Collège de France & Observatoire de Haute Provence (CNRS)
F-04870 Saint-Michel l'Observatoire, France
Large interferometric arrays of free-flying telescopes in space can provide snap-shot images at their recombined focus, using the concept of "densified-pupil imaging". Coronagraphic masks can be used for observing contrasted objects such as exo-planets and quasar host galaxies. Additional cleaning is possible with "dark-speckle" imaging. Visible and infra-red uses with baselines spanning 1 to 100 km are considered. 20x20 resolved elements are resolvable on a Jupiter-like planet at 5pc with a 20km baseline at visible wavelengths. The EED concept is compatible with DARWIN, in terms of interchanging recombiner optics to exploit both observing modes and access broader science.
Key words: space interferometer, exo-planets, coronagraph
In the early 1980's, my proposal for a space interferometer, called FLUTE  owing to its tubular shape with multiple viewing ports, was selected by the Centre National d'Etudes Spatiales in view of preliminary studies. As I started to think about detailed designs, I realized that free-flying elements, rather than a supposedly rigid structure, would be preferable in many respects for instruments larger than a dozen meters. I proposed a system of this sort called TRIO   and R.Stachnik  proposed another concept, called SAMSI, where three intersecting Earth orbits achieved a periodic baseline variation. These concepts were discussed in some detail at two ESA colloquia in Cargèse and Granada, and ESA started in-house and industrial studies in the mid 1990's. It concluded that free-flyer's arrays in orbit would be feasible and more economical than Moon-based arrays. DARWIN, an infra-red array of free-flying telescopes dedicated to extra-solar planet detection, was subsequently proposed by Leger & Mariotti. ) and Mennesson et al. .
This article describes a somewhat similar array concept, the Exo-Earth Discoverer (EED), using a different image recombiner principle. Because of the arraying flexibility offered by free-flying telescopes, it appears feasible to operate such arrays both in the DARWIN and the EED modes, using a pair of interchangeable focal instruments.
In ground-based arrays such as the IRAM sub-millimeter interferometer at plateau de Bures, elements have been progressively added to increase the performance. A similar capability is foreseen with the EED: it will be possible to upgrade it, starting with as few as only three apertures but preferably a dozen, before reaching 27 or even possibly 81. The imaging perfomance increases, in several respects, as the square of this number. Considerable observing power should result with the upgraded instrument, and snaphot images will be obtainable on a wide diversity of celestial objects. In addition to high-resolution images of galactic and extra-galactic sources, from the ultra-violet to the infra-red, coronagraphic images of close stars will be obtainable to detect their associated matter in the form of coronae, disks or planets.
Fig. 1. Proposed Exo Earth Discoverer, a 1-to-100km interferometric array in space. With the 36 free-flying telescopes shown here the exit pupil can be densified for efficient imaging and coronagraphy. Collimated coudé beams from telescopes Ti are reflected from flat mirrors SR towards the concave image recombination mirror FM. For optical path equality, the telescopes are located on a paraboloïdal surface, with focus at SR and curvature center at the metrology satellite MS. The arrangement provides a compact exit pupil XP which is a densified version of the diluted entrance pupil EP. The full densification achievable with hexagonal sub-pupils favors coronagraphic masking (Lyot , or Roddier type) in the recombined image and a relayed pupil downstream, at visible and infra-red wavelengths. In the densified pupil mode with N apertures, snapshot images can contain up to NxN resolved elements.
With suitable coronagraphic attachments and additional levels of nulling, achievable through adaptive apodisation and "dark speckle analysis", the EED is indeed expected to provide images of exo-planets, including Earth-like planets, at both visible and infra-red wavelengths. At some stage, baselines as large as 20 km will allow resolved images to be obtained on close planets, thus showing detail of their surface structure with about 20x20 resolved pixels in the case of the recently discovered planet of Gliese 876 , located at 5 pc, with 0.2 A.U. orbital radius and believed to have 1.5 Jupiter mass.
Longer baselines will be required to achieve similar resolution on Earth-like planets, but the imaging of continents is potentially feasible. At this stage, the associated spectro-imaging will be of interest to search for photosynthetic activity at the scale of sub-continents or oceanic regions which may be as green as the terrestrial Sargasso Sea.
Concept of Exo-Earth Discoverer
In space, optical interferometric arrays will be liberated from the size limitations imposed on Earth by site availability, atmospheric problems and the diurnal rotation of the terrestrial substrate. Sizes of one kilometer hundreds of kilometers are considered in the following discussion, but most design principles remain valid for larger sizes. Objects such as neutron stars, expected to have a high intrinsic brightness, may prove observable with 10,000 or 100,000 km baselines if a set of out-rigger mirrors, with nearly flat shape, are later added to the EED .
Given the moderate diameter, a few meters, of the interferometer sub-apertures, the total aperture will be highly diluted. If recombined in the simplest way, the Fizeau mode equivalent to operating a giant telescope with a mask defining the sub-apertures, the beams provide an image which is useless since its central interference peak is surrounded by a vast halo of side-lobes carrying most of the energy.
Instead, the pupil can be re-arranged in such a way that it appears more dense when seen from the detector, so as to provide a more favorably peaked interference pattern. Although Michelson's pioneering 20 feet and 50 feet interferometers already had such a "densified pupil", only recently was it shown  that many-element densified pupils can provide snap-shot images on compact objects. With its multiple free-flying collectors in space the EED allows an efficient implementation of this principle.
In addition to direct imaging, the optical design allows coronagraphic uses at visible and infra-red wavelengths for observing exo-planets, quasars and other contrasted objects.
The basic geometry considered is sketched in figure 1. It involves a number of free-flying telescopes, all feeding light in the form of afocal beams into a "focal" spaceship where flat mirrors feed a common focusing mirror. The images are thus recombined into a single high-resolution image. For equal optical paths, the telescopes are located on a paraboloidal surface, with the recombination satellite located at its focus. The system is analogous to a single giant telescope, although the densified-pupil limits the size of the field being imaged.
An adaptive optical system achieves the phasing required for fully constructive interference, using algorithms such as described by Pedretti et al. . Within the recombination satellite, the basic "densified pupil" recombiner shown in figure 1 can be interchanged with other focal instruments such as the beam-splitter arrangements designed for Bracewell's nulling technique and its improved versions   .
For snapshot imaging and coronagraphy at visible, ultra-violet and infra-red wavelengths, the "densified pupil" recombiner involves a polyhedral mirror followed by a concave paraboloidal mirror which refocuses the beams to form the recombined image. Instruments such as spectrographs or coronagraphs, or combined coro-spectro-imagers using micro-lens arrays to provide x,y,lambda information, can be installed downstream.
The principle of "densified pupil imaging" has been previously described . The method involves a phased recombination of the sub-images, i.e. the images obtained from each sub-aperture, with the exit pupil distorted in such a way that the sub-pupils are magnified with respect to their spacing, the pattern of their centers being conserved, as shown in the example of figure 1.
This pupil densification shrinks the halo of diffracted light otherwise generated by Fizeau-type recombiners, thereby concentrating the energy in the central peak and neighbouring sidelobes. The price to be paid is a smaller usable field, the size of which is adjustable and can be traded against luminosity if the relative size of the sub-pupils is adjustable, using for example zoom-lenses in each of them, or interchangeable Cassegrain secondary mirrors in each collecting telescope.
An extreme case of pupil densification is when sub-apertures become adjacent in the exit pupil. Hexagonal masks can be installed on the telescopes for filling exactly the exit-pupil (figure 1). This is of interest when applying coronagraphic "cleaning" to the final image, according to the classical scheme of Lyot where a focal and a pupil mask remove much of the diffracted light from the central object: in terms of its diffraction pattern, a compact densified pupil thus obtained indeed behaves like a single aperture, compatible with Lyot masking or other coronagraphic schemes.
The initial TRIO concept for interferometry with free-flying telescopes had small solar sails as the principal means of geometry control. It appeared suitable for the smooth micrometric motions needed when making stabilized exposures on an object, but had obvious limitations in terms of the accelerations needed for repointing large arrays. The subsequent studies pursued at the European Space Agency  considered novel FEEP ion thrusters for faster slewing. With such thrusters and Earth-trailing or Sun-Earth Lagrange orbital sites providing a smooth residual gravity, arrays spanning several kilometers can be operated efficiently. A metrology satellite, located at the center of curvature of the virtual giant mirror and launching laser beams towards retro-reflectors aboard each telescope, provides a simple approach to controlling the array geometry.
For reliability, a "sheep dog" satellite, which may also carry the communications antennas, can be added to capture and bring back any escaping spaceship. Umbrellas are needed for each spacecraft, especially if passively cooled infra-red operation is desired in addition to the visible operation.
In terms of optical performance, the possible trade-offs between the number of elements N and their size appear to favor N values larger than a few dozens. Indeed, the number of object points which can be imaged simultaneously in a snapshot exposure is of the order of N2.
A ring geometry will be preferred for most imaging situations.
Component telescopes in the size range from 1m to 8m or more can be considered. A strong requirement of the densified-pupil imaging concept is that all sub-apertures be of equal size and shape. The telescopes should preferally have adaptive optics, in addition to the inter-telescope piston correctors needed for fully phased imaging. If the recombined images are not phased but just coherent, observing remains possible with full angular resolution, but in the speckle interferometry mode, suitable only for simple objects and providing degraded images. This may allow some ultra-violet observations at wavelengths shorter than the adaptive correction range.
Coronagraphy with Exo Earth Discoverer
With its interference peak, the recombined image may be fed into coronagraphic optics, whether a classical Lyot masking device, a Roddier & Roddier  phase mask device, or an interference coronagraph. The former requires a compact pupil with little obscuration, which is in principle achievable with careful densification as sketched in figure 1. The densified-pupil imaging mode requires that the entrance pupil be an "exploded" version of the exit pupil, i.e. that the pattern of centers be identical, but with sub-pupils comparatively smaller in the entrance pupil with respect to their spacing. The free-flyers array therefore also has a hexagonal pattern with one, two, or three rings in this mode. Unlike Lyot's opaque mask which spreads over five diffraction rings at least, the Roddier-phase mask is smaller than the Airy peak, and can in principle allow planet detection closer to the star, down to the first dark ring. Ensuring a wide usable spectral band for the phase mask may prove feasible with a Bragg hologram or equivalent multi-layer dielectric films stacked as concentric discs.
The interference coronagraph invented by Gay & Rabbia  incorporates an ingenious phase reversal solution which accomodates a wide spectral band, but produces a double image, symmetrized with respect to the star position at the field center. It can accommodate any pupil shape, whether single or multiple, provided that it be centro-symetrical.
Coronagraphs of either type remove much of the diffracted light from a bright central object, and thus help imaging faint surrounding features. This first level of cleaning can be complemented by additional levels: optimized settings of actuators on the mirrors can tune them for minimal diffracted light in the halo region of interest .
A third level of cleaning is achievable with "dark-speckle imaging", a technique which exploits the presence of dark speckles in the diffracted halo . These speckles can be "boiled" by slightly readjusting the actuators. A cleaned image is then reconstructed by mapping the occurrence of dark speckles. Because of the incoherent addition of light, no dark speckle can appear at the location of a stellar companion or planet.
Recent ground-based observations   confirm that one gains significantly, beyond the limitations of adaptive coronagraphy, and higher gains are expected in space since the exposures can last seconds instead of milliseconds. Planets 25 magnitudes, or 1010 times, fainter than their parent star can in principle become detectable. Once located, a permanent dark speckle can be installed at their location in the field, and, with a suitably positioned spectrograph slit, or an integral field spectrograph, spectra can be recorded.
The EED equipped for dark-speckle coronagraphy is suitable for observations in the visible and the thermal infra-red up to perhaps 20 microns, assuming passive cooling techniques such as those considered for the Next Generation Telescope. At 10 microns, the dynamic range required to detect a Jupiter-like planet is only 106, but a multiple aperture as large as hundreds of meters is of interest to improve the planet's contrast against the contaminating zodiacal emission, as discussed below.
Advantage of long-baseline imaging for planet
detection in the presence of sky background and zodiacal light
In the visible, the sky background is expected to contribute negligibly in images of exo-planets produced by EED. Regarding the constrast of a point source imaged with an extended background, the classical gain of ordinary telescopes when their resolution increases indeed favors large instruments in space: a smaller Airy peak covers a smaller area of emissive sky.
In the thermal infra-red, the bright zodiacal and exo-zodiacal emissions are of more concern, and have justified some consideration for locating the DARWIN instrument at 5 AU from the Sun. With EED, the light concentration achieved on the planet by the interference peak from multiple phased apertures improves the situation, and 1 A.U. solar orbits are adequate.
The effect of contamination by an extended sky emission in densified-pupil imaging has been considered in the initial calculations . These are therefore applicable to the infra-red situation where the zodiacal emission from the observed star, and possibly of the solar system, tends to hide exo-planets.
In such cases, the object function may be considered as a sum of a uniform sky background S(x,y) and a Dirac peak O(x,y) representing the unresolved planet. The interference function of a phased interferometric array having many elements has a central peak surrounded by a wide halo of sidelobes, which may be considered as a sum of intensity distributions P(x,y) representing the peak and H(x,y) representing the remaining halo. According to the theory of densified-pupil imaging, one obtains the image by convolving the object and interference functions, and then multiplying by the sub-aperture's diffraction function. The convolution may be expanded to a sum of four terms:
The first three terms describe a nearly uniform background in the image "window" obtained after applying the final multiplication. The last term describes the planet image, which may be detectable above the photon and detector noise of the background.
Enlarging the array, by increasing the spacing of the entrance apertures, has no effect on the exit pupil, in the arrangement of figure 1. It therefore has no effect on the image. Increasing the number of apertures increases the peak/halo ratio in proportion, and thus the peak/sky ratio also in the same proportion.
Typically, a 200m array used with a fully densified exit pupil provides an infra-red image at 10-microns where the star is unresolved. An Earth-like planet at 10pc can appear as a faint peak, a million times fainter than the star, at about 10 Airy radii from the star's peak. The star's peak and rings are removed for the most part by the coronagraphic attachment, for example a phase-mask system which is little affected by the gaps in the densified pupil.
In the visible, the same star and planet provide interference peaks and envelopes shrunk about 20 times with respect to the star-planet spacing. The planet is angularly resolved by the sub-apertures, and cannot appear together with the star in the same high-resolution imaging window. Separate high-resolution images can be obtained as sketched in figure 3, and the star's image is typically resolved well enough to show some detail. The corresponding convolution destroys any dark speckles, and therefore makes their analysis inapplicable in this case.
Fig. 2. Phase mask coronagraphy with a 36-element EED. The Airy peak and diffraction rings in the star's image are markedly attenuated by the coronagraph installed downstream from the recombined focus. The coronagraph is similar to the classical Lyot design, but has a transparent phase-shifting dot replacing the opaque mask of Lyot. The transparent dot is smaller thant the Airy radius.
A wide-field variant of EED: the Moth- Eye Interferometric
If the collecting telescopes of EED are replaced by simple spherical mirrors, all concentric, then one benefits from the remarkable optical properties of Schmidt telescopes, at the scale of an array which may span hundreds of kilometers and can provide full coverage of the celestial sphere.The proposed design solution, sketched in figure 3, has similarities with the Arecibo radio-telescope, and again involves densified-pupil imaging.
The array being highly diluted, with its mirrors of 1-10m size spaced by hundreds or thousands of meters, mutual occultations by the elements do not occur frequently and thus cause a negligible loss of observing efficiency. The numerous focal stations which move to their assigned positions, as required by the parallel observing schedule, each provide a high-resolution image with a very small field containing NxN resolution elements, if N is the number of mirrors contributing to the image.
Figure 3. Moth- Eye Interferometric Array variant of EED providing full sky coverage. The array has spherical mirrors (fat lines), arranged concentrically as a diluted paving on a common sphere MS. A number of focal stations Ri (enlarged at right) containing recombination optics are located on the half-size focal sphere FS, and can be moved on this sphere to observe different fields. They contain differential delay lines to correct the spherical aberration of the mirror sphere MS, and to densify the pupil. A central metrology station emits laser beams to monitor positions of all elements. Sun shields (thin lines) also serving as solar sails are attached to each mirror segment and to the focal stations for baffling and for passive cooling to 50deg.K. No re-pointing being required for the collecting mirrors, and little motion being required for the focal stations if there are many of them, the attached solar sails may suffice for field exploration at a suitable rate.
The MEIA design for parallel independant observing in many directions provides the same observing efficiency as would be attainable with many separate steerable arrays, but uses fewer mirror elements since each simultaneously serves for different images. This form of mirror sharing will be most valuable once the need for observing many fields simultaneously will have emerged, but a modest initial configuration with a single focal station and limited sky coverage, will be expandable into a full MEIA. The Arecibo and the Hobby-Eberly telescopes are examples of such embryonic spherical telescope structures which cannot be expanded to a full sphere nor have many focal stations, but nevertheless prove useful.
Following the study work initiated by the European Space Agency, the forthcoming DS-3 test of small free-flying optical elements released from NASA's Space Shuttle will be a major step towards qualifying free-flyers as component of large future interferometers. The subsequent New Millenium Interferometer proposal , expected to provide a kilometric baseline with a pair of small collecting mirrors is also a highly desirable step. If successful, it will make it possible to tackle the ambitious goals discussed above.
Optimal combinations of ion thrusters with solar sails should be studied. The former are efficient for translating the free-flyers, as required when slewing the entire array, but the associated pollution tends to cause absorbtion lines in the stellar spectra. During an observation, low levels of acceleration are needed to maintain the stability, in a site with smooth gravity, and solar sails of the type described in Labeyrie et al.  may be optimal. Their role as umbrellas for passive cooling is of interest.
Regarding the optical concepts, much of the work towards a detailed design can be done through diffractive calculations and laboratory verifications on a simulation bench. The coronagraphic and dark-speckle attachments are also profitably simulated in the laboratory, as achieved for the ground-based dark-speckle program.
The encouraging results of the feasibility studies carried out by the ESA, regarding the operation of free-flyer arrays of telescopes, suggest that a many-element densified pupil imaging array can be built. It should prove most efficient for high resolution imaging as well as for coronagraphic imaging in the visible and the infra-red.The high spatial resolution achieved in the latter case helps removing the contamination from zodiacal light.
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