Two-aperture measurements for GEO-feeder adaptive optics pre-compensation optimization.

We present a method to estimate the pre-compensation phase of ground-to-geostationary orbit (GEO) optical links based on downlink phase and log-amplitude measurements from two ground apertures. This method allows us to reduce the point-ahead anisoplanatism that currently limits the telecom performance of GEO-feeder links. It is shown to reduce the anisoplanatic phase variance by 50%, hence improving the statistics of the coupled flux aboard the satellite. It also outperforms the one-aperture estimation method for very severe atmospheric conditions. Besides, only low-resolution amplitude measurements are required on the second aperture to reach the performance of the novel estimator.

Tbit/s line-rate satellite feeder links enabled by coherent modulation and full-adaptive optics.

Free-space optical (FSO) communication technologies constitute a solution to cope with the bandwidth demand of future satellite-ground networks. They may overcome the RF bottleneck and attain data rates in the order of Tbit/s with only a handful of ground stations. Here, we demonstrate single-carrier Tbit/s line-rate transmission over a free-space channel of 53.42 km between the Jungfraujoch mountain top (3700 m) in the Swiss Alps and the Zimmerwald Observatory (895 m) near the city of Bern, achieving net-rates of up to 0.94 Tbit/s. With this scenario a satellite-ground feeder link is mimicked under turbulent conditions. Despite adverse conditions high throughput was achieved by employing a full adaptive optics system to correct the distorted wavefront of the channel and by using polarization-multiplexed high-order complex modulation formats. It was found that adaptive optics does not distort the reception of coherent modulation formats. Also, we introduce constellation modulation - a new four-dimensional BPSK (4D-BPSK) modulation format as a technique to transmit high data rates under lowest SNR. This way we show 53 km FSO transmission of 13.3 Gbit/s and 210 Gbit/s with as little as 4.3 and 7.8 photons per bit, respectively, at a bit-error ratio of 1 ∙ 10-3. The experiments show that advanced coherent modulation coding in combination with full adaptive optical filtering are proper means to make next-generation Tbit/s satellite communications practical.

Phase estimation at the point-ahead angle for AO pre-compensated ground to GEO satellite telecoms.

We present a new method to estimate the off-axis adaptive optics pre-compensation phase of a ground to GEO satellite telecom link suffering from point-ahead anisoplanatism. The proposed phase estimator relies on the downlink phase and log-amplitude measurements that are available at the optical ground station. We introduce the analytical tools, extended from the literature, to build the estimator as well as a general modal formalism to express the reciprocal residual phase covariance matrix resulting from any estimation linear with measurements. We use this residual phase covariance matrix to generate independent coupled flux samples thanks to a pseudo-analytical approach and study the gain offered by the proposed estimator on the coupled flux statistics, in various atmospheric conditions. The estimator is shown to reduce the anisoplanatic residual phase variance by at least 35%, and 46% at best, with a greater impact on the lower modes, especially on the tip and tilt residual phase variances. The phase variance reduction brings a gain up to 15 dB on the cumulative density function at probability 10-3. This gain should allow to relax the power constraints on the link budget at the OGS and renews the interest in large aperture diameter (60 cm class telescopes) for GEO Feeder links by reducing the atmospheric turbulence impact on the uplink coupled signal.

Feasibility demonstration of AO pre-compensation for GEO feeder links in a relevant environment.

Optical technologies are extremely competitive candidates to achieve very-high throughput links between ground and GEO satellites; however, their feasibility relies on the ability to mitigate channel impairments due to atmospheric turbulence. For that purpose, Adaptive Optics (AO) has already proved to be highly efficient on the downlink. However, for the uplink, anisoplanatism induced by point-ahead angle (PAA) compromises AO pre-compensation efficiency to an extent that depends on propagation conditions. The ability to properly assess the anisoplanatism impact in a wide variety of conditions is thus critical in designing the optical ground terminals. In this paper, we demonstrate the consistency of experimental coupled flux statistics with results coming from performance and end-to-end models, on an AO pre-compensated 13 km slant path in Tenerife. This validation is demonstrated in a wide variety of turbulence conditions, hence consolidating propagation channel models that are of critical importance for the reliability of future GEO feeder links. We then compare experimental results to theoretical on-sky performance, and discuss to what extent such slant path or horizontal path experiments can be representative of real GEO links.

Linear controller error budget assessment for classical adaptive optics systems.

Understanding limitations of adaptive optics (AO) systems is crucial when designing new systems. In particular, analyzing the potential of different controllers is of great interest for the upcoming AO systems of the very large telescopes (VLTs) and extremely large telescopes (ELTs). This paper thus details a complete error budget assessment formalism, based on analytic formulas involving the disturbance temporal power spectral density (PSD) and the controller transfer function, and is applicable to any linear controller. This formalism is presented here for the special case of classical AO systems, but can be extended to any closed- or open-loop, single- or multi-conjugated AO configuration. Special attention is paid to the "control-dependent" errors, the importance of which is directly related to the type of control used in the AO system. The proposed method is applied to a NAOS/VLT-type single conjugated AO system, using disturbance PSD derived from a simulated turbulence trajectory or estimated from wavefront sensor measurements, enabling the construction of detailed error budgets for an integrator and different linear quadratic Gaussian controllers. Application to ELT-sized systems is discussed in the conclusion.

Fixational eye movement: a negligible source of dynamic aberration.

To evaluate the contribution of fixational eye movements to dynamic aberration, 50 healthy eyes were examined with an original custom-built Shack-Hartmann aberrometer, running at a temporal frequency of 236Hz, with 22 lenslets across a 5mm pupil, synchronized with a 236Hz pupil tracker. A comparison of the dynamic behavior of the first 21 Zernike modes (starting from defocus) with and without digital pupil stabilization, on a 3.4s sequence between blinks, showed that the contribution of fixational eye movements to dynamic aberration is negligible. Therefore we highlighted the fact that a pupil tracker coupled to an Adaptive Optics Ophthalmoscope is not essential to achieve diffraction-limited resolution.

Statistical properties of single-mode fiber coupling of satellite-to-ground laser links partially corrected by adaptive optics.

In the framework of satellite-to-ground laser downlinks, an analytical model describing the variations of the instantaneous coupled flux into a single-mode fiber after correction of the incoming wavefront by partial adaptive optics (AO) is presented. Expressions for the probability density function and the cumulative distribution function as well as for the average fading duration and fading duration distribution of the corrected coupled flux are given. These results are of prime interest for the computation of metrics related to coded transmissions over correlated channels, and they are confronted by end-to-end wave-optics simulations in the case of a geosynchronous satellite (GEO)-to-ground and a low earth orbit satellite (LEO)-to-ground scenario. Eventually, the impact of different AO performances on the aforementioned fading duration distribution is analytically investigated for both scenarios.

High temporal resolution aberrometry in a 50-eye population and implications for adaptive optics error budget.

We formed a database gathering the wavefront aberrations of 50 healthy eyes measured with an original custom-built Shack-Hartmann aberrometer at a temporal frequency of 236 Hz, with 22 lenslets across a 7-mm diameter pupil, for a duration of 20 s. With this database, we draw statistics on the spatial and temporal behavior of the dynamic aberrations of the eye. Dynamic aberrations were studied on a 5-mm diameter pupil and on a 3.4 s sequence between blinks. We noted that, on average, temporal wavefront variance exhibits a n-2 power-law with radial order n and temporal spectra follow a f-1.5 power-law with temporal frequency f. From these statistics, we then extract guidelines for designing an adaptive optics system. For instance, we show the residual wavefront error evolution as a function of the number of corrected modes and of the adaptive optics loop frame rate. In particular, we infer that adaptive optics performance rapidly increases with the loop frequency up to 50 Hz, with gain being more limited at higher rates.

Pupil motion analysis and tracking in ophthalmic systems equipped with wavefront sensing technology.

Our eyes are constantly in motion, even during "steady" fixation. In ophthalmic systems equipped with wavefront technology, both eye and head motion potentially degrade its performance and/or increase the cost and complexity, as they induce a movement of the entrance optical pupil of the system. Here, we characterize the pupil motion in an aberrometry setting, using a custom, high-speed pupil tracker (478 Hz), and draw conclusions on design considerations of future ophthalmic systems. We also demonstrate the feasibility of tracking such motion directly with a custom-built Hartmann-Shack sensor (236 Hz) using a method that offers certain benefits over previously suggested approaches, thereby paving the way to an efficient and cost-effective approach.

First on-sky SCAO validation of full LQG control with vibration mitigation on the CANARY pathfinder.

Adaptive optics provides real time correction of wavefront disturbances on ground based telescopes. Optimizing control and performance is a key issue for ever more demanding instruments on ever larger telescopes affected not only by atmospheric turbulence, but also by vibrations, windshake and tracking errors. Linear Quadratic Gaussian control achieves optimal correction when provided with a temporal model of the disturbance. We present in this paper the first on-sky results of a Kalman filter based LQG control with vibration mitigation on the CANARY instrument at the Nasmyth platform of the 4.2-m William Herschel Telescope. The results demonstrate a clear improvement of performance for full LQG compared with standard integrator control, and assess the additional improvement brought by vibration filtering with a tip-tilt model identified from on-sky data, thus validating the strategy retained on the instrument SPHERE at the VLT.

First on-sky results of the CO-SLIDAR C(2)(n) profiler.

COupled SLope and scIntillation Detection And Ranging (CO-SLIDAR) is a recent profiling method of the vertical distribution of atmospheric turbulence strength (C(2)(n) profile). It takes advantage of correlations of slopes and of scintillation, both measured with a Shack-Hartmann wavefront sensor on a binary star. In this paper, we present the improved CO-SLIDAR reconstruction method of the C(2)(n) profile and the first on-sky results of the CO-SLIDAR profiler. We examine CO-SLIDAR latest performance in simulation, taking into account the detection noise bias and estimating error bars along with the turbulence profile. The estimated C(2)(n) profiles demonstrate the accuracy of the CO-SLIDAR method, showing sensitivity to both low and high altitude turbulent layers. CO-SLIDAR is tested on-sky for the first time, on the 1.5 m MeO (Métrologie Optique) telescope at Observatoire de la Côte d'Azur (France). The reconstructed profiles are compared to turbulence profiles estimated from meteorological data and a good agreement is found. We discuss CO-SLIDAR's contribution in the C(2)(n) profilers' landscape and we propose some improvements of the instrument.

Fast computation of an optimal controller for large-scale adaptive optics.

The linear quadratic Gaussian regulator provides the minimum-variance control solution for a linear time-invariant system. For adaptive optics (AO) applications, under the hypothesis of a deformable mirror with instantaneous response, such a controller boils down to a minimum-variance phase estimator (a Kalman filter) and a projection onto the mirror space. The Kalman filter gain can be computed by solving an algebraic Riccati matrix equation, whose computational complexity grows very quickly with the size of the telescope aperture. This "curse of dimensionality" makes the standard solvers for Riccati equations very slow in the case of extremely large telescopes. In this article, we propose a way of computing the Kalman gain for AO systems by means of an approximation that considers the turbulence phase screen as the cropped version of an infinite-size screen. We demonstrate the advantages of the methods for both off- and on-line computational time, and we evaluate its performance for classical AO as well as for wide-field tomographic AO with multiple natural guide stars. Simulation results are reported.

Minimum-variance control for woofer-tweeter systems in adaptive optics.

The woofer-tweeter concept in adaptive optics consists in correcting for the turbulent wavefront disturbance with a combination of two deformable mirrors (DMs). The woofer corrects for temporally slow-evolving, spatially low-frequency, large-amplitude disturbances, whereas the tweeter is generally its complement, i.e., corrects for faster higher-order modes with lower amplitude. A special feature is that in general both are able to engender a common correction space. In this contribution a minimum-variance solution for the double stage woofer-tweeter concept in adaptive optics systems is addressed using a linear-quadratic-Gaussian approach. An analytical model is built upon previous developments on a single DM with temporal dynamics that accommodates a double-stage woofer-tweeter DM. Monte Carlo simulations are run for a system featuring an 8×8 actuator DM (considered infinitely fast), mounted on a steering tip/tilt platform (considered slow). Results show that it is essential to take into account temporal dynamics on the estimation step. Besides, unlike the other control strategies considered, the optimal solution is always stable.

Generalized aliasing and its implications in modal gain optimization for multi-conjugate adaptive optics.

The error of generalized aliasing associated with the limited sampling of the atmospheric turbulence volume due to the finite number of wavefront sensing directions in wide-field-of-view adaptive optics is formally defined. Following a modal approach, we extend the direct problem formulation of star-oriented multi-conjugate adaptive optics (MCAO) to model and quantify this error analytically. We show that the turbulence estimation with the least-squares reconstructor is subject to strong generalized aliasing, in particular affecting the badly seen modes, whereas with the minimum-mean-square-error reconstructor the estimation is little affected. Finally, we show that the application of modal gain optimization techniques in closed-loop MCAO systems is jeopardized by the generalized aliasing error.

Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors.

Noise effects induced by laser guide star (LGS) elongation have to be considered globally in a multi-LGS tomographic reconstruction analysis. This allows a fine estimation of performance and the comparison of different launching options. We present a modal analysis of the wavefront error with Shack-Hartmann wavefront sensors based on quasi-analytical matrix formalism. Including spot elongation and the Rayleigh fratricide effect, edge launching produces similar performance to central launching and avoids the risk of possible underestimation of fratricide scatter. Performance improves slightly with an optimized centroid estimator and is not affected by a slight field-of-view truncation of the subapertures. Finally we discuss detector characteristics for a LGS Shack-Hartmann wavefront sensor.

Wide field adaptive optics laboratory demonstration with closed-loop tomographic control.

HOMER, the new bench developed at ONERA devoted to wide field adaptive optics (WFAO) laboratory research, has allowed the first experimental validations of multi-conjugate adaptive optics (MCAO) and laser tomography adaptive optics (LTAO) concepts with a linear quadratic Gaussian (LQG) control approach. Results obtained in LTAO in closed loop show the significant gain in performance brought by LQG control, which allows tomographic reconstruction. We present a calibration and model identification strategy. Experimental results are shown to be consistent with end-to-end simulations. These results are very encouraging and demonstrate robustness of performance with respect to inevitable experimental uncertainties. They represent a first step for the study of very large telescope (VLT) and extremely large telescopes (ELT) instruments.

On the optimal reconstruction and control of adaptive optical systems with mirror dynamics.

In adaptive optics (AO) the deformable mirror (DM) dynamics are usually neglected because, in general, the DM can be considered infinitely fast. Such assumption may no longer apply for the upcoming Extremely Large Telescopes (ELTs) with DM that are several meters in diameter with slow and/or resonant responses. For such systems an important challenge is to design an optimal regulator minimizing the variance of the residual phase. In this contribution, the general optimal minimum-variance (MV) solution to the full dynamical reconstruction and control problem of AO systems (AOSs) is established. It can be looked upon as the parent solution from which simpler (used hitherto) suboptimal solutions can be derived as special cases. These include either partial DM-dynamics-free solutions or solutions derived from the static minimum-variance reconstruction (where both atmospheric disturbance and DM dynamics are neglected altogether). Based on a continuous stochastic model of the disturbance, a state-space approach is developed that yields a fully optimal MV solution in the form of a discrete-time linear-quadratic-Gaussian (LQG) regulator design. From this LQG standpoint, the control-oriented state-space model allows one to (1) derive the optimal state-feedback linear regulator and (2) evaluate the performance of both the optimal and the sub-optimal solutions. Performance results are given for weakly damped second-order oscillatory DMs with large-amplitude resonant responses, in conditions representative of an ELT AO system. The highly energetic optical disturbance caused on the tip/tilt (TT) modes by the wind buffeting is considered. Results show that resonant responses are correctly handled with the MV regulator developed here. The use of sub-optimal regulators results in prohibitive performance losses in terms of residual variance; in addition, the closed-loop system may become unstable for resonant frequencies in the range of interest.

Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis.

We present a comprehensive analysis of the linear quadratic Gaussian control approach applied to adaptive optics (AO) and multiconjugated AO (MCAO) based on numerical and experimental validations. The structure of the control law is presented and its main properties discussed. We then propose an extended experimental validation of this control law in AO and a simplified MCAO configuration. Performance is compared with end-to-end numerical simulations. Sensitivity of the performance regarding tuning parameters is tested. Finally, extension to full MCAO and laser tomographic AO (LTAO) through numerical simulation is presented and analyzed.

Tomographic reconstruction for wide-field adaptive optics systems: Fourier domain analysis and fundamental limitations.

Several wide-field-of-view adaptive optics (WFAO) concepts such as multi-conjugate AO (MCAO), multi-object AO (MOAO), and ground-layer AO (GLAO) are currently being studied for the next generation of Extremely Large Telescopes (ELTs). All these concepts will use atmospheric tomography to reconstruct the turbulent-phase volume. In this paper, we explore different reconstruction algorithms and their fundamental limitations, conducting this analysis in the Fourier domain. This approach allows us to derive simple analytical formulations for the different configurations and brings a comprehensive view of WFAO limitations. We then investigate model and statistical errors and their effect on the phase reconstruction. Finally, we show some examples of different WFAO systems and their expected performance on a 42 m telescope case.

First laboratory validation of vibration filtering with LQG control law for adaptive optics.

We present a first experimental validation of vibration filtering with a Linear Quadratic Gaussian (LQG) control law in Adaptive Optics (AO). A quasi-pure mechanical vibration is generated on a classic AO bench and filtered by the control law, leading to an improvement of the Strehl Ratio and image stability. Vibration filtering may be applied to any AO system, but these results are of particular interest for eXtrem AO, and for instance for the SPHERE AO design, where high performance is required.