Focal plane wavefront sensing (FPWFS) is appealing for several reasons. Notably, it offers high sensitivity and does not suffer from non-common path aberrations (NCPA). The price to pay is a high computational burden and the need for diversity to lift any phase ambiguity. If those limitations can be overcome, FPWFS is a great solution for NCPA measurement, a key limitation for high-contrast imaging, and could be used as adaptive optics wavefront sensor. Here, we propose to use deep convolutional neural networks (CNNs) to measure NCPA based on focal plane images. Two CNN architectures are considered: ResNet-50 and U-Net which are used respectively to estimate Zernike coefficients or directly the phase. The models are trained on labelled datasets and evaluated at various flux levels and for two spatial frequency contents (20 and 100 Zernike modes). In these idealized simulations we demonstrate that the CNN-based models reach the photon noise limit in a large range of conditions. We show, for example, that the root mean squared (rms) wavefront error (WFE) can be reduced to < $λ$/1500 for $2 \times 10^6$ photons in one iteration when estimating 20 Zernike modes. We also show that CNN-based models are sufficiently robust to varying signal-to-noise ratio, under the presence of higher-order aberrations, and under different amplitudes of aberrations. Additionally, they display similar to superior performance compared to iterative phase retrieval algorithms. CNNs therefore represent a compelling way to implement FPWFS, which can leverage the high sensitivity of FPWFS over a broad range of conditions.
We present a method to calibrate a high-resolution wavefront-correcting device with a single, static camera, located in the focal plane; no moving of any component is needed. The method is based on a localized diversity and differential optical transfer functions (dOTF) to compute both the phase and amplitude in the pupil plane located upstream of the last imaging optics. An experiment with a spatial light modulator shows that the calibration is sufficient to robustly operate a focal-plane wavefront sensing algorithm controlling a wavefront corrector with ~40 000 degrees of freedom. We estimat…
We present two complementary algorithms suitable for using focal-plane measurements to control a wavefront corrector with an extremely high spatial resolution. The algorithms use linear approximations to iteratively minimize the aberrations seen by the focal-plane camera. The first algorithm, Fast & Furious (FF), uses a weak-aberration assumption and pupil symmetries to achieve fast wavefront reconstruction. The second algorithm, an extension to FF, can deal with an arbitrary pupil shape; it uses a Gerchberg-Saxton style error reduction to determine the pupil amplitudes. Simulations and experi…
We investigate methods to calibrate the non-common path aberrations at an adaptive optics system having a wavefront-correcting device working at an extremely high resolution (larger than 150x150). We use focal-plane images collected successively, the corresponding phase-diversity information and numerically efficient algorithms to calculate the required wavefront updates. The wavefront correction is applied iteratively until the algorithms converge. Different approaches are studied. In addition of the standard Gerchberg-Saxton algorithm, we test the extension of the Fast & Furious algorithm th…
The photonic lantern (PL) is a tapered waveguide that can efficiently couple light into multiple single-mode optical fibers. Such devices are currently being considered for a number of tasks, including the coupling of telescopes and high-resolution, fiber-fed spectrometers, coherent detection, nulling interferometry, and vortex-fiber nulling (VFN). In conjunction with these use cases, PLs can simultaneously perform low-order focal-plane wavefront sensing. In this work, we provide a mathematical framework for the analysis of the photonic lantern wavefront sensor (PLWFS), deriving linear and hig…
We present a promising approach to the extremely fast sensing and correction of small wavefront errors in adaptive optics systems. As our algorithm's computational complexity is roughly proportional to the number of actuators, it is particularly suitable to systems with 10,000 to 100,000 actuators. Our approach is based on sequential phase diversity and simple relations between the point-spread function and the wavefront error in the case of small aberrations. The particular choice of phase diversity, introduced by the deformable mirror itself, minimizes the wavefront error as well as the comp…
Adaptive optics (AO) is critical in astronomy, optical communications and remote sensing to deal with the rapid blurring caused by the Earth's turbulent atmosphere. But current AO systems are limited by their wavefront sensors, which need to be in an optical plane non-common to the science image and are insensitive to certain wavefront-error modes. Here we present a wavefront sensor based on a photonic lantern fibre-mode-converter and deep learning, which can be placed at the same focal plane as the science image, and is optimal for single-mode fibre injection. By measuring the intensities of …
Focal plane wavefront sensing is an elegant solution for wavefront sensing since near-focal images of any source taken by a detector show distortions in the presence of aberrations. Non-Common Path Aberrations and the Low Wind Effect both have the ability to limit the achievable contrast of the finest coronagraphs coupled with the best extreme adaptive optics systems. To correct for these aberrations, the Subaru Coronagraphic Extreme Adaptive Optics instrument hosts many focal plane wavefront sensors using detectors as close to the science detector as possible. We present seven of them and com…
The differential Optical Transfer Function (dOTF) is a focal plane wavefront sensing method that uses a diversity in the pupil plane to generate two different focal plane images. The difference of their Fourier transforms recovers the complex amplitude of the pupil down to the spatial scale of the diversity. We produce two simultaneous PSF images with diversity using a polarizing filter at the edge of the telescope pupil, and a polarization camera to simultaneously record the two images. Here we present the first on-sky demonstration of polarization dOTF at the 1.0m South African Astronomical …
Future large space telescopes will be equipped with adaptive optics (AO) to overcome wavefront aberrations and achieve high contrast for imaging faint astronomical objects, such as earth-like exoplanets and debris disks. In contrast to AO that is widely used in ground telescopes, space-based AO systems will use focal plane wavefront sensing to measure the wavefront aberrations. Focal plane wavefront sensing is a class of techniques that reconstruct the light field based on multiple focal plane images distorted by deformable mirror (DM) probing perturbations. In this paper, we report an efficie…
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 pyramid 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 starligh…
Focal plane wavefront sensing and control is a critical approach to reducing non-common path errors between the a conventional astronomical adaptive optics (AO) wavefront sensor (WFS) detector and science camera. However, in addition to mitigating non-common path errors, recent focal plane wavefront 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 f…
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 fractio…
Australian Astronomical Optics, Macquarie University（澳大利亚天文光学，麦考瑞大学）；The Astrophysics and Space Technologies Research Centre, School of Mathematical and Physical Sciences, Macquarie University（麦考瑞大学数理学院天体物理与空间技术中心）；Research School of Astronomy and Astrophysics, Australian National University（澳大利亚国立大学天文与天体物理研究学院）
This article describes the implementation of a focal plane based wavefront control loop on the high-contrast imaging instrument SCExAO (Subaru Coronagraphic Extreme Adaptive Optics). The sensor relies on the Fourier analysis of conventional focal-plane images acquired after an asymmetric mask is introduced in the pupil of the instrument. This absolute sensor is used here in a closed-loop to compensate the non-common path errors that normally affects any imaging system relying on an upstream adaptive optics system.This specific implementation was used to control low order modes corresponding to…
High quality, repeatable point-spread functions are important for science cases like direct exoplanet imaging, high-precision astrometry, and high-resolution spectroscopy of exoplanets. For such demanding applications, the initial on-sky point-spread function delivered by the adaptive optics system can require further optimization to correct unsensed static aberrations and calibration biases. We investigated using the Fast and Furious focal-plane wavefront sensing algorithm as a potential solution. This algorithm uses a simple model of the optical system and focal plane information to measure …
The detection and characterization of Earth-like exoplanets is one of the major science drivers for the next generation of telescopes. Current direct imaging instruments are limited by evolving non-common path aberrations (NCPAs). The NCPAs must be compensated for by using the science focal-plane image. A promising sensor is the self-coherent camera (SCC). An SCC modifies the Lyot stop in the coronagraph to introduce a probe electric field. However, the SCC has a weak probe electric field due to the requirements on the pinhole separation. A spectrally modulated self-coherent camera (SM-SCC) is…
Demonstration of a photonic lantern focal-plane wavefront sensor: measurement of atmospheric wavefront error modes and low wind effect in the non-linear regime
High-contrast imaging instruments need extreme wavefront control to directly image exoplanets. This requires highly sensitive wavefront sensors which optimally make use of the available photons to sense the wavefront. Here, we propose to numerically optimize Fourier-filtering wavefront sensors using automatic differentiation. First, we optimize the sensitivity of the wavefront sensor for different apertures and wavefront distributions. We find sensors that are more sensitive than currently used sensors and close to the theoretical limit, under the assumption of monochromatic light. Subsequentl…
All coronagraphic instruments for exoplanet high-contrast imaging need wavefront correction systems to reject optical aberrations and create sufficiently dark holes. Since the most efficient wavefront correction algorithms (controllers and estimators) are usually model-based, the modeling accuracy of the system influences the ultimate wavefront correction performance. Currently, wavefront correction systems are typically approximated as linear systems using Fourier optics. However, the Fourier optics model is usually biased due to inaccuracies in the layout measurements, the imperfect diagnose…
The Low Wind Effect (LWE) refers to a phenomenon that occurs when the wind speed inside a telescope dome drops below $3$m/s creating a temperature gradient near the telescope spider. This produces phase discontinuities in the pupil plane that are not detected by traditional Adaptive Optics (AO) systems such as the pyramid wavefront sensor or the Shack-Hartmann. Considering the pupil as divided in 4 quadrants by regular spiders, the phase discontinuities correspond to piston, tip and tilt aberrations in each quadrant of the pupil. Uncorrected, it strongly decreases the ability of high contrast …
The performance of high-contrast imaging instruments is limited by wavefront errors, in particular by non-common path aberrations (NCPAs). Focal-plane wavefront sensing (FPWFS) is appropriate to handle NCPAs because it measures the aberration where it matters the most, that is to say at the science focal plane. Phase retrieval from focal-plane images results, nonetheless, in a sign ambiguity for even modes of the pupil-plane phase. The phase diversity methods currently used to solve the sign ambiguity tend to reduce the science duty cycle, that is, the fraction of observing time dedicated to s…
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 of 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 …
Optical imperfections, misalignments, aberrations, and even dust can significantly limit sensitivity in high-contrast imaging systems such as coronagraphs. An upstream deformable mirror (DM) in the pupil can be used to correct or compensate for these flaws, either to enhance Strehl ratio or suppress residual coronagraphic halo. Measurement of the phase and amplitude of the starlight halo at the science camera is essential for determining the DM shape that compensates for any non-common-path (NCP) wavefront errors. Using DM displacement ripples to create a series of probe and anti-halo speckles…
Current and future high contrast imaging instruments aim to detect exoplanets at closer orbital separations, lower masses, and/or older ages than their predecessors. However, continually evolving speckles in the coronagraphic science image limit contrasts of state-of-the-art ground-based exoplanet imaging instruments. For ground-based adaptive optics (AO) instruments it remains challenging for most speckle suppression techniques to attenuate both the dynamic atmospheric as well as quasi-static instrumental speckles on-sky. We have proposed a focal plane wavefront sensing and control algorithm …
High contrast imaging and spectroscopy provide unique constraints for exoplanet formation models as well as for planetary atmosphere models. But this can be challenging because of the planet-to-star small angular separation and high flux ratio. Recently, optimized instruments like SPHERE and GPI were installed on 8m-class telescopes. These will probe young gazeous exoplanets at large separations (~1au) but, because of uncalibrated aberrations that induce speckles in the coronagraphic images, they are not able to detect older and fainter planets. There are always aberrations that are slowly evo…
In this article we show that the vector-Apodizing Phase Plate (vAPP) coronagraph can be designed such that the coronagraphic point spread functions (PSFs) can act as a wavefront sensor to measure and correct the (quasi-)static aberrations, without dedicated wavefront sensing holograms nor modulation by the deformable mirror. The absolute wavefront retrieval is performed with a non-linear algorithm. The focal-plane wavefront sensing (FPWFS) performance of the vAPP and the algorithm are evaluated with numerical simulations, to test various photon and read noise levels, the sensitivity to the 100…
Exoplanet detection and characterization through extreme adaptive optics (ExAO) is a key science goal of future extremely large telescopes. This achievement, however, will be limited in sensitivity by both quasi-static wavefront errors and residual AO-corrected atmospheric wavefront errors. A solution to both of these problems is to use the science camera of an ExAO system as a wavefront sensor to perform a fast measurement and correction method to remove these aberrations as soon as they are detected. We have developed the framework for one such method, using the self-coherent camera (SCC), t…
Current and future high contrast imaging instruments aim to detect exoplanets at closer orbital separations, lower masses, and/or older ages than their predecessors, with the eventual goal of directly detecting terrestrial-mass habitable-zone exoplanets. However, continually evolving speckles in the coronagraphic science image still limit state-of-the-art ground-based exoplanet imaging instruments to contrasts at least two orders of magnitude worse than what is needed to achieve this goal. For ground-based adaptive optics (AO) instruments it remains challenging for most speckle suppression tec…
The ability to characterize exoplanets by spectroscopy of their atmospheres requires direct imaging techniques to isolate planet signal from the bright stellar glare. One of the limitations with the direct detection of exoplanets, either with ground- or space-based coronagraphs, is pointing errors and other low-order wavefront aberrations. The coronagraphic detection sensitivity at the diffraction limit therefore depends on how well low-order aberrations upstream of the focal plane mask are corrected. To prevent starlight leakage at the inner working angle of a phase mask coronagraph, we have …
Reaching the fundamental sensitivity limit of wavefront sensing on arbitrary apertures with the Phase Induced Amplitude Apodized Zernike Wavefront Sensor (PIAA-ZWFS)
The raw coronagraphic performance of current high-contrast imaging instruments is limited by the presence of a quasi-static speckle (QSS) background, resulting from instrumental non-common path errors (NCPEs). Rapid development of efficient speckle subtraction techniques in data reduction has enabled final contrasts of up to 10-6 to be obtained, however it remains preferable to eliminate the underlying NCPEs at the source. In this work we introduce the coronagraphic Modal Wavefront Sensor (cMWS), a new wavefront sensor suitable for real-time NCPE correction. This pupil-plane optic combines the…
Laser guide stars (LGS) are used in many adaptive optics systems to extend sky coverage. The most common wavefront sensor used in combination with a LGS is a Shack-Hartmann wavefront sensor (SHWFS). The Shack-Hartmann has a major disadvantage for extended source wavefront sensing because it directly samples the image. In this proceeding we propose to use the generalized-Optical Differentation Wavefront Sensor (g-ODWFS) a wavefront sensor for wavefront sensing of LGS. The g-ODWFS uses only 4 pixels per sub-aperture, has little to no aliasing noise and therefore no spurious low-order errors and …
Direct detection of exoplanets requires high dynamic range imaging. Coronagraphs could be the solution, but their performance in space is limited by wavefront errors (manufacturing errors on optics, temperature variations, etc.), which create quasi-static stellar speckles in the final image. Several solutions have been suggested for tackling this speckle noise. Differential imaging techniques substract a reference image to the coronagraphic residue in a post-processing imaging. Other techniques attempt to actively correct wavefront errors using a deformable mirror. In that case, wavefront aber…
Demonstration of simultaneous PIAA- coronagraphy and wavefront sensing using a single metasurface-based focal-plane optic
Leiden University（莱顿大学）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；University of Arizona（亚利桑那大学）；Flatiron Institute（平顿研究所）；Subaru Telescope, National Astronomical Observatory of Japan（日本国立天文台昴星团望远镜）；National Institutes of Natural Sciences（自然科学研究机构）；Northrop Grumman Corporation（诺斯罗普·格鲁曼公司）；Draper Laboratory（德拉珀实验室）；Kirtland Air Force Base（基尔兰空军基地）；Durham University（杜伦大学）
The shape of a focus-modulated point spread function (PSF) is used as a quick visual assessment tool of aberration modes in the PSF. Further analysis in terms of shape moments can permit quantifying the modal coefficients with an accuracy comparable to that of typical wavefront sensors. In this letter, the error of the moment-based wavefront sensing is analytically described in terms of the pixelation and photon/readout noise. All components highly depend on the (unknown) PSF shape, but can be estimated from the measured PSF sampled at a reasonable spatial resolution and photon count. Numerica…
Wavefront sensing in solar adaptive-optics is currently done with correlating Shack-Hartmann sensors, although the spatial- and temporal-resolutions of the phase measurements are then limited by the extremely fast computing required to correlate the sensor signals at the frequencies of daytime atmospheric-fluctuations. To avoid this limitation, a new wavefront-sensing technique is presented, that makes use of the solar brightness and is applicable to extended sources. The wavefront is sent through a modified Mach-Zehnder interferometer. A small, central part of the wavefront is used as referen…
Wavefront sensors encode phase information of an incoming wavefront into an intensity pattern that can be measured on a camera. Several kinds of wavefront sensors (WFS) are used in astronomical adaptive optics. Amongst them, Fourier-based wavefront sensors perform a filtering operation on the wavefront in the focal plane. The most well known example of a WFS of this kind is the Zernike wavefront sensor, and the pyramid wavefront sensor (PWFS) also belongs to this class. Based on this same principle, new WFSs can be proposed such as the n-faced pyramid (which ultimately becomes an axicone) or t…
In an effort to transcend the limitations of differential imaging of exoplanets in the era of extremely large telescopes (ELTs), the first paper in this series established a rigorous, fully polarimetric framework for determining the science camera (SC) image given a turbulent wavefront and unknown aberrations in multiple planes the optical system. This article builds on the structure developed in Paper I in order to rigorously express the polarimetric SC image in terms of the field impinging on the wavefront sensor (WFS), thereby providing a direct connection between the measurements made in b…
A new concept of using focus-diverse point spread functions (PSFs) for modal wavefront sensing (WFS) is explored. This is based on relatively straightforward image moment analysis of measured PSFs, which differentiates it from other focal-plane wavefront sensing techniques (FPWFS). The presented geometric analysis shows that the image moments are non-linear functions of wave aberration coefficients, but notes that focus-diversity (FD) essentially decouples the coefficients of interest from others, resulting in a set of linear equations whose solution corresponds to modal coefficient estimates.…
A new wavefront sensing approach, derived from the successful curvature wavefront sensing concept but using a non-linear phase retrieval wavefront reconstruction scheme, is described. The non-linear curvature wavefront sensor (nlCWFS) approaches the theoretical sensitivity limit imposed by fundamental physics by taking full advantage of wavefront spatial coherence in the pupil plane. Interference speckles formed by natural starlight encode wavefront aberrations with the sensitivity set by the telescope's diffraction limit lambda/D rather than the seeing limit of more conventional linear WFSs. …
Testing of machine learning wavefront sensing algorithms on the Tiny Observatory for Telescope Optimization (TOTO) testbed
Steward Observatory - The University of Arizona（亚利桑那大学斯图尔德天文台）；Wyant College of Optical Sciences - The University of Arizona（亚利桑那大学怀安特光学科学学院）；Department of Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校物理系）
Freezing the speckles: focal plane wavefront sensing with the spatially-clipped self-coherent camera
James C. Wyant College of Optical Sciences, University of Arizona（亚利桑那大学光学科学学院）；Steward Observatory, University of Arizona（亚利桑那大学斯图尔德天文台）；Leiden University, Leiden Observatory（莱顿大学莱登天文台）；Flatiron Center for Computational Astrophysics, Flatiron Institute（平顶山研究所计算天体物理中心）；Starfire Optical Range, Kirtland Air Force Base（基尔兰空军基地星光光学试验场）；Northrop Grumman（诺斯罗普·格鲁曼公司）
Fewer than 1% of all exoplanets detected to date have been characterized on the basis of spectroscopic observations of their atmosphere. Unlike indirect methods, high-contrast imaging offers access to atmospheric signatures by separating the light of a faint off-axis source from that of its parent star. Forthcoming space facilities, such as WFIRST/LUVOIR/HabEX, are expected to use coronagraphic instruments capable of imaging and spectroscopy in order to understand the physical properties of remote worlds. The primary technological challenge that drives the design of these instruments involves …
Space-based coronagraphs for future earth-like planet detection will require focal plane wavefront control techniques to achieve the necessary contrast levels. These correction algorithms are iterative and the control methods require an estimate of the electric field at the science camera, which requires nearly all of the images taken for the correction. We demonstrate a Kalman filter estimator that uses prior knowledge to create the estimate of the electric field, dramatically reducing the number of exposures required to estimate the image plane electric field. In addition to a significant re…
High contrast coronagraphic imaging of the immediate surrounding of stars requires exquisite control of low-order wavefront aberrations, such as tip-tilt (pointing) and focus. We propose an accurate, efficient and easy to implement technique to measure such aberrations in coronagraphs which use a focal plane mask to block starlight. The Coronagraphic Low Order Wavefront Sensor (CLOWFS) produces a defocused image of a reflective focal plane ring to measure low order aberrations. Even for small levels of wavefront aberration, the proposed scheme produces large intensity signals which can be easi…
The continual push to directly image exoplanets at lower masses and closer separations orbiting around bright stars remains limited by both quasi-static and residual adaptive optics (AO) aberration. In previous papers we have proposed a modification of the self-coherent camera (SCC) design to address both of these limitations, called the Fast Atmospheric SCC Technique (FAST). In this paper we introduce an additional modification to the FAST focal plane mask design, including the existing Tip/tilt and Gaussian components and adding a charge four Vortex (TGV) component. In addition to boosting S…
The ability to position multiple miniaturized wavefront sensors precisely over large focal surfaces are advantageous to multi-object adaptive optics. The Australian Astronomical Observatory (AAO) has prototyped a compact and lightweight Shack-Hartmann wavefront-sensor that fits into a standard Starbug parallel fibre positioning robot. Each device makes use of a polymer coherent fibre imaging bundle to relay an image produced by a microlens array placed at the telescope focal plane to a re-imaging camera mounted elsewhere. The advantages of the polymer fibre bundle are its high-fill factor, hig…
Experimentally-determined performance limits for joint imaging and wavefront sensing with a photonic lantern
University of California, Santa Cruz（加州大学圣克鲁兹分校）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Laboratoire d’Astrophysique de Marseille（马赛天体物理学实验室）；University of California, Los Angeles（加州大学洛杉矶分校）；The College of Optics & Photonics, University of Central Florida（中佛罗里达大学光学与光子学院）
