Hunting exoplanets ? try using two chessboards and one triangle
1er mars 2008
A team from Observatoire de Paris proposes a novel instrumental concept that could simplify future space experiments that aim at directly detecting exoplanets in mid-infrared. The originality of the concept is the use of chessboard mirrors whose cells positions and thickness are defined thanks to peculiar mathematical relations not usually found in optics.
Direct detection of an exoplanet (a planet outside our solar system) that is orbiting a star requires the stellar light to be dimmed as much as possible. This is due to the huge contrast in brightness (106–10) between the parent star and its orbiting planet, as well as the small angular separation (10−6 rd) between the two objects. In the mid-infrared, one way to image the planet against the background light of the star is by nulling interferometry, which uses at least two telescopes coherently recombined in the way proposed by Bracewell1, so that the brighter light from the star is cancelled out by light wave interference, hopefully allowing the orbiting planet to be seen. When a π phase shift is applied to one of the arms of the telescope, a system of fringes with a central dark fringe is projected onto the sky. The star image, put on the dark fringe, is strongly attenuated, while the planet, if on a bright fringe, can be detected. Obtaining a π phase shift that brings different wavelengths to focus together (is achromatic) is mandatory because the wavelength domain where spectroscopic life signatures are to be found is broad2 (typically 6-18 μm), and it’s a photon-starving experiment. Various methods3 have been presented in order to approach an achromatic π phase shift in a large domain of wavelength. Unfortunately, they typically make the two arms of the interferometer asymmetrical and introduce several additional optical components with sometimes a delicate adjustment. A new solution4,5 has then been proposed, using a twin mirror made of cells of different thicknesses transposed as a chessboard pattern. It is the peculiar distribution of the cells’ thickness that makes the π phase shift quasi-achromatic on a broad domain.
- Figure 1 : L’échiquier achromatique. La figure montre le schéma d’interféromètre considéré, en recombinaison multi-axiale. Les cellules d’un des miroirs-damier produisent des différences de chemin optique qui sont des multiples impairs de la moitié de la longueur d’onde centrale (λo / 2) et les cellules de l’autre, des multiples impairs. Ainsi, un déphasage de π est bien appliqué entre les deux branches pour λ = λo. Cliquer sur l’image pour l’agrandir
- Figure 2 : Structure des deux échiquiers de la paire de miroirs (impair et pair) lorsque n = 5.
The Pascal’s triangle solution provides the distribution in z of the cells, but it does not say anything on the distribution of cells in x and y (on the surface of the mirrors). A distribution has been found which is built according to a recursive scheme, also based on diophantine relations, and which is optimum in terms of darkening the residual point spread function of the star image. Figure 2 shows the resulting pattern for the pair of mirrors (odd and even) when n=5. Click on the image to enlarge it
- Cliquer sur l’image pour l’agrandir
Performances : A simulator was developed, based on a fully analytical solution to predict the performance of the configurations.
- Figure 3 : La figure montre la détection simulée d’une exoplanète (en bleu) un million de fois plus faible que son étoile (en jaune), lorsque la longueur d’onde diffère de λoà hauteur de 20%. Cliquer sur l’image pour l’agrandir
- Figure 4 : La figure compare, pour une planète un million de fois plus faible que son étoile, l’efficacité d’annulation en fonction de Δλ / λo pour les différentes tailles croissantes du damier optimum (en couleur). Il convient de noter le comportement relativement plat du rapport "résidu étoile sur résidu de la planète" en fonction de λ . La bande passante est typiquement [0,85 λo - 1,7 λo], c’est-à-dire une octave. On note qu’une erreur de phase réaliste est en plus introduite dans le modèle. Cliquer sur l’image pour l’agrandir
Conclusion This approach presents several advantages : a very compact and robust system, a fully symmetric design with respect to the two arms of the interferometer, and finally the concept can be extended to multi-telescope interferometers with a phase shift other than π. The use, in the future, of adaptive segmented mirrors based on micro optical electro mechanical systems (MOEMS) technology, could allow adjustment of the wavelength and a fine correction of error that would be beneficial to future exoplanet detection programs.
References 1. doi:10.1006/icar.1996.0155 3. doi:10.1051/eas:2004035 4. D. Rouan, D. Pelat, The achromatic chessboard, a new concept of phase shifter for Nulling Interferometry - I theory, Astron. Astroph., à paraître  (voir aussi : http://arxiv.org/abs/0802.3334) 5. http://spie.org/x19643.xml?highlight=x2418
Contact Daniel Rouan (Observatoire de Paris, LESIA et CNRS)
Didier Pelat (Observatoire de Paris, LUTH, et CNRS)
Dernière modification le 4 mars 2013