Info

Electronics Repair Manuals

Schematic Diagrams and Service Manuals

Get Instant Access

Fig. 2.25 Visibility functions for binary systems where the contrast is 1 (top left), 10 (top right), 100 (bottom left) and 1000 (bottom right) (After Borde, 2003.)

Star Planet

Star Planet

Fig. 2.26 Schematic diagram of a dark-fringe interferometer. Light arriving from the direction in which the instrument is aimed arrives simultaneously at the two telescopes. The achromatic dephaser, n, ensures destructive interference at the recombiner. Light from a point away from the target direction (from the planet) arrives at Telescope 1 with a delay relative to Telescope 2, because it has to cover an additional distance (D.sin 0). By altering the distance between the telescopes (by varying D), it is possible to compensate for the n phase shift by the additional optical path, such that the interference is constructive in the direction of the planet. We thus obtain an instrument where the transmission is zero along the direction in which the instrument is pointed, and adjustable between 0 and 1 around that axis

Fig. 2.26 Schematic diagram of a dark-fringe interferometer. Light arriving from the direction in which the instrument is aimed arrives simultaneously at the two telescopes. The achromatic dephaser, n, ensures destructive interference at the recombiner. Light from a point away from the target direction (from the planet) arrives at Telescope 1 with a delay relative to Telescope 2, because it has to cover an additional distance (D.sin 0). By altering the distance between the telescopes (by varying D), it is possible to compensate for the n phase shift by the additional optical path, such that the interference is constructive in the direction of the planet. We thus obtain an instrument where the transmission is zero along the direction in which the instrument is pointed, and adjustable between 0 and 1 around that axis

Let us consider two telescopes T1 and T2, which, because of diffraction are not able individually to resolve the star/planet pair. We point the two telescopes exactly in the direction of the star, and merge the beams of light from the two telescopes with an optical recombiner. In the direction of the star (i.e., where the two telescopes are pointing), the wavefront arrives simultaneously at T1 and T2. If we recombine the two beams, they will be in phase and will produce constructive interference. If we than add an achromatic dephaser, n, in one arm of the interferometer (for example, the path from T2), the light from the two telescopes will be recombined with opposite phases. In other words, the interference will be destructive and everything coming from the star's direction (in particular the star's flux) will be extinguished. In the direction of the planet (which typically lies at an angle 9 ~ 0.1 arcsec for a terrestrial analogue orbiting a star at a distance of 10 pc), we introduce a delay for Ti relative to T2 that is equal to D.sin(9), where D is the distance between the two telescopes. If D is altered (by moving the telescopes), this may be done so that at an average wavelength (for example at the centre of a spectral band, or at two wavelengths so chosen as to maximize the spectral coverage) the difference in the path-lengths D.sin(9) compensates for the dephasing that n introduces into the arm incorporating T2. This results in constructive interference in the direction of the planet. To summarize, such an instrument allows the observation of a faint object that lies outside the optical axis, where the theoretical transmission is zero. The response obtained with such an instrument is shown in Fig. 2.27. In its original version, the Bracewell interferometer was rotated such that the signal from the planet was modulated rel-

Fig. 2.27 Plot of the transmission of a dark-fringe interferometer with two telescopes (a Bracewell interferometer). The star is located on the dark fringe (it is extinguished), and the planet on a bright fringe

ative to the leakage of light from the star (because of the non-zero size of the star and of the finite size of the zone with zero transmission, the star is not perfectly extinguished).

In practice, a dark-fringe interferometer and its associated detection system (which may, in principle, be a single-pixel detector), behaves as a photometer with the spatial transmission shown in Fig. 2.27. In particular, measurements obtained with this instrument are measurements of the flux, which consists of several individual contributions:

• the off-axis object (for example, the planet),

• leaks from the star (because the central fringe is not perfectly dark and the star is not a perfect point), and the associated noise and fluctuations,

• other contributions related to the source, for example, a portion of the zodiacal disk in a planetary system,

• thermal emission from the instrument itself (in cases where such wavelengths are a problem).

The specific remedy that needs to be applied is to try to separate these different contributions to be able to isolate the component linked to the off-axis object that one is trying to detect and analyze. One classic technique consists of taking the geometry of the signals into account (the emission from a disk of zodiacal light is overall centrally symmetrical with respect to the plot of transmission, whereas that from the planet is not). To do this, the system is observed at several orientations of the interferometer, enabling discrimination of the different contributions. Another possibility is to use an internal modulation between several subsidiary interferometers.

This concept of a dark-fringe interferometer is the basis of the proposal for the DARWIN space mission and its American counterpart TPF (Terrestrial Planet Finder), described in Chap. 8.

It is interesting to note that from the instrumental point of view, the two inter-ferometric concepts: the 'measurement of visibility' and dark-fringe interferometry, may, potentially, be combined in a single instrument. In particular, the achromatic dephaser does not prohibit the measurement of the experimental visibility. In such a case, it is necessary to limit exploration of the interference fringes to a small number of fringes, the characteristics of which (the amplitude and the phase) have been determined by a method that is precisely comparable with the classic method of measuring the visibility.

2.3.4 Interferometry and Imagery: Hypertelescopes

We have seen that the spatial resolution of a telescope is intrinsically limited by diffraction and, in practice, by the diameter of the telescope. The size of instruments is limited by current technology to:

• telescopes between 10 and 42 metres in diameter (ESO's current Extremely Large Telescope projects). The largest current telescope is a multi-mirror system with an elliptical pupil (10 x 11m): the Hobby Eberly Telescope, which is slightly larger than the two Keck telescopes (10 m in diameter). The largest monolithic telescopes are the two mirrors of the Large Binocular Telescope (each 8.4 m in diameter);

• space telescopes of a few metres in diameter. (The JWST is to have a diameter of about 6.5 m. This is the largest space instrument observing in the visible or infrared that has ever been constructed or is in the course of construction.)

However, if we are to contemplate the observation of planetary systems in the thermal infrared, or even direct imagery of exoplanetary surfaces in the visible, we will require diameters that are distinctly larger, and also with significantly greater collecting surfaces, because the flux from planets is weak. We soon encounter the limit for monolithic instruments - or at least with unified pupils (all points of the pupil are available without leaving the pupil).

Table 2.6 gives the minimal baseline (diffraction limited) as well as the collecting surface required to image the surface of a planet such as the Earth at a distance of 10 parsecs, with the corresponding spatial resolution (given as the number of pixels). The assumptions used for these calculations are:

• image of a planet like the Earth orbiting a solar analogue in the visible/near IR spectral region (0.1 photon/s/m2 at the Earth, in the 0.3-1 ¡m spectral region, in three colours, to obtain chromatic information i.e., to differentiate vegetation, continents, oceans, etc.);

• the integration time should be sufficiently short to 'freeze' the planet's possible rotation and avoid a blurred image. In this calculation, the integration time is limited to one hour, but could be adapted according to the target if the rotation period were known;

• observation of the planet is limited by photon noise with a signal-to-noise ratio of 10 per pixel. As a result, an average flux of 100 planetary photons is required per bright pixel. (This relatively stringent assumption enables an estimate of the observation's minimal characteristics.);

• at 10 parsecs, an Earth-like body would have an angular diameter of 8.5 x 10~6 arcsec;

• the overall transmission of the photometric chain (including the telescope and the detector's efficiency) is assumed to be equal to 0.2.

Table 2.6 Parameters for imaging a terrestrial planet at a distance of 10 parsecs

Image size (pixels)

Collecting

Minimum

Integration

Was this article helpful?

0 0

Post a comment