No Arabic abstract
Advanced AO systems will likely utilise Pyramid wave-front sensors (PWFS) over the traditional Shack-Hartmann sensor in the quest for increased sensitivity, peak performance and ultimate contrast. Here, we wish to bring knowledge and quantify the PWFS theoretical limits as a means to highlight its properties and use cases. We explore forward models for the PWFS in the spatial-frequency domain for they prove quite useful since a) they emanate directly from physical-optics (Fourier) diffraction theory; b) provide a straightforward path to meaningful error breakdowns, c) allow for reconstruction algorithms with $O (n,log(n))$ complexity for large-scale systems and d) tie in seamlessly with decoupled (distributed) optimal predictive dynamic control for performance and contrast optimisation. All these aspects are dealt with here. We focus on recent analytical PWFS developments and demonstrate the performance using both analytic and end-to-end simulations. We anchor our estimates with observed on-sky contrast on existing systems and then show very good agreement between analytical and Monte-Carlo estimates for the PWFS. For a potential upgrade of existing high-contrast imagers on 10,m-class telescopes with visible or near-infrared PWFS, we show under median conditions at Paranal a contrast improvement (limited by chromatic and scintillation effects) of 2x-5x by replacing the wave-front sensor alone at large separations close to the AO control radius where aliasing dominates, and factors in excess of 10x by coupling distributed control with the PWFS over most of the AO control region, from small separations starting with the Inner Working Angle of typically 1-2 $lambda/D$ to the AO correction edge (here 20 $lambda/D$).
In this article, we compare a set of Wave Front Sensors (WFS) based on Fourier filtering technique. In particular, this study explores the class of pyramidal WFS defined as the 4 faces pyramid WFS, all its recent variations (6, 8 faces, the flattened PWFS, etc.) and also some new WFSs as the flattened cone WFS or the 3 faces pyramid WFS. In the first part, we describe such a sensors class thanks to the optical parameters of the Fourier filtering mask and the modulation parameters. In the second part, we use the unified formalism to create a set of performance criteria: size of the signal on the detector, efficiency of incoming flux, sensitivity, linear range and chromaticity. In the third part, we show the influence of the previous optical and modulation parameters on these performance criteria. This exhaustive study allows to know how to optimize the sensor regarding to performance specifications. We show in particular that the number of faces has influence on the number of pixels required to do the wave front sensing but no influence on the sensitivity and linearity range. To modify these criteria, we show that the modulation radius and the apex angle are much more relevant. Moreover we observe that the time spent on edges or faces during a modulation cycle allows to adjust the trade-off between sensitivity and linearity range.
The effects of photon noise, aliasing, wavefront chromaticity and scintillation on the point spread function (PSF) contrast achievable with ground based adaptive optics (AO) are evaluated for different wavefront sensing schemes. I show that a wavefront sensor (WFS) based upon the Zernike phase contrast technique offers the best sensitivity to photon noise at all spatial frequencies, while the Shack-Hartmann WFS is significantly less sensitive. In AO systems performing wavefront sensing in the visible and scientific imaging in the near-IR, the PSF contrast limit is set by the scintillation chromaticity induced by Fresnel propagation through the atmosphere. On a 8m telescope, the PSF contrast is then limited to 1e-4 to 1e-5 in the central arcsecond. Wavefront sensing and scientific imaging should therefore be done at the same wavelength, in which case, on bright sources, PSF contrasts between 1e-6 and 1e-7 can be achieved within 1 arcsecond on a 8m telescope in optical/near-IR. The impact of atmospheric turbulence parameters (seeing, wind speed, turbulence profile) on the PSF contrast is quantified. I show that a focal plane wavefront sensing scheme offers unique advantages, and I discuss how to implement it. Coronagraphic options are also briefly discussed.
One of the primary science goals of the Large UV/Optical/Infrared Surveyor (LUVOIR) mission concept is to detect and characterize Earth-like exoplanets orbiting nearby stars with direct imaging. The success of its coronagraph instrument ECLIPS (Extreme Coronagraph for Living Planetary Systems) depends on the ability to stabilize the wavefront from a large segmented mirror such that optical path differences are limited to tens of picometers RMS during an exposure time of a few hours. In order to relax the constraints on the mechanical stability, ECLIPS will be equipped with a wavefront sensing and control (WS&C) architecture to correct wavefront errors up to temporal frequencies >~1 Hz. These errors may be dominated by spacecraft structural dynamics exciting vibrations at the segmented primary mirror. In this work, we present detailed simulations of the WS&C system within the ECLIPS instrument and the resulting contrast performance. This study assumes wavefront aberrations based on a finite element model of a simulated telescope with spacecraft structural dynamics. Wavefront residuals are then computed according to a model of the adaptive optics system that includes numerical propagation to simulate a realistic wavefront sensor and an analytical model of the temporal performance. An end-to-end numerical propagation model of ECLIPS is then used to estimate the residual starlight intensity distribution at the science detector. We show that the contrast performance depends strongly on the target star magnitude and the spatio-temporal distribution of wavefront errors from the telescope. In cases with significant vibration, we advocate for the use of laser metrology to mitigate high temporal frequency wavefront errors and increase the mission yield.
Current and future high-contrast imaging instruments require extreme adaptive optics (XAO) systems to reach contrasts necessary to directly image exoplanets. Telescope vibrations and the temporal error induced by the latency of the control loop limit the performance of these systems. One way to reduce these effects is to use predictive control. We describe how model-free Reinforcement Learning can be used to optimize a Recurrent Neural Network controller for closed-loop predictive control. First, we verify our proposed approach for tip-tilt control in simulations and a lab setup. The results show that this algorithm can effectively learn to mitigate vibrations and reduce the residuals for power-law input turbulence as compared to an optimal gain integrator. We also show that the controller can learn to minimize random vibrations without requiring online updating of the control law. Next, we show in simulations that our algorithm can also be applied to the control of a high-order deformable mirror. We demonstrate that our controller can provide two orders of magnitude improvement in contrast at small separations under stationary turbulence. Furthermore, we show more than an order of magnitude improvement in contrast for different wind velocities and directions without requiring online updating of the control law.
In tomographic adaptive-optics (AO) systems, errors due to tomographic wave-front reconstruction limit the performance and angular size of the scientific field of view (FoV), where AO correction is effective. We propose a multi time-step tomographic wave-front reconstruction method to reduce the tomographic error by using the measurements from both the current and the previous time-steps simultaneously. We further outline the method to feed the reconstructor with both wind speed and direction of each turbulence layer. An end-to-end numerical simulation, assuming a multi-object AO (MOAO) system on a 30 m aperture telescope, shows that the multi time-step reconstruction increases the Strehl ratio (SR) over a scientific FoV of 10 arcminutes in diameter by a factor of 1.5--1.8 when compared to the classical tomographic reconstructor, depending on the guide star asterism and with perfect knowledge of wind speeds and directions. We also evaluate the multi time-step reconstruction method and the wind estimation method on the RAVEN demonstrator under laboratory setting conditions. The wind speeds and directions at multiple atmospheric layers are measured successfully in the laboratory experiment by our wind estimation method with errors below 2 ms. With these wind estimates, the multi time-step reconstructor increases the SR value by a factor of 1.2--1.5, which is consistent with a prediction from end-to-end numerical simulation.