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Register a new userInformation-theoretical Limits of Recursive Estimation and Closed-loop Control in High-contrast Imaging
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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 covariance 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.
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For imaging faint exoplanets and disks, a coronagraph-equipped observatory needs focal plane wavefront correction to recover high contrast. The most efficient correction methods iteratively estimate the stellar electric field and suppress it with active optics. The estimation requires several images from the science camera per iteration. To maximize the science yield, it is desirable both to have fast wavefront correction and to utilize all the correction images for science target detection. Exoplanets and disks are incoherent with their stars, so a nonlinear estimator is required to estimate both the incoherent intensity and the stellar electric field. Such techniques assume a high level of stability found only on space-based observatories and possibly ground-based telescopes with extreme adaptive optics. In this paper, we implement a nonlinear estimator, the iterated extended Kalman filter (IEKF), to enable fast wavefront correction and a recursive, nearly-optimal estimate of the incoherent light. In Princetons High Contrast Imaging Laboratory we demonstrate that the IEKF allows wavefront correction at least as fast as with a Kalman filter and provides the most accurate detection of a faint companion. The nonlinear IEKF formalism allows us to pursue other strategies such as parameter estimation to improve wavefront correction.
Adaptive optic (AO) systems delivering high levels of wavefront correction are now common at observatories. One of the main limitations to image quality after wavefront correction comes from atmospheric refraction. An Atmospheric dispersion compensator (ADC) is employed to correct for atmospheric refraction. The correction is applied based on a look-up table consisting of dispersion values as a function of telescope elevation angle. The look-up table based correction of atmospheric dispersion results in imperfect compensation leading to the presence of residual dispersion in the point-spread function (PSF) and is insufficient when sub-milliarcsecond precision is required. The presence of residual dispersion can limit the achievable contrast while employing high-performance coronagraphs or can compromise high-precision astrometric measurements. In this paper, we present the first on-sky closed-loop correction of atmospheric dispersion by directly using science path images. The concept behind the measurement of dispersion utilizes the chromatic scaling of focal plane speckles. An adaptive speckle grid generated with a deformable mirror (DM) that has a sufficiently large number of actuators is used to accurately measure the residual dispersion and subsequently correct it by driving the ADC. We have demonstrated with the Subaru Coronagraphic Extreme AO (SCExAO) system on-sky closed-loop correction of residual dispersion to < 1 mas across H-band. This work will aid in the direct detection of habitable exoplanets with upcoming extremely large telescopes (ELTs) and also provide a diagnostic tool to test the performance of instruments which require sub-milliarcsecond correction.
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.
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.
The Phase-Induced Amplitude Apodization (PIAA) coronagraph is a high performance coronagraph concept able to work at small angular separation with little loss in throughput. We present results obtained with a laboratory PIAA system including active wavefront control. The system has a 94.3% throughput (excluding coating losses) and operates in air with monochromatic light. Our testbed achieved a 2.27e-7 raw contrast between 1.65 lambda/D (inner working angle of the coronagraph configuration tested) and 4.4 lambda/D (outer working angle). Through careful calibration, we were able to separate this residual light into a dynamic coherent component (turbulence, vibrations) at 4.5e-8 contrast and a static incoherent component (ghosts and/or polarization missmatch) at 1.6e-7 contrast. Pointing errors are controlled at the 1e-3 lambda/D level using a dedicated low order wavefront sensor. While not sufficient for direct imaging of Earth-like planets from space, the 2.27e-7 raw contrast achieved already exceeds requirements for a ground-based Extreme Adaptive Optics system aimed at direct detection of more massive exoplanets. We show that over a 4hr long period, averaged wavefront errors have been controlled to the 3.5e-9 contrast level. This result is particularly encouraging for ground based Extreme-AO systems relying on long term stability and absence of static wavefront errors to recover planets much fainter than the fast boiling speckle halo.
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