A. LABEYRIE
Collège de France & Observatoire de Haute Provence
(CNRS)
F-04870 Saint-Michel l'Observatoire, France
CONTENTS
Large telescopes in space and the much larger interferometric arrays of telescopes currently studied will presumably provide images, spectra and resolved images of exoplanets. There is a huge potential for progress in this direction, and detailed information will be obtainable on planetary objects including possibly on their life-bearing characteristics.
The contrast problem in star/planet images
As seen from a distance of 10 parsecs, the solar system shows the Sun as a 5th magnitude star, with Earth appearing 0.1 arc-second away as a 30th magnitude source. Jupiter is 0.5 arc-second away and magnitude 27.5. Both planets are bright enough to be imageable with a Hubble-like Telescope, and spaced far enough from the Sun to be angularly resolved, but the contamination of the focal image with scattered light from the Sun would prevent the detection of the planets unless special precautions are taken.
If we expect a neighbouring star to have such planets (and one case was announced by M. Mayor after the Cargèse school [1]), we face a similar situation. In the 10 micron infra-red region, the planet's contrast is improved owing to its thermal emission, with 10-6 rather than 10-10 relative luminosity in the Earth's case, but the angular resolution is degraded 20 times and the zodiacal light emission, both in the observer's planetary system and in the target system, affect the planet's contrast.
Coronagraphy with opaque and phase masks
A similar problem of contamination by diffracted light long prevented the observation of the solar corona, which could be seen only during rare eclipses. A solution was found by astronomer Bernard Lyot in the 1930's [2], in the form of his coronagraph which provided excellent images of the corona, and films showing its evolution during hours of observation.
In addition to building a very clean lens, free from scratches and maintained free from dust, he tried to reduce the diffractive spreading of light from the disk into the image of the corona. In the telescope's focal plane, he installed an opaque mask blocking the disc's geometric image. Looking at the pupil through the mask (smaller than the pupil of his eye), he could locate the brighter areas which contributed most diffracted light around the mask. In the absence of dust, he could see a double bright ring circling the pupil, and had the idea of removing it with a mask slightly smaller than the pupil's image obtained with a relaying lens. With a second lens relaying the focal plane, he could thus obtain a cleaned image of the source. The corona, little affected by the field and pupil masks, became visible.
This empirically discovered method was subsequently justified analytically by a number of authors, using the powerful tool of the Fourier transformation to model diffraction effects. In coherent light, i.e. from a point source with monochromatic spectrum, the Fourier transform relates the vibration amplitude distributions in a pupil and the image. Bonneau et al. [3], Mauron [4] and Malbet [5], Ftaclas [6], Brown [7]) Clampin et al. [8], among others, have studied variants of the basic scheme. When attempting to use the method with large ground-based telescopes for observing stellar environments, it became necessary to implement adaptative corrections of atmospheric turbulence.
When the Hubble Space Telescope was being conceived by NASA in 1976, I proposed a Lyot coronagraphic camera to look for star's planets. I made laboratory tests on a new 1.5m spherical mirror which J. Texereau had just completed at Observatoire de Paris for Calern's Schmidt telescope; and our calculations [3] had indicated that it would be feasible, in a few hours of exposure, to detect exo-planets with the 3 m aperture then considered. NASA invited me to contribute to the project study as a member of its instrument definition teams, although it did not expres I therefore suggested to NASA that the instrument be built by the European Space Agency in exchange for a share of telescope time. This was agreed between NASA and ESA. I eventually resigned from my involvement with NASA, following its decision that the telescope would not be tested optically before launch. Given the absence of testing, the spherical aberration problem found after launch was no surprise to optical experts, but the corrective COSTAR optics subsequently added changed the pupil size and made the Lyot mask inoperant. The mirror size reduction, from 3 to 2.4 m, with respect to the initial plans had also made impossible the coronagraphic detection of a Jupiter-like planet, but some of the fast orbiting planets recently discovered are expected to be much brighter and may prove detectable with a 2.4 m space telescope and Lyot coronagraph.
Several ideas for improved coronagraphy emerged since. Claude and François Roddier [9] described the use of a phase-shifting mask replacing the occulting mask of Lyot. Suitably sized within the Airy peak, it can provide a destructive interference which cancels most of the star light in the relayed pupil. The light is rejected outside of the geometric pupil, and occulted with the same kind of aperture mask used by Lyot, as shown in figure 1. Its advantage, in theory, is that a planet as close as the first Airy ring can be imaged with a phase mask, whereas the Lyot mask cannot be made smaller than the third or fifth ring without losing much of its effect.
The classical representation of diffraction by Fourier transforms, if applied to the Lyot or the Roddier coronagraph, indicates that the residual starlight in the output image has an amplitude distribution which is a convolution of two complex distributions: the amplitude distribution just downstream from the occulting or phase-shifting mask, and the diffraction pattern from the Lyot diaphragm in the relayed pupil. This latter pattern is typically identical to the pattern just up-stream from the mask, but slightly wider in the usual case where the pupil diaphragm is made slightly smaller than the geometrical pupil to remove diffracted light.
This convolution description also applies to the case of a multiple aperture such as discussed in section 5.
Making the phase mask achromatic, for usability across a wide spectral band, requires a mask diameter and optical path shift proportional to wavelength. Reflective Bragg holograms (Denysiuk [10], Stroke & Labeyrie [11]) can in principle achieve the required non-interacting superposition of many color-selective masks. Equivalent structures can in principle be built through the vacuum deposition of multi-layer dielectric films, each layer having a radially graded refractive index.
Little practical testing has yet been reported for phase mask coronagraphy, and it is unclear whether the theoretical advantages can be materialized. It may be remarked that the micro-dips used to encode data bits in CD-ROM systems are also phase masks. Used in reflective fashion, they make the dips appear dark although the disc is uniformaly coated with relective aluminum.
Figure 1
Another idea which emerged in the way of improved coronagraphic devices is
the Achromatic Interference Coronagraph of Gay
[12].
It uses a beam splitter, according to a modified Michelson interferometer scheme,
to cancel the star's wavefront. It however produces a double image of the planet.
Dark hole and dark speckle imaging
Additional levels of cleaning are required to bring out planet images. Once basic coronagraphic cleaning is applied, most of the organized diffracted light is removed, i.e. the diffraction rings and the spikes caused by the structural spiders, but a speckled halo of residual starlight inevitably remains. It results mostly from residual bumpiness on the wavefront, and can be attenuated, in a selected region, by applying weak corrections to the shape of the main mirror, using actuators and the algorithm developped by Malbet, Yu and Shao [13].
The performance of this second cleaning step is limited by the accuracy of the wave mapping. Phase-contrast techniques may be considered for accurate wave mapping in this case, and they should be applied up-stream from the Roddier phase mask, where the pupil is uniformly illuminated. Phase-contrast is perhaps not applicable for wave sensing on ground-based telescopes since the high-altitude turbulence creates a shadow pattern which tends to confuse the phase contrast pattern.
Such optimization being made, which is easier said than done, there is again a residual speckled halo which still affects the detection of any faint Airy peak contributed by a planet. It cannot be further attenuated with actuators on the mirrors, but slight re-adjustments of the actuators, as caused by servo noise in the feedback loop, generate "boiling" of the speckle pattern.
Speckles are caused by interference of many vibrations having random phases, received from all parts of the mirror. The superposition can be more or less destructive or constructive, as one guesses from a vector representation of vibrations, where the addition amounts to a classical random walk. The speckle's scale size matches the width of the Airy peak. The two initial steps of darkening produce a highly destructive interference in the field zone considered. This is a random walk situation where the last step brings the walker very close to its starting point, and one guesses that very small phase shifts affecting randomly the numerous component vibrations suffice to affect significantly the intensity cancellation, making the system exquisitely sensitive to low-level disturbances such as residual "seeing" on Earth or fixed mirror bumpiness in space.
A long exposure, relative to the speckle lifetime, produces an image where the speckled halo becomes smoothed. This improves the visibility of underlying planet peaks, but photon noise ultimately limitates the detectable planet level: the planet should provide at least n1/2 photons if n photons are detected from the star in a speckle-sized area of the field [24].
Rather than long exposures, the "dark speckle" analysis method [14], [15] instead uses thousands of exposures shorter than the speckle life-time. In each exposure, the speckle pattern is different and dark speckles appear at different locations. A dark speckle appearing at the planet's location improves its detectability since the contaminating photon count n is decreased.
The reduction algorithm builds a map of dark speckle appearances, and the planet tends to stand out as a location where no dark speckles ever appears, owing to the addition of intensities from the star and the planet, their light being mutually incoherent.
The method therefore provides a third level of cleaning. It can be applied when observing on Earth with a telescope equipped with an adaptive coronagraph, where residual turbulence achieves the speckle "boiling". It has been recently proposed to NASA for the Hubble Space Telescope, in the form of a "Faint Source Coronagraphic Camera", but the instrument was not selected.
Another opportunity arises with the Next Generation Space Telescope, for which a "dark-speckle coronagraph" is again being proposed. Suitable adaptive optics can make it usable in the infra-red and in the visible as well. Calculations indicate that exo-planets will be imageable.
Once a planet is detected, the contrast of its image can be improved by creating a permanent dark speckle in the star light at the planet's location. This allows in principle to obtain low-resolution spectra of the planet: the above-mentioned planet detection condition may be written np > n1/2, np being the number of photons received from the planet, and implies that np / k > ( n / k2 )1/2. This indicates that the detection condition is still satisfied in each among k spectral channels, carrying k times fewer planet photons, if the star's light is attenuated k times in the white band, equivalent to k2 times in the spectral channel considered. If, following the planet's discovery with "boiling speckles", a permanent dark speckle is thus created to attenuate the local stellar contamination k=100 times, a 100-element spectrum of the planet becomes obtainable in the same time which it took to discover it.
This challenging prospect announces attempts to detect spectroscopic signatures of life, and particularly analogs of the broad spectral bands caused by chlorophyll on Earth. Assuming vegetated planets, the contrast of the broad photosynthetic bands to be expected depends highly on the average vegetation density, and can reach high values in forested areas. There are reasons to believe however that a cloud cover approaching 50% must be present on densely vegetated planets. Whether diurnal and seasonal variations of the cloud and vegetation spectra can help discriminating photosynthetic spectral features from mineral features remains to be investigated. On Earth, a diversity of photosynthetic pigments providing broad absorbtion bands in varied parts of the visible spectrum have evolved since the onset of photosynthetic life. Whether analogous photochemistry, or completely different photosynthetic systems, may have evolved on other planets is unclear, but much insight will be gained if corresponding spectral features can be detected.
Ground-based observations with dark-speckle techniques have been initiated on the 1.52m telescope at Haute Provence, using 80-element adaptive optics developped by the Office National d'Etudes et de Recherches Aérospatiales [15]. These are yet far from achieving the expected dynamic range, but improved photon-counting detectors and adaptive correction should allow significant progress.
Extension to interferometric arrays: towards an Exo-Earth
Discoverer
The option of using several free-flying elements for interferometry in space was first proposed in the early 1980's [16] and is now actively studied by the space agencies. Following a feasibility study by ESA [17], the agency is studying the proposal of Léger and Mariotti for DARWIN [18] [19], an infra-red array dedicated to the search for extra-solar planets. As described in the lectures of J.M. Mariotti, the coronagraphic cancelling of the star's light which he proposed extends and improves markedly the Bracewell scheme, where a beamsplitter recombines the plane waves from two apertures in opposite phases. The Terrestrial Planet Finder concept studied by american groups involves a similar optical principle, although initially ivolving a rigid beam-shaped structure to carry the optical elements.
A different coronagraphic approach is possible, also using a number of free-flying telescopes as collecting elements, according to the principle of the proposed "Exo-Earth Discoverer" [20]. As shown in figures 2,3,4 and 5 it involves a recombination scheme [21] [22] which violates the "golden rule" of W.Traub and J.Beckers . It causes a densification of the exit pupil, in comparison with the entrance pupil: the size/spacing ratio of the sub-pupils is considerably increased.
If certain conditions are met, and the wavefront elements properly phased, a directly usable recombined image is generated (figures 3, 4, 5). The conditions are:
The pupil densification avoids the problem encountered with highly diluted Fizeau interferometers. For the case of many apertures, mainly considered in this section, these have a spread function which has a sharp interference peak surrounded by a wide halo of side-lobes. The peak-to-halo ratio, in terms of intensity levels, is equal to N, the number of apertures, but most of the energy goes in the halo owing to its large diameter, thousands of times larger than the interference peak.
A multiple star or complicated object gives an image which is a convolution of this spread function (intensities) with the object's distribution of intensities. The halo makes the image useless, since its convolution tends to create a dominating uniform background, with little energy left in the convolved peak (figures 2, 3, 4).
With a densified pupil instead, the halo, being the sub-aperture's diffraction pattern, is shrunk and the energy concentrated. The central interference peak still dominates the halo by a factor N, but now carries a much larger fraction of the energy since it is wider compared to the size of the shrunk halo.
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The displacement of the diffraction function sketched in figure 3 is negligible when the pupil is highly densified, in which case the image of an extended object is a convolution of the intensity distributions in the object and the interference function, followed by a multiplication with the diffraction function.
The multiplication cancels most of the light in the feet of the latter function, and this causes a field limitation for the high resolution image, as seen in the simulations of figure 4 (bottom) where one of the stars seen at the edge of the simulated cluster in the Fizeau case vanishes from the densified-pupil image. The multiplication also darkens the vast halo of sidelobes found in Fizeau images, and since the total energy is conserved, the consequence is a strong intensification of the interference function appearing within the window.
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Figure 5
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Figure 5 illustrates the Earth and Moon, as they would appear in yellow light at the combined focus of the EED from a distance of 3 parsecs. A real pictures of these bodies, produced by the Galileo probe, was convolved with the interference function of a 150-eleme diffraction pattern of the sub-pupil. Further post-detection image processing is normally required for better rendering but these simulations verify the theoretical analysis21 previously mentioned. Its equation (6) gives the photon count in the | ||||||
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Depending on the aperture configurations, it requires at least 30 telescopes
of 3 meter size, arrayed across 100km, to produce images such as these. The
exposure time should not exceed 30mn to avoid rotational blurring, although
stroboscopy with repeated short exposures at diurnal intervals can be attempted
in the absence of fluctuating cloud cover. Light from the parent star must be
removed as much as possible to obtain such images, and this requires
coronagraphic masking, plus active dark-speckle implementation, in each
subpupil up-stream from the combining optics.
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C
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The method is also applicable in the infra-red, but baselines of several
thousand kilometers become needed, requiring rather large optics to retransmit
the beams from the collecting stations to the combiner. This difficulty is
avoided by the Moth-Eye Interferometer concept discussed below. Such images can be recorded through an integral field spectrograph to obtain independant spectra in each of their pixels. If spectral features analogous to the broad absorbtion bands of terrestrial photosynthetic pigments are present, their distribution on the planet can be mapped. |
The very small field extent obtained in the observing situation just discussed, tens or hundreds of micro-arc-seconds, requires that the planet's exact location be previously known from observations with smaller intruments. Relative to its parent star, the contrast of a planet is typically improved to 10-6 in the 10-micron infra-red, and coronagraphic observations in this range facilitate the detection. The 8m aperture of the planned NGST is however too small for separating planets correctly at 10 microns, although it should be attempted in the visible as mentioned above, hence the larger size of the DARWIN and the Terrestrial Planet Finder projects.
The EED can also provide efficient coronagraphy (figures 6), 7). Retracted configurations with 100m-1km size are adapted to the situation just mentioned. Much larger sizes are in principle also efficient for coronagraphy on neutron stars, active galactic nuclei and other luminous compact sources.
Classical coronagraphy involved a mask in the image plane, and a second mask to remove diffracted light in a relayed pupil. When EED has its exit pupil completely densified, i.e. with sub-pupils made exactly adjacent and possibly hexagonal in shape for full "paving", the coronagraph's effect on an unresolved source is the same as it would be in a conventional filled telescope with the same pupil pattern. Indeed, the densified pieces of the wavefront collected in the entrance pupil cannot be distinguished, in terms of diffraction, from the continuous wavefront in the exit pupil of a conventional telescope. Nearby sources such as exoplanets can be imaged without being significantly affected by the pair of masks.
Either the Lyot or the Roddier techniques can be used, the latter being more tolerant of gaps between the sub-pupils and providing higher resolution.
The "Exo Earth Discoverer" being proposed to the space agencies [20] follows these principles, and the concept can be made compatible with DARWIN, in terms of using a single set of free-flying telescopes to feed interchangeable focal optics so that both recombination principles be usable.
For a large usable field, the number of elements N should be as large as possible, and several kinds of ring, hexagonal or square paving geometries appear of interest. For coronagraphic uses, a periodic hexagonal diluted paving (figures 6)A and B) may be preferable, but the option of using a ring with a Roddier phase mask (figure 7) in the recombined image is also appealing and being studied. The amplitude convolution description of the cleaned stellar image, mentioned in section 3, indicates that a multi-aperture diaphragm matching the geometrical pupil, located downstream from the recombined field where a phase mask is inserted in the interference peak, causes a convolution of the amplitude distributions found just up-stream and do
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Figure 6
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For dark speckle imaging, a phase mask with a multitude of active elements, similar to a pupil-plane adaptive mirror but located in the field, may allow useful additional degrees of freedom, in addition to those provided by the pupil actuators. Changes of aperture size and geometry are equally achievable with free-flyer elements. |
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Also achievable is a progressive up-grading of the array with additional telescopes, as operating experience is gained. The array size can also be extended for observing compact objects having a high surface brightness. Low-brightness objects such as an exo-planet are in principle observable with 27 apertures of 8m, arrayed as a 20km circle. At 5 pc, a Jupiter is resolvable in 20x20 elements. Brigther objects are observable with smaller (1.5m) sub-apertures using 100 km baselines. |
Extension of EED towards a Moth Eye Interferometer
With their spherical symetry, Schmidt-type telescopes provide a wide field coverage. Similarly, a giant interferometer in space can provide high-resolution images with unlimited field if arranged as sketched in figure 8.
The collecting telescopes of EED are replaced by simple spherical mirrors, all part of a single giant sphere. The instrument requires no global pointing and keeps a fixed attitude, with only the focal stations being moved to produce high-resolution images of selected parts of the sky. Densified-pupil imaging is an essential part of the concept since the collectors are necessarily diluted, if only to avoid masking each other. Each focal station contains small mirrors and delay lines arranged to correct the huge spherical aberration of the large spherical reflector, together with the corresponding optical path differences. It also achieves the pupil densification, required to produce images such as those of figure 5. Coronagraphic masks can also be used in the focal station to clean either the sub-images or the combined image. The former case arises when attempting to image details, clouds or continents, of an exo-planet which is well separated from its parent star by
Figure 8
The Moth Eye Interferometer will be of obvious interest after the initial
operation of a pointable imaging interferometer such as the EED. Later, many
EEDs may become needed for observing many fields simultaneously, as currently
done on Earth with the multitude of existing telescopes, but the Moth Eye
Interferometer will provide a much more economical integrated approach since
each of its mirrors will contribute to simultaneous observing in many
directions, given as many focal stations.
Whether a first-generation EED should already be conceived as a "bare-bone" Moth-Eye Interferometer, suitable for later up-grading towards wider and wider sky coverage, remains to be investigated.
Feasibility of giant baselines
Figure 9
Objects of extremely high surface luminosity, such as the few known neutron
stars emitting visible light, can in principle be observed with extremely long
baselines. 100,000 km baselines thus appear usable on the few optical pulsars
known
[20].
As shown in figure
4,
auxiliary optics in the form of out-rigger mirrors could be added at some stage to the EED for this purpose. The fringe acquisition will be difficult, but probably not impossible: in the absence of a better method, one can always increase progressively th
Coronagraphic and interferometric approaches to the detection of exo-planets in images are actively developped by a number of groups. There is a potential for tremendous gains in this area. The goal of searching spectral signatures of photosynthetic life on exo-planets is quite challenging but does not appear unrealistic. Nor does it appear btain images showing surface details on an exo-planet. With free-flyer arrays, the required multi-kilometric sizes may be quickly achievable once smaller baselines become mastered.
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Figure 2
Figure 3
Figure 4
