Frederic Cassaing

Coupling of large telescopes and single-mode waveguides: application to stellar interferometry

The coupling between a turbulence-distorted optical beam and a single-mode waveguide is addressed. The coupling efficiency and the coupled phase are derived, both without aberrations and with small aberrations. These analytical expressions are validated by numerical simulations. Correction with adaptive optics is investigated. In the general case, the Strehl ratio is a pessimistic estimator, and the coupled phase is different and has a smaller variance than the classical phase averaged over the pupil. Application fields are heterodyne detection and stellar interferometry, for which spatial and modal filtering are distinguished.

AMBER: the near-infrared focal instrument for the Very Large Telescope Interferometer

AMBER is a focal instrument for the Very Large Telescope Interferometer working in the near infrared from 1.1 to 2.4 micrometers . It has been designed having in mind the General User of interferometric observations and the full range of his possible astrophysical programs. However the three programs used to define the key specifications have been the study of Young Stellar Objects, the study of Active Galactic Nuclei dust tori and broad line regions and the measure of masses and spectra of hot Extra Solar Planets. AMBER combines up to three beams produced by the VLTI 8 m Unit Telescopes equipped with Adaptive Optics and/or by the 1.8 m Auxiliary Telescopes. The fringes are dispersed with resolutions ranging from 35 to 10000. It is optimized for high accuracy single mode measurements of the absolute visibility, of the variation of the visibility and phase with wavelength (differential interferometry) and of phase closure relations with three telescopes. The instrument and its software are designed to allow a highly automated user friendly operation and an easy maintenance.

Optimized fringe tracker for the VLTI/PRIMA instrument

This paper presents new concepts for a Fringe Sensor Unit (FSU) optimized for high accuracy and low flux operation. This concept has been studied for the VLTI/PRIMA instrument in the H (and K) bands. To optimize both photon use and accuracy, an efficient spatial achromatic discrete modulation is chosen. For optical path difference measurements, most of the photons are used in a single polychromatic quadrature while the adjustable remaining part is dispersed for simultaneous group delay tracking. Integration time can be very short since no moving device is used. This FSU can also be turned to a classical two quadratures FSU if needed, for differential delay or visibility measurements. Optical designs for these FSUs are proposed. These simple designs are also very well suited to future space instruments. Theoretical performance and simulation results are finally given and compared to other existing devices.

Analytical solution to the phase-diversity problem for real-time wavefront sensing

High-resolution optical systems require a very accurate control of the optical paths. For the measurement of aberrations on extended objects, several iterative phase-diversity algorithms have been developed, based on aberration estimation from focal-plane intensity measurements. Here we present an analytical estimator in the case of small aberrations. Under this assumption, a quadratic criterion is derived that allows us to express the solution (phase and object) under a simple analytical form. We also compare the performance of our algorithm with the iterative phase diversity, demonstrating that the analytic estimator is appropriate for closed-loop operation.

Aperture configuration optimality criterion for phased arrays of optical telescopes

We address the optimization of the relative arrangement (aperture configuration) of a phased array of optical telescopes, coherently combined to form images of extended objects in a common focal plane. A novel optimality criterion, which is directly linked to the restoration error of the original object from the recorded image, is derived. This criterion is then refined into a second criterion to accommodate the possible knowledge of the noise spectrum. The optimal configuration is a function of the maximum spatial frequency of interest (or desired resolution) and takes into account the diameters of the elementary telescopes. Simulations illustrate the usefulness of this criterion for designing a synthetic-aperture optical instrument with three, four, and five telescopes.

Piston control with adaptive optics in stellar interferometry - Application to the GI2T interferometer and bimorph mirrors

The general purpose of an adaptive optics system is to correct for the wavefront corrugations due to atmospheric turbulence. When applied to a stellar interferometer, care must be taken in the control of the mean optical path length, commonly called differential piston. This paper defines a general formalism for the piston control of a deformable mirror in the linear regime. It is shown that the usual filtering of the piston mode in the command space is not sufficient, mostly in the case of a bimorph mirror. Another algorithm is proposed to cancel in the command space the piston produced in the pupil space. This analysis is confirmed by simulations in the case of the GI2T interferometer located on Plateau de Calern, France. The contrast of the interference fringes is severely reduced in the case of a classical wavefront correction, even in short exposures, but is negligible with our algorithm, assuming a realistic calibration of the mirror. For this purpose, a simple concept for the calibration of the piston induced by a deformable mirror is proposed.

Unambiguous phase retrieval as a cophasing sensor for phased array telescopes

Cophasing a multiple-aperture optical telescope (MAOT) or optical interferometer requires the knowledge of the tips/tilts and of the differential pistons on its subapertures. In this paper we demonstrate in the case of a point source object that a single focal-plane image is sufficient for MAOT cophasing. Adopting a least-square approach allows us to derive an analytic estimator of the subaperture aberrations, provided that these are small enough (typically for closed-loop operation) and that the pupil is diluted noncentrosymmetric. We then provide the validation of this estimator by simulations as well as a performance comparison with a more conventional iterative algorithm of phase retrieval. Finally, we present the experimental validation of both estimators on a laboratory test bench; our results, especially subnanometric repeatability, demonstrate that focal-plane sensors are appropriate for the cophasing of phased array telescopes.

Imaging with multi-aperture optical telescopes and an application

Abstract The two main types of Multi-Aperture Optical Telescopes (MAOTs) (so-called Michelson and Fizeau) and the two possible modes of optical beam combination are reviewed. Wide-field imaging with a Michelson instrument is studied and the constraints are identified. An example of application to Earth observation is given. Then, we address the optimization of the aperture configuration, a key issue in the design of a MAOT. We also stress the image restoration, a necessary component of such an instrument because of the shape of its point spread function. Finally, a MAOT seems to be a promising technical solution for high resolution Earth observation from Space on a high orbit such as a geostationary one.

Optical path difference sensors

Abstract In a synthetic aperture system, three main kinds of optical path difference (OPD) sensors can be distinguished: sensors used for astronomy and sensors used for the real-time correction of OPD disturbances, fed either by a star or an internal source. To select the best implementation, a general analysis of OPD measurement algorithms is made with a new vectorial formalism. For any modulation, demodulation algorithms can be derived and compared in terms of additive noise propagation and sensibility to systematic errors. Free parameters (the modulation, the number of samples and the demodulation algorithm) can be optimized for each kind of sensor. For best performance, these sensors must use different implementations and thus be distinct. This should be considered in the instrument early design, as illustrated with two examples.

Phasing segmented telescopes with long-exposure phase diversity images

One of the major issues in new Extremely Large Telescopes is the phasing of their primary segmented mirror. A cophasing sensor is mandatory to achieve the ultimate resolution of the telescope. Phase diversity (PD) is a light-hardware cophasing technique. In this paper, we show that this technique is suited to segmented pupil instruments, such as the E-ELT.