• Astrophysical issues
• Feasibility of exoplanet images and spectra
• The Dark Speckle Imager
• Adaptive coronagraphy
• Present performance of the dark-speckle coronagraph prototype
• Conclusion
• References

Images with extra-solar planets appearing as "pale dots" near their parent star can be produced by the Next Generation Space Telescope if it is equipped with a "dark-speckle" camera (Labeyrie 1995, Gezari et al. 1997). It exploits the self-destruction of stellar straylight, happening randomly at certain locations in the field, to improve the detectability of a planet peak when present at one of these locations. The camera also has adaptive optics to concentrate stellar light, as much as possible, in the central Airy peak, and adaptive coronagraphs to further attenuate the surrounding diffraction rings and speckles. Refined techniques of apodization and image analysis can darken the star's average halo level by several orders of magnitudes and thus they offer new hopes of detecting extra-solar planets and other faint features near stars, QSO's, etc... if installed on board of the Next Generation of Space Telescopes.

Astrophysical issues

The scientific objectives achievable with the proposed instrument cover a broad field, from stellar environments to extragalactic sources.

• Binary systems

  Binary systems can be imaged, even with a large magnitude difference between both companions; the distribution of white and brown dwarves in multiple systems can be derived. An extreme case is the detection of exoplanets. This is in principle achievable, and low resolution spectra of detected planets can in principle be obtained to gain information on the composition of their atmosphere (section 2).

• Disks and envelopes

  Circumstellar envelopes around evolved stars and dusty disks around young stellar objects also appear detectable and observable at high angular resolution. It will provide information in particular on the physical processes occuring during the formation of planetary systems.

• Galaxies and quasars

  In term of extragalactic sources, the dark-speckle coronagraph will also be able to observe quasar environments. The nature of the interaction with the host galaxy will be investigated, as well as the high resolution structure of active galaxy bulges.

• Einstein rings

  The NGST, with its diffraction-limited resolution reaching 10 milli-arcsecond at blue wavelengths, could provide images of Einstein rings associated to the closest stars and hypothetical planet-like dark bodies within a few parsecs from Earth. This will exploit the diffractive aspects of gravitational lensing (Labeyrie 1994), and the high intensification, reaching 1012, which they are expected to provide. For detecting flashes when pointed towards galaxies, as expected when a foreground "lost planet" crosses the line of sight, the required instrument is a field imager, equipped with fast detectors. A coronagraph, pointed to the faintest known close stars having a galaxy in their background is needed in this case.

• Detectability

  At luminosity levels of the order of 10^-9 to 10^-10 relative to their parent star, exo-planets are detectable if the star's diffracted halo can be brought down to 10^-6 or 10^-7, using adaptive optics for efficient apodization with Malbet's algorithm. A further gain of 100 or 1000 through "dar high-altitude "seeing". The conditions are much more favorable in space, given the stable spread function and the absence of shadow pattern. Excellent guiding, possibly involving a tip-tilt correction in the adaptive mirror, is needed.

  For a 4th magnitude star, with an 8m aperture, 20% quantum efficiency, a 1000 Angstrom bandwidth in red light, and a star light halo at the 10-6 level, a planet at relative level 1/R = 10-9 is imaged with SNR = 5 in 4 hours. The duration of the individual exposures is of the order of a few seconds. High efficiency photon-counting cameras or low noise CCDs are both of interest as detectors. If available in time for NGST use, the Super-conducting Tunnel Junction detector appears of considerable interest (Peacock et al. 1998).

  Numerical simulations performed for HST (Boccaletti 1998, Gezari 1997) have confirmed the feasibility of the exoplanet imaging and low-resolution spectroscopy. Figure 1 shows one example of an exoplanet simulated image.

  

  Figure 1: Simulated observation of an exo-planet 109 times fainter than its parent star, using the dark-speckle algorithm to remove a starlight halo 1000 times brighter than the planet. Assumptions: 2.4m telescope, 10-6 scattered light level, 20% quantum efficiency. The total integration time is 22 hours for a 0 magnitude star. The field covers a few Airy radii and the actuator refreshing time is 10 seconds. Left: conventional long exposure, dominated by the residual speckle contrast. Right: cleaned image, where the planet becomes visible.

• Visible contrast of exo-planet and exo-zodiacal light

  An Earth-like planet at 10pc, observed with an 8m telescope, is approximately 1500 times smaller than the telescope's resolution limit in visible wavelengths. In the image, its intensity will therefore appear equal to the local intensity of the exo-zodiacal cloud if this background luminosity is 15002 times fainter than the planet's luminosity, per unit area of the actual resolved planet and cloud. Because of this " dilution " at high angular resolutions, the exo-zodiacal cloud is not expected to affect significantly the detection of an Earth-like planet at 10pc.

  Regarding the solar zodiacal contribution to "sky" background, it is of the order of mv = 22 per square arc-second, and thus mv =32 per resolution element of 10 milli-arcsecond. If the star is solar-type and located at 10pc , its magnitude is mv = 4.8 and the planet's magnitude is 30, assuming 10-9 relative luminosity. The detectability of an exoplanet on the solar zodiacal light background is thus critical and favors visible wavelengths.

• Spectral bands from exo-planets

  Near-IR spectra of planets provide an extended view of the chemical composition of their atmospheres. Vibrational water bands, as well as methane, carbone dioxyde or ozone signatures are present in the range 1-10 microns. Even low-resolution spectra of the detected companion could therefore allow the analysis of its atmosphere, if present, and in particular it would allow the distinction of brown dwarfs and giant planets.

  In the visible range, oxygene absorption bands can be observed if present in the exoplanet atmosphere. Another feature of interest for the search of living systems is the spectroscopic signature of possible photosynthetic processes. On Earth, the chlorophyll absorption is seen at an average level of 1% in spectra taken from orbiting satellites. Long integrations are needed to detect comparable bands in exoplanets with the proposed instrument. If some unknown bands are detected, the difficulty will lie in the identification. The prospect raises several intriguing questions: (1) How shall one distinguish real photosynthetic absorption features from those of mineral or organic molecules not associated to life ? (2) Should chlorophylls and the associated carotenoid dyes be expected to be universally present in photosynthetic life forms ?

  Among the millions of possible photo-absorbing macro-molecules, having different spectral features, independent processes of life creation and evolution may have selected identical molecules if these amount to strong attractors in the evolutionary process. Our limited knowledge of the process prevents an estimate of the probability of such a convergence, but it cannot be ruled out.

• Instrument description

  The instrument consists of the following elements:

  • - an adaptive coronagraph: either an occulting mask and pupil stop, according to the Lyot design (1939) or a more recent phase-shifting mask (Roddier and Roddier 1997), or else an "Achromatic Interfero-Coronagraph" (Gay and Rabbia 1996). The re-imaged pupil pattern is very sensitive to the image centering and it is thus important to control it actively.
    
  • - a Wynne corrector or an integral field spectrograph, to prevent the speckle chromaticity.
    
  • - a photo-counting detector, or a very low noise CCD camera, for acquiring short exposures of the speckled halo.

  Several improvements of coronagraphic techniques have been suggested recently. The phase mask proposed by Roddier & Roddier (1997) shrinks the central blind spot to the size of the Airy peak, by replacing the opaque mask used since Lyot by a phase-shifting transparent mask. The light nulling thus achieved removes the diffraction rings with a comparable efficiency, while not masking the first few rings.

  A problem which remained to be solved is the fabrication of a wide-band phase mask. A holographic solution appears possible, using Bragg structures to provide a reflective hologram with a color-selective phase pattern.

  The Achromatic Interfero-Coronagraph of Gay & Rabbia (1996) brings a similar gain, but causes a problematic symmetrization of the image. This method is described in these proceedings (Rabbia et al. 1998).

  Malbet's active cleaning procedure creates a " dark hole " at the feet of the star's Airy peak, while the dark speckle imaging technique brings a further level of cleaning. The two or three stages of nulling thus applied to the stellar light contamination should in principle reach the extreme level of image cleaning required to image exo-planets and produce their spectra.

  The coronagraphic dark-speckle imager may accomodate directly a broad spectral bandwidth, or be linked to a spectrograph. In particular, an integral field spectrograph used downstream would serve two purposes:
  

  1. provide spectra of each pixel;
  2. deal with the spectral dependence of the speckled halo of star light.

  For operation in full bandwidth, the contrast of the rings is improvable if one compensates the variation due to the proportional scaling of the Airy diffraction pattern with wavelength. A Wynne corrector may be used, which makes the speckle pattern nearly wavelength-invariant (Wynne 1979). The Wynne design has recently been recalculated by D.Kohler at Observatoire de Haute Provence and used for ground-based " dark-speckle " imaging, where it proved efficient (Boccaletti et al. 1998).

  More elaborate arrangements of integral field spectrography can be used. The TIGRE concept developped at Marseilles observatory, using micro-lens arrays, is of particular interest (Bacon et al. 1995).

  The final step towards highly cleaned images, dark speckle analysis, exploits the occurrence of dark speckles in the residual star light (Labeyrie 1995, Boccaletti et al. 1998). By moving these speckles between exposures, those locations where a planet's peak prevents the formation of a dark speckle are statistically highlighted and displayed in the form of a cleaned image.

  Dark speckle imaging requires that the image be over-sampled, with a few hundreds of pixels per speckle area, the size of which is identical to the Airy radius. This, in addition to the short exposures and the light spreading achieved by the integral field spectrography, requires that the read-out noise of the detector be minimal. Interchangeable arrays of micro-lenses, mounted on a wheel, can provide optimal sampling for ordinary and dark speckle imaging.

• Operation in dark-speckle imaging mode

  If a small deformable mirror can be inserted in the system, the wavefront bumpiness can be reduced. It attenuates the speckled halo leftover in the coronagraphic image, possibly down to levels of the order of 10^-7 relative to the star's Airy peak. The guiding jitter can also be attenuated.

  The dark-speckle algorithm requires a sequence of exposures, the deformable mirror being slightly re-shaped from exposure to exposure. The shape has to remain fixed during each exposure, so as to avoid any "filling" of the darkest speckles. The re-shaping between exposures should involve a random or pseudo-random set of deformations with amplitudes comparable to the residual un-correctible bumpiness. Thus, the average halo level is kept close to the lowest achievable value, the speckles being only re-distributed at constant average intensity. Such random action, rather than a calculated action, is necessary at this stage since the weak residual scattered light does not allow an accurate measurement of residual phases on the wave. The RMS phase corrections to be achieved randomly should match the level of the residual uncorrectible wave bumpiness, to avoid increasing the halo level. With 10,000 exposures obtained in this way during a few hours, the speckle noise can be considerably reduced in the cleaned image.

  If a faint stellar companion, brown dwarf or planet, becomes detected, then those exposures which provided the best speckle darkening at the planet's location can be identified from the data sequence and reproduced, with much longer exposure duration, by repeating the corresponding settings. This is required for obtaining spectra.

• Phase-contrast for wave analysis

  The wave analysis must be very sensitive to the presence of straylight in the feet of the Airy pattern. A possible way of achieving this sensitivity involves Zernike's phase contrast using an attenuating phase quadrature mask, a few Airy radii in size, in the corrected focal plane, and a camera in the subsequent pupil image where the mirror figure is then mapped as an intensity distribution. Phase-contrast cannot be used for adaptive optics in ground-based telescopes since the shadow pattern of seeing on the aperture would contaminate the phase-contrasted pupil image.

  

  Figure 2: Principle of phase-contrast for wave analysis. A- vibration with a small phase shift represented in the complex plane with its real and imaginary components; B - same vibration where the imaginary component has been made real through a 90deg. phase shift. The resulting vibration has its modulus increased; C- pupil P, focal plane with lens L and relayed pupil P' with camera CCD. The uniform and non-uniform components of the pupil's wave bumpiness are separated in the focal plane, where a phase mask M is applied to the Airy peak carrying the uniform component.

  Sensitivity to mirror bumpiness levels approaching 1Å has been demonstrated with phase contrast.

• Directed darkening of a single speckle

  Suitable algorithms have been described by Labeyrie (1995) for a single speckle and by Malbet et al. (1995) for a group of speckles or "dark hole". The required destructive interference of the star's light is in principle achievable with slight readjustments of the actuators if the pupil phase map is accurately known. Its noise, and the actuator's response non-linearity (hysteresis, etc..) however limit the degree of darkening thus achievable. Another limitation is the assessment of the darkening achieved: it cannot be measured quickly, owing to the low photon rate.

  

  Figure 3: Full darkening of a nearly dark speckle, shown with Fresnel's representation of vibration addition. The near cancellation of the vector sum (A - only the 4 last vectors of the sum are shown), where the last vector nearly reaches the origin O can be improved (B) by adjusting slightly the phases [[phi]] and [[phi]]' of the last two vectors if these are approximately in quadrature. The adjustment of the corresponding pair of actuators can be guided by minimizing the residual intensity.

  For darkening a single speckle, a vernier technique which relaxes the actuator accuracy requirement is sketched in figure 3. It uses two among the actuators, chosen to provide vibration phases coarsely in quadrature at the planet's location. Re-adjusting slightly both actuators can cancel exactly the residual intensity. The two-parameter optimisation can be driven by minimizing the intensity measured in the speckle considered. Ways of extending the technique to groups of speckles, as discussed by Malbet et al. (1995), should also be explored.

• Limits to speckle darkness:

  The amount of darkening achievable through dark-speckle analysis is expected to be limited by:
  

  1. incoherent scattered light, as may be produced by reflections in the camera window, etc...;
  2. the guiding jitter, most of which can probably be removed with adaptive optics.
     
  A star having its angular diameter slightly resolved will have its speckled halo slightly convolved with the star's apparent disk. It tends to decrease the speckle contrast and to fill the dark speckles, the darkest beeing most affected.

• Fixed speckles and their removal

  Fixed stellar speckles tend to appear in images obtained with adaptive coronagraphy, whether in the long exposure mode where one expects the residual speckles to be smoothed into a uniform halo, or in the dark-speckle mode where a non-linear algorithm maps the brief occurrence of destructive speckles. The phenomenon is obviously influenced by the amplitude of the permanent bumpiness on the wave, which adds to the variable bumpiness resulting from servo noise in the adaptive optics. There is also a contribution from the fixed shadow pattern on the wave, as caused by the central obscuration, spider structures, etc...

  Let us consider the image of an unresolved star, formed by a single or multi-aperture telescope, equipped with N-element adaptive optics and a coronagraph. In the focal plane, upstream from the coronagraph, there is an Airy peak amidst a halo of speckles.

  At the peak's location, the complex amplitudes of vibrations received from all actuators are phased and thus add constructively. In the feet of the diffraction pattern, the addition is highly destructive. A small variable phase , with zero mean, is added to each permanent phase received from the actuators at position x,y in the halo part of the image plane. The complex amplitude of the star is:

  

  since is small, the intensity in the focal plane may be written as:

  

  where and are the contributions to the permanent and the variable bumpiness.

  In the long exposure, the variable speckles integrated in the second contribute a smoothed halo, the smoothness of which improves as the square root of the integration time. With increasing observing time, the fixed speckles eventually become the dominant limitation to finding Airy peaks from faint stellar companions or planets. Their spatially averaged intensity is proportional to where is the " median " gain of the adaptive coronagraphic optics, i.e. the peak/halo intensity ratio with all actuators set to their average setting, which differs from the optimal setting due to unavoidable offset errors. The intensity of the smooth halo is proportional to where is the mean square phase of the actuator jitter. The average intensity of the residual speckles, relative to the halo, is therefore which may also be expressed as if one uses Marechal's expression for the scattered light level, where is the mean square permanent phase error on the pupil.

  Decreasing the amount of fixed bumpiness on the wave is thus critical for attenuating the fixed speckles. These should be attenuated as much as possible before attempting to subtract them from the long exposure, using a reference star.

  The ground-based situation considered by Angel (1994), involves 10,000 actuators expected to achieve a halo 106 times fainter than the peak, and becoming uniform within 10-3 in long exposures. According to the last expression, this requires a level of fixed bumpiness 30 times lower than the variable bumpiness, here amounting to 0.1 radian, with the prevailing photon noise in the wave analyzer. Ensuring such a low level of fixed bumpiness, of the order of 100 nm in red light, would require internal monitoring of the telescope's optical train to map accurately the permanent bumpiness, including any errors or biases in the deformable mirror. A laser guide star can provide this information. Offset corrections can be applied to attenuate the permanent speckles.

  The permanent amplitude pattern on the pupil, as caused by mirror edges, the secondary mirror obstruction and its suporting spider, also contributes to the fixed speckle pattern, and increasingly so in the central part of the image. The variable amplitude pattern on the pupil, which occurs in ground based telescopes due to high altitude turbulence, only contributes to the smooth halo, as discussed by Angel.

  Up to this point, photon noise has been neglected. In long exposures, it affects the detection of stellar companions if the fluctuations which it causes in the smooth halo are higher than the fixed speckles or their subtracted residuals. As previously shown (Boccaletti et al., 1998), a better performance is achievable with the dark speckle algorithm if there are enough detected photons per speckle in a short exposure.

The exact performance of the proposed instrument can be conveniently verified in the laboratory, using the same kind of artificial star and simulation techniques which have proved successful for speckle interferometry and adaptive optics. This is an essential step in the development of a space instrument.

The present performance of the dark speckle coronagraph is rather promising, since it was able to detect easily in the laboratory a companion at a separation 0.5" with magnitude difference larger than 6 (Boccaletti et al., in preparation). This is the preliminary result of the last simulations performed at ONERA (Office National d'Etudes et de Recherches Aérospatiales) with a turbulence generator followed by adative optics. It was obtained in half an hour integration.

The dark-speckle coronagraph has also been tested on the sky, at the Observatoire de Haute Provence 152cm telescope, in october 1997. The stellar beam from the telescope entered the adaptive optics bench BOA, of the ONERA. The target star [[eta]] Psc was compared to a reference star and the image is the subtraction of both taken in similar atmospheric conditions. The highest magnitude difference between both companions was 4, at a separation as small as 0.5".

Figure 4: Coronagraphic images of an artificial binary star obtained on the turbulence generator at ONERA. a: cleaned image of the binary; b: cleaned image of the reference single star; c: unmasked reference; d: normalised subtraction of both top maps. The faint companion is evidenced at a separation of 0.51" (arrow); the magnitude difference estimate is 6.4.

Our results were affected by the presence of static optical defects mostly due to the pupil stop and to the adaptive system, which limits the speckle smoothing. The fixed residual speckles remain the dominant source of noise in these coronagraphic data and should be removed from future systems.

A wide range of astrophysical topics can be addressed with advanced coronagraphic techniques on board NGST. Exoplanet, brown dwarves, circumstellar envelopes, as well as extragalactic objects are observable. The central (stellar or galactic) light cancellation is achieved in three steps: advanced coronagraphy with the Achromatic Interfero-Coronagraph or the Phase-mask occultation; adaptive apodisation; and a final cleaning step using the dark-speckle algorithm. A chromatic correction for full bandwith detection or an integral field spectrograph would allow either high-contrast imaging or spectral analysis of the detected sources.

In the longer term, these principles of coronagraphic nulling can be extended to the future diluted telescopes, i.e. interferometric arrays of free-flying telescopes spanning one to tens of kilometers. A so-called " densified pupil " imaging mode will provide a recombined focal image where the field will be restricted by a window effect (Labeyrie 1996), but which can be exploited with the same instrument proposed here for NGST, with an obvious gain in angular resolution.

Acknowledgments: This article borrows from the team work achieved for preparing an HST proposal. We thank particularly F. Malbet, F. Vakili, P. Nisenson, K. Dohlen, R. Ragazzoni, D. Gezari, D. Kohler, R. Stachnik, F. and C.Roddier, M. Northcott, W. Danchi, M. Harwitt, for their contributions.

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