The PRIMA facility phase-referenced imaging and micro-arcsecond astrometry

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Abstract

This article describes dual-field interferometry, in particular PRIMA, the phase-referenced imaging and micro-arcsecond astrometry facility of the very large telescope interferometer. It uses the simultaneous detection of fringes of two stars in a narrow angle and the accurate measurement of their respective positions. PRIMA aim is threefold: (i) to increase the VLTI limiting magnitude with off-axis fringe tracking, (ii) to reconstruct images with a resolution of 2 mas in K-band, 10 mas in N-band, and (iii) to perform differential narrow-angle astrometry with an accuracy of 10 μas. This article exposes the fundamental and technical limitations of such a technique and presents how PRIMA will try to solve the practical problems of measuring 100-m long optical paths with nanometric accuracy in a ground based interferometer.

Introduction

Ground based interferometer performance is mainly limited by the atmospheric turbulence. Variable index of refraction of the air column above each telescope changes randomly both the angle of arrival and the time of arrival of the coherent photons on each aperture. The time of arrival variation results in a fast jitter of the observed fringe positions in the beam combiner. The order of magnitude of this jitter reaches more than 40 μm peak-to-valley (PTV) and has a typical time-scale of some milli-seconds (for the K-band). The jitter of the angle of arrival induces a problem to superimpose the beams coming from various telescopes on top of each other or to inject them into monomode optical fibers. To get a good efficiency and limit the photometric losses, an angle or tip-tilt tracker has to be used with a bandwidth of typically 10 Hz. Thus, to observe fringes, one is obliged to take short exposures both in the fringe tracker and in the angle tracker and the sensitivity of the interferometer is strongly limited as shown in (Shao and Colavita, 1992, Haniff, 2007).

The fringe jitter results in loosing as well a very important information: the position (phase) of the fringes. The absolute position of the fringes is linked to both the position of the object photo-center on the sky (astrometry) and to shape of the object (Haniff, 2007, Quirrenbach, 2001). Indeed one measurement by a two-telescope interferometer (one baseline) is giving one point (and its symmetric relative to the center) of the Fourier transform of the object image. The visibility of the fringes is the amplitude of the complex number in the Fourier transform; the position of the fringes is the phase of this complex number. It can be shown that most of the information on the object shape is contained in the phase.

Thus it is very important to recover the phase information from the fringes with an accuracy much better than 2π (or one wavelength). Two strategies can be applied: phase-closure and phase-referenced imaging (Booth, 1985). Phase-closure is based on the simultaneous observation with three or more telescopes. It can be shown that the sum of the phases on any baseline triangle is independent of the atmospheric turbulence (Monnier, 2000). This technique is used by AMBER, the near-infrared instrument of the very large telescope interferometer (VLTI) and by many other optical and infrared interferometers in the world. Phase-referenced imaging measures, one baseline at a time, the phase of the object with respect to a reference star whose phase is assumed null (i.e., is centro-symmetric) (Ulvestad, 1999). The differential astrometric information is also included in the measurement.

PRIMA, the phase-referenced imaging and micro-arcsecond astrometry facility, has been developed since 2000 in order to fight the effects of the atmospheric turbulence and to bring the imaging and astrometric capabilities to the VLTI instruments. The principle of narrow-angle differential interferometry is described in Section 2. PRIMA scientific goals, with emphasis on the observation of circumstellar disks and the detection of planets, are given in Section 3 and the high level requirements to reach these goals in Section 4. Of course such a technique has some physical limitations in terms of accuracy, limiting magnitude, sky coverage, etc. that are detailed in Section 5. Moreover, operating an interferometer on the ground, in the air (i.e., not under vacuum) and with real telescopes that can shake and bend, is not as simple as predicted by theory. The technical problems that have been experienced on the VLTI and that PRIMA will have to fight are described in Section 6. Finally, the various sub-systems of PRIMA, how they interact and how to operate the full system to get the best accuracy possible are presented in Sections 7 PRIMA system description, 8 PRIMA operation, calibration and data reduction, respectively.

Section snippets

Principle of narrow-angle dual-feed interferometry

PRIMA is a narrow-angle dual-feed interferometric method based on the simultaneous observation of two stars within the same telescope field of view (see Section 5 for the limitations on this field of view). The method is presented and described in detail in (Shao and Colavita, 1992). The bright star is used for fringe tracking: short exposures on this star allow measuring the atmospheric turbulence and stabilizing the fringes thanks to a closed loop. One can then integrate longer on the fainter

Scientific goals

PRIMA has therefore three capabilities:

  • Faint object observation by fringe tracking on a close-by bright star. Both stars have to be within the same narrow-angle field (see Section 5). The theoretical limits for fringe tracking is K  13 on the UTs (unit telescopes, 8 m diameter), and K  10 on the ATs (auxiliary telescopes, 1.8 m diameter). Due to various disturbances (see Section 6), this is probably impossible to reach and the current PRIMA goal is a fringe tracking limiting magnitude of K  10 on

High-level requirements

To reach an astrometric accuracy of 10 μas necessary to detect a Jupiter-like planet, when using a baseline of 200 m (longest VLTI baseline), Eq. (1) shows that all terms have to be measured or to be averaged out at better than 5 nm rms. The astrometric measurements have to be taken for two significantly different baseline orientations (ideally at 90° from each other) in order to get the two-dimensional angle vector on sky.

In order to get good reconstructed images of the object, one needs both

Physical limitations

The main limitations of dual-field interferometry are linked to the atmospheric turbulence. First, the coherence time τ0 of the turbulence on the bright star determines at which frequency one has to measure the fringe phase in order to be able to stabilize them. In good nights, τ0 is of the order of 20–30 ms in K-band. Thus a sampling frequency of 200 Hz is needed for a good stabilization. As fringes can be measured reliably with a 100 SNR (signal to noise ratio), this imposes the minimum number

Beam stability

Despite adaptive optics on the UTs and tip-tilt stabilization on the ATs, the beam arriving at the fringe sensor in the laboratory are not perfectly stabilized: some tip-tilt or higher order residuals are still present and the internal air turbulence (inside the light ducts and tunnels of the interferometric complex) affects the beam stability as well. The problem is that one wants to inject the beams coming from the telescopes into monomode fibers. A slight error of pointing (e.g., on 20 

PRIMA system description

PRIMA main functions are the following:

  • To select, pick up and track two stars in a 2′ field of view at the Coudé focus of the telescopes (UT or AT). This is done by the so-called star separators (STS).

  • To introduce the differential delay between the two stars. Indeed as both stars passing by the same delay lines, only one delay can be applied to both. This is the role of the differential delay lines (DDL).

  • To measure and track the fringes on the bright star (and on the faint object if possible).

PRIMA operation, calibration and data reduction

The most stringent goal of PRIMA in terms of performance, is the 10 μas narrow-angle astrometry for planet detection. Thus, this goal is driving the way we want to operate, calibrate and reduce the data. All the problems mentioned above have to be taken into account. Some of them are several order of magnitude larger than the signal that we want to measure. To get the final accuracy, PRIMA is based on multiple differential measurements that have to be done cleanly, and as much as possible at

Conclusions

PRIMA is a very challenging project, especially in its ultimate goal of micro-acrsecond astrometry. It is also a complex system, interfering with the current VLTI infrastructure at many level and places. However, it will significantly enhance the VLTI performance and capabilities by increasing the limiting magnitude and providing phase-referenced imaging and astrometric functionalities. This will make the VLTI a really unique facility in the world. Moreover, PRIMA sub-systems have been designed

Acknowledgements

The development of PRIMA has been done by a large team at ESO and in the European Interferometric Community. Here is a non-exhausitive list of people/institutes who worked/are working specifically on PRIMA: R. Abuter, L. Andolfato, P. Ballester, J. de Jong, F. Derie, N. di Lieto, R. Frahm, S. Lévêque, S. Ménardi,, J.-M. Moresmau, R. Palsa, T. Phan, D. Popovic, E. Pozna, F. Puech, J. Sahlmann, N. Schuhler, G. van Belle, G. Vasisht, the PAOS-DDL Consortium (Geneva Observatory, Max-Planck Institut

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