these instruments operating in this adaptive optics mode.

On-sky tests of the CuReD and HWR fast wavefront reconstruction algorithms with CANARY

CuReD (Cumulative Reconstructor with domain Decomposition) and HWR (Hierarchical Wavefront Reconstructor) are novel wavefront reconstruction algorithms for the Shack–Hartmann wavefront sensor, used in the single-conjugate adaptive optics. For a high-order system they are much faster than the traditional matrix–vector-multiplication method. We have developed three methods for mapping the reconstructed phase into the deformable mirror actuator commands and have tested both reconstructors with the CANARY instrument. We find out that the CuReD reconstructor runs stably only if the feedback loop is operated as a leaky integrator, whereas HWR runs stably with the conventional integrator control. Using the CANARY telescope simulator we find that the Strehl ratio (SR) obtained with CuReD is slightly higher than that of the traditional least-squares estimator (LSE). We demonstrate that this is because the CuReD algorithm has a smoothing effect on the output wavefront. The SR of HWR is slightly lower than that of LSE. We have tested both reconstructors extensively on-sky. They perform well and CuReD achieves a similar SR as LSE. We compare the CANARY results with those from a computer simulation and find good agreement between the two.

A new cumulative wavefront reconstructor for the Shack–Hartmann sensor

Abstract. We present a new direct algorithm for the reconstruction of the optical wavefront from the Shack–Hartmann sensor measurements in Single Conjugate Adaptive Optics (SCAO) systems. The computational complexity of this method which is based on linear triangular finite elements is linear in the number of unknowns. Moreover, due to its simple structure, the cumulative reconstructor is pipelinable and parallelizable, which makes the effective computation even faster. Error estimates are given in dependence of the number of the subapertures and the data noise.

Adaptive Optics Simulations for Siding Spring

AbstractUsing an observationally derived model of optical turbulence profile, we have investigated the performance of adaptive optics (AO) at Siding Spring Observatory, Australia. The simulations cover the performance for AO techniques of single-conjugate adaptive optics (SCAO), multi-conjugate adaptive optics (MCAO), and ground-layer adaptive optics (GLAO). The simulation results presented in this paper predict the performance of these AO techniques as applied to the Australian National University (ANU) 2.3-m and Anglo-Australian Telescope (AAT) 3.9-m telescopes for astronomical wavelength bands J, H, and K. The results indicate that the AO performance is best for the longer wavelengths (K band) and in the best seeing conditions (sub 1 arcsec). The most promising results are found for GLAO simulations (field of view of 180 arcsec), with the field RMS for encircled energy 50% diameter (EE50d) being uniform and minimally affected by the free-atmosphere turbulence. The GLAO performance is reasonably good over the wavelength bands of J, H, and K. The GLAO field mean of EE50d is between 200 and 800 mas, which is a noticeable improvement compared with the nominal astronomical seeing (870–1 700 mas).

Wavefront reconstruction for extremely large telescopes via CuRe with domain decomposition

The Cumulative Reconstructor is an accurate, extremely fast reconstruction algorithm for Shack-Hartmann wavefront sensor data. But it has shown an unacceptable high noise propagation for large apertures. Therefore, in this paper we describe a domain decomposition approach to deal with this drawback. We show that this adaptation of the algorithm gives the same reconstruction quality as the original algorithm and leads to a significant improvement with respect to noise propagation. The method is combined with an integral control and compared to the classical matrix vector multiplication algorithm on an end-to-end simulation of a single conjugate adaptive optics system. The reconstruction time is 20n (number of subapertures), and the method is parallelizable.

Computational performance comparison of wavefront reconstruction algorithms for the European Extremely Large Telescope on multi-CPU architecture

The European Southern Observatory (ESO) is studying the next generation giant telescope, called the European Extremely Large Telescope (E-ELT). With a 42 m diameter primary mirror, it is a significant step from currently existing telescopes. Therefore, the E-ELT with its instruments poses new challenges in terms of cost and computational complexity for the control system, including its adaptive optics (AO). Since the conventional matrix-vector multiplication (MVM) method successfully used so far for AO wavefront reconstruction cannot be efficiently scaled to the size of the AO systems on the E-ELT, faster algorithms are needed. Among those recently developed wavefront reconstruction algorithms, three are studied in this paper from the point of view of design, implementation, and absolute speed on three multicore multi-CPU platforms. We focus on a single-conjugate AO system for the E-ELT. The algorithms are the MVM, the Fourier transform reconstructor (FTR), and the fractal iterative method (FRiM). This study enhances the scaling of these algorithms with an increasing number of CPUs involved in the computation. We discuss implementation strategies, depending on various CPU architecture constraints, and we present the first quantitative execution times so far at the E-ELT scale. MVM suffers from a large computational burden, making the current computing platform undersized to reach timings short enough for AO wavefront reconstruction. In our study, the FTR provides currently the fastest reconstruction. FRiM is a recently developed algorithm, and several strategies are investigated and presented here in order to implement it for real-time AO wavefront reconstruction, and to optimize its execution time. The difficulty to parallelize the algorithm in such architecture is enhanced. We also show that FRiM can provide interesting scalability using a sparse matrix approach.

A benchmark for multiconjugated adaptive optics: VLT-MAD observations of the young massive cluster Trumpler 14★

MAD is the first multi-conjugated adaptive optics system at the VLT. We present H and Ks observations of the young massive cluster Trumpler 14 revealing the power of MCAO systems by providing a homogeneous Strehl ratio over a large field of view. Mean Strehl ratios of 6.0 and 5.9 per cent with maximum Strehl ratios of 9.8 and 12.6 per cent in H and Ks, respectively, show significant improvement of the spatial PSF stability compared to single-conjugated adaptive optics systems. Photometry of our observations cover a dynamic range of ~10 mag including 2-3 times more sources than comparable seeing-limited observations. The colour-magnitude diagram reveals that the massive cluster originated in a recent starburst-like event 1+/-0.5 Myr ago. We tentatively detect hints for an older population of 3 Myr suggesting that low intensity star formation might have been going on in the HII region for a few Myr. We derive the luminosity function and mass function between 0.1 M_sun and 3.2 M_sun and identify a change of the power law slope of the mass function at m_c~0.53(+0.12/-0.10) M_sun. The MF appears shallow with power law slopes of Gamma1=-0.50+/-0.11 above m_c and Gamma2=0.63+/-0.32 below m_c.

An E-ELT case study: colour–magnitude diagrams of an old galaxy in the Virgo cluster

One of the key science goals for a diffraction limited imager on an Extremely Large Telescope (ELT) is the resolution of individual stars down to faint limits in distant galaxies. The aim of this study is to test the proposed capabilities of a multi-conjugate adaptive optics (MCAO) assisted imager working at the diffraction limit, in IJHK$_s$ filters, on a 42m diameter ELT to carry out accurate stellar photometry in crowded images in an Elliptical-like galaxy at the distance of the Virgo cluster. As the basis for realistic simulations we have used the phase A studies of the European-ELT project, including the MICADO imager (Davies & Genzel 2010) and the MAORY MCAO module (Diolaiti 2010). We convolved a complex resolved stellar population with the telescope and instrument performance expectations to create realistic images. We then tested the ability of the currently available photometric packages STARFINDER and DAOPHOT to handle the simulated images. Our results show that deep Colour-Magnitude Diagrams (photometric error, $\pm$0.25 at I$\ge$27.2; H$\ge$25. and K$_s\ge$24.6) of old stellar populations in galaxies, at the distance of Virgo, are feasible at a maximum surface brightness, $\mu_V \sim$ 17 mag/arcsec$^2$ (down to M$_I > -4$ and M$_H \sim$ M$_K > -6$), and significantly deeper (photometric error, $\pm$0.25 at I$\ge$29.3; H$\ge$26.6 and K$_s\ge$26.2) for $\mu_V \sim$ 21 mag/arcsec$^2$ (down to M$_I \ge -2$ and M$_H \sim$ M$_K \ge -4.5$). The photometric errors, and thus also the depth of the photometry should be improved with photometry packages specifically designed to adapt to an ELT MCAO Point Spread Function. We also make a simple comparison between these simulations and what can be expected from a Single Conjugate Adaptive Optics feed to MICADO and also the James Webb Space Telescope.

Cumulative wavefront reconstructor for the Shack-Hartmann sensor

We present a new direct algorithm aiming at the reconstruction of the opticalwavefront from the Shack-Hartmann sensor measurements in Single ConjugateAdaptive Optics (SCAO) systems. The objective of an adaptive optics systemdesigned for a large telescope can be only achieved if the wavefrontreconstruction is sufficiently fast. Our scheme does not contain any explicitregularization for the reconstruction process but is still able to provide agood quality of reconstruction. The analysis of quality is given for threevarying parameters: the diameter of the telescope, the number of subaperturesand the level of photon noise. It has been shown both analytically andnumerically that the quality of the reconstruciton, measured by the Strehlratio, is reasonable for the small photon noise level and increases with theincreasing number of subapertures for the same telescope size. The impact of thephoton noise on the reconstruction gets higher with the increasing telescopediameter. The computational complexity of the method is linear in the number ofunkowns. Counting all summation and multiplication steps the scaling factor is$14$. Moreover, due to its simple structure, the cumulative reconstructor ispipelinable and parallelizable, which makes the effective computation evenfaster.

Performance comparison of wavefront reconstruction and control algorithms for Extremely Large Telescopes

Extremely Large Telescopes (ELTs) are very challenging with respect to their adaptive optics (AO) requirements. Their diameters and the specifications required by the astronomical science for which they are being designed imply a huge increment in the number of degrees of freedom in the deformable mirrors. Faster algorithms are needed to implement the real-time reconstruction and control in AO at the required speed. We present the results of a study of the AO correction performance of three different algorithms applied to the case of a 42-m ELT: one considered as a reference, the matrix-vector multiply (MVM) algorithm; and two considered fast, the fractal iterative method (FrIM) and the Fourier transform reconstructor (FTR). The MVM and the FrIM both provide a maximum a posteriori estimation, while the FTR provides a least-squares one. The algorithms are tested on the European Southern Observatory (ESO) end-to-end simulator, OCTOPUS. The performance is compared using a natural guide star single-conjugate adaptive optics configuration. The results demonstrate that the methods have similar performance in a large variety of simulated conditions. However, with respect to system misregistrations, the fast algorithms demonstrate an interesting robustness.

Extreme adaptive optics in the mid-IR: The METIS AO system

METIS, the Mid-infrared ELT Imager and Spectrograph, is currently in its phase A study as one of the candidate first-light instruments for the European Extremely Large Telescope. METIS will feature several observational modes, ranging from diffraction limited imaging in L, M and N-bands to high-resolution Integral Field spectroscopy for the L and M-bands. METIS in its current design gives sensitivities similar to Spitzer in imaging and low-resolution spectroscopy and with its high-resolution spectrograph will provide unprecedented line sensitivity. The design of METIS is optimized for both galactic science cases (e.g. conditions in the early solar system, formation and evolution of proto-planetary disks and properties of exoplanets) and extragalactic science cases (e.g. the growth of Supermassive Black Holes). METIS will require a high-order adaptive optics (AO) system to meet its scientific goals, both to provide correction for atmospheric turbulence as well as reduce the impact of wind shake, leading to a residual image motion of 3 - 5 mas rms. METIS is expected to feature both an internal Single Conjugate AO system as well as an external Laser Tomography AO system. The challenges for the METIS AO system are mainly in the broad correction range, an excellent image stability required for coronagraphy and in providing a high sky coverage to be available for as many science targets as possible. An additional challenge for METIS is the need to compensate for composition turbulence, mainly in the form of fast fluctuations in water vapor concentration. Water vapor fluctuations impact the performance of METIS in several ways: Atmospheric dispersion causes a broadening of the point-spread function, both in the science channel and the wavefront channel, but can be corrected using a Atmospheric Dispersion Corrector. Variations in the water vapor composition cannot be corrected this way and are currently estimated to give a residual image motion of ≤10 mas rms. This effect can, especially for coronagraphy, not be neglected. Chromatic optical path difference errors, caused by changes in the index of refraction along the path through the atmosphere were found to be negligible in the case of METIS due to attenuation by the outer scale (at typical values of 25 m). Chromatic anisoplanatism is the effect that the light at different wavelengths travels through a slightly different light path through the atmosphere and can be–at least partly–corrected. The last effect is composition turbulence, mainly caused by fast (> 1 Hz) fluctuations in the water vapor content. Based on data for ALMA and radiometer probes, this leads to a maximum loss in Strehl ratio between 5 and 10%. This mainly has an impact on coronagraphy and the METIS AO team is actively investigating ways to compensate also water vapor turbulence. The main challenge is currently obtaining reliable data on the distribution and magnitude of precipitable water vapor fluctuations.

MAD: practical implementation of MCAO concepts

The European Southern Observatory (ESO) together with external research institutes have built a Multi-Conjugate Adaptive Optics (MCAO) Demonstrator (MAD) to perform wide field-of-view adaptive optics correction (2′ in K band). The aim of MAD is to demonstrate the on-sky feasibility of the MCAO technique and to evaluate its critical aspects in the framework of both the 2nd generation instrumentation for the Very Large Telescope (VLT) and the Overwhelmingly Large Telescope (OWL). The MAD module will be installed on the VLT to perform on-sky observations. MAD comprises two deformable mirrors and two different multi-reference wavefront sensors with natural guide stars. In this article we present the MAD design, some aspects of the MAD calibration and the first closed-loop results in the laboratory in Single Conjugated Adaptive Optics (SCAO) and Ground Layer Adaptive Optics (GLAO) configurations. To cite this article: E. Marchetti et al., C. R. Physique 6 (2005).