The Zernike wavefront sensor (ZWFS) is a concept belonging to the wide class Fourier-filtering wavefront sensor (FFWFS). The ZWFS is known for its extremely high sensitivity while having a low dynamic range, which makes it a unique sensor for second
stage adaptive optics (AO) systems or quasi-static aberrations calibration sensor. This sensor is composed of a focal plane mask made of a phase shifting dot fully described by two parameters: its diameter and depth. In this letter, we aim to improve the performance of this sensor by changing the diameter of its phase shifting dot. We begin with a general theoretical framework providing an analytical description of the FFWFS properties, then we predict the expected ZWFS sensitivity for different configurations of dot diameters and depths. The analytical predictions are then validated with end-to-end simulations. From this, we propose a variation of the classical ZWFS shape which exhibits extremely appealing properties. We show that the ZWFS sensitivity can be optimized by modifying the dot diameter and even reach the optimal theoretical limit, with a trade-off for low spatial frequencies sensitivity. As an example, we show that a ZWFS with a 2{lambda}/D dot diameter (where {lambda} is the sensing wavelength and D the telescope diameter), hereafter called Z2WFS, exhibits a sensitivity twice higher than the classical 1.06{lambda}/D ZWFS for all the phase spatial components except for tip-tilt modes. Furthermore, this gain in sensitivity does not impact the dynamic range of the sensor, and the Z2WFS exhibits a similar dynamical range as the classical 1.06{lambda}/D ZWFS. This study opens the path to the conception of diameter-optimized ZWFS.
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
. 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 perform a fast tracking of the PyWFS non-linearities, the so-called optical gains (OG). We show that this additional focal plane imaging path only requires a small fraction of the total flux, while representing a robust solution to estimate the PyWFS OG. Finally, we demonstrate the gain brought by our method with the specific examples of bootstrap and Non-Common Path Aberrations (NCPA) handling.
Direct imaging of Earth-like planets from space requires dedicated observatories, combining large segmented apertures with instruments and techniques such as coronagraphs, wavefront sensors, and wavefront control in order to reach the high contrast o
f 10^10 that is required. The complexity of these systems would be increased by the segmentation of the primary mirror, which allows for the larger diameters necessary to image Earth-like planets but also introduces specific patterns in the image due to the pupil shape and segmentation and making high-contrast imaging more challenging. Among these defects, the phasing errors of the primary mirror are a strong limitation to the performance. In this paper, we focus on the wavefront sensing of segment phasing errors for a high-contrast system, using the COronagraphic Focal plane wave-Front Estimation for Exoplanet detection (COFFEE) technique. We implemented and tested COFFEE on the High-contrast imaging for Complex Aperture Telescopes (HiCAT) testbed, in a configuration without any coronagraph and with a classical Lyot coronagraph, to reconstruct errors applied on a 37 segment mirror. We analysed the quality and limitations of the reconstructions. We demonstrate that COFFEE is able to estimate correctly the phasing errors of a segmented telescope for piston, tip, and tilt aberrations of typically 100nm RMS. We also identified the limitations of COFFEE for the reconstruction of low-order wavefront modes, which are highly filtered by the coronagraph. This is illustrated using two focal plane mask sizes on HiCAT. We discuss possible solutions, both in the hardware system and in the COFFEE optimizer, to mitigate these issues.
Current designs for all three extremely large telescopes show the overwhelming adoption of the pyramid wavefront sensor (P-WFS) as the WFS of choice for adaptive optics (AO) systems sensing on natural guide stars (NGS) or extended objects. The key ad
vantages of the P-WFS over the Shack-Hartmann are known and are mainly provided by the improved sensitivity (fainter NGS) and reduced sensitivity to spatial aliasing. However, robustness and tolerances of the P-WFS for the ELTs are not currently well understood. In this paper, we present simulation results for the single-conjugate AO mode of HARMONI, a visible and near-infrared integral field spectrograph for the European Extremely Large Telescope. We first explore the wavefront sensing issues related to the telescope itself; namely the island effect (i.e. differential piston) and M1 segments phasing errors. We present mitigation strategies to the island effect and their performance. We then focus on some performance optimisation aspects of the AO design to explore the impact of the RTC latency and the optical gain issues, which will in particular affect the high-contrast mode of HARMONI. Finally, we investigate the influence of the quality of glass pyramid prism itself, and of optical aberrations on the final AO performance. By relaxing the tolerances on the fabrication of the prism, we are able to reduce hardware costs and simplify integration. We show the importance of calibration (i.e. updating the control matrix) to capture any displacement of the telescope pupil and rotation of the support structure for M4. We also show the importance of the number of pixels used for wavefront sensing to relax tolerances of the pyramid prism. Finally, we present a detailed optical design of the pyramid prism, central element of the P-WFS.
Quasi-static aberrations in coronagraphic systems are the ultimate limitation to the capabilities of exoplanet imagers both ground-based and space-based. These aberrations - which can be due to various causes such as optics alignment or moving optica
l parts during the observing sequence - create light residuals called speckles in the focal plane that might be mistaken for a planets. For ground-based instruments, the presence of residual turbulent wavefront errors due to partial adaptive optics correction causes an additional difficulty to the challenge of measuring aberrations in the presence of a coronagraph. In this paper, we present an extension of COFFEE, the coronagraphic phase diversity, to the estimation of quasi-static aberrations in the presence of adaptive optics-corrected residual turbulence. We perform realistic numerical simulations to assess the performance that can be expected on an instrument of the current generation. We perform the first experimental validation in the laboratory which demonstrates that quasistatic aberrations can be corrected during the observations by means of coronagraphic phase diversity.
The segmentation of the telescope pupil (by spiders & the segmented M4) create areas of phase isolated by the width of the spiders on the wavefront sensor (WFS), breaking the spatial continuity of the wavefront. The poor sensitivity of the Pyramid WF
S (PWFS) to differential piston leads to badly seen and therefore uncontrollable differential pistons. In close loop operation, differential pistons between segments will settle around integer values of the average sensing wavelength. The differential pistons typically range from one to ten times the sensing wavelength and vary rapidly over time, leading to extremely poor performance. In addition, aberrations created by atmospheric turbulence will contain large amounts of differential piston between the segments. Removing piston contribution over each of the DM segments leads to poor performance. In an attempt to reduce the impact of unwanted differential pistons that are injected by the AO correction, we compare three different approaches. We first limit ourselves to only use the information measured by the PWFS, in particular by reducing the modulation. We show that using this information sensibly is important but will not be sufficient. We discuss possible ways of improvement by using prior information. A second approach is based on phase closure of the DM commands and assumes the continuity of the correction wavefront over the entire unsegmented pupil. The last approach is based on the pair-wise slaving of edge actuators and shows the best results. We compare the performance of these methods using realistic end-to-end simulations. We find that pair-wise slaving leads to a small increase of the total wavefront error, only adding between 20-45 nm RMS in quadrature for seeing conditions between 0.45-0.85 arcsec. Finally, we discuss the possibility of combining the different proposed solutions to increase robustness.
The imaging and spectroscopy of habitable worlds will require large-aperture space-based telescopes, to increase the collecting area and the angular resolution. These large telescopes will necessarily use segmented primaries to fit in a rocket. Howev
er, these massively segmented mirrors make high-contrast performance very difficult to achieve and stabilize, compared to more common monolithic primaries. Despite space telescopes operating in a friendlier environment than ground-based telescopes, remaining vibrations and resonant modes on the segments can still deteriorate the performance. In this context, we present the Pair-based Analytical model for Segmented Telescopes Imaging from Space (PASTIS) that enables the establishment of a comprehensive error budget, both in term of segment alignment and stability. Using this model, one may evaluate the influence of the segment cophasing and surface quality evolution on the final images and contrasts, and set up requirements for any given mission. One can also identify the dominant modes of a given geometry for a given coronagraphic instrument and design the feedback control systems accordingly. In this paper, we first develop and validate this analytical model by comparing its outputs to the images and contrasts predicted by an end-to-end simulation. We show that the contrasts predicted using PASTIS are accurate enough compared to the end-to-end propagation results, at the exo-Earth detection level. Second, we develop a method for a fast and efficient error budget in term of segment manufacturing and alignment that takes into account the disparities of the segment effects on the final performance. This technique is then applied on a specific aperture to provide static and quasi-static requirements on each segment for local aberrations. Finally we discuss potential application of this new technique to future missions.
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 calculat
ion 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 and propose the synthesis of a distributed Kalman filter to mitigate both aniso-servo-lag and aliasing errors whilst 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 $sim$60 nm rms error reduction can be achieved with the distributed Kalman filter embodying anti- aliasing reconstructors on 10 m class high-order AO systems, leading to contrast improvement factors of up to three orders of magnitude at few ${lambda}/D$ separations ($sim1-5{lambda}/D$) for a 0 magnitude star and reaching close to one order of magnitude for a 12 magnitude star.
