Antoine Labeyrie
Collège de France & Observatoire de Haute Provence (CNRS),
F-04870 Saint Michel l'Observatoire, France
E-mail: labeyrie@obs-hp.fr
The "densified pupil" imaging mode, now developed for large multi-telescope interferometers 1, will provide images and spectro-images of compact objects, directly at the recombined focus. It requires telescopes of identical sizes and allows trading field for luminosity. The principle is applicable to dilute arrays of small, medium or large telescopes, 0.2m to beyong 25m in size, using similar recombination systems and cophasing methods. Design solutions are discussed for each case, and particularly for the medium-scale Optical Very Large Array of 27 telescopes, spanning one kilometer, studied at Haute Provence. We build a prototype 1.5m OVLA element. Solutions for the beam recombiner are discussed, and will be assessed with a test-bed interferometer involving 27 small mobile heliostats. forming a 100 or 300m ring.
Larger versions of the OVLA, employing unit telescopes of 10 to 25 m, are also considered, in connexion with the large telescope study iniated by the Lund group. In space, arrays of free-flying telescopes can in principle resolve continental detail of exo-planets. Equipped with additional out-rigger mirrors providing baselines of 10,000 to 100,000 kilometers, such space arrays can in principle provide images of pulsars and naked neutron stars.
keywords:optical, interferometry, multi-telescope; imaging, densified pupil
The extraordinary science potential of multi-telescope interferometric arrays
has been stressed for two decades, but some ingredients were missing to
implement them:
We discuss ways of building instruments with 27 apertures or more. Their size may be modest or large, but has to be homogeneous for efficient imaging according to the densified-pupil principle. The instruments thus considered are: a modest "Micromegas" array involving 27 mirrors of 20 cm size, and spanning a few hundred meters; a more powerful "Optical Very Large Array", previously described 5, 15 but now upgraded to provide densified-pupil imaging; and a more ambitious array of large telescopes, 10 to 25m in size and spanning 10 to 20 kilometers. The latter is capable, in principle, of producing images of extra-solar planets where detail such as their continents would be resolved 1. Space versions of such instruments, spanning as much as 10,000 to 100,000 km when observing neutron stars, are also discussed.
The more modest "Micromegas" array is expected to serve initially as a test-bed for the central recombination system of the OVLA, but should also produce useful snapshot images of bright stars and their surroundings. It also appears applicable to solar imaging with 5 milli-arcsecond resolution.
The OVLA, capable of spectro-imaging with high spatial and spectral resolution, has obvious uses in stellar physics, and should access the brighter extra-galactic sources. If fully equipped with adaptive optics and laser guide stars on each sub-aperture, it is expected to exceed visual magnitude 20.
Arrays of 10-25m adaptive telescopes will address the kind of science considered by Mountain 6. They will provide detailed images of stellar surfaces and their environment, of galactic features, of extra-galactic and cosmological sources with resolution levels eventually reaching 10 micro-arcseconds. Objects such as the remote galaxies appearing in the Hubble Deep Field, although very faint, can in principle be imaged with sub-milliarcsecond resolution, considering the high degree of light concentration achievable with an adaptively-phased densified pupil.
In space, densified-pupil arrays of small or large telescopes will likely have free-flying elements 7. In the absence of residual "seeing", their coronagraphic and dark-hole 8 imaging performance can be markedly improved with respect to the above-mentioned ground-based interferometers. When the parent star is unresolved, dark-speckle imaging 9 will also be applicable to further improve the coronagraphic sensitivity. Operating 10,000 to 100,000 km baselines appears feasible, with remote out-rigger collectors, and these can provide nano-arc-second resolution on neutron stars and other small objects of high intrinsic luminosity.
As explained elsewhere 1, 2, 3 , densified-pupil imaging involves the kind of image recombination originally used by Michelson and Pease at the 20-feet interferometer, but with many rather than just two beams, and a conserved pattern of sub-pupil centers in the exit pupil, where sub-pupils are proportionally larger than in the entrance pupil. With adequate phasing, sub-pupil orientations being preserved for polarisation homogeneity, the image of a point source becomes dominated by a central interference peak. A usable image is also obtained on resolved sources if, and only if, the pattern of sub-pupil centers in the exit pupil is a scaled-down version of the pattern in the entrance pupil.
With a strongly densified pupil, the energy otherwise dispersed in a wide halo of side-lobes becomes concentrated in a smaller halo.
Efficient images, concentrating most of the collected energy, can thus be produced with highly diluted arrays of many sub-apertures. The analysis 1 indicates that snapshot images of extended objects, formed in such conditions, can have NxN resolved elements if N is the number of sub-apertures. These image elements can be contiguous, as is the case when observing the apparent disk of a star, or separated as would be the case for a cluster of unresolved stars. However, more than N2 such stars within the Airy disk of an entrance sub-pupil causes their interference peaks to vanish amidst the side-lobes of their added halos. The limitation already exists in a N-aperture Fizeau interferometer, owing to the S1/2 growth of the halo's speckle noise when S unresolved sources are present in the halo field. For imaging extended objects, the sub-apertures of a Fizeau array should be larger than D/N, if D is the array size. This implies nearly contiguous sub-apertures for a ring-shaped array. With a densified exit pupil, the entrance sub-pupils cannot be contiguous, and no extended object can provide snapshot images unless it fits within the NxN pixel high-resolution field of the recombined image. Multiple exposures or observations with different aperture patterns improves things, although not as much as would a comparable multiplication of N, by smoothing the halo in the resulting image where intensities are summed.
All this indicates that densified pupils are suitable for star clusters and compact resolved objects of moderate complexity. For large arrays in the kilometric or multi-kilometric size range, densified pupil imaging can intensify the interference peak 104 to 106 times with respect to Fizeau imaging.
To best suit the type of object observed, the trade-off between luminosity and field can be made adjustable, using zoom lenses in each sub-pupil.
In the absence of adaptive phasing, the interference function is a speckle pattern, which may be exploited according to the principles of speckle interferometry, and can similarly provide images if the oject is simple.
Figure 1
Ring arrays are mainly considered here since they provide efficient spread
functions and can be operated without delay lines, if the collecting telescopes or
heliostats are movable, but the discussion also applies to multi-ring or
square-grid aperture geometries, which can provide more compact exit pupils once
densified.
The interference function of a ring array resembles the Airy pattern of the giant filled aperture, with a narrow central peak surrounded by a few rings, becoming broken into a speckle pattern of side-lobes at increasing distances from the peak (figure 1).
The image can be exploited directly, and can also be deconvolved post-detection with deconvolution codes such as CLEAN or WIPE 10. Coronagraphic techniques involving a phase mask 11 and dark-speckle analysis 12, 9 are also potentially applicable for detecting faint stellar companions, or exo-planets. The sensitivity thus achievable, on Earth and in space, should be compared with that expected for other schemes such as Bracewell's "nulling interferometer" 13 and Gay's Achromatic Interference Coronagraph 14.
The arrays considered here, whether using large or small elements, consist of many (27 to perhaps 81 or 243) telescopes which are movable and concentrate light at a common coudé focus where all images are superposed. The motion capability serves for changing the array size and geometry, and also for compensating the optical path difference variations caused by Earth rotation. Telescopes arranged along an elliptical ring thus require no delay lines if the ring shape is made to change during the observation in such a way as to maintain equal optical paths. The coarse mechanical motion is supplemented with a fast adaptive-optics correction of coherence and phase errors among the telescopes.
On bright and moderately resolved stars, the level of positioning accuracy needed to acquire the fringes does not have to be much better than a millimeter. The spectro-imaging camera, with the set of partial images involving 3, 9, etc. sub-pupils (figures 2, 4) can indeed have enough spectral resolution to find fringes with optical path differences reaching a millimeter.
A more accurate definition of the array's geometry is obviously possible with metrological laser systems. A system where each telescope receives 3 laser beams had been considered and tested 16, but found difficult to operate. The principle is also part of NASA's initial design for the Space Interferometry Mission, in which a "metrology boom" carries coherent laser sources, at least three of them illuminating each collecting element.
Railway tracks, oriented radially, are used at the GI2T interferometer, and can certainly be adopted for larger multi-telescope systems. More flexible solutions, also lower in cost, involve hexapod translators, resembling in some respects the hydraulic "walking" translators which have been used for moving nuclear submarines.
Figure 2
Versions of the recombiner system, applicable to arrays of small or
large telescopes, are shown in figure
2.
A multi-element Fizeau interferometer, being equivalent to a giant telescope with an aperture mask, a dispersive prism in the exit pupil can fully correct the atmospheric dispersion, as would a giant prism on top of the entrance aperture. With a densified pupil, the prismatic correction required in the exit pupil is larger for the interference function than for the diffraction function. Both can be corrected at the same time in the exit pupil with a large prism having facets at the sub-pupil locations, in such a way that the sub-pupils have a locally reduced prism angle and different thicknesses of glass. The equivalent implementation shown in figure 2 has Risley prisms of adjustable angle and thickness in each sub-pupil. Any residual dispersion caused by inadequate matching of glass and air dispersions is removable in software, at little cost in signal-to-noise ratio, from the multi-spectral x,y, lambda image.
Vacuum tunnels are used in other interferometric systems to equalize all lengths of horizontal light propagation in air, thus compensating the dispersion of the interference function. For the long and variable baselines considered here, up to 10 or perhaps 20km long, the cost of variable-length tunnels would be prohibitive.
Obtaining spatial and spectral information simultaneously is of utmost interest for fringe acquisition, for adaptive phasing, and for the science derived from the high-resolution images. In our situation where the number of spatially resolved elements in the image is small, of the order of NxN, the spectro-imaging devices developed at Marseilles by G. Courtès 17 and his group are particularly attractive Micro-lenses arrayed in the recombined image, several of them per resolution element, produce an array of micro-pupils serving as entrance apertures of a spectrograph. Diffraction through the micro-lens apertures smoothes the geometric dotted-ring shape of the micro-pupils.
With current concepts of active and adaptive telescopes, the passive stability traditionally provided by supporting piers is no longer needed. Instead of using optical delay lines to equalize the optical path lengths, moving the telescopes themselves simplifies the optical train. It does however affect the positioning freedom of the telescopes, since an elliptical ring is generally required on a flat platform, but introduces other degrees of freedom regarding the array size and the azimuthal location of the telescopes. The ring constraint has little impact when there are many telescopes. Hybrid solutions with M rings and (M-1) delay-lines are also possible for more uniformly filled apertures.
Several types of hexapod systems appear capable of the smooth and accurate translation required, on the natural ground on pre-aligned posts (figure 3). We have built working models of leg mechanisms allowing zero-energy motion, a condition which is equivalent to specifying a constant height for the load. Steps are taken towards building a full size hexapod for the prototype OVLA telescope.
Figure 3
Michelson's original method for finding the fringes, by looking at them through
a dispersive prism, can be automated
18,
and extended to triplets of apertures, and triplets of triplets, etc. In
monochromatic light, a triplet produces honeycomb-like fringes. The x,y,lambda
pattern is thus an array of vertical rods, tilted if the optical paths are unequal.
Its tri-dimensional Fourier transform has six points forming a hexagon around
the origin, the tilt parameters of which are a measure of the two optical path
difference errors. For fringe acquisition and coherence tracking, square moduli
of Fourier transforms made from short-exposure images can be averaged in time.
Once near-zero optical path difference is achieved, the adaptive phasing system
can utilize the instantaneous phases in the 6 points as the error signal.
Similar processing is achievable with a triplet of triplets, i.e. nine sub-apertures, to center the fine honeycomb appearing within the central cell of three superposed broader honeycombs. Three such images can again be superposed, forming a 27-aperture image, and processed in the same way if the object is moderately resolved at these later stages involving the longer baselines. 81 or 243 apertures could be phased in a similar way with one or two more levels of triplet formation. On well resolved objects, the finer fringe components become attenuated, but image sharpness criteria applied to the triplet levels have been found to achieve the phasing rather efficiently 4, even on some color-dependant objects. The complications arising with color-dependant objects deserve further investigation.
Figure 4
shows a beam-splitter scheme providing the hierarchy of simultaneous
triplet images together with the complete image. It is desirable to record the
image and triplet sub-images on a single photon-counting camera, in the
spectro-imaging mode, and this appears feasible with adequate sampling.
Arrayed telescopes larger than Fried's parameter r0 are expected to include adaptive optics, so that the sub-pupils in the recombiner be uniform in phase. Large collecting telescopes, if equipped with laser stars 19, 20 may provide such adaptively phased sub-pupils on arbitrarily faint objects, and this would improve the limiting magnitude for inter-aperture phasing in the recombined image. A simple extrapolation of the limiting magnitude mv = 13 to 15 usually considered achievable when phasing r0 = 10cm seeing cells in conventional telescopes indicates that the limit should reach mv = 23-25 if the apparent r0 is enlarged by the adapative optics of 10m telescopes to match their pupil size.
The encouraging results obtained by Coudé du Foresto 21, and Perrin 22 indicate that optical fibers can replace conventional coudé trains. The principle of densified-pupil imaging remains applicable through fibers and can provide directly usable images at the output if used according to figure 5. Fibers would be of most interest if they could directly connect the telescope's foci to the central recombiner, nearly equal lengths of fiber being used for chromatic balance.
Figure 5
A modest implementation of the above principles, using for example 27 collectors of
only 20cm arrayed on a 100-300m ring, should already produce dramatic science.
It would provide snapshot images and spectro-images of bright stars, with for example
27x27 resolved elements, which is of considerable interest for stellar physics.
Such small apertures are usable efficiently with low-order adaptive optics correcting
tilt, defocus, and piston errors, or even only the latter at the expense of some
efficiency loss.
The Micromegas concept, named in relation to its small elements and great power, follows these specifications. It can also serve as a test-bed for techniques to be used in more ambitious projects such as the OVLA and the ARGUS array of 10-25m telescopes described below. Either heliostats or telescopes can be used as collectors.
The OVLA project, involving 1.5m telescopes mobile on hexapods, has been previously described 15, and the design is being up-graded to allow densified pupil imaging. The construction of a prototype telescope is described elsewhere at a simultaneous conference 5.
Current plans involve:
The science potential of the test-bed will possibly justify its continued use as a Micromegas imaging array dedicated to solar and bright star observations.
With glass achromats in the recombiner, for a simplified optical train, the wavelength range accessible to the OVLA may cover 400 to 2500nm, using visible and infra-red cameras on both sides of a dichroic beam-splitter. Specialized observing modes, such as coronagraphy and polarimetry, will be achievable with interchangeable modules.
After the GI2T to GI3T conversion, scheduled in 2000, suitable sites, with adequate flatness at the kilometer scale, will have to be found for building the OVLA. The flatness requirement is relaxed to tens of meters since the recombining optics accepts slant incoming beams.
Current ideas and developments towards mosaïc mirrors and new mount types announce the feasibility of ambitious interferometric arrays having for example 27 telescopes of 25m. Calculations 1 of signal and noise in such arrays show that a Jupiter-like planet is in principle imageable at 5pc distance with 27x27 resolved elements. The impressive science achievable at visible and infra-red wavelengths justifies broad collaborative efforts towards their study and implementation.
In the wake of the Keck telescopes, a further drastic reduction of telescope weight and cost appears possible with mosaïc mirror techniques involving thin and active segments made from ordinary glass 5. The study of a 40m telescope, pursued in Sweden 23, 24, 25 and the recent work undertaken at ESO to study a 100m telescope 26 suggest that such large instruments are feasible within reasonable cost limits.
The complementarity of isolated giants and interferometric arrays deserves a careful evaluation. Mountain 6 concludes that more science is likely to be achievable with large multi-element interferometers than with filled super-telescopes of equal area. An interferometric array having movable telescopes can observe with the elements either arranged close together or widely spaced, and can therefore have the advantages of both: a comparatively wide field at minimal resolution, and a restricted field of NxN resolved elements at high resolution (10 to 100 micro-arc-second). The retracted observing configuration has imaging properties approaching those of a monolithic telescope with equivalent collecting area, and also allows incoherent observing with minutes of field. Used separately when seeing is too fast for efficient interferometric observing, the numerous large telescopes will also provide much neded observing time for conventional imaging and spectroscopy.
The studies undertaken in Sweden
23,
24,
25
for 25-50m telescopes thus suggest the following strategy, for which our group is
committing to a collaborative effort:
A similar approach allowed IRAM to build a 30m millimetric dish in Spain and a 6-element interferometer with 15m dishes in France, the excellent results of which have now triggered the study of the 64-element Large Sub-millimeter Array. Adding elements thus proves a low-risk strategy towards very ambitious instruments.
Preliminary results of the large telescope study are reported by A. Ardeberg at this series of conferences. Our expected contribution at Haute Provence will bear on the use of active glass segments for the large mosaïc mirrors, based upon the current work for the OVLA prototype telescope. It will also bear upon the design of large telescope mounts suitable for interferometry.
Figure 6
Skeletal spherical mounts providing three angular degrees of freedom allow a
simple coudé train involving a single flat mirror, located at the center
of the sphere and driven around one axis.
To avoid "dome seeing", the spherical frame structure should preferably remain open. Adjustable louvers can also be installed on the spherical frame, for controlling the wind velocity near the mirror. The mount can also be equipped with a hexapod translator.
The design of an "Argus" interferometer using such large telescopes is considered at Haute Provence. These must be capable of both compact and highly diluted arraying, for array sizes reaching perhaps 20 km. A difficult problem is the selection of good mountain sites with adequate flatness at this scale. The flatness specification is tens of meters, and no attempt will be made to level the site if the natural ground texture allows direct operation of the hexapod translators.
Low-resolution observing modes require a compact configuration of the array, with minimal distances between the telescopes. With 36 telescopes, a 3-ring hexagonal array may for example be obtained, and it can provide a nearly filled hexagon as the exit pupil (figure 6), an extreme case of "densified pupil" recombination. This mode provides maximal field and requires two delay lines to equalize the optical paths among the 3 rings of movable telescopes.
27 movable telescopes of 25m can also be arrayed as a single 300m ring, providing a less compact exit pupil but requiring no delay lines. At the other extreme, a ring as large as 10 km, and even possibly 20km in the infra-red, appears operable if the site allows.
For faint objects in the mv = 30 to 35 range, interferometric arrays of large telescopes will heavily depend on laser guide stars to activate the separate adaptive optics residing in each telescope. The huge concentration of stellar light thus achieved from sub-apertures 250 times wider than the prevailing r0 extends the magnitude range for co-phasing the N sub-apertures in the central station.
The low-cost mirror technology developped for the OVLA 5 may prove applicable to large mosaics. Hexagonal elements, about 1.5m in size and 24mm thick, can be made of ordinary float glass, slumped, annealed and polished. Active supports, about 30 of them, make the mirror shape insensitive to flexures of the supporting structure, temperature changes, etc. Continuous shape monitoring appears possible with a light source at the center of curvature.
Given the very small field usable for interferometric observations, a Mersenne-type configuration, i.e. with parabolic M1 and M2 mirrors, can be used. However, more field is of interest to observe simultaneously a reference star, its coudé beam being made nearly coincident with the main object's beam.
An interesting optical solution with a f/0.95 spherical primary mirror has been calculated by the Lund group 25. Other solutions calculated at Marseilles are presented at these conferences 28, 29.
Figure 7
In space, the concept of free-flyers arrays proposed in the 1980's
7 ,
is now studied in more detail by ESA and NASA. With many elements and densified-pupil
imaging, instruments of considerable power can be foreseen. Baselines reaching some
100 km should prove operable on ordinary stellar and galactic sources, while the few
known pulsars and isolated neutron stars, with their extraordinary surface luminosity,
should allow baselines as long as 100,000 km if no surrounding nebulosity hides the
central source, and this should allow resolved images to be formed.
NASA has announced plans to operate an array of free-flying 8m telescopes in space after the initial NGST. With the kind of pupil densification shown in figure 7), coronagraphic imaging can be avchieved, using Lyot masks or a phase-mask 11 complemented by dark-speckle techniques. The prospect of exo-planet images showing resolved detail, continents for example, is in principle obtainable, and equivalents of Earth's chlorophyll absorbtion bands can be evidenced if photosynthetic life occurs. The complementarity of these techniques with those utilizing beam splitters for light nulling 13 should be investigated.
For implementing the 10,000 to 100,000 km baselines needed for resolving neutron stars, a free-flyers array can serve as the core instrument, with "out-rigger" mirrors arranged as shown in figure 7). The metrology requirements for such giant baselines, although difficult, can probably be met with the help of forthcoming astrometric catalogues, the position of the outrigger mirrors being monitored by boresight alignment with respect to background stars seen from the central telescopes.
With adaptive optics and "densified pupil" imaging, interferometric arrays of many elements will provide extensive spectro-imaging data on bright and faint objects. Whether modest arrays of small mirrors, ambitious arrays of very large telescopes spread kilometers apart, or intermediate systems such as the OVLA, most of the standing problems which heretofore prevented such projects from emerging are now being solved, and the time has come for practical attempts. Pending major projects such as a multi-25m ARGUS, the moderate cost of an OVLA allows its construction in the near future. Many groups in different countries have now acquired the skills needed for such projects. As done successfully by the radio-astronomy community, it is now time to join efforts towards designing, modelling and building truly powerful instruments. Possible sites, suitably flat at the scale of 10 kilometers, are difficult to find and systematic surveys should be undertaken shortly.
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