Prof. E. Aristidi, P. Martinez & M. Carbillet
(S2, compulsory, 6 ECTS)
|This course is composed of 3 parts: Fourier optics: the aim of this course is to provide the basics of Fourier optics for astronomers. The theory of diffraction and image formation makes an extensive use of tools related to Fourier analysis and signal processing, such as the Fourier transform, convolution and frequency filtering. During this course we present mathematical formalism as well as applications to image formation, long baseline interferometry, Abbe-Porter optical filtering and Lyot coronography. The course is completed by laboratory sessions, using optical benches with lasers, lenses and cameras. We also give a small introduction to a scientific computing language (python) and use it for numerical exercises and processing of data obtained during lab sessions.
Telescope optics: The aim of this course is to provide the basics of telescope optics for astronomers. Astronomy distinguishes itself from other disciplines by the fact that it mainly relies on observations, as most experiments are impossible by nature. It is thus fundamental to have an in-depth understanding of the instrument that exploits the sky that naked eye is not able to catch. During this course, based on the theory of diffraction and image formation, the impact of the telescope optical and mechanical characteristics in the image formation will be studied. The course will cover modern-day telescopes through monolithic and segmented primary mirror configurations.
Astronomical imaging:The aim of this course is to provide knowledge in image formation through atmospheric optical turbulence, a problem which is faced by any ground-based instrumentation when high-angular resolution (HAR) is desired.
The phenomenon of atmospheric optical turbulence will first be reviewed through the classical Kolmogorov model and its von Karman modification. Numerical modelling of the last will be performed, and its consequences on the image formation at HAR will be analyzed, for what concerns spatial coherence in the pupil plane and the corresponding “seeing” in the image plane.
Detection noises will also be modelized in the framework of astronomical image formation, and statistical techniques permitting to overcome the optical turbulence effects will be approached.
In fine, an introduction to adaptive optics (AO) will be given, and a numerical study on one of the main errors contributing to the post-AO error budget when wide fields of observation (wide with respect to the atmospheric isoplanatic patch) will be performed by the students.
|Knowledge and Understanding:
|Learn how to perform efficient analytical calculations using Fourier properties and tools. Understand the theory of diffraction, image formation and optical filtering, and their application to astrophysics. Learn how to align an optical bench, work with lasers and cameras and process images.
Learn how wavefront errors and telescope architectures impact image quality and translate into the point-spread function structure. Understand the definition and relevance of various image quality metrics. Diagnose image quality and diffraction signatures recorded by various telescopes. Understand and illustrate the theory of diffraction and image formation.
Learn how atmospheric optical turbulence degrades image quality through theoretical lectures and practical numerical modeling. The impact of detection noises will also be understood, and the specific problem of anisoplanatism with respect to observational field of view will be fully considered.
|Applying Knowledge and Understanding:
|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. Knowledge and understanding of the theoretical part of the lectures will be directly utilized within the numerous numerical modeling and subsequent studies performed all along this course.
|Mathematical knowledge: Integrals, Fourier transform and convolution Basic knowledge in wave optics (plane waves, interferences, coherence, diffraction)
|Part 1: Fourier optics
– Reminders on Fourier analysis – Fraunhofer diffraction – Fourier properties of lenses – Optical coherent filtering – Image formation in incoherent light
Part 2: Telescope optics
1. Evolution of telescopes 2. Basic in telescope optics
– wave interference and diffraction
– wavefront errors and fabrication errors
– primary mirror central obscuration and secondary mirror support structures
– point spread function, encircled energy, modulation transfer function, Strehl ratio
3. Segmented telescope optics
– segment shape and size
– geometrical considerations
– piston, tip/tilt misalignments
– diffraction in segmented telescopes
4. Image quality and external disturbances
– external disturbances (system and operation, atmosphere) – active and adaptive optics (introduction)
5. Example of space-based and ground-based telescopes
– Actual observatories (VLT, Keck, etc.)
– Extremely large telescopes (ELT, TMT, etc.)
– Space telescopes (HST, JWST, LUVOIR, etc.)
– Laboratory facilities
Part 3: Astronomical imaging
1. High-angular resolution imaging in astronomy
2. Atmospheric turbulence
3. Numerical modeling of perturbed wavefronts
4. Formation of resulting image (+detector noises)
5. Introduction to speckle interferometry
6. Introduction to adaptive optics
7. Anisoplanatism error study (ideal AO system)
|Description of how the course is conducted
|The Fourier optics course consists of a series of short lectures, followed by concrete exercises chosen in topics related to astronomical optics. Lectures are completed by a PDF handbook providing the full, detailed version of the course, as well as exercises solutions. Two laboratory sessions of 3h are proposed. Students work by pair and perform a set of experiments about Fraunhofer diffraction and optical filtering.
The telescope optics course consists of a series of lectures, followed by concrete classwork/homework assignments using numerical simulations. Upon availability, hands-on experiences with the SPEED facility (Segmented Pupil Experiment for Exoplanet Detection) will be made possible. Lectures are completed by a PDF handbook providing the full, detailed version of the course. Active learning is expected through reading assignments, homework and classwork assignments, experimental hands-on. Understanding will be evaluated by written/oral questions or oral presentations to their classmates.
The course consists in a series of lectures, performed along with numerous IDL-based and CAOS-aided (see lagrange.oca.eu/caos) numerical physical modelling and concrete simulation studies.
|Description of the didactic methods
|Academic lectures are made as short as possible, presenting the context of the addressed topics, important results and examples of application. The aim is that students learn by practicing on exercises. Quizz are proposed at the beginning of every course to evaluate the good understanding of the previous lesson.
In addition, students work on a mini-project consisting in the analysis of a research article. Students are asked to understand and reproduce the results of the article. Eventually they give short presentations to explain the article to their classmates. This constitutes good preparation for a future scientific work (scientific papers, technical reports, parts of Master or PhD dissertations).
|Description of the evaluation methods
|Exam, oral presentation (article work, mini project), lab reports, quiz. For the part 3, the mini-project consists in a numerical simulation study (and a written report)
|“The Fourier Transform and its application”, R. N. Bracewell, eds. McGraw Hill Higher Education “Introduction to Fourier Optics”, Goodman, J.W. “The design and construction of large optical telescopes”, Pierre Y. Bely, A&A Library, Springer “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) CAOS website https://lagrange.oca.eu/caos