For ExAO instruments for the Giant Segmented Mirror Telescopes (GSMTs), alternative architectures of WFS are under consideration because there is a tradeoff between detector size, speed, and noise that reduces the performance of GSMT-ExAO wavefront c
ontrol. One option under consideration for a GSMT-ExAO wavefront sensor is a three-sided PWFS (3PWFS). The 3PWFS creates three copies of the telescope pupil for wavefront sensing, compared to the conventional four-sided PWFS (4PWFS) which uses four pupils. The 3PWFS uses fewer detector pixels than the 4PWFS and should therefore be less sensitive to read noise. Here we develop a mathematical formalism based on the diffraction theory description of the Foucault knife edge test that predicts the intensity pattern after the PWFS. Our formalism allows us to calculate the intensity in the pupil images formed by the PWFS in the presence of phase errors corresponding to arbitrary Fourier modes. We then use the Object Oriented MATLAB Adaptive Optics toolbox (OOMAO) to simulate an end-to-end model of an adaptive optics system using a PWFS with modulation and compare the performance of the 3PWFS to the 4PWFS. In the case of a low read noise detector, the Strehl ratios of the 3PWFS and 4PWFS are within 0.01. When we included higher read noise in the simulation, we found a Strehl ratio gain of 0.036 for the 3PWFS using Raw Intensity over the 4PWFS using Slopes Maps at a stellar magnitude of 10. At the same magnitude, the 4PWFS RI also outperformed the 4PWFS SM, but the gain was only 0.012 Strehl. This is significant because 4PWFS using Slopes Maps is how the PWFS is conventionally used for AO wavefront sensing. We have found that the 3PWFS is a viable wavefront sensor that can fully reconstruct a wavefront and produce a stable closed-loop with correction comparable to that of a 4PWFS, with modestly better performance for high read-noise detectors.
A lower bound on unbiased estimates of wavefront errors (WFE) is presented for the linear regime of small perturbation and active control of a high-contrast region (dark hole). Analytical approximations and algorithms for computing the closed-loop co
variance of the WFE modes are provided for discrete- and continuous-time linear WFE dynamics. Our analysis applies to both image-plane and non-common-path wavefront sensing (WFS) with Poisson-distributed measurements and noise sources (i.e., photon-counting mode). Under this assumption, we show that recursive estimation benefits from infinitesimally short exposure times, is more accurate than batch estimation and, for high-order WFE drift dynamical processes, scales better than batch estimation with amplitude and star brightness. These newly-derived contrast scaling laws are a generalization of previously known theoretical and numerical results for turbulence-driven Adaptive Optics. For space-based coronagraphs, we propose a scheme for combining models of WFE drift, low-order non-common-path WFS (LOWFS) and high-order image-plane WFS (HOWFS) into closed-loop contrast estimates. We also analyze the impact of residual low-order WFE, sensor noise, and other sources incoherent with the star, on closed-loop dark-hole maintenance and the resulting contrast. As an application example, our model suggests that the Roman Space Telescope might operate in a regime that is dominated by incoherent sources rather than WFE drift, where the WFE drift can be actively rejected throughout the observations with residuals significantly dimmer than the incoherent sources. The models proposed in this paper make possible the assessment of the closed-loop contrast of coronagraphs with combined LOWFS and HOWFS capabilities, and thus help estimate WFE stability requirements of future instruments.
The MagAO-X instrument is a new extreme adaptive optics system for high-contrast imaging at visible and near-infrared wavelengths on the Magellan Clay Telescope. A central component of this system is a 2040-actuator microelectromechanical deformable
mirror (DM) from Boston Micromachines Corp. that operates at 3.63 kHz for high-order wavefront control (the tweeter). Two additional DMs from ALPAO perform the low-order (the woofer) and non-common-path science-arm wavefront correction (the NCPC DM). Prior to integration with the instrument, we characterized these devices using a Zygo Verifire Interferometer to measure each DM surface. We present the results of the characterization effort here, demonstrating the ability to drive tweeter to a flat of 6.9 nm root mean square (RMS) surface (and 0.56 nm RMS surface within its control bandwidth), the woofer to 2.2 nm RMS surface, and the NCPC DM to 2.1 nm RMS surface over the MagAO-X beam footprint on each device. Using focus-diversity phase retrieval on the MagAO-X science cameras to estimate the internal instrument wavefront error (WFE), we further show that the integrated DMs correct the instrument WFE to 18.7 nm RMS, which, combined with a 11.7% pupil amplitude RMS, produces a Strehl ratio of 0.94 at H$alpha$.
High-contrast imaging observations are fundamentally limited by the spatially and temporally correlated noise source called speckles. Suppression of speckle noise is the key goal of wavefront control and adaptive optics (AO), coronagraphy, and a host
of post-processing techniques. Speckles average at a rate set by the statistical speckle lifetime, and speckle-limited integration time in long exposures is directly proportional to this lifetime. As progress continues in post-coronagraph wavefront control, residual atmospheric speckles will become the limiting noise source in high-contrast imaging, so a complete understanding of their statistical behavior is crucial to optimizing high-contrast imaging instruments. Here we present a novel power spectral density (PSD) method for calculating the lifetime, and develop a semi-analytic method for predicting intensity PSDs behind a coronagraph. Considering a frozen-flow turbulence model, we analyze the residual atmosphere speckle lifetimes in a MagAO-X-like AO system as well as 25--39 m giant segmented mirror telescope (GSMT) scale systems. We find that standard AO control shortens atmospheric speckle lifetime from ~130 ms to ~50 ms, and predictive control will further shorten the lifetime to ~20 ms on 6.5 m MagAO-X. We find that speckle lifetimes vary with diameter, wind speed, seeing, and location within the AO control region. On bright stars lifetimes remain within a rough range of ~20 ms to ~100 ms. Due to control system dynamics there are no simple scaling laws which apply across a wide range of system characteristics. Finally, we use these results to argue that telemetry-based post-processing should enable ground-based telescopes to achieve the photon-noise limit in high-contrast imaging.
The search for exoplanets is pushing adaptive optics systems on ground-based telescopes to their limits. One of the major limitations at small angular separations, exactly where exoplanets are predicted to be, is the servo-lag of the adaptive optics
systems. The servo-lag error can be reduced with predictive control where the control is based on the future state of the atmospheric disturbance. We propose to use a linear data-driven integral predictive controller based on subspace methods that is updated in real time. The new controller only uses the measured wavefront errors and the changes in the deformable mirror commands, which allows for closed-loop operation without requiring pseudo-open loop reconstruction. This enables operation with non-linear wavefront sensors such as the pyramid wavefront sensor. We show that the proposed controller performs near-optimal control in simulations for both stationary and non-stationary disturbances and that we are able to gain several orders of magnitude in raw contrast. The algorithm has been demonstrated in the lab with MagAO-X, where we gain more than two orders of magnitude in contrast.
Starlight subtraction algorithms based on the method of Karhunen-Lo`eve eigenimages have proved invaluable to exoplanet direct imaging. However, they scale poorly in runtime when paired with differential imaging techniques. In such observations, refe
rence frames and frames to be starlight-subtracted are drawn from the same set of data, requiring a new subset of references (and eigenimages) for each frame processed to avoid self-subtraction of the signal of interest. The data rates of extreme adaptive optics instruments are such that the only way to make this computationally feasible has been to downsample the data. We develop a technique that updates a pre-computed singular value decomposition of the full dataset to remove frames (i.e. a downdate) without a full recomputation, yielding the modified eigenimages. This not only enables analysis of much larger data volumes in the same amount of time, but also exhibits near-linear scaling in runtime as the number of observations increases. We apply this technique to archival data and investigate its scaling behavior for very large numbers of frames $N$. The resulting algorithm provides speed improvements of $2.6times$ (for 200 eigenimages at $N = 300$) to $140 times$ (at $N = 10^4$) with the advantage only increasing as $N$ grows. This algorithm has allowed us to substantially accelerate KLIP even for modest $N$, and will let us quickly explore how KLIP parameters affect exoplanet characterization in large $N$ datasets.
Here we review the current conceptual optical mechanical design of GMagAO-X --the extreme AO (ExAO) system for the Giant Magellan Telescope (GMT). The GMagAO-X tweeter deformable mirror (DM) design is novel in that it uses an optically distributed se
t of pupils that allows seven commercially available 3000 actuator BMC DMs to work in parallel to effectively create an ELT-scale ExAO tweeter DM --with all parts commercially available today. The GMagAO-X parallel DM tweeter will have 21,000 actuators to be used at ~2kHz update speeds enabling high-contrast science at ~5 mas separations in the visible and NIR of the spectrum (0.6-1.7 microns). To prove our concept for GMagAO-X several items must be lab tested: the optical/mechanical concept for the parallel DM; phasing of the GMT pupil; and solving the GMTs isolated island effect will all be demonstrated on an optical testbed at the University of Arizona. Here we outline the current design for this GMT High-Contrast Testbed that has been proposed jointly by GMTO and the University of Arizona which leverages the existing, operational, MagAO-X ExAO instrument to verify our approach to phase sensing and AO control for high-contrast GMT NGS science. We will also highlight how GMagAO-X can be mounted on the auxiliary port of the GMT and so remain gravity invariant. Since it is gravity invariant GMagAO-X can utilize a floating optical table to minimize flexure and NCP vibrations.
Precision wavefront control on future segmented-aperture space telescopes presents significant challenges, particularly in the context of high-contrast exoplanet direct imaging. We present a new wavefront control architecture that translates the grou
nd-based artificial guide star concept to space with a laser source aboard a second spacecraft, formation flying within the telescope field-of-view. We describe the motivating problem of mirror segment motion and develop wavefront sensing requirements as a function of guide star magnitude and segment motion power spectrum. Several sample cases with different values for transmitter power, pointing jitter, and wavelength are presented to illustrate the advantages and challenges of having a non-stellar-magnitude noise limited wavefront sensor for space telescopes. These notional designs allow increased control authority, potentially relaxing spacecraft stability requirements by two orders of magnitude, and increasing terrestrial exoplanet discovery space by allowing high-contrast observations of stars of arbitrary brightness.
One of the main pursuits of the MagAO-X project is imaging planets around nearby stars with the direct detection method utilizing an extreme AO system and a coronagraph and a large telescope. The MagAO-X astronomical coronagraph will be implemented o
n the 6.5 meter Clay Magellan Telescope in Chile. The 22 mirrors in the system require a high level of mirror stability. Our goal is less than 1 microradian drift in tilt per mirror per one degree Celsius change in temperature. There are no commercial 2inch kinematic optical mounts that are truly zero-drift from 0-20C. Our solution to this problem was to develop a locking clamp to keep our optics stable and fulfill our specifications. After performing temperature variation and thermal shock testing, we conclude that this novel locking clamp significantly increases the thermal stability of stainless steel mounts by ~10x but still allows accurate microradian positioning of a mirror. A provisional patent (#62/632,544) has been obtained for this mount.
The Magellan extreme adaptive optics (MagAO-X) instrument is a new extreme adaptive optics (ExAO) system designed for operation in the visible to near-IR which will deliver high contrast-imaging capabilities. The main AO system will be driven by a py
ramid wavefront sensor (PyWFS); however, to mitigate the impact of quasi-static and non-common path (NCP) aberrations, focal plane wavefront sensing (FPWFS) in the form of low-order wavefront sensing (LOWFS) and spatial linear dark field control (LDFC) will be employed behind a vector apodizing phase plate (vAPP) coronagraph using rejected starlight at an intermediate focal plane. These techniques will allow for continuous high-contrast imaging performance at the raw contrast level delivered by the vAPP coronagraph 6 x 10^-5. We present simulation results for LOWFS and spatial LDFC with a vAPP coronagraph, as well as laboratory results for both algorithms implemented with a vAPP coronagraph at the University of Arizona Extreme Wavefront Control Lab.
