Hunting exoplanets ? try using two chessboards and one triangle |
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Hunting exoplanets ? try using two chessboards and one triangle
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: The achromatic chessboard. The figure depicts the two-telescope interferometer considered in a multi-axial recombination mode, equipped with the two chessboard mirrors. On one mirror, the cells produce optical path differences (OPDs) that are odd multiples of half the central wavelength (λo/2) while they are even multiples on the other mirror. Thus, a π phase shift between the two arms is applied for λ = λo. Among the various distributions of thickness, a special one, defined by the Pascal's triangle - i.e. the terms of the polynomial (1+1)n- allows to extend this property to wavelengths rather far from λo. This happens thanks to a peculiar equality between sums of powers of odd and even integers. Such relations are said diophantine, from the name of the alexandrian mathematician Diophantus, who lived during the 3rd century. and who studied some of them. Since they appear in other problems of optics already examined6, the team proposes to give the name of diophantine optics to this new branch of optics.
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Figure 2: Structure of the two chessboards of the mirror pair when 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.
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Figure 3: The Figure shows the simulated detection of a planet (in blue) one million times dimmer than its parent star (in yellow) when Δλ/λo = 20%.
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Performances : A simulator was developed, based on a fully analytical solution to predict the performance of the configurations.
Figure 4: The figure compares, for a planet 10−6 fainter than its star, the nulling efficiency versus Δλ/λo for different increasing orders (colors) of the best chessboard. It is worth noting the relative flatness of the star-to-planet ratio versus λ for the highest orders. The bandpass is typically [0.85λo − 1.7λo], i.e. one octave. Note that a realistic phase error between the two arms is introduced in the model.
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Figure 5: An 8×16 device with a cell pitch of 600 μm was manufactured by the company SILIOS-France using an electron etching technique. The two masks (odd and even) are put side by side. The first images – in Fizeau recombination – show, as expected, a central dark fringe which is close to the model prediction, but more important which is fixed when λ ≠ λo, as illustrated in this Figure. (The dark fringe would shift with classical mirrors.)
Click on the image to enlarge itConclusion
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
2. A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider,Could We Search for Primitive Life on Extrasolar Planets in the Near Future? , Icarus 123, pp. 249-255, 1996.doi:10.1006/icar.1996.01553. Y. Rabbia,7. http://spie.org/x19643.xml?highlight=x2418Nulling Interferometry: from the Bracewell scheme to the ESA-Darwin mission , EAS Publications Series 12, pp. 215-234, 2004.doi:10.1051/eas:2004035
Contact
Daniel Rouan (Observatoire de Paris, LESIA et CNRS)
Didier Pelat (Observatoire de Paris, LUTH, et CNRS)
