Prof. M. Carbillet, P. Martinez, S. Robbe & M. Turconi
(S2, elective, 6 ECTS)
|Learning Outcomes:||The course is composed of 3 parts. Part 1: Optical Long Baseline Interferometry: Requirements for new breakthroughs in astrophysics (S. Robbe-Dubois) The course aims to make the students understand the technique of stellar interferometry and the process to define the optical concept. They will learn how to build such an instrument within the requirements necessary to reach significant advances in the various fundamental research fields in astrophysics. Observing with an optical long baseline interferometer gives access to very high angular resolution. Measurements of accurate observables are expected, from which parameters related to the scientific target are deduced. For example, we will show that visibility measurements allow us to determine angular diameters. Indeed, the interferometric observables are affected by the instrumental response. The different parameters affecting the instrumental transfer function are well identified and methods are applied to minimize their effect. The goal is to achieve the most stable and reliable instrument. The successful spectro-interferometer MATISSE located at the observatory of the Very Large Telescope in the Atacama desert, Chile, and its precursors provide a very good representative for this course.|
Part 2: Adaptive and cophasing optics (M. Carbillet, P. martinez) The aim of this course is to provide knowledge in (1) astronomical adaptive optics (AO), at a time in which any ground-based telescope with high-angular resolution goals is equipped (or about to be) with such systems, (2) cophasing optics, at a time in which increasing the telescope diameter from a few meters class telescopes towards tens of meters and beyond, gets segmentation increasingly important in order to keep the telescope mechanically and optically feasible. The basic principles of astronomical AO systems will be presented in detail, for what concerns its complete error budget and its consequences on the post-AO point-spread function morphology. Hence, the “hard(ware)” side of AO systems will be learnt from its main characteristics (wavefront sensing, real-time reconstruction and command/control, wavefront correction), and detailed numerical modeling will be studied (AO system dimensioning, end-to-end modeling, performance evaluation). The basic principles of cophasing segmented optics for astronomers will be presented in detail. Deploying segmented optics on large scale structures turns active and adaptive optics into cophasing optics that strives for aligning multiple optical paths in real time operation. Cophasing optics that correct for the misalignment of individual segments of the primary segmented mirror is a key optical process to reach exquisite image quality and stability. The course will cover the fundamental principles of active optics, phasing sensors, and detailed the active control implementation.
Part 3: Gravitational Wave Detection by Laser Interferometry (M. Turconi) After a long maturation, “multi-messenger astronomy” has recently emerged after the ground-breaking detections of the gravitational waves (GW) emitted in catastrophic astrophysical processes, such as binary black hole mergers, binary neutron star mergers, etc. Detections have been realized first by the LIGO detector and later by the European detector, Virgo. This course aims at providing a view on the various optical interferometric techniques which have brought to GW detection. GW are recorded as tiny modifications of an interference state, which can then be exploited by astrophysicists to calculate physical properties of the sources, for instance the mass of the merging bodies. The course will present these giant, complex interferometers that are the operating, ground-based interferometers, and the space project LISA.
|Knowledge and Understanding:||Part 1: understand the domain of long-baseline stellar interferometry, the applications, the technique, the constraints and limitations. Learn how to conduct a system study of an interferometer, which part can be applied to any other optical instruments, to ensure its performance.|
Part 2: the students will learn how astronomical optics systems are conceived through theoretical lectures and practical numerical modeling. In addition to basics and on the adaptive optics side, the two somehow orthogonal types of advanced systems, wide-field AO systems and extreme AO systems will be considered, implying study of the use of artificial stars (Laser Guide Star), and its drawbacks, comparison between different wavefront sensing concepts, the performance of deformable correctors, and possible developments. On the cophasing optics side, the students will also learn how segmented telescope architectures impact image quality and translate into the point-spread function structure. Understand how segment misalignments impact the image quality and what are the conditions for optimal performances. Diagnose image quality and understand phasing sensor landscape. Study active optics architectures, phasing sensor signal properties, cophasing steps and accuracy, control algorithm and operation strategy, performance evaluation and metrics.
Numerical modelling and testing will be fundamental contributors to acquiring knowledge and understanding from this course.
Part 3: the students will understand the principles of laser interferometric GW detectors and the limitations that lead to the frequency range of the measurable GWs, as illustrated by the “sensitivity curves” of each detector. It will be shown how, despite the fact that the most stable laser sources show a much larger frequency instability, exceedingly small (10-23) distortions of space time can be detected, measured, and exploited to draw astrophysical observations. Indeed, each detector implements a variety of techniques that, combined, will give to the interferometric signal the unique signature of a gravitational wave. The student will be familiar with techniques and concepts linked to laser interferometry such as: laser stabilization and control, signal processing, noise characterisation and rejection, systematic errors.
|Applying Knowledge and Understanding:||Part 1: knowledge and understanding of the theoretical part of the lectures will be directly utilized within the numerous numerical modelling and subsequent studies performed all along this course. The students will have to communicate with others to transfer their experience-building, providing an opportunity to demonstrate the depth of their new knowledge and understanding through meaningful application and sharing with an audience. They will explain concepts, principles, and processes, interpret data, texts, and experience, apply by effectively using and adapting, and propose perspectives.|
Part 2: knowledge and understanding of the theoretical part of the lectures will be directly utilized within the numerous numerical modelling and subsequent studies performed all along this course.
Part 3: the student will have acquired the necessary knowledge to run and design high-end laser interferometric set-ups. The acquired knowledge can find applications in different areas of technology or of fundamental physics, including gravitational wave detection, vacuum birefringence measurement, or search for light particles coupled to the photon, a class of experiments that also test “the optical properties of the vacuum”.
|Prerequisites||Basic knowledge in geometrical optics and wave optics (plane waves, interferences, coherence, diffraction) Completed Fourier optics course Completed “Telescope optics” course (for part 2) Completed “Image formation through turbulence” course (for part 2) Mathematical knowledge: double and triple integrals – Fourier Transforms|
|Program||Part 1: long baseline interferometry 1 . Introduction Interference between two waves Definition of intensity, contrast Amplitude and wavefront interferometers 2. Why a stellar interferometer? Resolution History Astrophysical programs 3. Choice of the general configuration Wavelength/spectral coverage Telescope number Maximal baseline u-v coverage 4. Constraints Terrestrial atmosphere Mechanics/vibrations Noise 5. Optical concept Definition of the requirements: from high to low level From the requirements to the concept Spatial filtering V-diagram method 6. Data analysis: from raw data to observables|
Part 2: Adaptive and cophasing optics
I – Adaptive Optics Standard AO system basics Post-AO error budget Laser guide star AO Quality of correction? Post-AO point-spread function morphology Wavefront sensors Deformable correctors Possible improvements Focus on numerical modelling (using CAOS) Ground-layer AO vs. eXtreme AO II – Cophasing Optics Segmented telescope optics (image quality, performances, sensitivity analysis) Active optics (principles, architectures, phasing sensor, signal properties, accuracy) Active control implementation (interaction & control matrix, close-loop operation) Applications (operational strategies, telescopes, testbed)
Part 3: Gravitational waves Introduction on GW: What are gravitational waves? What are their sources, and why it is important to detect them?
– Introduction to GW detection. GW detection by laser interferometry. State of the art on GW detection and multi-messenger astronomy.
– The Michelson interferometer; rejection of the laser frequency noise.
– The Fabry-Perot (FP) interferometer; optical cavities.
– Laser frequency stabilisation by locking the laser to a FP cavity: Pound-Drever-Hall method.
– Ground-based GW detectors: a Michelson interferometer involving FP cavities.
– Power recycling cavity. Adding a recycling mirror to the Michelson interferometer results in an additional gain in sensitivity
– Optical techniques for laser beam cleaning: mode cleaner cavities, triangular cavities.
– Thermal noise.
– The signals in a GW detector: the true life of a GW interferometric detector.
– Laser Interferometer Space Antenna (LISA): main characteristics.
– LISA: Unequal-arms interferometer and time-delayed interferometry
|Description of how the course is conducted||The course consists of lectures accompanied by concrete examples, so that concepts do not remain too abstract. A global introduction on interferometry is presented. After explaining how a long-baseline interferometer is defined in its general configuration, details are provided on constraints and limits, methods to minimize their effects and to reach the required performance are presented, resulting on a detailed opto-mechanical study of the instrumentation. The course consists in a series of lectures, performed along with numerous numerical physical modelling and concrete simulation studies. A gravitational wave detector is a complex instrument, in which different ideas have been implemented to both improve sensitivity and reduce noise. The course will introduce one by one these ideas, and the modelling of the corresponding optical system. The (often implicit) assumptions which are made to model the system under study, and the domain of validity for each assumption will be highlighted.|
|Description of the didactic methods||The courses consist of lectures presented on blackboard. Slide presentations will be used for the course introduction and for showing relevant images and plots. The good understanding by the students of the addressed topics will be evaluated through analysis of documents which constitute a good preparation for a future scientific work (scientific papers, technical reports, parts of Master or PhD dissertations). Laboratory works will also be conducted. A numerical work will be performed through examples of data analysis provided by the MATISSE instrument. Active learning is expected through reading assignments, homework and classwork assignments, numerical modelling, and simulation projects.|
|Description of the evaluation methods||Reports, oral examinations, tutorial questions. Understanding will be evaluated by an informal oral presentation of a specific point of the theoretical part developed in some article, and, mostly, by a final written simulation study report or lab reports. The evaluation is done with an oral exam. The students will be asked to read in advance a scientific paper concerning GW detection. The exam includes the paper presentation and three or four questions on different topics of the course with open answers.|
|Recommended readings||The Fourier Transform and its application, R. N. Bracewell, eds. McGraw Hill Higher Education Optics, E. Hecht, several editions « Astrophysique – Méthodes physiques de l’observation » (in French), P. Léna, CNRS Éd. (1996) “Teaching astronomical speckle techniques”, C. Aime, Eur. J. Phys. 22, 169 (2001) “Modélisation des effets optiques de la turbulence atmosphérique pour les grands télescopes et les observations à haute résolution angulaire » (in French), J. Maire, PhD thesis of the Université de Nice Sophia-Antipolis (2007) “Numerical modelling of atmospherically perturbed phase screens: new solutions for classical fast Fourier transform and Zernike methods”, M. Carbillet & A. Riccardi, App. Optics 49 (31), G47 (2010) “On the difference between seeing and image quality: when the turbulence outer scale enters the game”, P. Martinez, The Messenger 41, 5 (2010) “The design and construction of large optical telescopes”, Pierre Y. Bely, A&A Library, Springer The VIRGO physics book, https://www.ego-gw.it/public/events/vesf/2010/Presentations/Interferometer_Materials-Vinet.pdf “Astronomical adaptive optics”, F. Rigaut, PASP 127, 1197 (2015) CAOS website https://lagrange.oca.eu/caos “The design and construction of large optical telescopes”, Pierre Y. Bely, A&A Library, Springer The SPEED project: https://lagrange.oca.eu/en/lag-speed-home|