本文针对泽尼克波前传感器动态范围受限的问题，提出非线性重建算法并结合相位排序干涉测量与多波长测量，将动态范围提升至1.4 rad rms，使其成为理想的第二级波前传感器。
摘要：
背景：极大望远镜（ELT）和巨型麦哲伦望远镜（GMT）等望远镜将与极端自适应光学（AO）仪器一起使用，以直接对类地行星成像。为了对地球孪生体成像，AO系统需要在基本极限下工作。一个关键部件是波前传感器。干涉式波前传感器，如泽尼克波前传感器（ZWFS），已被证明其性能接近基本灵敏度极限。然而，灵敏度是以线性度为代价的；ZWFS具有很强的非线性行为。目的：本工作的目标是通过使用非线性重建算法，并结合相位排序干涉测量（PSI）和多波长测量，来提高类泽尼克波前传感器的动态范围。方法：对ZWFS的响应进行了分析和数值研究。结果：所提出的迭代（非）线性重建器对于小像差（<0.25 rad rms）达到机器精度。将非线性重建算法与PSI耦合，将ZWFS的动态范围提高了三倍，达到约0.75 rad rms。增加多个波段再次使动态范围翻倍，达到1.4 rad rms。结论：ZWFS是最灵敏的波前传感器之一，但动态范围有限。如果与所提出的非线性重建算法相结合，ZWFS将是理想的第二级波前传感器。
英文摘要：
Context: Telescopes like the Extremely Large Telescope (ELT) and the Giant Magellan Telescope (GMT) will be used together with extreme adaptive optics (AO) instruments to directly image Earth-like planets. The AO systems will need to perform at the fundamental limit in order to image Earth twins. A crucial component is the wavefront sensor. Interferometric wavefront sensors, such as the Zernike wavefront sensor (ZWFS), have been shown to perform close to the fundamental sensitivity limit. However, sensitivity comes at the cost of linearity; the ZWFS has strong nonlinear behavior. Aims: The aim of this work is to increase the dynamic range of Zernike-like wavefront sensors by using nonlinear reconstruction algorithms combined with phase sorting interferometry (PSI) and multi-wavelength measurements. Methods: The response of the ZWFS is explored analytically and numerically. Results: The proposed iterative (non)linear reconstructors reach the machine precision for small aberrations (<0.25 rad rms). Coupling the nonlinear reconstruction algorithm with PSI increases the dynamic range of the ZWFS by a factor of three to about 0.75 rad rms. Adding multiple wavebands doubles the dynamic range again, to 1.4 radians rms. Conclusion: The ZWFS is one of the most sensitive wavefront sensors, but has a limited dynamic range. The ZWFS will be an ideal second-stage wavefront sensor if it is combined with the proposed nonlinear reconstruction algorithm.
Reaching the fundamental sensitivity limit of wavefront sensing on arbitrary apertures with the Phase Induced Amplitude Apodized Zernike Wavefront Sensor (PIAA-ZWFS)
This paper studies the effects on Zernike coefficients of aperture scaling, translation and rotation, when a given aberrated wavefront is described on the Zernike polynomial basis. It proposes a new analytical method for computing the matrix that enables the building of the transformed Zernike coefficients from the original ones. The technique is based on the properties of Zernike polynomials Fourier Transform and, in the case of a full aperture without central obstruction, the coefficients of the matrix are given in terms of integrals of Bessel functions. The integral formulas are exact and d…
Future space telescopes with coronagraph instruments will use a wavefront sensor (WFS) to measure and correct for phase errors and stabilize the stellar intensity in high-contrast images. The HabEx and LUVOIR mission concepts baseline a Zernike wavefront sensor (ZWFS), which uses Zernike's phase contrast method to convert phase in the pupil into intensity at the WFS detector. In preparation for these potential future missions, we experimentally demonstrate a ZWFS in a coronagraph instrument on the Decadal Survey Testbed in the High Contrast Imaging Testbed facility at NASA's Jet Propulsion Lab…
In space-based gravitational wave detection, the estimation of far-field wavefront error of the distorted beam is the precondition for the noise reduction. Zernike polynomials is used to describe the wavefront error of the transmitted distorted beam. The propagation of a laser beam between two telescope apertures is calculated numerically. Far-field wavefront error is estimated with the absolute height of the peak-to-valley phase deviation between distorted Gaussian beam and a reference distortion-free Gaussian beam. The results show the pointing jitter is strongly related to the wavefront err…
We present an enhanced version of the Zernike wavefront sensor, that simultaneously measures phase and amplitude aberrations. The 'vector-Zernike' wavefront sensor consists of a patterned liquid-crystal mask, which imposes $\pm π/2$ phase on the point spread function core through the achromatic geometric phase acting with opposite sign on opposite circular polarizations. After splitting circular polarization, the ensuing pupil intensity images are used to reconstruct the phase and the amplitude of the incoming wavefront. We demonstrate reconstruction of the complex wavefront with monochromatic…
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）
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 …
Segmented aperture telescopes require an alignment procedure with successive steps from coarse alignment to monitoring process in order to provide very high optical quality images for stringent science operations such as exoplanet imaging. The final step, referred to as fine phasing, calls for a high sensitivity wavefront sensing and control system in a diffraction-limited regime to achieve segment alignment with nanometric accuracy. In this context, Zernike wavefront sensors represent promising options for such a calibration. A concept called the Zernike unit for segment phasing (ZEUS) was pr…
The next generation of large ground- and space-based optical telescopes will have segmented primary mirrors. Co-phasing the segments requires a sensitive wavefront sensor capable of measuring phase discontinuities. The Zernike wavefront sensor (ZWFS) is a passive wavefront sensor that has been demonstrated to sense segmented-mirror piston, tip, and tilt with picometer precision in laboratory settings. We present the first on-sky results of an adaptive optics fed ZWFS on a segmented aperture telescope, W.M. Keck Observatory's Keck II. Within the Keck Planet Imager and Characterizer (KPIC) light…
The Roman Coronagraph Community Participation Program: Using the Zernike wavefront sensor for a full characterisation of the Roman Space Telescope and the Coronagraph Instrument
Aix Marseille Univ, CNRS, CNES, LAM（艾克斯马赛大学）；Space Telescope Science Institute（太空望远镜科学研究所）；Laboratoire Lagrange, Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS（拉格朗日实验室，蔚蓝海岸大学，蔚蓝海岸天文台）；Jet Propulsion Laboratory, California Institute of Technology（喷气推进实验室，加州理工学院）
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 consi…
On-sky demonstration of a vector Zernike wavefront sensor in a cascaded adaptive optics system
ONERA（法国航空航天研究院）；Aix Marseille University, CNRS, CNES, LAM（艾克斯-马赛大学，法国国家科学研究中心，法国国家空间研究中心，拉格朗日实验室）；Aix Marseille Univ, CNRS, Pytheas, OHP, Observatoire de Haute-Provence（艾克斯-马赛大学，法国国家科学研究中心，皮泰亚斯，上普罗旺斯天文台）；Department of Physics, University of Oxford（牛津大学物理系）；W. M. Keck Observatory（W.M.凯克天文台）；Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange（蔚蓝海岸大学，蔚蓝海岸天文台，法国国家科学研究中心，拉格朗日实验室）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）
Combining large segmented space telescopes, coronagraphy and wavefront control methods is a promising solution to produce a dark hole (DH) region in the coronagraphic image of an observed star and study planetary companions. The thermal and mechanical evolution of such a high-contrast facility leads to wavefront drifts that degrade the DH contrast during the observing time, thus limiting the ability to retrieve planetary signals. Lyot-style coronagraphs are starlight suppression systems that remove the central part of the image for an unresolved observed star, the point spread function, with a…
Future Extremely Large Telescopes will adopt segmented primary mirrors with several hundreds of segments. Cophasing of the segments together is essential to reach high wavefront quality. The phasing sensor must be able to maintain very high phasing accuracy during the observations, while being able to phase segments dephased by several micrometers. The Zernike phase contrast sensor has been demonstrated on-sky at the Very Large Telescope. We present the multi-wavelength scheme that has been implemented to extend the capture range from \pmlambda/2 on the wavefront to many micrometers, demonstra…
Mid-order wavefront control for exoplanet imaging: preliminary characterization of the segmented deformable mirror and Zernike wavefront sensor on HiCAT
Analytical decomposition of Zernike and hexagonal modes over an hexagonal segmented optical aperture
ONERA The French Aerospace Laboratory（法国航空航天实验室）；Aix Marseille Université, CNRS, CNES, Laboratoire d’Astrophysique de Marseille (LAM)（艾克斯马赛大学）；Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange（蔚蓝海岸大学）
Imaging exo-Earths is an exciting but challenging task because of the 10^-10 contrast ratio between these planets and their host star at separations narrower than 100 mas. Large segmented aperture space telescopes enable the sensitivity needed to observe a large number of planets. Combined with coronagraphs with wavefront control, they present a promising avenue to generate a high-contrast region in the image of an observed star. Another key aspect is the required stability in telescope pointing, focusing, and co-phasing of the segments of the telescope primary mirror for long-exposure observa…
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）
ELT-HARMONI is the first light visible and near-IR integral field spectrograph (IFS) for the ELT. It covers a large spectral range from 450nm to 2450nm with resolving powers from 3500 to 18000 and spatial sampling from 60mas to 4mas. It can operate in two Adaptive Optics modes - SCAO (including a High Contrast capability) and LTAO - or with NOAO. The project is preparing for Final Design Reviews. The High Contrast Module (HCM) will allow HARMONI to perform direct imaging and spectral analysis of exoplanets up to one million times fainter than their host star. Quasi-static aberrations are a lim…
Demonstration of a photonic lantern focal-plane wavefront sensor: measurement of atmospheric wavefront error modes and low wind effect in the non-linear regime
Closing the loop on-sky with a vector-Zernike wavefront sensor using a convolutional neural network as phase reconstructor
Aix Marseille Univ, CNRS, CNES, LAM（艾克斯马赛大学、法国国家科学研究中心、法国国家空间研究中心、天体物理学与行星学实验室）；DOTA, ONERA, Université Paris Saclay（ONERA航空航天研究院、巴黎萨克雷大学）；DTIS, ONERA, Université Paris Saclay（ONERA航空航天研究院、巴黎萨克雷大学）；School of Electrical Engineering, Pontificia Universidad Católica de Valparaíso（智利天主教瓦尔帕莱索大学电气工程学院）
If the optical system of a telescope is perturbed from rotational symmetry, the Zernike wavefront aberration coefficients describing that system can be expressed as a function of position in the focal plane using spin-weighted Zernike polynomials. Methodologies are presented to derive these polynomials to arbitrary order. This methodology is applied to aberration patterns produced by a misaligned Ritchey Chretian telescope and to distortion patterns at the focal plane of the DESI optical corrector, where it is shown to provide a more efficient description of distortion than conventional expans…
Cascade adaptive optics with a second stage based on a Zernike wavefront sensor for exoplanet observations II. Validation in broadband light on the ESO/GHOST testbed
Université Côte d’Azur, Observatoire de la Côte d’Azur（蔚蓝海岸大学，蔚蓝海岸天文台）；Aix Marseille Université（艾克斯-马赛大学）；European Southern Observatory (ESO)（欧洲南方天文台）；University of Arizona（亚利桑那大学）
Calibration of MEMS DM actuator gains using a Zernike wavefront sensor on the HiCAT testbed and implications for Habitable Worlds Observatory operations
Space Telescope Science Institute（太空望远镜科学研究所）；Max Planck Institute for Astronomy（马克斯·普朗克天文学研究所）；Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange（蔚蓝海岸大学、蔚蓝海岸天文台、法国国家科学研究中心、拉格朗日实验室）
Second-generation exoplanet imagers using extreme adaptive optics and coronagraphy have demonstrated their great potential for studying close circumstellar environments and for detecting new companions and helping to understand their physical properties. However, at very small angular separation, their performance in contrast is limited by several factors: diffraction by the complex telescope pupil not perfectly canceled by the coronagraph, residual dynamic wavefront errors, chromatic wavefront errors, and wavefront errors resulting from noncommon path aberrations (NCPAs). In a previous work, …
Millimeter-wave adaptive optics: Demonstrating closed-loop correction for lowest Zernike modes
Nagoya University（名古屋大学）；Kitami Institute of Technology（北见工业大学）；Kanazawa University（金泽大学）；Japan Women’s University（日本女子大学）；National Astronomical Observatory of Japan（日本国立天文台）；Kyoto University（京都大学）；Osaka Metropolitan University（大阪公立大学）
Future large segmented space telescopes and their coronagraphic instruments are expected to provide the resolution and sensitivity to observe Earth-like planets with a 10^10 contrast ratio at less than 100 mas from their host star. Advanced coronagraphs and wavefront control methods will enable the generation of high-contrast dark holes in the image of an observed star. However, drifts in the optical path of the system will lead to pointing errors and other critical low-order aberrations that will prevent maintenance of this contrast. To measure and correct for these errors, we explore the use…
The estimation of atmospheric turbulence parameters is of relevance for: a) site evaluation & characterisation; b) prediction of the point spread function; c) live assessment of error budgets and optimisation of adaptive optics performance; d) optimisation of fringe trackers for long baseline optical interferometry. The ubiquitous deployment of Shack-Hartmann wavefront sensors in large telescopes makes them central for atmospheric turbulence parameter estimation via adaptive optics telemetry. Several methods for the estimation of the Fried parameter and outer scale have been developed, most of…
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 …
Context. Several exoplanet direct imaging instruments will soon be in operation. They use an extreme adaptive optics (XAO) system to correct the atmospheric turbulence and provide a highly-corrected beam to a near-infrared (NIR) coronagraph for starlight suppression. The performance of the coronagraph is however limited by the non-common path aberrations (NCPA) due to the differential wavefront errors existing between the visible XAO sensing path and the NIR science path, leading to residual speckles in the coronagraphic image. Aims. Several approaches have been developed in the past few years…
Adaptive optics (AO) is a technique allowing to drastically improve ground-based telescopes angular resolution. The wavefront sensor (WFS) is one of the key components of such systems, driving the fundamental performance limitations. In this paper, we focus on a specific class of WFS: the Fourier-filtering wavefront sensors (FFWFS). This class is known for its extremely high sensitivity. However, a clear and comprehensive noise propagation model for any kind of FFWFS is lacking. Considering read-out noise and photon noise, we derive a simple and comprehensive model allowing to understand how t…
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）
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…
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…
The Extremely Large Telescopes will require hundreds of actuators across the pupil for high Strehl in the visible. We envision a triple-stage AO (TSAO) system for GMT/GMagAO-X to achieve this. The first stage is a 4K DM controlled by an IR pyramid wavefront sensor that provides the first order correction. The second stage contains the high-order parallel DM of GMagAO-X that has 21000 actuators and contains an interferometric delay line for phasing of each mirror segment. This stage uses a Zernike wavefront sensor for high-order modes and a Holographic Dispersed Fringe Sensor for segment piston…
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 …
Circumstellar environments are now routinely observed by dedicated high-contrast imagers on large, ground-based observatories. These facilities combine extreme adaptive optics and coronagraphy to achieve unprecedented sensitivities for exoplanet detection and spectral characterization. However, non-common path aberrations (NCPA) in these coronagraphic systems represent a critical limitation for the detection of giant planets with a contrast lower than a few $10^{-6}$ at very small separations ($<$0.3$^{\prime\prime}$) from their host star. In 2013 we proposed ZELDA, a Zernike wavefront sensor …
High-contrast imager for complex aperture telescopes (HiCAT): 8. Dark zone demonstration with simultaneous closed-loop low-order wavefront sensing and control
Coronagraphic imaging of exoplanets using ground-based instruments on large telescopes is intrinsically limited by speckles induced by uncorrected aberrations. These aberrations originate from the imperfect correction of the atmosphere by an extreme adaptive optics system; from static optical defects; or from small opto-mechanical variations due to changes in temperature, pressure, or gravity vector. More than the speckles themselves, the performance of high-contrast imagers is ultimately limited by their temporal stability, since most post-processing techniques rely on difference of images ac…
Q1: Why deploy N wavefront sensors on a three mirror anastigmat (TMA) and not N + 1? Q2: Why measure M Zernike coefficients and not M + 1? Q3: Why control L rigid body degrees of freedom (total) on the secondary and tertiary and not L + 1? The usual answer: "We did a lot of ray tracing and N,M, and L seemed OK." We show how straightforward results from aberration theory may be used to address these questions. We consider, in particular, the case of a three mirror anastigmat.
