Giant telescopes: segments manufacturing with stress polishing 

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Instrumental needs for modern astrophysics

Searching for exoplanets and for life

Are we alone in the Universe? Answering this question would be an immense progress in our way to comprehend the Universe. The search for exoplanets has started in the 90’s at the Observatoire de Haute Provence, in France where the first exoplanet has been discovered, orbiting around the star 51Pegasus. This Jupiter-mass companion has been indirectly detected thanks to its influence on the host star [Mayor and Queloz, 1995]. Since this day, more than 700 exoplanets have been detected, most of them with indirect methods, such as transit, radial velocity or astrometry and a few with direct imaging (Figure 1.4) [Perryman, 2011].
The search for exoplanets illustrates well the synergy between Earth and Space based observato-ries. The two main space missions, CoRoT and Kepler, are detecting planet candidates and their follow-up with Earth spectrographs installed on large telescopes, such as HARPS and SOPHIE, allow their validation. Giant planet detection is also possible with high contrast and high angu-lar resolution imaging, and two new generation instruments, GPI [Macintosh et al., 2006] and SPHERE [Beuzit et al., 2010], are currently in development to exploit such techniques for the direct detection of exoplanets.
With an impressive array of tools, the field of exoplanets is in constant evolution, bringing new dis-coveries almost every day. But the detection of biosignatures in the atmosphere of terrestrial-mass
exoplanets will require a combination of high spatial resolution, high sensitivity and high contrast. The four drivers dictating the need for a space telescope for this application are summarized by Postman et al. [2012]. Firstly, the projected angular radius of an Habitable Zone around a star is typically lower than 100 mas. The adequate sampling of such a zone to isolate an exoplanet re-quires an angular resolution between 10 and 25 mas. Secondly, the Earth-mass planets are around 25 magnitude fainter than their host stars, it requires then high-contrast imaging to detect them, with a starlight suppression factor of 10−9 or 10−10. It can be achieved either with an internal coronograph or an external occulter, but only with high wave-front and pointing stability, impossi-ble to reach with ground-based telescopes [Guyon, 2005]. Thirdly, the detection of a biosignature, such as the presence of oxygen in the atmosphere, requires a direct low resolution spectroscopy of the extremely faint source, with a Signal to Noise Ratio better than 10. Fourthly, the planet harbor-ing life are probably rare, the sample size is then an important issue. A successful search for life will require the observation of hundreds of stars [Kasting et al., 2009]. The number of stars with a possible detection of an exoplanet spectrum is proportional to D3, D being the telescope optical aperture. The target primary mirror diameter is currently 8m, which will allow the observation of 100 star systems, 3 times each, in 5 years with 20% of the telescope time.
As a conclusion, the detection of signs of life in a star habitable zone requires at least a 8m-class space telescope, providing a SNR around 10, a 10−9 starlight suppression, a 0.1 nm wave-front error stability, a 1.5 mas pointing stability and a sensitivity from 0.3 to 2.4 m with broadband imaging and spectroscopic modes.


During the last century, our understanding of the universe has significantly improved. The ob-servations converge toward a cosmological model, called ΛCDM, and indicate that the universe is in accelerated expansion [Riess et al., 1998]. This expansion is explained by the dark energy, representing 70% of the universe density. This dark energy can be modeled by the cosmological constant of the general relativity theory. Our knowledge of galaxies and Universe formation and evolution stays quite limited, due to the difficulty to observe far back in time. The history of the universe, as understood today, is shown on Figure 1.5. After the emission of the Cosmological Mi-crowave Background (CMB), the Universe went through an epoch called dark ages during which it was neutral. The birth of primordial galaxies has allowed the universe re-ionization, making it observable. For such an observation, we need to go back in time, at 10 billions light years distance, which corresponds to high redshift observations (z > 7).
To explain the galaxies rotation curves, that are flat far from the center instead of decreasing, an-other component of the Universe needs to be introduced: dark matter, representing 25% of the universe density. The structure and kinematics of these components need to be probed in order to improve their understanding.
The current technological evolutions allow the preparation of large cosmological surveys that will identify billions of galaxies throughout the observable sky. Such missions, as EUCLID in space or BigBOSS on earth, will probe a larger and deeper volume of the universe.
Probing dark matter requires combining proper motions of stars in galaxies with their radial ve-locities [Strigari et al., 2007]. Once again, this can be achieved by coupling space and earth observations [Postman et al., 2012]. The high number of velocities required to efficiently charac-terize the dark matter necessitates large primary mirror diameter, only accessible on Earth. The measurement of proper motions with an accuracy better than 10 km/s requires an extremely pre-cise astrometry, at 0.1 mas. This will only be doable in Space, with an excellent thermal stability, coupled with wave-front sensing and controlling, maintaining the focal plane metrology below a 0.01 pixel error. In addition, a wide field of view, containing thousands galaxies, is needed to ensure a sufficient number of background astrometric references.
As a conclusion, a wide field imager, at high angular resolution and high stability, will provide the observation of thousands distant objects, with their internal structures, in a single exposure time. It will increase the data allowing the comprehension of the origin of the Universe.

Galaxy physics and star formation

Many questions about stars formation and evolution or about the growth of structures in galaxies and in the Universe remain unanswered. The star formation rate density has peaked at a moment observable at redshifts around 2 and 3. At this moment, the galaxies have formed most of their content in stellar mass. These astrophysical processes emit in the entire electromagnetic spectrum, so some observations must be done in space to recover data inaccessible from Earth, in the UV or mid and far Infra-Red for instance [Sembach et al., 2009]. Figure 1.6 presents the results of the observation of a same galaxy at different wavelengths. Revealing different structures, these observations are complementary and allow to explain the different phases of the galaxies and stars history.
Stellar formation mechanisms are studied through the observation of the Inter Stellar Medium (ISM). The ISM is constituted of gas and dust, mainly composed of hydrogen in different phases. If a molecular cloud is massive enough that the gas pressure is insufficient to support it, it will col-lapse to form stars. So, the early stages of a star’s life are observed through the infrared light from dust and clouds. For instance, observing in the far infrared, the 3.5 m Herschel Space Observa-tory studies stars and galaxies formation. Moreover, high angular resolution observations of these clouds are required to analyze the assembling processes and the collapse of interstellar clouds.
Galaxies formation studies can be achieved with high spatial resolution and sensitive spectroscopy [Giavalisco et al., 2009]. The absorption and emission lines observed thanks to spectroscopy char-acterize the galaxies’ components. The main diagnostic lines are OVI, SiIII, Lyα, NV and SiIV for the local universe (redshift inferior to 0.3), they are observed in the UV. At higher redshift (that is to say at longer wavelength), the diagnostic lines are Hα, Lyα and OIII. The observational challenge is then to acquire data of sufficient spatial sampling to identify fine structures and with enough spectral resolution and exposure time to detect the diagnostic lines.
As a conclusion, observations from UV to IR, with high angular and spectral resolutions, together with high sensitivity will reveal different features, characterizing the formation and evolution of stars and galaxies.


Earth observation

Hundreds of satellites are orbiting around Earth, observing it for many applications such as cartog-raphy, defense and security, risk prevention, surveillance, urbanism or Earth sciences (oceanog-raphy, hydrology, forestry, atmospheric studies, etc). The biggest need would be a large field of view and high angular resolution, to see small details in wide areas. There also can be a need for temporal repetitiveness, to observe the same target several times a day, or even continuously [La-try and Delvit, 2009]. We can differentiate missions in low earth orbit (LEO), in geostationnary orbit (GEO) and in intermediate orbit (MEO), the operation altitude depending on the requirement in area covering and revisit. The technologies developed for the Earth observation can also be applied for the exploration of our solar system planets.
For Earth observation, the ultimate achievable resolution is 10 cm, under this value, the observa-tion will be limited by the atmospheric turbulence.
The low orbit satellites are used for imaging. In order to have detailed cartography, the target resolution is 20 cm, which corresponds to a 2 m diameter optical aperture.
The target resolution for geostationnary satellites is around 10 m, also leading to 2 m diameter apertures. The main applications are for security, such as the preventions or follow-up of natural disasters and the ships monitoring.
In any cases, it is also important to have a wide spectral range, in order to image various struc-ture, such as vegetation, seaside or hot points for instance. Furthermore, stereoscopic capabilities, with high resolution in z, will allow the acquisition of 3 dimensional datas, for topography. Large footprint are intended, the swath will be given by the instrument’s field of view compared to its orbit. A pointing stability is required to have quality images. The satellites agility is also im-portant, the system must be responsive to specific user requirements. This can be achieved with dynamic image acquisition programming and revisit capacity. Intermediate elliptical orbits bring some instrumental challenges due to the variation of the illumination, the observing altitude and the projection speed.
The Pleiades satellites describe well the current state of the art in the Earth observation domain. It is a 2 satellites constellation (one is currently flying, the other will be launched this year) pro-viding a coverage of Earth’s surface with a repeat cycle of 26 days. They are Korsch telescopes, with a 650 mm diameter aperture and a focal ratio of 20. They operate in the visible, on a sun-synchronous, near circular orbit, at a mean altitude of 694 km. The satellites have a swath width of 20 km and can provide an image acquisition anywhere within a 800-km-wide ground strip with a 50 cm resolution [Lamard et al., 2004]. As we can see in Figure 1.8, the images quality achieved with Pleiades is exceptional.
As a conclusion, Earth observation requires agile telescopes with large field of view, high res-olution and wide spectral range. The instrumental innovations developed for Earth observation applications could then be adapted for Universe observations.

Conclusion: instrumental needs

The main requirement for future telescopes is the access to higher resolution and higher sensitivity with a high wave-front stability. It implies then larger optical aperture. But the scaling of the existing telescope is prohibitive due to mass and bulk. Then, the use of thin or lightweight mirrors, and eventually of deployable structures, becomes mandatory. However, this solution does not facilitate the achievement of stable structures.
In this context, active optics will allow a technological breakthrough by providing a mean to ensure the optical quality in future large telescopes.

Active optics: an overview

Active optics systems provide excellent optical quality by adjusting the wave-front through the deformation of mirrors. Therefore, the knowledge of mirrors’ mechanical behavior has a major role. In this section the elasticity theory, used for the deformable mirror conception, is introduced, and we will see how the optical aberrations theory can be translated in term of mirrors shapes. Then, the Finite Element Analysis method used in this manuscript to optimize active systems is presented. Finally, the three main fields of application of active optics are highlighted.

Table of contents :

1 Active optics for large-scale instrumental projects 
1.1 Image quality in telescopes
1.1.1 Image quality: definition
1.1.2 Optical aberrations theory
1.1.3 Telescope quality: ground versus space
1.2 Instrumental needs for modern astrophysics
1.2.1 Searching for exoplanets and for life
1.2.2 Cosmology
1.2.3 Galaxy physics and star formation
1.2.4 Earth observation
1.2.5 Conclusion: instrumental needs
1.3 Active optics: an overview
1.3.1 Active optics: a link between optical aberrations and elasticity theories
1.3.2 Active optics design with Finite Element Analysis
1.3.3 Access to optimal performance thanks to active optics
1.4 Active Optics for large telescopes
1.4.1 The Very Large Telescope: the most advanced Visible/Infra-Red telescope
1.4.2 Toward large segmented active telescopes: ELT and JWST
1.5 Conclusion
2 Correcting active mirror for space telescope : MADRAS project 
2.1 Large space observatories context
2.1.1 Space telescope evolution and needs
2.1.2 MADRAS project
2.2 MADRAS mirror design
2.2.1 Multimode Deformable Mirror: principle
2.2.2 Final design
2.3 FEA performance
2.3.1 Influence Functions and Eigen Modes
2.3.2 Mode correction
2.3.3 Global WFE correction
2.3.4 Conclusion on the Finite Element Analysis
2.4 Hardware specification and integration
2.4.1 Actuators
2.4.2 Estimating geometric sensitivities with FEA
2.4.3 Complete mirror system
2.4.4 System integration
2.5 Complete mirror system validation with interferometry
2.5.1 Test set-up
2.5.2 Influence Function
2.5.3 Performance of the complete mirror system
2.6 Conclusion
3 MADRAS mirror performance in closed loop
3.1 Test bed overview
3.1.1 Objectives
3.1.2 Design
3.1.3 Data analysis
3.2 Test bed characterization
3.2.1 WFE generation
3.2.2 Aberrations of the bench
3.3 Active correcting loop calibration
3.3.1 Interaction Matrix and Control Matrix
3.3.2 Loop Noise
3.3.3 Flattening
3.4 Mode correction
3.4.1 Operation
3.4.2 Specified modes
3.4.3 Stability in open loop
3.5 Representative WFE correction
3.5.1 Linearity
3.5.2 Mode combination
3.5.3 Global performance
3.6 Conclusion
4 Giant telescopes: segments manufacturing with stress polishing 
4.1 The E-ELT and its large segmented primary mirror
4.1.1 A 5 mirror telescope
4.1.2 A 39 m diameter primary mirror
4.1.3 Segment prototype with stress mirror polishing
4.2 Warping harness design
4.2.1 System description and modeling
4.2.2 Design optimization and FEA performance
4.2.3 Error sources characterization
4.2.4 Overall system performance and specifications
4.3 Experimental testing
4.3.1 Prototype
4.3.2 Testing means
4.4 Conclusion
5 Optimized active systems: 1 actuator – 1 mode 
5.1 Adapting the influence functions to the correction requirements
5.1.1 System simplification: context
5.1.2 System simplification: design
5.1.3 System simplification: optimization method
5.2 “Variable Off-Axis paraboLA” system (VOALA)
5.2.1 Application domain
5.2.2 Focus and Coma generation
5.2.3 Astigmatism generation
5.2.4 Modes combination and alternative design
5.3 “Correcting Optimized Mirror with a Single Actuator” system (COMSA)
5.3.1 Application domain
5.3.2 Contour adaptation
5.3.3 Thickness distribution
5.3.4 Actuation point location
5.4 Examples of application
5.4.1 Field compensation in an interferometer
5.4.2 Off-Axis Parabola generation
5.4.3 Zoom system
5.5 Conclusion


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