Astronomical Adaptive Optics Systems Research Articles

Pupil calibration for pyramid wavefront sensors based on a wavefront corrector.

The pyramid wavefront sensor (PWS) presents numerous advantages, such as high energy utilization, exceptional spatial resolution, and adjustability. Precise calibration of the pupil's position and size in advance is essential for accurately extracting wavefront slope information from the captured pupil image by the PWS. What we believe to be a novel calibration method is proposed using a wavefront corrector to enhance the sharpness of the pupil images in the PWS. An experimental setup using a crystal spatial light modulator (SLM) is established to validate this method. Both physical experiments and simulated results demonstrate that our proposed method can achieve accurate calibration of the pupil image with an error within 4 pixels for pupil size and not exceeding 3 pixels for position, meeting practical application requirements. The proposed PWS calibration method exhibits excellent repeatability and robustness, making it directly applicable in astronomical adaptive optics systems.

A Method of Superimposing Subapertures for Shark–Hartmann Wave Front Sensing with Faint Objects

Abstract For the astronomical adaptive optics systems, the observation condition is always in a regime of low photon flux. We present a method of superimposing subapertures for the Shark–Hartmann wave front sensing with faint objects. This approach significantly improves the signal-to-noise ratio (S/N) of the spot pattern by superimposing adjacent subapertures, thus circumventing the invalid wave front sensing with faint object, enhancing the accuracy of the wave front detection. In addition, we demonstrate that the validity of this approach is not an incidental result under a specific condition, which can be explained theoretically by exploiting the atmospheric turbulence model. Then we validate the approach with simulations and experimental realization under weak-light and bright-light conditions. Results show that the proposed subaperture superposition approach can achieve accurate wave front reconstruction for low S/N or faint object even in cases beyond the ability of conventional methods. It brings out a new idea, besides long exposure and variable sampling, that comes with a tradeoff between temporal sampling frequency and spatial resolution. In addition, this method is also valid for extended objects; we preliminarily validate this method on a 600 mm aperture solar telescope, achieving stable closed-loop control with lower-contrast objects.

High-speed Focal Plane Wave Front Sensing with an Optical Chopper

Focal plane wave front sensing and control is a critical approach to reducing noncommon path errors between a conventional astronomical adaptive optics (AO) wave front sensor (WFS) detector and a science camera. However, in addition to mitigating noncommon path errors, recent focal plane wave front sensing techniques have been developed to operate at speeds fast enough to enable “multi-WFS” AO, where residual atmospheric errors are further corrected by a focal plane WFS. Although a number of such techniques have been recently developed for coronagraphic imaging, here we present one designed for noncoronagraphic imaging. Utilizing conventional AO system components, this concept additionally requires (1) a detector imaging the focal plane of the WFS light source and (2) a pupil plane optical chopper device that is the noncommon path to the first WFS and is synchronized to the focal plane imager readout. These minimal hardware requirements enable the temporal amplitude modulation to resolve the sine ambiguity of even wave-front modes for low, mid, and high wave front spatial frequencies. Similar capabilities have been demonstrated with classical phase diversity by defocusing the detector, but such techniques are incompatible with simultaneous science observations. This optical chopping technique, however, enables science imaging at up to 50% duty cycle. We present both simulations and laboratory validation of this concept on SEAL, the Santa Cruz Extreme AO Laboratory testbed.

Study of a Shack-Hartmann wavefront sensor with adjustable spatial sampling based on spherical reference wave

For the astronomical adaptive optics systems, the observation condition is constantly changing or in a regime of low photon flux. Besides, for various brightness seeing conditions, the Shack-Hartmann wavefront sensor has a matching spatial sampling that avoids extra wavefront reconstruction error. To integrate advantageous spatial samplings, we propose a novel Shack-Hartmann wavefront sensor with adjustable spatial sampling (ASS-WFS) based on spherical reference wave. In principle, only a simple movement of the microlens array (MLA) and the CCD detector in the direction of the optical axis is required to achieve variable spatial sampling. This is also obviously advantageous in the adaptive optics performance as it allows the wavefront sensor to dynamically match brightness of the observation. To demonstrate the performance of the ASS-WFS, we present the sensor in terms of the principles, the simulation, and the experiment. Results show that the ASS-WFS is able to precisely measure and reconstruct the wavefront, and also demonstrate that advantages resulting from adjusting the spatial samplings can efficiently reduce the disadvantages of low signal-to-noise ratio to boost wavefront reconstruction accuracy.

Deep phase retrieval for astronomical Shack–Hartmann wavefront sensors

ABSTRACT We present a high-speed deep learning-based phase retrieval approach for Shack–Hartmann wavefront sensors used in astronomical adaptive optics. It reconstructs the Zernike modal coefficients from the image captured by the wavefront sensor with a lightweight convolutional neural network. Compared to the traditional slope-based wavefront reconstruction, the proposed approach uses the image captured by the sensor directly as inputs for more high-order aberrations. Compared to the recently developed iterative phase retrieval methods, the speed is much faster with the computation time less than 1 ms for a 100-aperture configuration, which may satisfy the requirement of an astronomical adaptive optics system. Simulations have been done to demonstrate the advantages of this approach. Experiments on a 241-unit deformable-secondary-mirror AOS have also been done to validate the proposed approach.

A low-cost and high-performance technique for adaptive optics static wavefront correction

Non-Common Path Error (NCPE) is one of the factors that limit an Adaptive Optics (AO) system from delivering ultra-high performance. To correct the NCPE associated static aberration, we propose a simple but robust and high-performance pupil-plane based wavefront measurement and correction technique, which can copy a single-mode fiber generated perfect wavefront to the AO system via an iteration optimization process, and the NCPE can be effectively corrected by directly commanding the Deformable Mirror (DM) of the AO system. Compared with the previous focal-plane based approach that uses focal plane based Point Spread Function (PSF) for correction evaluation, the pupil-plane based approach can be reliably and rapidly converged to a global optimization result and provides better performance, in particular for an AO system with a large initial static wavefront error. This technique we proposed can be implemented in astronomical AO systems where extremely high performance is required.

Focal-plane-assisted pyramid wavefront sensor: Enabling frame-by-frame optical gain tracking

Aims. With its high sensitivity, the pyramid wavefront sensor (PyWFS) is becoming an advantageous sensor for astronomical adaptive optics (AO) systems. However, this sensor exhibits significant non-linear behaviours leading to challenging AO control issues. Methods. In order to mitigate these effects, we propose to use in addition to the classical pyramid sensor a focal plane image combined with a convolutive description of the sensor to fast track the PyWFS non-linearities, the so-called optical gains (OG). Results. We show that this additional focal plane imaging path only requires a small fraction of the total flux while representing a robust solution to estimating the PyWFS OG. Finally, we demonstrate the gain that our method brings with specific examples of bootstrapping and handling non-common path aberrations.

Disturbance Modelling for Minimum Variance Control in Adaptive Optics Systems Using Wavefront Sensor Sampled-Data.

Modern large telescopes are built based on the effectiveness of adaptive optics systems in mitigating the detrimental effects of wavefront distortions on astronomical images. In astronomical adaptive optics systems, the main sources of wavefront distortions are atmospheric turbulence and mechanical vibrations that are induced by the wind or the instrumentation systems, such as fans and cooling pumps. The mitigation of wavefront distortions is typically attained via a control law that is based on an adequate and accurate model. In this paper, we develop a modelling technique based on continuous-time damped-oscillators and on the Whittle’s likelihood method to estimate the parameters of disturbance models from wavefront sensor time-domain sampled-data. On the other hand, when the model is not accurate, the performance of the minimum variance controller is affected. We show that our modelling and identification techniques not only allow for more accurate estimates, but also for better minimum variance control performance. We illustrate the benefits of our proposal via numerical simulations.

Cascading optofluidic phase modulators for performance enhancement in refractive adaptive optics

We discuss the implementation and performance of an adaptive optics (AO) system that uses two cascaded deformable phase plates (DPPs), which are transparent optofluidic phase modulators, mimicking the common woofer/tweeter-type astronomical AO systems. One of the DPPs has 25 electrodes forming a keystone pattern best suited for the correction of low-order and radially symmetric modes; the second device has 37 hexagonally packed electrodes better suited for high-order correction. We also present simulation results and experimental validation for a new open-loop control strategy enabling simultaneous control of both DPPs, which ensures optimum correction for both large-amplitude low-order, and complex combinations of low- and high-order aberrations. The resulting system can reproduce Zernike modes up to the sixth radial order with stroke and fidelity up to twice better than what is attainable with either of the DPPs individually. The performance of the new AO configuration is also verified in a custom-developed fluorescence microscope with sensorless aberration correction.

Artificial guide stars for adaptive optics using unmanned aerial vehicles

Astronomical adaptive optics systems are used to increase effective telescope resolution. However, they cannot be used to observe the whole sky since one or more natural guide stars of sufficient brightness must be found within the telescope field of view for the AO system to work. Even when laser guide stars are used, natural guide stars are still required to provide a constant position reference. Here, we introduce a technique to overcome this problem by using rotary unmanned aerial vehicles (UAVs) as a platform from which to produce artificial guide stars. We describe the concept, which relies on the UAV being able to measure its precise relative position. We investigate the adaptive optics performance improvements that can be achieved, which in the cases presented here can improve the Strehl ratio by a factor of at least 2 for a 8~m class telescope. We also discuss improvements to this technique, which is relevant to both astronomical and solar adaptive optics systems.

Efficient, nonlinear phase estimation with the nonmodulated pyramid wavefront sensor.

The sensitivity of the pyramid wavefront sensor (PyWFS) has made it a popular choice for astronomical adaptive optics (AAO) systems. The PyWFS is at its most sensitive when it is used without modulation of the input beam. In nonmodulated mode, the device is highly nonlinear. Hence, all PyWFS implementations on current AAO systems employ modulation to make the device more linear. The upcoming era of 30-m class telescopes and the demand for ultra-precise wavefront control stemming from science objectives that include direct imaging of exoplanets make using the PyWFS without modulation desirable. This article argues that nonlinear estimation based on Newton's method for nonlinear optimization can be useful for mitigating the effects of nonlinearity in the nonmodulated PyWFS. The proposed approach requires all optical modeling to be pre-computed, which has the advantage of avoiding real-time simulations of beam propagation. Further, the required real-time calculations are amenable to massively parallel computation. Numerical experiments simulate a PyWFS with faces sloped 3.7° to the horizontal, operating at a wavelength of 0.85μm, and with an index of refraction of 1.45. A singular value analysis shows that the common practice of calculating two "slope" images from the four PyWFS pupil images discards critical information and is unsuitable for the nonmodulated PyWFS simulated here. Instead, this article advocates estimators that use the raw pixel values not only from the four geometrical images of the pupil, but from surrounding pixels as well. The simulations indicate that nonlinear estimation can be effective when the Strehl ratio of the input beam is greater than 0.3, and the improvement relative to linear estimation tends to increase at larger Strehl ratios. At Strehl ratios less than about 0.5, the performances of both the nonlinear and linear estimators are relatively insensitive to noise since they are dominated by nonlinearity error.

Controlling the Laser Guide Star power density distribution at Sodium layer by combining Pre-correction and Beam-shaping

The Sodium laser guide star (LGS) plays a key role in modern astronomical Adaptive Optics Systems (AOSs). The spot size and photon return of the Sodium LGS depend strongly on the laser power density distribution at the Sodium layer and thus affect the performance of the AOS. The power density distribution is degraded by turbulence in the uplink path, launch system aberrations, the beam quality of the laser, and so forth. Even without any aberrations, the TE00 Gaussian type is still not the optimal power density distribution to obtain the best balance between the measurement error and temporal error. To optimize and control the LGS power density distribution at the Sodium layer to an expected distribution type, a method that combines pre-correction and beam-shaping is proposed. A typical result shows that under strong turbulence (Fried parameter (r0) of 5 cm) and for a quasi-continuous wave Sodium laser (power (P) of 15 W), in the best case, our method can effectively optimize the distribution from the Gaussian type to the “top-hat” type and enhance the photon return flux of the Sodium LGS; at the same time, the total error of the AOS is decreased by 36% with our technique for a high power laser and poor seeing.

Simulations of return flux of polychromatic laser guide stars based on Bloch equations

Sodium laser guide star (LGS) becomes an essential part in modern astronomical adaptive optics system, especially for the next generation extremely large ground based telescope. The LGS technology has experienced the developmental stages as natural guide star, Rayleigh LGS, sodium LGS and constellation of LGS. The sky coverage is still limited in that the LGS cannot not be used to detect the tip/tilt aberrations. While the polychromatic laser guide star (PLGS) is one of the most effective ways to enlarge the sky coverage to 100%. Previous simulation models are insufficient for the accurate calculation of the return flux, especially for the simulation model of PLGS which is generated by one-photon excitation of mesospheric sodium atoms. The simulation model based on Bloch equations proposed in this paper can be used to compute the return flux of one-photon excited PLGS precisely. Doppler broadening, beam atom exchanging, collisions and recoil are taken into account in the model. The return flux is validated by the return efficiency. The simulation results indicate that with one-photon excitation of sodium atoms, a return efficiency of 330 nm is minimum compared with those of other wavelengths; the saturation power density will decrease with recoil increasing and increase with collision rate increasing; an optimal line-width exists up to maximum the photon return efficiency. In the best case, when the power density is 10 W/m2 at the sodium layer, the maximum return efficiency at 330 nm is 0.907 photons/s/sr/atom/(W/m2) with an optimal laser line-width of 18 MHz.

Modeling astronomical adaptive optics performance with temporally filtered Wiener reconstruction of slope data.

We build on a long-standing tradition in astronomical adaptive optics (AO) of specifying performance metrics and error budgets using linear systems modeling in the spatial-frequency domain. Our goal is to provide a comprehensive tool for the calculation of error budgets in terms of residual temporally filtered phase power spectral densities and variances. In addition, the fast simulation of AO-corrected point spread functions (PSFs) provided by this method can be used as inputs for simulations of science observations with next-generation instruments and telescopes, in particular to predict post-coronagraphic contrast improvements for planet finder systems. We extend the previous results presented in Correia and Teixeira [J. Opt. Soc. Am. A31, 2763 (2014)JOAOD60740-323210.1364/JOSAA.31.002763] to the closed-loop case with predictive controllers and generalize the analytical modeling of Rigaut etal. [Proc. SPIE3353, 1038 (1998)PSISDG0277-786X10.1117/12.321649], Flicker [Technical Report (W. M. Keck Observatory, 2007)], and Jolissaint [J. Eur. Opt. Soc.5, 10055 (2010)1990-257310.2971/jeos.2010.10055]. We follow closely the developments of Ellerbroek [J. Opt. Soc. Am. A22, 310 (2005)JOAOD60740-323210.1364/JOSAA.22.000310] and propose the synthesis of a distributed Kalman filter to mitigate both aniso-servo-lag and aliasing errors while minimizing the overall residual variance. We discuss applications to (i)analytic AO-corrected PSF modeling in the spatial-frequency domain, (ii)post-coronagraphic contrast enhancement, (iii)filter optimization for real-time wavefront reconstruction, and (iv)PSF reconstruction from system telemetry. Under perfect knowledge of wind velocities, we show that ∼60 nm rms error reduction can be achieved with the distributed Kalman filter embodying antialiasing reconstructors on 10m class high-order AO systems, leading to contrast improvement factors of up to three orders of magnitude at few λ/D separations (∼1-5λ/D) for a 0 magnitude star and reaching close to one order of magnitude for a 12 magnitude star.

Turbulence velocity profiling for high sensitivity and vertical-resolution atmospheric characterization with Stereo-SCIDAR

As telescopes become larger, into the era of ~40 m Extremely Large Telescopes, the high- resolution vertical profile of the optical turbulence strength is critical for the validation, optimization and operation of optical systems. The velocity of atmospheric optical turbulence is an important parameter for several applications including astronomical adaptive optics systems. Here, we compare the vertical profile of the velocity of the atmospheric wind above La Palma by means of a comparison of Stereo-SCIntillation Detection And Ranging (Stereo- SCIDAR) with the Global Forecast System models and nearby balloon-borne radiosondes. We use these data to validate the automated optical turbulence velocity identification from the Stereo-SCIDAR instrument mounted on the 2.5 m Isaac Newton Telescope, La Palma. By comparing these data we infer that the turbulence velocity and the wind velocity are consistent and that the automated turbulence velocity identification of the Stereo-SCIDAR is precise. The turbulence velocities can be used to increase the sensitivity of the turbulence strength profiles, as weaker turbulence that may be misinterpreted as noise can be detected with a velocity vector. The turbulence velocities can also be used to increase the altitude resolution of a detected layer, as the altitude of the velocity vectors can be identified to a greater precision than the native resolution of the system. We also show examples of complex velocity structure within a turbulent layer caused by wind shear at the interface of atmospheric zones.

Comparison of the Shack–Hartmann and plenoptic sensor in closed-loop adaptive optics system

The wavefront sensor is used in adaptive optics (AO) to detect the atmospheric distortion, which feeds back to the deformable mirror to compensate for this distortion. While the Shack–Hartmann sensor has been widely used, the plenoptic sensor was proposed in recent years. The two different wavefront sensing methods have different interpretations and numerical consequences, though they are both slope-based. The plenoptic sensor is compared with the Shack–Hartmann sensor in a closed-loop AO system. Simulations are performed to investigate their performances under closed-loop conditions. The plenoptic sensors both without and with modulation are discussed. The results show that the closed-loop performance of the plenoptic sensor without modulation is worse than that of the Shack–Hartmann sensor when the star for observation is brighter than magnitude 7, but better when the star is fainter. The closed-loop performance of the plenoptic sensor could be improved by modulation, except for the faint star. In summary, the limiting magnitude of the astronomical AO system may be improved by using the plenoptic sensor instead of the Shack–Hartmann sensor, and the modulation of the plenoptic sensor is more suitable for the bright star.

Photon Return On-Sky Test of Pulsed Sodium Laser Guide Star with D2b Repumping

Sodium laser guide star (LGS) system has become one of the critical components in modern astronomical adaptive optics system (AOS), especially for the next-generation extremely large telescopes, such as the Thirty Meter Telescope and the European Extremely Large Telescope. Since the wavefront detection performance of AOS is directly related to the brightness of LGS, it is important for AOS to maximize its photon generation efficiency by all means. Sodium D2b line repumping is such a technique that can greatly increase the returned photons for either sodium continuous wave (CW) laser or pulsed laser. This technique has been studied theoretically and field tested with a 20 W CW laser by European Southern Observatory team. However, field test results of a 20 W class pulsed laser with D2b repumping have not been reported yet. In this paper, our latest field test results with theoretical comparison of D2b repumping with a 20 W quasi-continuous wave (QCW) pulsed laser will be presented. With a linearly polarized beam, approximate 40% photon return enhancement was achieved when 10% of laser power was detuned to D2b line, which agreed well with results from a rate equation-based Monte Carlo photon return simulation program. Both experiment and simulation results indicate that with a higher laser intensity projected at the sodium layer, the D2b repumping will be more effective.

Analysis of electron multiplying charge coupled device and scientific CMOS readout noise models for Shack–Hartmann wavefront sensor accuracy

In recent years, detectors with subelectron readout noise have been used very effectively in astronomical adaptive optics systems. Here, we compare readout noise models for the two key faint flux level detector technologies that are commonly used: electron multiplying charge coupled device (EMCCD) and scientific CMOS (sCMOS) detectors. We find that in almost all situations, EMCCD technology is advantageous, and that the commonly used simplified model for EMCCD readout is appropriate. We also find that the commonly used simple models for sCMOS readout noise are optimistic, and we recommend that a proper treatment of the sCMOS root mean square readout noise probability distribution should be considered during instrument performance modeling and development.

Real-time generation of atmospheric turbulence phase screen with non-uniform fast Fourier transform

High fidelity Monte Carlo simulation of atmospheric turbulence phase screens is important for performance testing of astronomical adaptive optics systems. With a sparse spectrum model and an optimal sampling method, it is possible to generate an atmospheric turbulence phase screen with high fidelity. However, the phase screen generation speed is limited by the algorithm structure of this technique. A non-uniform fast Fourier transform technique is proposed in this paper to accelerate phase screen generation speed. This method is able to generate huge atmospheric turbulence phase screens with high fidelity and an acceptable time-cost enabling practical adaptive optics simulations of forthcoming Extremely Large Telescopes.

Anti-aliasing Wiener filtering for wave-front reconstruction in the spatial-frequency domain for high-order astronomical adaptive-optics systems.

Computationally efficient wave-front reconstruction techniques for astronomical adaptive-optics (AO) systems have seen great development in the past decade. Algorithms developed in the spatial-frequency (Fourier) domain have gathered much attention, especially for high-contrast imaging systems. In this paper we present the Wiener filter (resulting in the maximization of the Strehl ratio) and further develop formulae for the anti-aliasing (AA) Wiener filter that optimally takes into account high-order wave-front terms folded in-band during the sensing (i.e., discrete sampling) process. We employ a continuous spatial-frequency representation for the forward measurement operators and derive the Wiener filter when aliasing is explicitly taken into account. We further investigate and compare to classical estimates using least-squares filters the reconstructed wave-front, measurement noise, and aliasing propagation coefficients as a function of the system order. Regarding high-contrast systems, we provide achievable performance results as a function of an ensemble of forward models for the Shack-Hartmann wave-front sensor (using sparse and nonsparse representations) and compute point-spread-function raw intensities. We find that for a 32×32 single-conjugated AOs system the aliasing propagation coefficient is roughly 60% of the least-squares filters, whereas the noise propagation is around 80%. Contrast improvements of factors of up to 2 are achievable across the field in the H band. For current and next-generation high-contrast imagers, despite better aliasing mitigation, AA Wiener filtering cannot be used as a standalone method and must therefore be used in combination with optical spatial filters deployed before image formation actually takes place.