Ground based optical telescopes are seriously affected by atmospheric turbulence induced aberrations. Understanding properties of these aberrations is important both for instruments design and image restoration methods development. Because the point spread function can reflect performance of the whole optic system, it is appropriate to use the point spread function to describe atmospheric turbulence induced aberrations. Assuming point spread functions induced by the atmospheric turbulence with the same profile belong to the same manifold space, we propose a non-parametric point spread function -- PSF-NET. The PSF-NET has a cycle convolutional neural network structure and is a statistical representation of the manifold space of PSFs induced by the atmospheric turbulence with the same profile. Testing the PSF-NET with simulated and real observation data, we find that a well trained PSF--NET can restore any short exposure images blurred by atmospheric turbulence with the same profile. Besides, we further use the impulse response of the PSF-NET, which can be viewed as the statistical mean PSF, to analyze interpretation properties of the PSF-NET. We find that variations of statistical mean PSFs are caused by variations of the atmospheric turbulence profile: as the difference of the atmospheric turbulence profile increases, the difference between statistical mean PSFs also increases. The PSF-NET proposed in this paper provides a new way to analyze atmospheric turbulence induced aberrations, which would be benefit to develop new observation methods for ground based optical telescopes.
Taiyuan University of Technology（太原理工大学）；Durham University（杜伦大学）；Nanjing Institute of Astronomical Optics and Technology CAS（中国科学院南京天文光学技术研究所）；Silesian University of Technology（西里西亚工业大学）
The point spread function (PSF) reflects states of a telescope and plays an important role in development of data processing methods, such as PSF based astrometry, photometry and image restoration. However, for wide field small aperture telescopes (WFSATs), estimating PSF in any position of the whole field of view is hard, because aberrations induced by the optical system are quite complex and the signal to noise ratio of star images is often too low for PSF estimation. In this paper, we further develop our deep neural network (DNN) based PSF modelling method and show its applications in PSF e…
AIM（天体物理与方法研究所）；CEA（法国原子能和替代能源委员会）；CNRS（法国国家科学研究中心）；Université Paris-Saclay（巴黎萨克雷大学）；Université de Paris（巴黎大学）
In astronomy, upcoming space telescopes with wide-field optical instruments have a spatially varying point spread function (PSF). Specific scientific goals require a high-fidelity estimation of the PSF at target positions where no direct measurement of the PSF is provided. Even though observations of the PSF are available at some positions of the field of view (FOV), they are undersampled, noisy, and integrated into wavelength in the instrument's passband. PSF modeling represents a challenging ill-posed problem, as it requires building a model from degraded observations that can infer a super-…
Laboratoire AIM, UMR CEA-CNRS-Paris 7（AIM实验室，CEA-CNRS-巴黎第七大学联合研究单位）；CEA Saclay（法国原子能和替代能源委员会萨克莱研究中心）
In large-scale spatial surveys, such as the forthcoming ESA Euclid mission, images may be undersampled due to the optical sensors sizes. Therefore, one may consider using a super-resolution (SR) method to recover aliased frequencies, prior to further analysis. This is particularly relevant for point-source images, which provide direct measurements of the instrument point-spread function (PSF). We introduce SPRITE, SParse Recovery of InsTrumental rEsponse, which is an SR algorithm using a sparse analysis prior. We show that such a prior provides significant improvements over existing methods, e…
Deblurring is a fundamental inverse problem in bioimaging. It requires modelling the point spread function (PSF), which captures the optical distortions entailed by the image formation process. The PSF limits the spatial resolution attainable for a given microscope. However, recent applications require a higher resolution, and have prompted the development of super-resolution techniques to achieve sub-pixel accuracy. This requirement restricts the class of suitable PSF models to analog ones. In addition, deblurring is computationally intensive, hence further requiring computationally efficient…
This Point spread function (PSF) plays a crucial role in many computational imaging applications, such as shape from focus/defocus, depth estimation, and fluorescence microscopy. However, the mathematical model of the defocus process is still unclear. In this work, we develop an alternative method to estimate the precise mathematical model of the point spread function to describe the defocus process. We first derive the mathematical algorithm for the PSF which is used to generate the simulated focused images for different focus depth. Then we compute the loss function of the similarity between…
We propose a compact snapshot monocular depth estimation technique that relies on an engineered point spread function (PSF). Traditional approaches used in microscopic super-resolution imaging such as the Double-Helix PSF (DHPSF) are ill-suited for scenes that are more complex than a sparse set of point light sources. We show, using the Cramér-Rao lower bound, that separating the two lobes of the DHPSF and thereby capturing two separate images leads to a dramatic increase in depth accuracy. A special property of the phase mask used for generating the DHPSF is that a separation of the phase mas…
The point-spread function (PSF) of an imaging system describes the response of the system to a point source. Accurately determining the PSF enables one to correct for the combined effects of focussing and scattering within the imaging system, and thereby enhance the spatial resolution and dynamic contrast of the resulting images. We present a semi-empirical semi-blind methodology to derive a PSF from partially occulted images. We partition the two-dimensional PSF into multiple segments, set up a multi-linear system of equations, and directly fit the system of equations to determine the PSF wei…
In this paper we present the testing of a back-illuminated development Euclid Visible Instrument (VIS) Charge-Coupled Device (CCD) to measure the intrinsic CCD Point Spread Function (PSF) characteristics using a novel modelling technique. We model the optical spot projection system and the CCD273-84 PSF jointly. We fit a model using Bayesian posterior probability density function, sampling to all available data simultaneously. The generative model fitting is shown, using simulated data, to allow good parameter estimations even when these data are not well sampled. Using available spot data we …
CSST-PSFNet: A Point Spread Function Reconstruction Model for the CSST Based on Deep Learning
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Institute of Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学前沿交叉科学研究院）；Zhejiang Lab（浙江实验室）；Center For Astrophysics, Guangzhou University（广州大学天体物理中心）
We present an analysis of six independent on-sky datasets taken with the Keck-II/NIRC2 instrument. Using the off-axis point spread function (PSF) reconstruction software AIROPA, we extract stellar astrometry, photometry, and other fitting metrics in order to characterize the performance of this package. We test the effectiveness of AIROPA to reconstruct the PSF across the field of view in varying atmospheric conditions, number and location of PSF reference stars, stellar crowding and telescope position angle (PA). We compare the astrometric precision and fitting residuals between a static PSF …
Weak gravitational lensing is one of the most powerful tools for cosmology, while subject to challenges in quantifying subtle systematic biases. The Point Spread Function (PSF) can cause biases in weak lensing shear inference when the PSF model does not match the true PSF that is convolved with the galaxy light profile. Although the effect of PSF size and shape errors - i.e., errors in second moments - is well studied, weak lensing systematics associated with errors in higher moments of the PSF model require further investigation. The goal of our study is to estimate their potential impact for…
Ground-based astronomy is severely limited by the atmospheric turbulence, resulting in a large Point-Spread-Function (PSF) and poor imaging resolution. Even imaging with Adaptive Optics (AO) cannot completely correct the aberrated wavefront, and a residual turbulence still corrupts the observation. Thus the consequences of the turbulence on the PSF is of first interest when building any ground-based telescope. The Power Spectral Density (PSD) of a spatially stationary turbulent phase carries all the information needed for describing the long-exposure PSF. We then develop an analytical descript…
The knowledge of the point spread function (PSF) of imaging instruments represents a fundamental requirement for astronomical observations. The Herschel PACS PSFs delivered by the instrument control centre are obtained from observations of the Vesta asteroid, providing a characterisation of the central part therefore excluding fainter features. However, in many cases information on both the core and the wings of the PSFs is needed. With this aim, we combine Vesta and Mars dedicated observations and obtain PACS PSFs with an unprecedented dynamic range $(\sim 10^6)$, at slow and fast scan speeds…
Point spread function (PSF) reconstruction (PSF-R) is a well established technique to determine reliably and accurately the PSF from Adaptive Optics (AO) control loop data. We have successfully applied this technique to improve the precision on photometry and astrometry to observation of NGC6121 obtained with SPHERE/ZIMPOL as it will be presented in a forthcoming letter. Firstly, we present the methodology we followed to reconstruct the PSF combining pupil-plane and focal-plane measurements using using our PSF-R method PRIME (Beltramo-Martin et al. 2019), with upgrade of both the model and bes…
We describe a rapid and direct method for regularizing, post-facto, the point-spread function (PSF) of a telescope or other imaging instrument, across its entire field of view. Imaging instruments in general blur point sources of light by local convolution with a point-spread function that varies slowly across the field of view, due to coma, spherical aberration, and similar effects. It is possible to regularize the PSF in post-processing, producing data with a homogeneous ``effective PSF'' across the entire field of view. In turn, the method enables seamless wide-field astronomical mosaics at…
Uncertainty in the wide-angle Point Spread Function (PSF) at large angles (tens of arcseconds and beyond) is one of the dominant sources of error in a number of important quantities in observational astronomy. Examples include the stellar mass and shape of galactic halos and the maximum extent of starlight in the disks of nearby galaxies. However, modeling the wide-angle PSF has long been a challenge in astronomical imaging. In this paper, we present a self-consistent method to model the wide-angle PSF in images. Scattered light from multiple bright stars is fitted simultaneously with a backgr…
Galaxy imaging surveys observe a vast number of objects that are affected by the instrument's Point Spread Function (PSF). Weak lensing missions, in particular, aim at measuring the shape of galaxies, and PSF effects represent an important source of systematic errors which must be handled appropriately. This demands a high accuracy in the modelling as well as the estimation of the PSF at galaxy positions. Sometimes referred to as non-parametric PSF estimation, the goal of this paper is to estimate a PSF at galaxy positions, starting from a set of noisy star image observations distributed over …
A robust and extended characterization of the point spread function (PSF) is crucial to extract the photometric information produced by deep imaging surveys. Here, we present the extended PSFs of the Sloan Digital Sky Survey (SDSS), one of the most productive astronomical surveys of all time. By stacking ~1000 images of individual stars with different brightness, we obtain the bidimensional SDSS PSFs extending over 8 arcmin in radius for all the SDSS filters(u, g, r, i, z). This new characterization of the SDSS PSFs is near a factor of 10 larger in extension than previous PSFs characterization…
The desire for wide-field of view, large fractional bandwidth, high sensitivity, high spectral and temporal resolution has driven radio interferometry to the point of big data revolution where the data is represented in at least three dimensions with an axis for spectral windows, baselines, sources, etc; where each axis has its own set of sub-dimensions. The cost associated with storing and handling these data is very large, and therefore several techniques to compress interferometric data and/or speed up processing have been investigated. Unfortunately, averaging-based methods for visibility …
We examined the anisotropic point spread function (PSF) of Suprime-Cam data utilizing dense star field data. We decomposed the PSF ellipticities into three components, the optical aberration, atmospheric turbulence, and chip-misalignment in an empirical manner, and evaluated the amplitude of each component. We found that, for long-exposure data, the optical aberration has the largest contribution to the PSF ellipticities, which could be modeled well by a simple analytic function based on the lowest-order aberration theory. The statistical properties of PSF ellipticities resulting from the atmo…
Modern Giant Segmented Mirror Telescopes (GSMT) like the Extremely Large Telescope (ELT), currently under construction depend heavily on Adaptive Optics (AO) systems to correct for atmospheric turbulence. To be able to correct wider fields of view (FoV), Multi-Conjugate Adaptive Optics (MCAO) systems were introduced, which use multiple guide stars to obtain an almost uniform correction over the FoV. However, a residual blur remains in the astronmical images due to the time delay stemming from the wavefront sensor (WFS) integration time and temporal response of the deformable mirror(s) (DM). Th…
Point spread function modelling for astronomical telescopes: a review focused on weak gravitational lensing studies
CEA（法国原子能和替代能源委员会）；CNRS（法国国家科学研究中心）；AIM（天体物理与宇宙学研究所）；University College London (UCL)（伦敦大学学院）；Mullard Space Science Laboratory（穆拉德空间科学实验室）；Institute of Astrophysics（天体物理研究所）
Adaptive optics (AO) restore the angular resolution of ground-based telescopes, but at the cost of delivering a time- and space-varying point spread function (PSF) with a complex shape. PSF knowledge is crucial for breaking existing limits on the measured accuracy of photometry and astrometry in science observations. In this paper, we concentrate our analyses on anisoplanatism signature only onto PSF: for large-field observations (20") with single- conjugated AO, PSFs are strongly elongated due to anisoplanatism that manifests itself as three different terms for Laser-guide star (LGS) systems:…
Context. Adaptive optics (AO) systems greatly increase the resolution of large telescopes, but produce complex point spread function (PSF) shapes, varying in time and across the field of view. This PSF must be accurately known since it provides crucial information about optical systems for design, characterisation, diagnostics and image post processing. Aims. We develop here a model of the AO long exposure PSF, adapted to various seeing conditions and any AO system. This model is made to match accurately both the core of the PSF and its turbulent halo. Methods. The PSF model we develop is base…
We present the results of an on-sky point spread function reconstruction (PSF-R) experiment for the Gemini North telescope adaptive optics system, Altair, in the simplest mode, bright on-axis natural guise star. We demonstrate that our PSF-R method does work for system performance diagnostic but suffers from hidden telescope and system aberrations that are not accounted for in the model, making the reconstruction unsuccessful for Altair, for now. We discuss the probable origin of the discrepancy. In the last section, we propose alternative PSF-R methods for future multiple natural and laser gu…
Here we describe a simple, efficient, and most importantly fully operational point-spread-function(PSF)-reconstruction approach for laser-assisted ground layer adaptive optics (GLAO) in the frame of the Multi Unit Spectroscopic Explorer (MUSE) Wide Field Mode. Based on clear astrophysical requirements derived by the MUSE team and using the functionality of the current ESO Adaptive Optics Facility we aim to develop an operational PSF-reconstruction (PSFR) algorithm and test it both in simulations and using on-sky data. The PSFR approach is based on a Fourier description of the GLAO correction t…
Modelling the Point Spread Function of ILMT images
Aryabhatta Research Institute of Observational Sciences (ARIES)（阿里亚巴塔观测科学研究所）；Mahatma Jyotiba Phule Rohilkhand University（马哈特马·乔提巴·普尔罗希勒坎德大学）；Physical Research Laboratory（物理研究实验室）；National University of Uzbekistan（乌兹别克斯坦国立大学）；Ulugh Beg Astronomical Institute of the Uzbek Academy of Sciences（乌兹别克斯坦科学院乌鲁伯格天文研究所）；Institute of Astrophysics and Geophysics, Liège University（列日大学天体物理学与地球物理学研究所）；Department of Physics and Astronomy, The University of British Columbia（不列颠哥伦比亚大学物理与天文学系）；Outer Space Institute, The University of British Columbia（不列颠哥伦比亚大学外层空间研究所）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学柯夫利天体物理学研究所）；Department of Applied Optics and Photonics, University of Calcutta（加尔各答大学应用光学与光子学系）
Context. Future weak lensing surveys, such as the Euclid mission, will attempt to measure the shapes of billions of galaxies in order to derive cosmological information. These surveys will attain very low levels of statistical error, and systematic errors must be extremely well controlled. In particular, the point spread function (PSF) must be estimated using stars in the field, and recovered with high accuracy. Aims. The aims of this paper are twofold. Firstly, we took steps toward a nonparametric method to address the issue of recovering the PSF field, namely that of finding the correct PSF …
The point spread function reconstruction (PSF-R) capability is a deliverable of the MICADO@ESO-ELT project. The PSF-R team works on the implementation of the instrument software devoted to reconstruct the point spread function (PSF), independently of the science data, using adaptive optics (AO) telemetry data, both for Single Conjugate (SCAO) and Multi-Conjugate Adaptive Optics (MCAO) mode of the MICADO camera and spectrograph. The PSF-R application will provide reconstructed PSFs through an archive querying system to restore the telemetry data synchronous to each science frame that MICADO wil…
Context: The unprecedented astrometric precision of the Gaia mission relies on accurate estimates of the locations of sources in the Gaia data stream. This is ultimately performed by point spread function (PSF) fitting, which in turn requires an accurate reconstruction of the PSF. Gaia Early Data Release 3 (EDR3) will, for the first time, use a PSF calibration that models several of the strongest dependences, leading to signficantly reduced systematic errors. Aims: We describe the PSF model and calibration pipeline implemented for Gaia EDR3, including an analysis of the calibration results ove…
Modeling the Point Spread Function (PSF) of wide-field surveys is vital for many astrophysical applications and cosmological probes including weak gravitational lensing. The PSF smears the image of any recorded object and therefore needs to be taken into account when inferring properties of galaxies from astronomical images. In the case of cosmic shear, the PSF is one of the dominant sources of systematic errors and must be treated carefully to avoid biases in cosmological parameters. Recently, forward modeling approaches to calibrate shear measurements within the Monte-Carlo Control Loops ($M…
We describe here a new full 2-D parameterization of the PSFs of the three XMM-Newton EPIC telescopes as a function of instrument, energy, off-axis angle and azimuthal angle, covering the whole field-of-view of the three EPIC detectors. It models the general PSF envelopes, the primary and secondary spokes, their radial dependencies, and the large-scale azimuthal variations. This PSF model has been constructed via the stacking and centering of a large number of bright, but not significantly piled-up point sources from the full field-of-view of each EPIC detector, and azimuthally filtering the re…
One of the problems often encountered in X-ray mirror manufacturing is setting proper manufacturing tolerances to guarantee an angular resolution - often expressed in terms of Point Spread Function (PSF) - as needed by the specific science goal. To do this, we need an accurate metrological apparatus, covering a very broad range of spatial frequencies, and an affordable method to compute the PSF from the metrology dataset. [...] However, the separation between these spectral ranges is difficult do define exactly, and it is also unclear how to affordably combine the PSFs, computed with different…
We make the in-orbit calibration to the point-spread functions (PSFs) of the collimators of the Hard X-ray Modulation Telescope with the scanning observation of the Crab. We construct the empirical adjustments to the theoretically calculated geometrical PSFs. The adjustments contain two parts: a rotating matrix to adjust the directional deviation of the collimators and a paraboloidal function to correct the inhomogeneity of the real PSFs. The parameters of the adjusting matrices and paraboloidal functions are determined by fitting the scanning data with lower scanning speed and smaller interva…
A ground-layer adaptive optics system (GLAO) uses a single adaptive mirror to partially correct the wavefront for atmospheric and telescope aberrations over a wide field of view. Instead of reaching diffraction limit on a narrow field, the idea is to provide partial improvement of the PSF over a wide field appropriate for multi-object spectrographs or wide field imagers. We derive an analytic formulation for the GLAO corrected PSF and then apply that in developing a methodology for calculating sensitivity improvement for astronomical instruments.
Point-spread function (PSF) estimation in spatially undersampled images is challenging because large pixels average fine-scale spatial information. This is problematic when fine-resolution details are necessary, as in optimal photometry where knowledge of the illumination pattern beyond the native spatial resolution of the image may be required. Here, we introduce a method of PSF reconstruction where point sources are artificially sampled beyond the native resolution of an image and combined together via stacking to return a finely sampled estimate of the PSF. This estimate is then deconvolved…
AnisoCADO is a Python package for generating images of the point spread function (PSF) for the european extremely large telescope (ELT). The code allows the user to set many of the most important atmospheric and observational parameters that influence the shape and strehl ratio of the resulting PSF, including but not limited to: the atmospheric turbulence profile, the guide star position for a single conjugate adaptive optics (SCAO) solution, differential telescope pupil transmission, etc. Documentation can be found at https://anisocado.readthedocs.io/en/latest/
Gaia Data Release 4: Modelling of drift-scan related effects in Gaia's point spread function
Institute for Astronomy, School of Physics and Astronomy, University of Edinburgh（爱丁堡大学物理与天文学学院天文研究所）；Lund Observatory, Division of Astrophysics, Department of Physics, Lund University（隆德大学物理系天体物理学部隆德天文台）；DAPCOM for Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB)（巴塞罗那大学宇宙科学研究所（ICCUB）DAPCOM项目）；ESA, European Space Astronomy Centre（欧洲空间局欧洲航天飞行中心）；Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (UB)（巴塞罗那大学宇宙科学研究所）；Departament de Física Quàntica i Astrofísica (FQA), Universitat de Barcelona (UB)（巴塞罗那大学量子物理与天体物理学系）；Institute of Astronomy, University of Cambridge（剑桥大学天文研究所）
Point spread function wavefront recovery from in-focus stellar observations
AIM, CEA, CNRS, Université Paris-Saclay, Université de Paris（天体物理与分子天文学研究所, 法国原子能与替代能源委员会, 法国国家科学研究中心, 巴黎萨克雷大学, 巴黎大学）；Institutes of Computer Science and Astrophysics, Foundation for Research and Technology Hellas (FORTH)（计算机科学与天体物理研究所, 希腊研究基金会）；IRFU, CEA, Université Paris-Saclay（核物理研究所, 法国原子能与替代能源委员会, 巴黎萨克雷大学）
The imaging sharpness of an X-ray telescope is chiefly determined by the optical quality of its focusing optics, which in turn mostly depends on the shape accuracy and the surface finishing of the grazing-incidence X-ray mirrors that compose the optical modules. To ensure the imaging performance during the mirror manufacturing, a fundamental step is predicting the mirror point spread function (PSF) from the metrology of its surface. Traditionally, the PSF computation in X-rays is assumed to be different depending on whether the surface defects are classified as figure errors or roughness. [...…
Context: in astronomy, observing large fractions of the sky within a reasonable amount of time implies using large field-of-view (fov) optical instruments that typically have a spatially varying Point Spread Function (PSF). Depending on the scientific goals, galaxies images need to be corrected for the PSF whereas no direct measurement of the PSF is available. Aims: given a set of PSFs observed at random locations, we want to estimate the PSFs at galaxies locations for shapes measurements correction. Contributions: we propose an interpolation framework based on Sliced Optimal Transport. A non-…
The shear measurement is a crucial task in the current and the future weak lensing survey projects. And the reconstruction of the point spread function(PSF) is one of the essential steps. In this work, we present three different methods, including Gaussianlets, Moffatlets and EMPCA to quantify their efficiency on PSF reconstruction using four sets of simulated LSST star images. Gaussianlets and Moffatlets are two different sets of basis functions whose profiles are based on Gaussian and Moffat functions respectively. Expectation Maximization(EM) PCA is a statistical method performing iterative…
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.…
The Mid Infra Red Instrument (MIRI) is one of the four instruments onboard the James Webb Space Telescope (JWST), providing imaging, coronagraphy and spectroscopy over the 5-28 microns band. To verify the optical performance of the instrument, extensive tests were performed at CEA on the flight model (FM) of the Mid-InfraRed IMager (MIRIM) at cryogenic temperatures and in the infrared. This paper reports on the point spread function (PSF) measurements at 5.6 microns, the shortest operating wavelength for imaging. At 5.6 microns the PSF is not Nyquist-sampled, so we use am original technique th…
Modeling the optical point spread function (PSF) is particularly challenging for adaptive optics (AO)-assisted observations owing to the its complex shape and spatial variations. We aim to (i) exhaustively demonstrate the accuracy of a recent analytical model from comparison with a large sample of imaged PSFs, (ii) assess the conditions for which the model is optimal, and (iii) unleash the strength of this framework to enable the joint estimation of atmospheric parameters, AO performance and static aberrations. We gathered 4812 on-sky PSFs obtained from seven AO systems and used the same fitti…
