This tutorial paper describes the problem of image reconstruction from interferometric data with a particular focus on the specific problems encountered at optical (visible/IR) wavelengths. The challenging issues in image reconstruction from interferometric data are introduced in the general framework of inverse problem approach. This framework is then used to describe existing image reconstruction algorithms in radio interferometry and the new methods specifically developed for optical interferometry.
The advent of enhanced technologies in radio interferometry and the perspective of the SKA telescope bring new challenges in image reconstruction. One of these challenges is the spatio-spectral reconstruction of large (Terabytes) data cubes with high fidelity. This contribution proposes an alternative implementation of one such 3D prototype algorithm, MUFFIN (MUlti-Frequency image reconstruction For radio INterferometry), which combines spatial and spectral analysis priors. Using a recently proposed primal dual algorithm, this new version of MUFFIN allows a parallel implementation where comput…
This paper provides a general introduction to the problem of image reconstruction from interferometric data. A simple model of the interferometric observables is given and the issues arising from sparse Fourier data are discussed. The effects of various regularizations are described. In the proposed general framework, most existing algorithms can be understood. For an astronomer, such an understanding is crucial not only for selecting and using an algorithm but also to ensure correct interpretation of the resulting image.
Astronomical optical interferometers (OI) sample the Fourier transform of the intensity distribution of a source at the observation wavelength. Because of rapid atmospheric perturbations, the phases of the complex Fourier samples (visibilities) cannot be directly exploited , and instead linear relationships between the phases are used (phase closures and differential phases). Consequently, specific image reconstruction methods have been devised in the last few decades. Modern polychromatic OI instruments are now paving the way to multiwavelength imaging. This paper presents the derivation of a…
We describe a "spatio-spectral" deconvolution algorithm for wide-band imaging in radio interferometry. In contrast with the existing multi-frequency reconstruction algorithms, the proposed method does not rely on a model of the sky-brightness spectral distribution. This non-parametric approach can be of particular interest for the new generation of low frequency radiotelescopes. The proposed solution formalizes the reconstruction problem as a convex optimization problem with spatial and spectral regularizations. The efficiency of this approach has been already proven for narrow-band image reco…
The number of publications of aperture-synthesis images based on optical long-baseline interferometry measurements has recently increased due to easier access to visible and infrared interferometers. The interferometry technique has now reached a technical maturity level that opens new avenues for numerous astrophysical topics requiring milli-arcsecond model-independent imaging. In writing this paper our motivation was twofold: 1) review and publicize emblematic excerpts of the impressive corpus accumulated in the field of optical interferometry image reconstruction; 2) discuss future prospect…
For sensitive infrared interferometry, it is crucial to control the differential piston evolution between the used telescopes. This is classically done by the use of a fringe tracker. In this work, we develop a new method to reconstruct the temporal piston variation from the atmosphere, by using real-time data from adaptive optics wavefront sensing: the Piston Reconstruction Experiment (P-REx). In order to understand the principle performance of the system in a realistic multilayer atmosphere it is first extensively tested in simulations. The gained insights are then used to apply P-REx to rea…
More than sixty years after the first intensity correlation experiments by Hanbury Brown and Twiss, there is renewed interest for intensity interferometry techniques for high angular resolution studies of celestial sources. We report on a successful attempt to measure the bunching peak in the intensity correlation function for bright stellar sources with 1 meter telescopes (I2C project). We propose further improvements of our preliminary experiments of spatial interferometry between two 1 m telescopes, and discuss the possibility to export our method to existing large arrays of telescopes.
Optical long baseline interferometry is a technique that has generated almost 850 refereed papers to date. The targets span a large variety of objects from planetary systems to extragalactic studies and all branches of stellar physics. We have created a database hosted by the JMMC and connected to the Optical Long Baseline Interferometry Newsletter (OLBIN) web site using MySQL and a collection of XML or PHP scripts in order to store and classify these publications. Each entry is defined by its ADS bibcode, includes basic ADS informations and metadata. The metadata are specified by tags sorted …
We present a compact setup based on a three-dimensional integrated optical component, allowing the mea- surement of spectrally resolved complex-visibilities for three channels of polychromatic light. We have tested a prototype of the component in R band and showed that accurate complex visibilities could be retrieved over a bandwidth of 50 nm centered at 650 nm (resolution: R=130). Closure phase stability in the order of $λ$/60 was achieved implying that the device could be used for spectro-interferometry imaging.
This paper summarizes some of the major calibration and image reconstruction techniques used in radio interferometry and describes them in a common mathematical framework. The use of this framework has a number of benefits, ranging from clarification of the fundamentals, use of standard numerical optimization techniques, and generalization or specialization to new algorithms.
The present notes refer to a lecture delivered on 27 September 2017 in Roscoff during the 2017 Evry Schatzman School. It concerns a general introduction to optical/IR interferometry, including a brief history, a presentation of the basic principles, some important theorems and relevant applications.The layout of these lecture notes is as follows. After a short introduction, we proceed with some reminders concerning the representation of a field of electromagnetic radiation. We then present a short history of interferometry, from the first experiment of Fizeau and Stefan to modern optical inter…
Bandwidth smearing is a chromatic aberration due to the finite frequency bandwidth. In long-baseline optical interferometry terms, it is when the angular extension of the source is greater than the coherence length of the interferogram. As a consequence, separated parts of the source will contribute to fringe packets that are not fully overlapping; it is a transition from the classical interferometric regime to a double or multiple fringe packet. While studied in radio interferometry, there has been little work on the matter in the optical, where observables are measured and derived in a diffe…
With the advent of infrared long-baseline interferometers with more than two telescopes, both the size and the completeness of interferometric data sets have significantly increased, allowing images based on models with no a priori assumptions to be reconstructed. Our main objective is to analyze the multiple parameters of the image reconstruction process with particular attention to the regularization term and the study of their behavior in different situations. The secondary goal is to derive practical rules for the users. Using the Multi-aperture image Reconstruction Algorithm (MiRA), we pe…
Optical long-baseline interferometry is a unique and powerful technique for astronomical research. Since 2004, optical interferometers have produced an increasing number of scientific papers covering various fields of astrophysics. As current interferometric facilities are reaching their maturity, we take the opportunity in this paper to summarize the conclusions of a few key meetings, workshops, and conferences dedicated to interferometry. We present the most persistent recommendations related to science cases and discuss some key technological developments required to address them. In the er…
During some thirty years, 1980-2010, technical studies of optical interferometry from instruments in space were pursued as promising for higher spatial resolution and for higher astrometric accuracy. Nulling interferometry was studied for both high spatial resolution and high contrast. These studies were great dreams deserving further historical attention. ESA's interest in interferometry began in the early 1980s. The studies of optical interferometry for the global astrometry mission GAIA began in 1993 and ended in 1998 when interferometry was dropped as unsuited for the purpose, and the Gaia…
Intensity interferometry permits very long optical baselines and the observation of sub-milliarcsecond structures. Using planned kilometric arrays of air Cherenkov telescopes at short wavelengths, intensity interferometry may increase the spatial resolution achieved in optical astronomy by an order of magnitude, inviting detailed studies of the shapes of rapidly rotating hot stars with structures in their circumstellar disks and winds, or mapping out patterns of nonradial pulsations across stellar surfaces. Signal-to-noise in intensity interferometry favors high-temperature sources and emissio…
High resolution imaging is achieved using increasingly larger apertures and successively shorter wavelengths. Optical aperture synthesis is an important high-resolution imaging technology used in astronomy. Conventional long baseline amplitude interferometry is susceptible to uncontrollable phase fluctuations, and the technical difficulty increases rapidly as the wavelength decreases. The intensity interferometry inspired by HBT experiment is essentially insensitive to phase fluctuations, but suffers from a narrow spectral bandwidth which results in a lack of detection sensitivity. In this stu…
Université de Nice Sophia Antipolis（尼斯索菲亚·安提波利斯大学）；CNRS（法国国家科学研究中心）；Observatoire de la Côte d’Azur（蔚蓝海岸天文台）；Université de Lyon（里昂大学）；Université Lyon 1（里昂第一大学）；Observatoire de Lyon（里昂天文台）；Centre de Recherche Astrophysique de Lyon（里昂天体物理研究中心）；École Normale Supérieure de Lyon（里昂高等师范学院）
Astronomical optical interferometers sample the Fourier transform of the intensity distribution of a source at the observation wavelength. Because of rapid perturbations caused by atmospheric turbulence, the phases of the complex Fourier samples (visibilities) cannot be directly exploited. Consequently, specific image reconstruction methods have been devised in the last few decades. Modern polychromatic optical interferometric instruments are now paving the way to multiwavelength imaging. This paper is devoted to the derivation of a spatio-spectral (3D) image reconstruction algorithm, coined P…
Observations of Binary Stars with the 1.3-m Devasthal Fast Optical Telescope Using Speckle Interferometry: An Attempt
Aryabhatta Research Institute of Observational Sciences（阿亚巴塔观测科学研究所）；School of Applied Sciences, Centurion University of Technology and Management（中央技术与管理大学应用科学学院）；Inter-University Centre for Astronomy and Astrophysics（跨大学天文学与天体物理学中心）；Physik-Institut, University of Zurich（苏黎世大学物理学院）
Radio interferometry has always faced the problem of incomplete sampling of the Fourier plane. A possible remedy can be found in the promising new theory of compressed sensing (CS), which allows for the accurate recovery of sparse signals from sub-Nyquist sampling given certain measurement conditions. We provide an introductory assessment of optimal arrays for CS in snapshot-mode radio interferometry, using orthogonal matching pursuit (OMP), a widely used CS recovery algorithm similar in some respects to CLEAN. We focus on centrally condensed (specifically, Gaussian) arrays versus uniform arra…
This paper describes version 2 of the OI Exchange Format (OIFITS), the standard for exchanging calibrated data from optical (visible/infrared) interferometers. This IAU-endorsed standard has been in use for 10 years at most of the past and current optical interferometer projects, including COAST, NPOI, IOTA, CHARA, VLTI, PTI and the Keck interferometer. Software is available for reading, writing and merging OI Exchange Format files. This version 2 provides definitions of additional data tables (e.g. for polarisation measurements), addressing the needs of future interferometric instruments. Als…
Conventional ground-based astronomical observations suffer from image distortion due to atmospheric turbulence. This can be minimized by choosing suitable geographic locations or adaptive optical techniques, and avoided altogether by using orbital platforms outside the atmosphere. One of the promises of optical intensity interferometry is its independence from atmospherically induced phase fluctuations. By performing narrowband spectral filtering on sunlight and conducting temporal intensity interferometry using actively quenched avalanche photon detectors (APDs), the Solar $g^{(2)}(τ)$ signat…
Imaging Atmospheric Cherenkov Telescopes (IACTs) currently in operation feature large mirrors and order of 1 ns time response to signals of a few photo-electrons produced by optical photons. This means that they are ideally suited for optical interferometry observations. Thanks to their sensitivity to visible wavelengths and long baselines optical intensity interferometry with IACTs allows reaching angular resolutions of tens to microarcsec. We have installed a simple optical setup on top of the cameras of the two 17 m diameter MAGIC IACTs and observed coherent fluctuations in the photon inten…
Optical imaging with microarcsecond resolution will reveal details across and outside stellar surfaces but requires kilometer-scale interferometers, challenging to realize either on the ground or in space. Intensity interferometry, electronically connecting independent telescopes, has a noise budget that relates to the electronic time resolution, circumventing issues of atmospheric turbulence. Extents up to a few km are becoming realistic with arrays of optical air Cherenkov telescopes (primarily erected for gamma-ray studies), enabling an optical equivalent of radio interferometer arrays. Pio…
High-resolution observations by visible and near-infrared interferometers of both single stars and binaries have made significant contributions to the foundations that underpin many aspects of our knowledge of stellar structure and evolution for cool stars. The CS16 splinter on this topic reviewed contributions of optical interferometry to date, examined highlights of current research, and identified areas for contributions with new observational constraints in the near future.
We propose a method for optical interferometry in telescope arrays assisted by quantum networks. In our approach, the quantum state of incoming photons along with an arrival time index is stored in a binary qubit code at each receiver. Nonlocal retrieval of the quantum state via entanglement-assisted parity checks at the expected photon arrival rate allows for direct extraction of the phase difference, effectively circumventing transmission losses between nodes. Compared to prior proposals, our scheme (based on efficient quantum data compression) offers an exponential decrease in required enta…
The closest examples of high-mass star birth occurs in deeply embedded environments at kiloparsec distances. Although much progress has been made, an observationally validated picture of the dominant processes which allows the central hydrostatic object to grow in mass has yet to be established. The observational technique of optical interferometry has demonstrated its potential in the field of high-mass star formation by delivering a milli-arcsecond infrared view on the complex accretion environment. We provide an overview of the scientific results obtained with multi-aperture telescope array…
IRIS: A Bayesian Approach for Image Reconstruction in Radio Interferometry with expressive Score-Based priors
Université de Montréal（蒙特利尔大学）；Mila - Quebec Artificial Intelligence Institute（米拉-魁北克人工智能研究所）；Ciela - Montreal Institute for Astrophysical Data Analysis and Machine Learning（CIELA-蒙特利尔天体物理数据分析与机器学习研究所）；University of Oxford（牛津大学）；Flatiron Institute - Center for Computational Astrophysics（弗拉蒂伦研究所-计算天体物理中心）；Perimeter Institute（圆周理论物理研究所）；McGill University（麦吉尔大学）；University of Manchester（曼彻斯特大学）；The Alan Turing Institute（阿兰·图灵研究所）
本文提出贝叶斯成像框架 IRIS，将星系光学图像训练的基于分数模型先验与 uv 空间高斯似然结合，用于 ALMA DSHARP 原行星盘可见度重建，并通过模拟覆盖率测试验证后验校准。
Generating images from very long baseline interferometric observations poses a difficult, and generally not unique, inversion problem. This problem is simplified by the introduction of constraints, some generic (e.g., positivity of the intensity) and others motivated by physical considerations (e.g., smoothness, instrument resolution). It is further complicated by the need to simultaneously address instrumental systematic uncertainties and sparse coverage in the u-v plane. We report a new Bayesian image reconstruction technique in the parameter estimation framework Themis that has been develop…
Eliminating photon transport in long-baseline optical interferometry using quantum memories
NASA Glenn Research Center（美国国家航空航天局格伦研究中心）；University of Maryland, College Park（马里兰大学帕克分校）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算机科学联合中心，美国国家标准与技术研究院/马里兰大学）；Joint Quantum Institute, NIST/University of Maryland（量子研究所联合机构，美国国家标准与技术研究院/马里兰大学）；NSF NOIRLab（美国国家科学基金会NOIR实验室）
We report on observations of the extended environment of the bright Be star $γ$-Cas performed using intensity interferometry measurements within its H$α$ emission line. These observations were performed using a modified version of the I2C intensity interferometry instrument installed onto the 1.54 meter MéO optical metrology telescope and a portable 1-meter telescope (T1M). In order to better constrain the extent of the H$α$ envelope, observations were performed for two different positions of the T1M telescope, corresponding to an intermediate and long baselines in which the extended region wa…
Quantum-enabled optical large-baseline interferometry: applications, protocols and feasibility
RMIT University（皇家墨尔本理工大学）；University of Technology Sydney（悉尼科技大学）；Macquarie University（麦考瑞大学）；University of Strathclyde（斯特拉斯克莱德大学）；The University of Sheffield（谢菲尔德大学）
Generative imaging for radio interferometry with fast uncertainty quantification
Mullard Space Science Laboratory (MSSL)（穆拉德空间科学实验室）；University College London (UCL)（伦敦大学学院）；Leiden Observatory（莱顿天文台）；Leiden University（莱顿大学）；IRFU CEA Université Paris-Saclay（CEA巴黎-萨克雷大学IRFU）；Department of Computer Science（计算机科学系）；Alan Turing Institute（艾伦·图灵研究所）
Deep frequency modulation interferometry combines optical minimalism with multi-fringe readout. Precision however is key for applications such as optical gradiometers for satellite geodesy or as dimensional sensor for ground-based gravity experiments. We present a single-component interferometer smaller than a cubic inch. Two of these are compared to each other to demonstrate tilt and displacement measurements with a precision of less than $20\,\mathrm{nrad}/\sqrt{\mathrm{Hz}}$ and $1\,\mathrm{pm}/\sqrt{\mathrm{Hz}}$ at frequencies below $1\,\mathrm{Hz}$.
After decades of experimental projects and fast-paced technical advances, optical / infrared (O/IR) interferometry has seen a revolution in the last years. The GRAVITY instrument at the VLTI with four 8 meter telescopes reaches thousand times fainter objects than possible with earlier interferometers, and the CHARA array routinely offers up to 330 meter baselines and aperture-synthesis with six 1 meter telescopes. The observed objects are fainter than 19 magnitude, the images have sub-milliarcsecond resolution, and the astrometry reaches micro-arcsecond precision. We give an overview of breakt…
The compatibility of higher-order Laguerre-Gauss (LG) modes with interferometric technologies commonly used in gravitational wave detectors is investigated. In this paper we present the first experimental results concerning the performance of the LG33 mode in optical resonators. We show that the Pound-Drever-Hall error signal for a LG33 mode in a linear optical resonator is identical to that of the more commonly used LG00 mode, and demonstrate the feedback control of the resonator with a LG33 mode. We succeeded to increase the mode purity of a LG33 mode generated using a spatial-light modulato…
We introduce a new class of iterative image reconstruction algorithms for radio interferometry, at the interface of convex optimization and deep learning, inspired by plug-and-play methods. The approach consists in learning a prior image model by training a deep neural network (DNN) as a denoiser, and substituting it for the handcrafted proximal regularization operator of an optimization algorithm. The proposed AIRI (``AI for Regularization in radio-interferometric Imaging'') framework, for imaging complex intensity structure with diffuse and faint emission from visibility data, inherits the r…
Using kilometric arrays of air Cherenkov telescopes, intensity interferometry may increase the spatial resolution in optical astronomy by an order of magnitude, enabling images of rapidly rotating stars with structures in their circumstellar disks and winds, or mapping out patterns of nonradial pulsations across stellar surfaces. Intensity interferometry (pioneered by Hanbury Brown and Twiss) connects telescopes only electronically, and is practically insensitive to atmospheric turbulence and optical imperfections, permitting observations over long baselines and through large airmasses, also a…
Highest resolution imaging in astronomy is achieved by interferometry, connecting telescopes over increasingly longer distances, and at successively shorter wavelengths. Here, we present the first diffraction-limited images in visual light, produced by an array of independent optical telescopes, connected electronically only, with no optical links between them. With an array of small telescopes, second-order optical coherence of the sources is measured through intensity interferometry over 180 baselines between pairs of telescopes, and two-dimensional images reconstructed. The technique aims a…
