The design of starshades, i.e. external occulters for stellar coronography, relies on the fast and precise computation of their associated diffraction patterns of incoming plane waves in the telescope aperture plane. We present here a method based on a polygonal approximation of the occulter’s shape, that allows fast computation of their diffraction patterns in the Fresnel approximation, without aliasing artefacts. It is competitive with respect to methods based on direct 2D Fourier transforms, or Boundary Diffraction Wave algorithms.
Solar and stellar externally occulted coronagraphs share similar concepts, but are actually very different because of geometric characteristics. Solar occulters were first developed with a simple geometric model of diffraction perpendicular to the occulter edges. We apply this mere approach to starshades, and introduce a simple shifted circular integral of the occulter which allows to illustrate the influence of the number of petals on the extent of the deep central dark zone. We illustrate the reasons for the presence of an internal coronagraph in the solar case and its absence in the exoplanet case.
The ESA formation Flying mission Proba-3 will y the giant solar coronagraph ASPIICS. The instrument is composed of a 1.4 meter diameter external occulting disc mounted on the Occulter Spacecraft and a Lyot-style solar coronagraph of 50mm diameter aperture carried by the Coronagraph Spacecraft positioned 144 meters behind. The system will observe the inner corona of the Sun, as close as 1.1 solar radius. For a solar coronagraph, the most critical source of straylight is the residual diffracted sunlight, which drives the scientific performance of the observation. This is especially the case for ASPIICS because of its reduced field-of-view close to the solar limb. The light from the Sun is first diffracted by the edge of the external occulter, and then propagates and scatters inside the instrument. There is a crucial need to estimate both intensity and distribution of the diffraction on the focal plane. Because of the very large size of the coronagraph, one cannot rely on representative full scale test campaign. Moreover, usual optics software package are not designed to perform such diffraction computation, with the required accuracy. Therefore, dedicated approaches have been developed in the frame of ASPIICS. First, novel numerical models compute the diffraction profile on the entrance pupil plane and instrument detector plane (Landini et al., Rougeot et al.), assuming perfect optics in the sense of multi-reflection and scattering. Results are confronted to experimental measurements of diffraction. The paper reports the results of the different approaches.
The hypertelescope construction initiated in the Southern Alps (Labeyrie et al., this conference) has
provided some preliminary operating experience indicating that larger versions, up to perhaps
1200m, are probably feasible at suitable sites. The Arecibo-like architecture of such instruments
does not require the large mount and dome which dominate the cost of a 40m ELT. For the same
cost, an "Extremely Large Hyper Telescope” ( ELHyT) may therefore have a larger collecting area.
It may thus in principle reach higher limiting magnitudes, both for seeing-limited and, if equipped
with a Laser Guide Star and adaptive phasing, for high-resolution imaging with gain as the size ratio,
i.e. about 30 with respect to a 40m ELT. Like the radio arrays of antennas, such instruments can be
grown progressively. Also, they can be up-graded with several focal gondolas, independently
tracking different sources. Candidate sites have been identified in the Himalaya and the Andes. We
describe several design options and compare the science achievable for both instruments, ELTs and
ELHyTs. The broad science addressed by an ELHyT covers stellar chromospheres, transiting exoplanets
and those requiring a high dynamic range, achieved by array apodization or coronagraphy.
With a Laser Guide Star, it extends to faint compact sources beyond the limits of telescopes having a
smaller collecting area, supernovae, active galactic nuclei, gamma ray bursts. The sparse content of
remote galaxies seen in the Hubble Deep Field appears compatible with the crowding limitations of
an ELHyT having 1000 apertures.
KEYWORDS: Stars, Apodization, Coronagraphy, Telescopes, Signal to noise ratio, Nulling interferometry, Planets, Sun, Point spread functions, Space telescopes
Nuller coronagraphs such as the Achromatic-Interfero-Coronagraph (AIC) can perfectly cancel the starlight by destructively
interfering it with itself, if the star is unresolved and exactly on-axis. Small pointing errors as well as the finite stellar
diameter of the targeted star may however greatly degrade the performance of this type of coronagraph. Observed at 600nm
with an AIC behind a 10 m telescope, the Sun at 10 pc would present an apparent angular diameter of 0.001" that would
induce a star-leakage of 10-6 times the maximum intensity of the star at 0.1". The expected flux ratio between a Sun-like
star and an Earth-like planet is however much lower (10-10 in the visible). We show through an analytical formalism that
an apodized nuller coronagraph (ANC) can achieve planet detections with much higher contrasts. Expressions of the local
contrast ratio and of the signal-to-noise ratio are derived. We first use for demonstrative purposes Sonine profiles and
spheroidal prolate profiles. Concentric ring profiles, obtained through a numerical optimization, are also presented. The
efficiency of these 3 types of apodizations is discussed.
We propose to use a Mach-Zehnder interferometer to greatly simplify and make achromatic the four quadrants
phase mask coronagraph. The interferometer is used to get the achromatic π phase term. Two complementary
binary masks of transmission 1 and 0 for quadrants of the same parity are set in the focal plane formed inside
the interferometer. There is an equipartition of the energy in the exit aperture images, one being similar to
the entrance aperture, the other being coronagraphied. We present preliminary results obtained with a coherent
light. The current throughput of the experiment is 25 % only, but we give indications to improve it.
An apodized aperture should make it possible to observe the solar corona without the need of a Lyot coronagraph. We
show in this communication that Sonine functions are much better apodizers for the observation of the solar corona than
the generalized prolate spheroidal functions previously proposed. For a perfect circular aperture of diameter unity operated
in space, a simple Sonine apodization of the form (1 - 4r2), with |r| ≤ 1/2 should sufficiently reduce the diffraction halo
produced by the solar disc to observe the corona very close to the solar limb (a few arcsec). The throughput is just one
third of the clear aperture.
We describe the multiple-stage Lyot coronagraph first proposed by Aime, Soummer and Ferrari (A&A 2002, 389,334344) for the detection of exoplanets. This coronagraph uses several stages. The first stage is a Prolate Apodized Lyot Coronagraph (PALC). It produces a residual wavefront on the aperture that is proportional to the entrance prolate spheroidal apodized wavefront. This permits the use of a second stage of coronagraphy, needing only a Lyot mask, identical to the first one, without any further aperture apodization. The resulting extinction factor is the square of the initial PALC. Using several stages permits to obtain considerable rejection factors for small-size coronagraphic masks and good overall throughput.
KEYWORDS: Coronagraphy, Adaptive optics, Speckle, Planets, Point spread functions, Diffraction, Wavefronts, Speckle pattern, Photon counting, Signal to noise ratio
In this communication we study the utility and limitations of ground based coronagraphy with adaptive optics (AO). In very high AO correction regimes, residual speckles are pinned on the diffraction rings of the Airy pattern. It can be shown that these speckles are due to small defaults of the wavefront, amplified by the coherent part of the wave. Their statistics can be described by a modified Rice distribution, under reasonable physical assumptions. Using properties of the Moment Generating Function (MGF), simple expressions are obtained for the variances of the noise at high flux and at photon counting levels. We discuss the relative importance of speckle and photon noise and present conclusions on the limits of coronagraphy for the detection of an exoplanet. The total variance can be partitioned into two contributions: one that can be suppressed by a coronagraph and one that cannot, and different regimes can be identified. These results enable analysis of when a coronagraph can defeat the noise variance, and they provide a criterion for effectiveness of such instruments.
Amplitude apodization of a telescope's pupil can be used to reduce the diffraction rings (Airy rings) in the PSF to allow high contrast imaging. Rather than achieving this apodization by selectively removing light at the edges of the pupil, we propose to produce the desired apodized pupil by redistributing the pupil's light. This lossless apodization concept can yield a high contrast PSF which allows the efficient detection of Earth-sized planets around stars at ~10pc with a 2m visible telescope in space. We review the current status of a JPL-funded study of this concept for the Terrestrial Planet Finder (TPF) mission, including a lab experiment and extensive computer simulations.
This communication deals with apodization and coronagraphy. For
apodization alone, we present analytical studies of point spread
functions obtained with a rectangular or a circular telescope
apodized by cross-linear or circular prolate spheroidal functions,
respectively. Results are compared with sonine apodizations
investigated by Nisenson and Papaliolios (2001) for the Apodized
Square Aperture project. For coronagraphy, prolate functions are
the optimal apodizers for rectangular and circular apertures. With the
Roddier & Roddier phase mask technique, these apodizations can
produce a total extinction of the star light. For Lyot coronagraphy, the extinction, not complete, is surprisingly good for a reasonable mask size. A comparison between coronagraphy and apodization alone for different telescope aperture shape is in favor to the use of a coronagraph with a circular aperture.
The one-dimensional point spread function for long-exposure frames of the whole system atmosphere - instrument is calculated from solar limb observations using data recorded at OCA Observatory (France). It is then compared to the theoretical one deduced from the Von Karman model and various wave-front structure functions. Good agreement is found allowing to deduce the spatial coherence outer scale L0 and the Fried parameter r0.
We propose regularized versions of Maximum Likelihood algorithms for Poisson process with non-negativity constraint. For such process, the best-known (non- regularized) algorithm is that of Richardson-Lucy, extensively used for astronomical applications. Regularization is necessary to prevent an amplification of the noise during the iterative reconstruction; this can be done either by limiting the iteration number or by introducing a penalty term. In this Communication, we focus our attention on the explicit regularization using Tikhonov (Identity and Laplacian operator) or entropy terms (Kullback-Leibler and Csiszar divergences). The algorithms are established from the Kuhn-Tucker first order optimality conditions for the minimization of the Lagrange function and from the method of successive substitutions. The algorithms may be written in a `product form'. Numerical illustrations are given for simulated images corrupted by photon noise. The effects of the regularization are shown in the Fourier plane. The tests we have made indicate that a noticeable improvement of the results may be obtained for some of these explicitly regularized algorithms. We also show that a comparison with a Wiener filter can give the optimal regularizing conditions (operator and strength).
KEYWORDS: Fractal analysis, Holograms, Diagnostics, Correlation function, Diffraction, 3D image reconstruction, Chaos, Optical signal processing, Data processing, Analog electronics
The present-day state of fractalometry and fractalography is considered. Fractalographic techniques based on referenceless holograms and off-axis quadric holograms are introduced. The original technique for measurement of a chaos correlation dimension at the field is proposed as well as possibilities provided by implementation of this technique.
This communication deals with the problem of image reconstruction in astronomy by means of a statistical analysis of the intensity of speckle patterns present at the focus of a large ground-based telescope. It emphasizes the importance of the order of the statistical analysis to be performed. Twofold and threefold statistical analyses are commonly used in speckle interferometry and in speckle masking, this later technique taking advantage of a phase closure effect for full recovery of the astronomical object. The question may arise on the interest of higher order analyses. Making use of simplifying hypotheses, we give a partial answer to this question. Under the assumption that the N points defining the object are well separated one another regard to the telescope resolution, we show that a statistical analysis of order N completely defines the statistical properties of the image speckle pattern. This result is based upon the fact that the characteristic function (CF) of order N + 1 can be written as function of CF's of order N and that the cumulant of order N + 1 is equal to zero.
The effect of atmospheric turbulence on the imaging of scenes, for a horizontal propagation of the light over a distance of 20 km, 15 meters above the sea surface, was analyzed at visible wavelength using a 20 cm telescope. Point-sources images were recorded during the night, and the fried parameter r0 was derived leading to values ranging from 1.5 to 3.6 cm. A very high level of scintillation was observed. Studies of correlations between close-by sources lead to a very small domain of isoplanatism. Daytime observations of an extended source area are also performed; an image motion of small spatial coherent length seems to be drawn by a horizontal wind producing wave-like distortion of horizontal lines and boiling-like of vertical ones.
The object of this communication is to compare two inversion algorithms in their application to the blind deconvolution problem. After a brief summary of the previous works in this field, we describe the Richardson-Lucy and the steepest descent algorithms and we introduce these methods in the basic error reduction algorithm of Ayers and Dainty. These algorithms are compared when used for blind deconvolution of simulated binary objects convolved by a point spread function and corrupted by a Gaussian additive noise. We consider the effects of the noise level on the reconstruction error, together with the effects of the algorithmic parameters (inner and outer iteration numbers). Particular effects occurring during the reconstruction process are also shown.
An analytical method to recover the high light level probability density function (PDF) of a random field from its PDF in counting mode is presented. The high light PDF is related to the photo-detected PDF by the Poisson transform. The inversion of this transformation is performed as follows: the characteristic function (CF), the Fourier transform of the PDF, is first calculated as a Taylor type series where the coefficients are the photo-counting PDF. Unfortunately the limited number of p(n) that can be obtained experimentally makes this expression of (Phi) ((omega) ) valid only for very low values of (omega) , and prevents the recovering of the PDF by an inverse Fourier transform. We have proposed recently to use Pade approximants to overcome this problem and to extend the validity of the expression of (Phi) ((omega) ) towards the high values of (omega) where the Taylor series diverges. We propose here a summary of this technique and its generalization to two dimensions. A procedure making use of the application of physical constraints allows us to select the most appropriate rational approximation of the CF. We present applications of this method to astronomical speckle interferometry and show that good results can be obtained for simulated data in the case of one and two fold PDFs.
We report in this communication experimental results obtained by the technique of probability imaging applied to double stars in the near-infrared. Intensity ratios and relative positions of components are obtained for six double stars. The two-fold probability density function of one-dimensional images is used to reconstruct the binary system. The data reduction is made with a parametric approach, by minimizing a distance between observed two-fold probability density functions and modelled ones, obtained by using a close-by reference star.
We present in this communication an introduction to the speckle technique of probability imaging. The technique is aimed at performing the reconstruction of astronomical images from ground based observations; it makes use of a complete statistical analysis of the speckle field by means of probability density functions and related quantities such as characteristic functions. The technique is first described for the simple case of imaging a binary star and simplifying assumptions for the statistics of the speckle pattern. Then the general case is considered, and it is shown how the characteristic function of the extended object speckle pattern can be modeled as a central slice of a higher order characteristic function of the point source speckle pattern. Corresponding relations for probability density functions are given. Effects of noise in the measurement are examined for the two cases of additive noise and photon noise. Relations between probability imaging, speckle interferometry, and speckle masking are presented.
The aim of this communication is to show how the Richardson-Lucy deconvolution algorithm can be applied to the blind deconvolution problem. After a brief description of the R.L algorithm itself, we start from the basic papers of Ayers and Dainty (1988) and Lane (1992) and introduce in their approach the R.L algorithm in several different ways. We show that the general behaviour of the proposed methods is analogous to that of the error-reduction algorithms and that good solutions can be obtained. The unregularized behaviour of the RL algorithm is overcame by a limitation of the iteration number. Moreover we compare the structures of the various algorithms proposed here and emphasise the main differences. The proposed algorithms are used to blindly deconvolve two types of objects (point-like and extended objects) blurred by simulated point spread functions similar to those observed at the focus of a small telescope in presence of at- mospheric turbulence. The error reduction term is given as a function of the iteration number.
We report in this Communication the current progress in development at the Nice University of the technique of Probability Imaging based on a complete statistical analysis of the speckle pattern observed at the focus of a large telescope. The technique, which was first proposed for the imaging of double and multiple stars, is here generalized to the image reconstruction of any general extended astronomical object. Making use of a technique of orthonormal expansion currently employed in statistical optics, a mathematical expression for the characteristic function of any order of the speckle pattern is given as the inverse of the determinant of a matrix whose elements are defined by the spatial correlation function of the amplitude of the point source speckle pattern and a diagonal matrix representing the astronomical object. Recent results obtained for the bright infrared double star ? Aqr and simulations of the implementation of the algorithm for optical photon-counting detectors with clipping problems are given. The use of the technique for synthesized apertures is also considered.
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