Adaptive optics for high resolution spectroscopy

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Thesis

Reference

Adaptive optics for high resolution spectroscopy

CONOD, Uriel Gwendal

Abstract

In this thesis, I explore an innovative way of designing high resolution spectrograph using Adaptive Optics. Most of the RV spectrographs are installed on 4 meter class telescopes and are working in seeing-limited conditions, however, a strong limitation for the adaptation of this instrumentation onto large telescope exists. Telescopes and radial-velocity spectrographs size issue as well as the technology proposed to overcome this problem (Adaptive Optics) are addressed in this thesis. With adaptive optics the telescope optical étendue can be reduced without loosing photons, thus allow us to build very compact spectrographs, cheaper and easier to stabilized. Moreover, a direct application of this concept is presented through this thesis with the NIRPS instrument.

CONOD, Uriel Gwendal. Adaptive optics for high resolution spectroscopy . Thèse de doctorat : Univ. Genève, 2018, no. Sc. 5300

URN : urn:nbn:ch:unige-1145145

DOI : 10.13097/archive-ouverte/unige:114514

Available at:

http://archive-ouverte.unige.ch/unige:114514

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UNIVERSITÉ DEGENÈVE FACULTÉ DESSCIENCES

Département d’Astronomie Professeur Francesco Pepe Dr. François Wildi

Adaptive Optics for High Resolution Spectroscopy

T

HÈSE

présentée à la Faculté des Sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences,

mention Astronomie et Astrophysique

par

Uriel C

ONOD de

Genève (GE, Suisse)

Thèse N^o5300

GENÈVE

Observatoire Astronomique de l’Université de Genève 2018

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Les causes primordiales ne nous sont point connues;

mais elles sont assujetties à des lois simples et constantes, que l’on peut découvrir par l’observation, et dont l’étude est l’objet de la philosophie naturelle.

— Baron Jean-Baptiste-Joseph Fourier

A mon père qui nous a quitté malheureusement trop tôt A ma mère qui m’a toujours soutenu

A Alexia que j’aime tant

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Summary

Progress in the astronomical instrumentation was always followed by majors discoveries.

The first detection of an exoplanet was indeed due to a number of instrumental techniques improving the precision of stellar radial-velocity measurements. Trying to answer one of the fundamental questions regarding the unicity of Humanity, the constant development of the exoplanet instrumentation is now motivated by the search for life. After decades since the first exoplanet detection, today, more than 3500 exoplanets are confirmed and the detection era is moving towards an era of exoplanets characterization. Radial-velocity spectrographs are now at the state of the art in the visible domain and near-infrared precise radial-velocity instruments are currently being developed. The interest for infrared wavelengths is motivated by the recent discovery of the very high occurence rate for exoplanets around M-Dwarfs. The smaller M-Dwarf size compared to Solar-type stars makes of the M-Dwarfs, solid candidates for the search for Earth-size exoplanet in their habitable zone. The habitable zone being the distance of an exoplanet around its host star, whereH₂Oon its surface (if present) would be liquid.

Astroclimatic conditions, wavelength range, spectral resolution as well as the size of the telescopes play important role in the design of radial-velocity spectrographs. Most of the RV spectrographs are installed on 4 meter class telescopes and are working in seeing-limited conditions, however, a strong limitation for the adaptation of this instrumentation onto large telescope exists. Telescopes and radial-velocity spectrographs size issue as well as the technology proposed to overcome this problem (adaptive optics) are addressed in this PhD.

The first part of this work discusses the link between telescopes size and the size of the spectrographs when working in seeing-limited conditions. For a given resolution, the size of the telescope primary diameter will drive the diameter of the light beam inside the spectrograph and thus will affect the overall instrumental size, cost and complexity.

The second part of this thesis presents an alternative way of designing spectrographs using adaptive optics. Using an AO system will allow to reduce the telescope size impact on the design of high-resolution spectrographs. Generalizing the problem as much as possible, this study conduced in a first author publication (submitted and currently in revision) where important results were found. An adaptive optics system dedicated for spectroscopy applications has not the same metric of interest as, for instance, imaging applications. The goal of this

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fiber (which is essentially the same as demonstrated in this thesis). The use of an AO system is therefore advantageous for many spectroscopic applications.

In addition, a direct application to the use of AO for high-resolution spectroscopy is presented with the NIRPS instrument. NIRPS is an AO-assisted high-resolution radial-velocity spectrograph operating in the near-infrared and aiming the 1 m/s precision. This instrument will be (soon) installed on the ESO 3.6m Telescope allowing simultaneous observations with HARPS.

Thanks to the generic study presented previously, the relevant AO parameters were explored for the case of NIRPS. The design of the AO module conduced also in a first author publication where the essential points are addressed. The NIRPS AO module, is able to couple 50% of the star light in median seeing condition at La Silla, for star magnitude up to I=12, and consists of a Shack-Hartmann wavefront sensor (with 14x14 subapertures) coupled to a deformable mirror (with 15x15 actuators) operating at a frequency of 250Hz up to 1kHz. Moreover, the hardware components of the NIRPS AO module were characterized with a dedicated test bench. The results obtained on the bench are in agreements with the simulation performed in the design phase of the AO module. Using astandardcomputer (i5, 3.3 GHz), the loop was closed at a frequency of 800 Hz with a 2 ms loop delay. Other useful tools for the future NIRPS operations on sky were developed, tested and validated on the bench.

Furthermore, other specific application cases with the use of AO for spectroscopy were explored and presented in the thesis. Severals already existing spectrographs such as SOPHIE, CORALIE, and ESPRESSO could benefit of an AO system. Such a system could either significantly improve the coupling efficiency into the already existing fibers or conduce to new observing modes using a fiber size optimized with respect to the AO. I also can mentioned my contribution to a slightly different application case of the adaptive optics which consist of combining the high-contrast and the high-resolution techniques.

Conclusion as well as an outlook of this thesis are finally given. The objectives of the thesis were fully accomplished and the path to a next generation of AO-assisted high-resolution spectrographs is now traced.

Key words: Instrumentation, Telescopes, High Resolution Spectroscopy, Adaptive Optics, Radial Velocities, Exoplanets

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Résumé

Les progrès de l’instrumentation astronomique ont toujours été suivis de découvertes ma- jeures. La première détection d’une exoplanète était en effet due à un certain nombre de techniques instrumentales améliorant la précision des mesures de vitesse radiale stellaire.

Tentant de répondre à l’une des questions fondamentales concernant l’unicité de l’humanité, le développement constant de l’instrumentation dans le domaine des exoplanètes est désor- mais motivé par la recherche de la vie. Après des décennies depuis la détection des premières exoplanètes, plus de 3 500 exoplanètes sont aujourd’hui confirmées et l’ère de la détection s’achemine vers une ère de caractérisation. Les spectrographes à vitesse radiale (VR) sont maintenant à la pointe de la technologie dans le domaine visible et des instruments à vitesse radiale précise dans le proche infrarouge sont en cours de développement. L’intérêt pour les longueurs d’onde infrarouges est motivé par la découverte récente de très haut taux d’occur- rence pour les exoplanètes autour des Naines-M. La taille plus petite des Naines-M comparée aux étoiles de type solaire en fait d’intéressant candidats pour la recherche d’exoplanètes de la taille de la Terre dans leur zone habitable. La zone habitable étant la distance d’une exoplanète autour de son étoile hôte, oùH2Oà la surface (si présent) serait liquide.

Les conditions astroclimatiques, la couverture en longueurs d’onde, la résolution spectrale ainsi que la taille des télescopes jouent un rôle important dans la conception des spectrographes à vitesse radiale. La plupart des spectrographes à VR sont installés sur des télescopes de classe 4 mètres, et fonctionnent dans un régime ditseeing-limited. Cependant, il existe une forte limitation pour l’adaptation de cette instrumentation sur de grand télescopes. La question de la taille des télescopes et des spectrographes à vitesse radiale, ainsi que la technologie proposée pour surmonter ce problème (optique adaptative) sont abordés dans cette thèse.

La première partie de ce travail traite du lien entre la taille des télescopes et la taille des spectrographes lorsque les conditions sontseeing-limited. Pour une résolution donnée, la taille du diamètre primaire du télescope déterminera le diamètre du faisceau lumineux à l’intérieur du spectrographe et affectera donc la taille globale de l’instrument, son coût et sa complexité.

La deuxième partie de cette thèse présente une nouvelle approche pour la conception des spectrographes en utilisant l’optique adaptative (OA). L’utilisation d’un système OA permet de réduire l’impact de la taille du télescope sur la conception des spectrographes à haute résolution. Généralisant le problème autant que possible, une étude a été réalisée et a conduit

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spectroscopie n’a pas la même métrique d’intérêt que, par exemple, les applications d’ima- gerie. Le but de cette publication est de présenter les paramètres pertinents et impliqués dans la conception des systèmes OA et leur comportement vis-à-vis de la métrique d’intérêt : l’énergie encerclée ou le couplage avec une fibre (ce qui est essentiellement la même chose, ceci étant démontré dans cette thèse). L’utilisation d’un système OA est donc avantageux pour de nombreuses applications spectroscopiques.

En outre, une application directe à l’utilisation de l’OA pour la spectroscopie haute résolution est présentée avec l’instrument NIRPS. NIRPS est un spectrographe à vitesse radiale assisté par OA, fonctionnant dans le proche infrarouge et visant une précision de 1 m/s. Cet instrument sera (bientôt) installé sur le télescope ESO de 3,6 m permettant des observations simultanées avec HARPS. Grâce à l’étude générique présentée précédemment, les paramètres OA pertinents ont été explorés dans le cas de NIRPS. La conception du module OA a également été présentée dans une publication en premier auteur où sont abordés les points essentiels. Le module NIRPS OA peut coupler 50% de la lumière de l’étoile en condition moyenne deseeing à La Silla, pour une magnitude jusqu’à I = 12, et consiste en un analyseur de front d’onde Shack-Hartmann (avec 14 x 14 sous-ouvertures) couplé à un miroir déformable (avec 15x15 actionneurs) fonctionnant à une fréquence de 250Hz à 1kHz. De plus, les composants du module NIRPS OA ont été caractérisés avec un banc de test dédié. Les résultats obtenus sur le banc sont en accord avec les simulations effectuées lors de la phase de conception du module OA. En utilisant un ordinateurstandard(i5, 3,3 GHz), la boucle a été fermée à une fréquence de 800 Hz avec un délai de boucle de 2 ms. D’autres outils utiles pour les futures opérations de NIRPS sur le ciel ont été développés, testés et validés sur le banc.

De plus, d’autres cas d’application spécifiques avec l’utilisation de l’OA pour la spectroscopie ont été explorés et présentés dans cette thèse. Plusieurs spectrographes déjà existants tels que SOPHIE, CORALIE et ESPRESSO pourraient bénéficier d’un système OA. Un tel système pourrait soit améliorer de manière significative l’efficacité du couplage dans les fibres déjà existantes, soit conduire à de nouveaux modes d’observation utilisant une taille de fibre op- timisée. Je peux également mentionner ma contribution à un cas d’application légèrement différent de l’optique adaptative consistant à combiner les techniques de haut contraste et de haute résolution spectrale.

La conclusion ainsi que la perspective de cette thèse sont finalement données. Les objec- tifs de la thèse ont été pleinement atteints et le chemin vers une nouvelle génération de spectrographes haute résolution assistés par OA est maintenant tracé.

Mots clefs :Instrumentation, Téléscopes, Spectroscopie à haute résolution, Optique Adapta-

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List of Figures

1.1 Evolution of the radial-velocity measurement error over time. . . 5

1.2 Portion of a high-resolution Solar spectrum taken with the HELIOS-HARPS instrument. . . 7

1.3 ESPRESSO raw stellar spectrum obtained the 27 of November 2017 during the first light. . . 9

1.4 Reflexion grating spectrograph layout. . . 9

1.5 Grating equation illustration. . . 11

1.6 Projection of the spectrograph’s slit onto the detector. . . 12

1.7 HARPS échelle-grating temperature over a period of 20 days. . . 14

1.8 Fabry-Pérot and ThAr spectra obtained with HARPS. From Wildi et al. (2010). . 15

1.9 Double scrambler optical layout. From Brown (1990). . . 16

1.10 (a) HARPS optical layout. (b) HARPS Spectral format.. . . 18

1.11 (a) HARPS vacuum vessel. (b) HARPS grating. . . 18

1.12 (a) SPIRou optical layout. (b) SPIRou spectral format.. . . 19

1.13 Moffat versus Gaussian seeing limited PSF energy profile. . . 21

1.14 Illustration of the Equation 1.13 for an R4 échelle grating. . . 21

2.1 La Nuit étoilée, Van Gogh, 1889. (b) Jupiter Great Red Spot. . . . 25

2.2 (a) Typical Earth atmosphere temperature profile. (b) MedianC_N² profile at Cerro Paranal, Chile. . . 26

2.3 Illustration of the anisoplanatism effect. Credits: ESO. . . 29

2.4 Surface plots of the Zernike polynomial sequence up to 10 orders. . . 32

2.5 (a) Covariance matrix for the 200 first Zernike modes. (b) Variance of the modes. 33 2.6 Left:pupil function. Right: Associated diffraction PSFs. . . 36

2.7 NASA ADS query results for the keyword: Adaptive Optics.. . . 38

2.8 AO image binary stars in open and closed loop obtained with COME-ON. . . . 39

2.9 Left:AO image of Neptune obtain with the VLT AOF.Right:Comparable image taken by Hubble. . . 40

2.10 Adaptive optics system principle, from Davies & Kasper (2012).. . . 40

2.11 Residual wavefront rms computed from Noll (1976). . . 42

2.12Left:Simulated instantaneous atmospheric wavefronts.Right:Associated PSFs. 43 2.13 Types of wavefront sensor.. . . 44

2.14 Comparison between the pyramid and the Shack-Hartmann WFS. . . 46

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2.15 (a) SPHERE 41x41 actuator stacked array DM. (b) Subaru 188 electrode bimorph

DM. . . 47

2.16 Block-diagram representing an AO system. From Madec (1999). . . 48

2.17 Example of a Bode diagram for an open loop transfer function. . . 50

2.18 Closed loop transfer function examples. . . 50

2.19 Closed loop error transfer function examples. . . 51

2.20 Illustration of the cone effect. Credits: ESO . . . 53

3.1 Profile of the four fundamental wavefront errors. . . 59

3.2 Illustrative example of PSF intensity profiles.. . . 61

3.3 Illustrative example of PSF EE profiles. . . 61

3.4 Typical CAOS GUI, here is for the simulation of the NIRPS AO module. . . 64

3.5 Strehl ratio versus the diameter for 50% EE for differentD/r0(λ). . . 65

4.1 Simulated NIRPS planet population in the projected separation/contrast plane. 84 4.2 NIRPS Front End optical principle.. . . 87

4.3 (a)NIRPS Front End mechanical structure. (b) NIRPS Front End optical components. . . 88

4.4 (a) NIRPS spectrograph optical layout. (b) NIRPS spectral format. . . 89

4.5 HARPS (in bue) versus NIRPS (in red) optical layout at the same scale.. . . 89

4.6 Comparison between residual SR and EE in 0.4" diameter.. . . 91

4.7 Wavefront residual phase rms error for different NGS magnitudes. . . 91

4.8 Diameter for the EE=50% in function of the number of linear actuators.. . . 92

4.9 Typical NIRPS AO-corrected PSF profiles. . . 93

4.10 (a) Loop frequency impact. (b) Impact of the loop pure delay. . . 94

4.11 (a) Off-axis performances atλ=1.0µm. (b) Same as (a) atλ=1.8µm. . . . 94

4.12 Encircled energy in 0.4" versus wavelength for a I=12 NGS. . . 95

4.13 EE in 0.4" atλ= 950nm for various Zernike polynomials.. . . 96

4.14 EE for different external scales values (L0= [20m,100m,∞(noL0)] in color code). 97 4.15 (a) Peak to Valley mirror deformations with anL0of 20m. b) Same as (a) for an L0=100m. . . 97

4.16 Impact of the delay for different loop frequency (500Hz and 1kHz). . . 98

4.17 Compliance matrix coming from the NIRPS DM241 (High-speed version). . . . 99

4.18 Compliance matrix of the detector coming from the OCAM2K test report. . . . 100

4.19 NIRPS WFS and DM configuration at the telescope.. . . 101

5.1 NIRPS AO test bench optical layout. Credits: Nicolas Blind . . . 112

5.2 NIRPS AO test bench.. . . 112

5.3 Rejection transfer function of the Zernike mode number 3. . . 113

5.4 Same as Figure 5.3 but for the Zernike mode number 8. . . 114

5.5 Principle of the residual wavefront construction used to compute the PSF. . . . 114

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List of Figures

5.8 Strehl meter performance for different simulated AO PSFs. . . 117

5.9 (a) NCPA corrected PSF. (b) NCPA corrected PSF x and y profile. . . 118

5.10 Structure function of the phase mask measured using NIRPS WFS.. . . 119

5.11 Structure function of the phase mask measured using the HASO. . . 119

5.12 Wavefront decomposition principle illustrated for given random frame.. . . 121

5.13 Typical wavefront rms output coming from the turbulence generators. . . 121

5.14 Block diagram schema representing the control loop of the AO system. . . 122

5.15 Principle of the noise determination. . . 124

5.16 Principle of the optimal gain determination for a given mode. . . 125

5.17 Optimal gain obtained from the CAOS NIRPS telemetry. . . 126

5.18 (a) Optimal gains for I=12 performance. (b) Same as (a) for I=13 . . . 126

5.19 (a) Optimal gains performances for I=14 at 250Hz. (b) Optimal gains performances for I=14 at 100Hz. . . 127

5.20 Residual and corrected phase. . . 129

5.21 Closed-loop RTF for one frequency disturbance. . . 130

5.22 Picture of the two DC motors with eccentric masses used to generate vibrations on the bench. . . 131

5.23 (a) One frequency perturbation using the DC motor. (b) One frequency gener- ated with the DC motor and one via the DM. . . 132

6.1 Planet to star contrast in reflected light for known exoplanets. . . 134

6.2 (a) Simulated SPHERE PSF normalized in log scale. (b) Same as (a) but zoomed by a factor 5. . . 135

6.3 Proxima b simulated spectrum assuming 60 nights of observation on VLT with SPHERE+ESPRESSO. . . 136

6.4 (a) Picture of the 193cm telescope at OHP. (b) SOPHIE spectrograph. . . 137

6.5 Principle of the SOPHIE’s fiber injection module. . . 138

6.6 Atmospheric conditions at OHP. . . 139

6.7 Diameter for EE=50% in function of the number of linear actuators. . . 140

6.8 EE in a 3.0" fiber for different seeing conditions.. . . 140

6.9 EE in a 1.5" fiber for different seeing conditions.. . . 141

6.10 (a)The EULER telescope. (b) The optical layout of CORALIE . . . 146

6.11 Diameter for 50% EE as a function of the number of WFS subapertures. . . 148

6.12 (a) EE profile for a star magnitude of V=12. (b) EE profile for a V=12. . . 148

6.13 (a) Artist view of the ELT. (b) The optical system of the ELT. . . 150

6.14 HIRES layout and ray tracing of the BVRI module. From Oliva et al. (2018) . . . 151

6.15 Encircled energy profiles for a seeing of 0.8". . . 152

6.16 (a) AO corrected PSF for I=6. (b) Same as (a) but for a star magnitude of I=14. . 153

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List of Tables

1.1 List of new precise RV spectrographs. Adapted from Wright & Robertson (2017). 8 2.1 Zernike-Kolmogorov residual errors for up to 20 corrected modes, from Noll

(1976).. . . 41

4.1 Difference in detecting an Earth twin around the Sun and a M5V star. . . 82

4.2 Summary of the expected performance of the NIRPS AO module. The values are the mean EE (1.0-1.8µm) for different NGS magnitude and seeing conditions.. 95

6.1 Used parameters for the simulation. . . 143

6.2 Summary of the simulations results for a seeing of 1.5" and 2.0". . . 144

6.3 Summary of the simulations results for a seeing of 2.5" and 3.0". . . 145

6.4 Used parameters for the simulation. . . 147

6.5 Summary of the expected performance for V=10 star with a 8x8 subapertures WFS at 500 Hz in median seeing conditions (0.9"). . . 149 6.6 Summary of the expected performance for the ELT-AO in seeing conditions of 0.8".153

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Introduction

In June 2014, the National Centers of Competence in Research (NCCR) PlanetS was established by the Swiss National Science Foundation (SNSF) for a period of four years, and depending on the results, renewable two additional times. The Swiss astronomy community in the field of the exoplanets was supported by the Swiss Confederation, with the goal of bringing together researchers from the Universities of Berne (Leading House), Geneva (co-Leading House), and Zürich as well as ETHs Zürich and Lausanne. This thesis contributes to one of the key aspects needed for addressing a core goal of the NCCR PlanetS: pushing forward the expertise of the Swiss astronomy community in the era of exoplanet discovery and characterization.

The development of instrumentation in the exoplanet field is crucial in the quest for habitabil- ity and precise radial-velocity spectrographs remain one of the key tools to characterize the exoplanets. The Observatoire Astronomique de l’Université de Genève is well-established in designing and building such instruments for the community. However, as telescopes gradually get bigger and better, there is a need to reconsider the classical design of such instruments for the community. The goal of this thesis was to explore new and alternative radial-velocity spectrographs designs, using adaptive optics.

The thesis is organized as follows. Chapter 1 introduces the problem linking the high resolution spectrographs and telescopes, as well as, the consequences for the next generation of instruments to be installed on extremely large telescopes. Chapter 2 presents the theoretical aspects needed to understand the solution proposed to overcome the instrumental issue.

Features such as to the atmospheric turbulence, generating images in presence of turbulence and adaptive optics, are approached in this chapter. The core of the thesis, which is the impact of adaptive optics on the design of the spectrographs, as well as, the ways to design an adaptive optics system dedicated for high resolution spectroscopy, is addressed in chapter 3. Chapter 4 is an application case of the general approach presented in the previous chapter. The NIRPS instrument is AO-assisted and can be see as a first example of the use of adaptive optics for high resolution spectroscopy. Chapter 5, presents the laboratory characterization of the NIRPS AO module and development of tools that will be used for NIRPS operation on sky. A collection of different instrumental cases, for which I studied how using adaptive optics would benefit them is presented in chapter 6. Finally, I conclude and give an outlook in chapter 7.

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1 Radial Velocity Spectrographs in the Era of Extremely Large Telescopes

One of the main drivers of this thesis is the following question:What would be the benefits of using an adaptive optics to couple the light of a telescope into a radial-velocity spectrograph ? Before answering to this question, for instance, several other induced questions have to be addressed:

• What is a radial-velocity spectrograph and which are the relevant parameters ?

• What is the impact of the telescope size on a spectrograph ?

• How do we couple/fed the light of a telescope efficiently to a spectrograph ?

All these questions arise naturally in an era where the exoplanet research is pushing the instrumental precision to new limits. Ultra-stable and high-resolution spectrographs are required to detect and characterize exoplanets using radial-velocity (RV) technique. Today, most of the radial-velocity spectrographs are mounted on 4 meter class telescopes. The telescope size plays an important role in the design of such spectrographs and is a strong limitation for the adaptation of this instrumentation on 8-10 meter class telescopes and even greater for the next generation of 40 meter class telescopes. The design of RV spectrographs for large telescopes have to be completely reviewed and have to differ from the 4 meter telescopes mainly due to manufacturer’s limitations on the hardware (optics, dispersive elements, and detectors) and simply because of the instrument overall size and costs.

Furthermore, with current and future exoplanet dedicated space missions such as KEPLER (Borucki et al.,2010), TESS (Ricker et al.,2016), CHEOPS (Broeg et al.,2013) and PLATO (Rauer et al.,2014), thousands of candidates will be revealed and become accessible for follow-up.

These missions are using the transit technique to detect exoplanet candidates, however, only the radius and the period are accessible. To confirm and obtain the density of these candidates, also the mass of the planet must be measured. One and probably the most effective technique, is the one of measuring precise stellar radial velocities. Therefore, the exoplanet community looks for high-fidelity RV spectrographs to do massive follow-up and candidates confirmation.

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In addition, there is now a strong interest to observe M-type stars with RV spectrographs, however, the visible wavelengths are a limitation. For M-type stars, most of the stellar flux is accessible in the near-infrared. Up to now there are only few near-infrared RV spectrographs, for instance: CARMENES (in operation, northern hemisphere), GIARPS (in operation, northern hemisphere), IRD (in operation, northern hemisphere), SPIRou (in commissioning, northern hemisphere), iSHELL (in operation, northern hemisphere), PARVI (planned for the end of 2019, northern hemisphere) and NIRPS (planned for the end of 2019, southern hemisphere), see Table1.1for details and references.

To understand all the challenges related to these questions, severals important aspects have to be introduced to the reader. For which I will firstly present a short introduction on the spectroscopy and RV instrumentation used for the detection and characterization of exoplanets.

Some of the state of the art RV spectrographs (HARPS for the visible and SPIRou for the near infra-red) are presented in order to well understand their designs. The requirements driven by RV spectrographs are discussed and finally a first order comparison between seeing-limited and AO coupled RV spectrographs is made.

1.1 Spectroscopy

The history of spectroscopy began with Isaac Newton in 1672 when he describes an experiment where the sunlight passes through a small hole followed by a prism. He observed that the sunlight is made of a mixture of all the colors of a rainbow. Later, with the work of Joseph von Fraunhofer, this technique became more precise and accessible until reaching today a significant role on different scientific domains such as chemistry, physics, and astronomy. In astronomy, spectroscopy consists of measuring the spectra of astronomical objects such as planets, stars, nebulae, galaxies, and active galactic nuclei, supernovae, etc.. The power of spectroscopy resides in the fact that light emitted from the objects contains a considerable amount of information. From a stellar spectrum, many properties can be extract, such as stellar chemical composition, stellar effective temperature, density of interstellar medium, stellar mass, stellar distance, stellar luminosity, and the relative stellar motion using radial- velocity measurements (see Section1.1.1). Moreover a spectrum also contains information coming from the Earth’s atmosphere.

1.1.1 Radial Velocities

Good reviews on the the importance of stellar radial velocities in exoplanet science can be found inLovis & Fischer(2010), Hatzes(2016) andBenatti(2018). Starting in the19th century, this technique was firstly used to demonstrate that the Doppler theory applies to electromagnetic waves propagation from stars. The change in colors observed by a stars moving toward or forward the line of sight is generally called aDoppler shift. It is used as an

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1.1. Spectroscopy

needed. The Doppler shift is computed from the displacement of the stellar spectrum and gives direct access to the radial velocity of the star, i.e. its velocity relative to Earth projected along the line of sight. If influenced by the presence of a companion orbiting the star, the RV changes can in turn be converted using Kepler’s equation into orbital parameters such as a lower limit for the planetary massempsini, where i is the orbital inclination along the line of sight, the period of the planet’s orbit and its eccentricity.

The first detection of an exoplanet was made thanks to this technique,Mayor & Queloz(1995).

However, it took a long time to develop instruments of precision sufficient for such a discovery.

On Figure1.1the evolution of the RV measurement error over time as well as examples of RV signals induced by planets of different mass and period. Starting in the fifties, spectrographs equipped with photographic plates had the precisions of severals km/s. The subsequent impressive evolution of the precision is mainly due to majors developments on electronic detectors. Nevertheless, it is also due to different techniques such as the usage of (wide-band) cross-dispersed échelle spectrographs and spectral calibration and reference techniques to control instrumental effects. Today the best radial-velocity spectrographs are able to reach precisions below the 1 m/s.

Figure 1.1: Evolution of the radial-velocity measurement error over time. The horizontal lines mark the reflex motion of a Jupiter, a Neptune and a Super Earth (5M_⊕) mass companions orbiting at 1 AU around a solar mass star. Adapted fromHatzes(2016).

Historically, one of the first RV dedicated spectrograph was the radial-velocity spectrome- ter at the coudé reflector of the Cambridge 36-inch telescope,Griffin(1967). Followed by

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CORrelation-RAdial-VELocities (CORAVEL,Baranne et al.(1979)), using awhite pupildesign firstly introduced byBaranne & Duchesne(1972) with an échelle grating as the main dispersive element to achieve high resolution. This first generation of RV spectrographs delivered 200-500 m/s precision. Later, using the same design with ELODIE,Baranne et al.(1996) achieved a precision better than 15 m/s.Pepe et al.(2014),Fischer et al.(2016) andWright & Robertson (2017) reviewed the present and future radial-velocity spectrographs. The Table1.1shows a non-exhaustive list of the new and forthcoming precise RV spectrographs with references in it.

1.2 RV Spectrographs

In principle, any spectrograph can provide spectra from which a measurement of radial velocities can be done. In practice, however, several instrumental parameters such as spectral resolution play an important role. Moreover, the spectral (stellar) lines have to be resolved and the number of observed stellar absorption lines maximized in order to maximize the information content and thus increase the RV precision,Bouchy et al.(2001). Consequently, high resolutionR=_∆λ^λ Ê50000 and large band width are fundamental requirements for precise RV spectrographs. The intrinsic stability of the instrument as well, e.g. variations in pressure and temperature of the opto-mechanical structure. Indeed all these effects can change the refractive index of the air as the light passes inside the spectrograph and therefore will affect position of the spectrum on the scientific detector and thus the measured radial velocity.

Ergo, the spectrographs must be installed in a controlled environment. The calibration and the wavelength solution also have to be very precise, in order to be able to assign to each detector pixel a precise and possibly also accurate wavelength which should be valid for any subsequent astronomical measurement. Since however this can be hardly guaranteed at this level of stability, a simultaneous spectral reference in order to track the possible instrumental drifts is also required. Also, it should be recalled that a spectrograph is an optical system that forms the (monochromatic) image of its entrance (white) slit on the scientific detector. The RV measurements is nothing else as a measurement of the photo-center of this image. If the stability of the spectrograph illumination is compromised during an exposure, it could induce photo-center shifts and thus mimic RV signals. Nevertheless, I would like to summarize a few basic characteristics of high-precision spectrographs that will be relevant for my further work:

• High resolution:R=_∆λ^λ Ê50000

• Wide and continuous wavelength coverage

• Stabilized instrument: pressure and temperature control, stable opto-mechanics, fixed configuration, etc.

• Precise calibration and availability of simultaneous reference or absorption cells

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1.2. RV Spectrographs

Telescope size, magnitude limit, as well as, astroclimatic conditions also heavily constrain the design of RV spectrographs. In the following, I shall discuss how these elements and parameters influence the design of the instrument and finally determine its size, costs and complexity.

1.2.1 Resolution and Etendue

An astronomical spectrograph is fed by the telescope though its slit or fiber located in the focal plane of the telescope. After the slit (or at the output of the optical fiber), the light beam is collimated and prepared for dispersion. The collimated light then passes through a disperser and is eventually focused through acameraonto a detector. The detector is formed by either a 1-D or 2-D array of pixels (individual small detectors) which record, due to their different position, different colors (wavelengths) of the dispersed beam. By its concept a spectrograph essentially forms a monochromatic image of the slit/fiber entrance over its wavelength range at a given resolution. Figure1.2and1.3show examples of astronomical high resolution spectra obtained with different spectrographs (see respective captions). Along the continuous stellar spectrum we can distinguish darker features (negativeof slit/fiber images) corresponding to absorption spectral lines at different wavelengths.

Figure 1.2: Portion of a High resolution Solar spectra taken with the HELIOS-HARPS instrument. Credits: Xavier Dumusque

Since high resolving power is a major requirement, the use of an échelle grating as the dispersive element seems to be the most adequate design for a compact and powerful instrument.

On Figure1.4the working principle of a grating spectrograph is shown, we can distinguish the main elements of the instrument: the telescope, the slit/fiber, the grating and the detector.

Generally, after the main dispersion of the light into several spectral orders by the échelle grating, they all are superimposed and need to be separated in the, so-called, cross-dispersion

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Instrument DateoffullWavelengthTelescopeExpectedReferenceoperationrange[µm]aperture[m]precision[m/s]

SALT/HRSearly20180.37-0.8910É3Crauseetal.(2014)MINERVA11/20160.48-0.694x0.70.9Swiftetal.(2015)Veloce20200.38-0.954É1Gilbertetal.(2018)PFS2mid20180.38-0.696.5∼0.5Craneetal.(2010)PARAS-2mid20200.38-0.692.50.5–HARPS-3early20200.38-0.692.5É0.5Thompsonetal.(2016)TOU10/20170.38-0.901.27∼0.8Geetal.(2016)iSHELL10/20161.10-5.303É5Rayneretal.(2016)MINERVA-R3/20180.82-0.920.7É1Sliskietal.(2017)MAROON-X5/20190.50-0.908.2É1Seifahrtetal.(2016)iLocater12/20190.97-1.272x8.2É0.7Creppetal.(2016)PARVIfall20191.25-1.805.10.3goal–NIRPSfall20190.98-1.803.6É1Wildietal.(2017)SPIRou8/20180.98-2.353.6É1Donatietal.(2017)HPF11/20170.81-1.29∼101Mahadevanetal.(2014)IRD10/20170.97-1.758.21Kotanietal.(2014)CARMENES01/20160.52-1.713.51Quirrenbachetal.(2014)GIARPSmid20180.34-2.453.61(vis),3(NIR)Claudietal.(2017)NEIDmid20190.38-1.003.5∼0.3Schwabetal.(2016)EXPRES12/20170.38-0.684.3É0.3Fischeretal.(2017)ESPRESSO1/10/20180.38-0.78(4x)80.1Pepeetal.(2013)KPF1/20200.44-0.85100.5Gibsonetal.(2016)

Table1.1:ListofnewpreciseRVspectrographs.AdaptedfromWright&Robertson(2017).

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Figure 1.3: ESPRESSO raw stellar spectra obtained the 27 of November 2017 during the first light. On the zoomed part, we can see the stellar spectrum (continuous lines) and the Fabry-Pérot etalon as the simultaneous reference (dots). Each spectrum is doubled due to a special optical device, the Anamorphic Pupil Slicer Unit (APSU,Conconi et al.(2013)). Credits:

ESPRESSO team.

Figure 1.4: Reflexion grating spectrograph layout.

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(perpendicular) direction in order to spread the spectrum on the scientific detector.

Resolving power

A spectrograph analyses the spectral content of light by separating (dispersing) the different colors (wavelengths). The dispersive element in the spectrograph, in this case the échelle grating, converts wavelengths into beam direction. In order to avoidconfusion, the incoming beam must therefore be prepared, such that all the wavelengths have initially the same propagation direction; in other words, the beam must be collimated. However, in practice the collimated beam is never perfectly collimated. This can be due, for instance, to the limited diameter of the beam which produces through diffraction a beam divergence

δφ=1.22λ

h, (1.1)

whereλis the wavelength andhis the collimated beam diameter as shown on Figure1.4.

Another reason for beam divergence is the finite size of the slit, which produces an angular divergence

δΘ= s f1

(1.2) wheresis the physical slit/fiber size andf1is the focal length of the collimator. in principle all the light coming from the same direction, and thus corresponding to one single color, into only singlepointor position of the detector. In practice however, and due to the angular divergence caused by the finite diameter or slit/fiber size is then translated into an image of finite size d x=f2δΘord x=f2δφ, depending on which of the two divergence causes is dominant, and wheref₂is the focal length of the camera.

Using the above definitions, it is then possible to express the resolution of the spectrograph.

For a given angular dispersionD=dβ/dλ, the resolving powerR_maxdefined as the maximum spectral resolution obtainable for a slit/fiber sizes=0, thus the angular divergence is limited by diffraction due to the limited beam diameter. This provides a resolving power of

Rmax= λ δλ= λ

δφ/D = λ δφ

dβ

dλ (1.3)

In most astronomical spectrographs the slit will have however a considerable size, since the goal is to collect most of the light in the (seeing-limited) stellar image in the focal plane of the spectrograph. For this reason it can be easily verified that the divergence caused by the finite slit width is dominant and that the effective resolving power becomes

R= λ δλ= λ

δΘ/D = λ δΘ

dβ

dλ (1.4)

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Dispersion

The main purpose of a spectrograph is to spatially disperse the light by wavelength; this is the role of the grating.

Figure 1.5: Illustration of the geometry of diffraction in the case of planar wavefronts. The parallel rays, labeled 1 and 2, are incident on the grating one groove spacingd apart and are in phase with each other at wavefront A. Upon diffraction, the principle of constructive interference implies that these rays are in phase at diffracted wavefront B if the difference in their path lengths,dsinα+dsinβ, is an integral number of wavelengths; this in turn leads to the grating equation. FromPalmer & Loewen(2005).

The grating equation governs the angular repartition of the constructive interferences when light of wavelengthλis diffracted from a grating. This equation is illustrated on Figure1.5, whereαis the incident angle between the collimated beam an the grating andβthe reflected angle,dis the distance between the grooves andρ=1/dis the groove density. FromPalmer &

Loewen(2005), the grating equation is

mρλ=sinα+sinβ , (1.5)

wheremis the diffraction or spectral order, and is an integer. Assuming the incident angleα constant and by differentiating the grating equation, we can express the angular dispersionD as

D=dβ dλ= mρ

cosβ (1.6)

At a given wavelengthλand orderm, the linear dispersion can be expressed as dλ

d x =dλ dβ

dβ

d x = cosβ mρf2

(1.7)

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Etendue

Now let me introduce a fundamental optical property known as theconservation of the étendue.

The étendueEis defined as the product of the area of the source and the solid angle that the system’s entrance pupil subtends as seen from the source. Equivalently, and from the system point of view, it is the areaSof the entrance pupil times the solid angleΩthe source subtends as seen from the pupil.

E=SΩ[m²st er ad i ans] (1.8)

whereΩ=4πsin(θ/2)²andθis the half-angle of the circular cone with its vertex on a point on the surface of the source.

Figure 1.6: Projection of the spectrograph’s slit onto the detector.

This quantity has to be conserved in all optical systems and without this, a loss of photons will occur in the system. Using the conservation of the étendue it is possible to calculate the size of the image of the slit/fiber on the spectrograph’s detector a shown on Figure1.6. In this case, the conservation of the étendue appears in the form:θs=θ⁰s⁰, whereθ=D_T/f_T and θ⁰=D2/f2. The image of the slit/fiber is therefore defined as follows

s⁰=sθ θ⁰=sF₂

FT

(1.9) for the so-called F-number definitionFi=fi/Di. It is now possible to expressδλ(the width of the image of the slit in wavelength units) as follows

δλ= µdλ

d x

¶

s⁰= cosβ mρf2

sF2

FT =cosβsDT

mρD2fT = s

mρFTW (1.10)

whereW is the length of the intersection between the the collimated beam and the plane of the grating defined as

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Defining the resolution as R= λ

δλ=mρλFTW

s (1.12)

Assuming a system inLittrow configuration, whereα=βand using the grating equation; it is now possible from the projection of the slit/fiber on sky (s=φfT) and the conservation of the optical étendue between the telescope and the spectrograph to establish a relation linking important instrumental parameters such as the effective resolving powerRmax, the blaze angleβ, the slit/fiber size projected on skyφ, the telescope diameter sizeDT and the beam diameter sizeh=D₂inside the spectrograph

Rmax=2·t anβ·h φ·DT

(1.13)

It is from this equation that the first reflections and the motivations of this thesis have origi- nated, hence the importance to take the time to explain the implications of such a relation.

The main point is that for a given resolution and a given échelle grating blaze angleβ, the size of the collimated beam is directly linked to the size of the telescopes primary mirror. The size of a spectrograph, its optics and the échelle grating are driven by the collimated beam diameter h. Therefore, increasing the telescope size while keeping the same spectral resolution implies an increasing beam size which drives a greater spectrograph volume footprint. However, it is difficult and very expensive to increase the beam size drastically, the limitation coming from the of the optical elements and in particular the échelle grating. Indeed, the manufacturer capabilities due to the ruling machines and the replica process clearly limits the size of such optical elements (seePalmer & Loewen(2005) for more details). The presented equation implies therefore, a trade-off between spectrograph size, spectral resolution, and slit efficiency for the design of a spectrograph.

1.2.2 Stabilized environment

The stabilized environment can be achieved using different strategies. One method consists in using a vacuum vessel stabilized in temperature and pressure. Temperature stabilization is required at the order of the milli Kelvin to reach 1 m/s. On Figure1.7the HARPS échelle grating temperature measured over a period of 18 days is shown. We can notice the extreme stability reached with variations up to 3-5 milli-degree with a rms of 1 milli-degree. Most modern spectrograph aiming at extreme precision follow the path of HARPS by adopting a design concept ensuring the highest-possible thermo-mechanical stability of the instrument.

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Figure 1.7: HARPS échelle grating temperature for a period of 20 days (1.08.2018-20.08.2018) corresponding to more than 1500 measurements. Note that the temperature sensor has a resolution of 1 milli-degree.

1.2.3 Calibration and simultaneous reference

The calibration of the instrument plays an important role on the RV measurement. Its goal is to transform detector pixel position into a wavelength. The so-called wavelength solution is generally performed using arc lamp spectra. Thorium-neon (ThNe) and Thorium-argon (ThAr) hollow-cathode lamps are the standard for wavelength calibration of visible astronomical spectrographs. This is due to the large number of spectral features over the visible and near- infrared domains in addition to the narrow and highly symmetric line profile. In refer here to Lovis & Pepe(2007) andCoffinet et al.andCersullo et al.for details on how the wavelength calibration is performed and has been improved over time in the case of HARPS.

Once the calibration is done, the instrument will perform measurements despite the fact that, the instruments generally maydriftand suffer from a shift or distortion of the wavelength scale (wavelength solution). If not controlled or measured, these shifts in wavelength solution will directly produce afakeradial-velocity change in the observed target and heavily affect the measurement. In order to remove this effect on (unstabilized and slit-fed) spectrographs, Griffin & Griffin(1973) proposed a solution: pass the starlight through an absorbing medium before the entering of the spectrograph. The absorbing medium will superimpose spectral absorption line on the stellar spectrum, and both spectra willseethe same instrumental profile. Therefore, the absorption line reference will suffer the same instrumental shifts and distortions as the stellar spectrum. Theabsorbing celltechnique has been successfully used by different teams (Campbell & Walker,1979;Marcy & Butler,1992) to achieve precisions better than 3 m/s (Butler et al.(1996)), and is today considered to be able to achieve sub-m/s

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Seemann et al.(2014). Using this technique holds a note worthy consequence nonetheless: the spectral band width and the overall throughput of the instrument are significantly reduced. An alternative technique has been proposed and employed successfully to overcome this problem, thesimultaneous referencetechniqueBaranne et al.(1996). The idea is to use a second fiber coming from a spectral reference source and inject it directly into the spectrograph in order to create a second spectrum on the detector simultaneously alongside the stellar spectrum. Being present on all raw frames both the calibration and the scientific exposures, the simultaneous spectral reference will be able to track possible drifts of the spectrograph and allow us to correct for the wavelength solution. The simultaneous reference does not affect the throughput of the instrument, however, certainly increases the demand of pixels on the detector. Also, this technique requires a fiber feed (it won’t work on a slit spectrograph, since the illumination of the spectrograph by the stellar object will be affected by strong motions not monitored by the simultaneous reference) and requires the continuous operation of a spectral lamp. At the beginning it was the Th-Ar calibration lamp itself that was used during observations, but recently the usage of Fabry-Pérot etalon has been adopted to improve photon precision and safethe high-purity metallic thorium lamps, which are not anymore available on the market, in visble (Wildi et al.,2010) or in the near infraredCersullo et al.(2017) is promising. On Figure1.8Fabry-Pérot and ThAr spectra are shown on the HARPS detector. The Fabry-Pérot spectrum is much richer than the thorium spectrum, therefore, being a better tracker of the instrumental drifts. The forthcoming laser frequency comb is also a promising technique, Obrzud et al.(2017).

Figure 1.8: Fabry-Pérot and ThAr spectra obtained with HARPS. FromWildi et al.(2010).

1.2.4 Spectrograph illumination stability

For a better stability of the spectrograph illumination optical fiber-feed instead of a slit illumination is chosen for the design of RV spectrographs. The fibers also allow to decouple the telescope and the spectrograph such that the spectrograph can be placed in a separate room where thermal control can be achieved in a gravity-invariant environment. As mentioned previously, fibers offer a good and efficient way of scrambling the light coming from the tele-

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scope, i.e. obtain a stable an uniform illumination of the fiber at the spectrograph’s entrance.

However, it is challenging to couple the star light into small fibers."It is like trying to put the light of a star coming from a few meters telescope into an hair, even if I have no more." Sir Pepe.

Due to the telescope tracking imperfection, vibrations or optics, an additional guiding system is generally used. It is made of a pierced-mirror and an imaging camera. The fiber is located in the the back of hole of the mirror. The system is coupled to a tip-tilt actuator working in closed loop.

A differential drift between the stellar and the reference spectrum can arise from a differential and varying illumination of the two fibers fed with the calibration/stellar and the simultaneous reference, respectively. Guiding errors, the seeing or variations of the pupil illumination (e.g., vignetting) can produce both near-field and far-field variations during an observation. To mitigate this illumination effect, the usage of a double scramblerBrown (1990) appears to be a necessity. Its principle is to invert the near-field and the far-field of the light beam using an optical device. Figure1.9shows the optical layout of such a device.

It remains important to have a good scrambling of the light for both the scientific light and

Figure 1.9: Double scrambler optical layout. FromBrown(1990).

the calibration/simultaneous-reference light (Chazelas et al.,2012), since all of them can be affected by illumination variations.

It should be recalled that a major limitation in precision for RV instrument remained for a long time the imperfect scrambling of the light by circular fibers. Using square and octagonal

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1.3. HARPS

a much better option to scramble the light beam and has become today a standard solution (HARPS-N, ESPRESSO, etc.).

1.2.5 The throughput

The throughput of an instrument is the ratio of the photons recorded by the scientific detector to the photons fed into the instrument within a given spectral bands. As an astronomical spectrograph is made of severals optical elements and due to imperfect reflections or trans- missions of these elements, a certain amount of light is lost. The throughput will indeed affect the limiting magnitude of the scientific target. As consequences, the throughput of the instrument has to be carefully studied and aimed to be as high as possible. The telescope size and the seeing condition of the observatory as well as the choice of the slit/fiber size are very important parameters, (see Section1.5). A strict minimum of optics is mandatory and the coupling of the telescope and the fibers have to be optimized to minimize the focal ratio degradation FRD. For precise RV spectrographs, the throughput is very low, generally below 10%. SeePepe et al.(2014) for a general discussion of spectrographs and their throughputs.

1.3 HARPS

The High-Accuracy Radial velocity Planetary Searcher (HARPS,Mayor et al.(2003)) is an

"instrument dedicated to the search for extrasolar planets with an unequalled precision of 1 m/s".

With more than then years of operation, this instrument remains the world reference in matter of precision. The recent discovery of a low mass planet candidate around Proxima was also made with HARPS data,Anglada-Escudé et al.(2016). Even more than only search for exoplanet it demonstrates also exoplanet atmosphere characterization capabilities,Wyttenbach et al.

(2015) andWyttenbach et al.(2017) as example.

HARPS is a high-resolution (R=115000) fiber-fed cross-dispersed échelle spectrograph installed on the ESO 3.6-metre telescope at La Silla, Chile. The field of view of the spectrograph?s fiber is 1.0". The spectral domain continuously covers the visible wavelengths from 0.38-0.69 µm. Its design is very similar to the other RV spectrographs by using a white pupil design and an R4 échelle grating (R4 define the blaze angleαof the grating as follow: tan(α)=4). Figure 1.10ashows the optical design layout of the HARPS spectrograph. The spectrograph is made of a triple pass parabola, an R4 échelle grating (840 mm x 214mm, with a blaze angle of 75^◦and a groove density of 31.6 gr/mm), a folding mirror, a cross disperser (FK5 grism, 257.17 gr/mm blazed at 480 nm), a refractive camera and a detector. To ensure the intrinsic stability of the instrument in temperature as well as in pressure, the optical bench is placed in a vacuum vessel, Figure1.11a.

Owing to upgrades of the instrument (laser frequency comb (LFC), octagonal fibers, data eduction software (DRS)), the HARPS precision is expected to reach close to or even better than 0.5 m/s for bright stars,Lo Curto et al.(2015). It should be noticed that before the

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installation of the Fabry-Perot etalon Wildi et al.(2010), the ThAr lamp was used for the simultaneous reference source.The optical fiber link of HARPS was upgraded in 2015 for octagonal fibers (Lo Curto et al.,2015). Further details regarding the calibration process of HARPS can be found inLovis & Pepe(2007) and Coffinet et al. submitted.

(a) (b)

Figure 1.10: (a) HARPS optical layout. The design is made of a triple pass parabola and a white pupil. (b) HARPS Spectral format. The gray rectangles represent a mosaic of two 2k4 CCDs.

(a) (b)

Figure 1.11: (a) HARPS vacuum vessel. (b) HARPS grating made of a mosaic of two replica of the ESO UVES (Dekker et al.,2000) grating.

1.4 SPIRou

The SpectroPolarimètre Infra-Rouge (SPIRou,Donati et al.(2017),Artigau et al.(2014)) is

"a near-infrared spectropolarimeter and a high-precision velocimeter optimized for both the detection of habitable Earth twins orbiting around nearby red dwarf stars, and the study of

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1.5. Seeing limited RV spectrographs

Hawaii. The spectrograph delivers a continuous high-resolution (R=75000) spectrum covering the 0.98 - 2.35µmrange. As the wavelength range goes beyond 2.0µm, fluoride (ZrF4) fibers are required to ensure a good transmission. The radial velocity precision is expected to beÉ1 m/s.

The spectrograph is made of one parabola, an échelle grating (R2), a train of cross disperser prisms (in double pass), a flat folding mirror, a refractive camera and a detector. The Figure 1.12ashows the optical design layout of the spectrograph. Its design differs from HARPS in severals points which are mainly the resolution, the wavelength range, the opto-mechanical design (grating, prisms in double path and the horizontal optical bench)

(a) (b)

Figure 1.12: (a) SPIRou optical layout. The design is made of a double pass parabola and a white pupil. Credits: SPIRou team. (b) SPIRou spectral format (4kx4k detector). FromArtigau et al.(2014).

1.5 Seeing limited RV spectrographs

Having a better understanding of what is a RV spectrograph and the impact of the telescope size on these instruments, I will define in the following more precisely what is the coupling and why AO can help in optimizing the spectrograph design. For seeing-limited RV spectrographs, and according to equation1.13, the fiber sizeφdepends on the telescope size. Typically, a fiber size corresponding to the median seeing value of the site is chosen; a value of 0.5 up to 2 arcseconds allows for the best example of astronomical observatory site seeing values. The seeing represents the full width at half maximum (FWHM) of the intensity profile of the long exposure point spread function (PSF) in presence of atmospheric turbulences (see Section 2.2.2for a precise definition of the seeing). By design, the spectrographs generally have a fiber size corresponding to this value. The coupling is the ratio of photons entering in the fiber with respect to the photons collected by the telescope. At first approximation level, a Gaussian profile for the seeing PSF is assumed. However, it appears from the study ofTrujillo et al.(2001) that a better model to fit the seeing limited profile is the Moffat function. Its intensity profile is

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given by

IMo f(A,r,α,β)=A· µ

1+³r α

´2¶_−β

(1.14) whereF W H M =2αp

2^1/^β−1. Trujillo et al.(2001) found an optimal value ofβ=4.765 for atmospheric seeing PSF profile. The difference between a seeing limited PSF using Gaussian and a Moffat approximation is illustrated on Figure1.13. While 50% of the energy is encircled at the FWHM with a Gaussian, only 42% is encircled considering a Moffat profile.

The choice of the fiber size depends on several aspects which are almost philosophical and related to the equation1.13. Figure1.13can help to understand the choice of slit/fiber size when the PSF has a seeing-limited profile. The diameter to collect around 50% of the PSF energy corresponds to the inflection point of the curves, thus collecting more energy will require larger fiber diameter. Losing approximately half of the stellar flux while maintaining a reasonable instrument size is often considered acceptable, however losing a greater percent- age is rarely accepted. Coupling more energy drives on the other hand large instrumental beam size for a given spectral resolution. The Figure1.14shows the fiber size impact on the collimated beam diameter for different spectral resolution and telescope sizes, assuming an R4 échelle grating and the equation1.13. It is important to notice that the overall spectrograph size and its optics are driven by the collimated beam diameter inside the instrument. As explained earlier, the beam size is critical in terms of feasibility, stability and costs of the instrument.

From an étendue point of view, the atmospheric turbulences will increase the size of the object image (this will be discussed at greater length in the next chapter). Conserving the energy will require a larger slit/fiber and will result in an increased size of the collimated beam in the spectrograph (resolution and grating blaze angle assumed fixed). Opposite, it is possible to reduce the slit/fiber size in seeing limited regime, however the downside is a reduction of the encircled energy in the slit/fiber. As I will demonstrate in this thesis, using an adaptive optic system can help in reducing the optical étendue of the telescope without affecting the overall throughput of the system. In others words, the FWHM of the PSF can be reduced using adaptive optics, therefore the fiber size of the spectrographs can be significantly reduced, increasing its stability, reducing instrumental complexity and costs, while allowing precise RV measurements with high throughput.

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1.5. Seeing limited RV spectrographs

Figure 1.13: Moffat versus Gaussian seeing limited PSF energy profile. For both functions the FWHM = seeing = 1.0".

Figure 1.14: Illustration of the Equation1.13for an R4 échelle grating. The colors represents different resolutions while the line style is for the fiber size.

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2 Atmospheric Turbulences, Image For- mation and Adaptive Optics

I presented in the previous chapter the problem of the telescope size for high resolution spectrograph working in seeing limited regime. To fight this issue I recommend the use of an adaptive optics system.

This chapter will introduce the general theory needed to understand the atmospherical turbulences as well as their impact on the image formation. The last part will convey how to compensate the turbulences for ground based observations using Adaptive Optics.

The relevant aspects of the turbulence theory needed to understand the principles and the behavior of an AO system are coming from reviews on the subject given byRoddier(1981), Fried(1994),Hardy(1998) andRoddier(1999).

2.1 Definition and notations

This section is dedicated to the definition of the mathematical tools used in this chapter.

2.1.1 Structure Function

For a random functionf, depending on a variablex, the structure function is defined as Df(ρ)=

|f(x+ρ)−f(x)|²®

(2.1) the operator〈〉is the mean value of this random process, assumed stationary. The covariance of f is

B_f(ρ)=

f(x)·f^∗(x+ρ)®

(2.2) the structure function and the covariance are linked by the relation

Df(ρ)=2£

Bf(0)−Bf(ρ)¤

(2.3)

Adaptive optics for high resolution spectroscopy

Thesis

Reference

Adaptive optics for high resolution spectroscopy

CONOD, Uriel Gwendal

CONOD, Uriel Gwendal. Adaptive optics for high resolution spectroscopy . Thèse de doctorat : Univ. Genève, 2018, no. Sc. 5300

URN : urn:nbn:ch:unige-1145145

DOI : 10.13097/archive-ouverte/unige:114514

Adaptive Optics for High Resolution Spectroscopy

T

Uriel C

Summary

Résumé

Contents

List of Figures

List of Tables

Introduction

1 Radial Velocity Spectrographs in the Era of Extremely Large Telescopes

1.1 Spectroscopy

1.2 RV Spectrographs

1.3 HARPS

1.4 SPIRou

1.5 Seeing limited RV spectrographs

2 Atmospheric Turbulences, Image For- mation and Adaptive Optics

2.1 Definition and notations