In this paper I provide a brief introduction to astronomical interferometry at optical and infrared wavelengths. Two key concepts, central to understanding the basis and practice of interferometry are introduced: image formation with conventional telescopes, in particular the Fourier decomposition of images, and the nature and utility of measurements of the coherence function or mutual intensity. Thereafter I focus on optical/infrared interferometry, outlining how measurements of the coherence function are made at these wavelengths, how they can be used to interpret a source's structure, and what the principles of interferometric imaging tell us about the limitations expected for the current generation of arrays such as the VLTI.

This chapter is a first step towards visibility modeling. It describes analytical expressions for visibility curves derived from "classical" brightness distributions. It describes first some general useful tools for this kind of computation and then discusses several widely used morphologies. Finally, some practical issues of visibility modeling are discussed.

The Practice sessions of the EuroWinter School "Observing with the Very Large Telescope Interferometer" held at Les Houches in February 2002 relied on the use of ASPRO, an observing preparation tool crafted for optical interferometry, developed at the Jean-Marie Mariotti Center. This Tutorial serves as an introduction to the basic uses of this tool.

The following exercices are aimed to get trained to the link between the object intensity distribution and the corresponding visibility curves. They were intended to be the practical application of the seminar "Introduction to visibility modeling" (Berger same volume). This practical session was initially meant to be done with the ASPRO software (see Duvert same volume), uv tables and the fits file can be donwloaded from the ASPRO website. However, any image processing or mathematical software (Idl, Yorick, Mathlab, Mathematica...) associated with the object equations given in Berger can be used for most exercises.

In this second lecture I review some of the practical considerations associated with developing and implementing ground-based interferometry at optical and near-infrared wavelengths. Familiarity with these logistical concerns is relevant not only for understanding how arrays such as the VLTI actually operate but also for identifying the most important questions that need to addressed when planning a campaign of interferometric observations. I outline some of the strategies that have been adopted to address these issues and point to some areas ripe for future development.

Observing with an optical stellar interferometer is more complicated than observing with a single dish telescope. Several "hardware" constraints are added, such as the optical path difference compensation with delay lines as well as possible telescope vignetting. A more fundamental constraint is the coverage of the uv-plane. Its sampling costs a lot of observing time and thus should be optimized for each scientific source. These issues will be addressed in this tutorial and in Exercize number 2.

This exercize is divided into two main parts. The first one intends to give a clear idea about the UV coverage with baselines of different orientations and targets of different declinations. It also emphasizes on the delay lines constraints for a 2 and a 3-telescope array. In the second part, different array configurations have to be selected to efficiently measure the radius of 3 close M dwarfs and the parameters (ρ, Θ, Δmag) of a binary system.

The Very Large Telescope (VLT) Observatory on Cerro Paranal (2635 m) in Northern Chile is approaching completion. After the four 8-m Unit Telescopes (UT) individually saw first light in the last years, two of them were combined for the first time on October 30, 2001 to form a stellar interferometer, the VLT Interferometer. The remaining two UTs will be integrated into the interferometric array later this year, so that any two UTs can be used for interferometry. In this article, we will describe the subsystems of the VLTI and the planning for the following years.

AMBER is the General User near infrared focal instrument of the Very Large Telescope Interferometer. It is a single mode, dispersed fringes, three telescopes instrument. His limiting magnitude of the order of H=13 will allow him to tackle two dozens of extragalactic targets. His extremely high accuracy, in particular in phase closure and differential mode give good hope for very high dynamic range observation, possibly including hot extra solar planets. His relatively high spectral resolution will allow some stellar activity observations. Between this extreme goals, AMBER should have a wide range of applications including Young Stellar Objects, Evolved Stars, circumstellar material and many others. This papers tries to introduce AMBER to its future users and insists on what AMBER measures, how it calibrates it and how this could give the reader ideas for applications.

We report in this paper on the current status of the mid-infrared beam combiner of the VLTI: MIDI. We explain the interest of VLTI for this range of wavelentghs and give an overview of the main characteristics of MIDI and present its scientific targets.

The objective of this exercise is to learn how to compute error bars on visibility estimations computed with the ASPRO software in order to investigate the feasibility of an observations with the VLTI.

By construction, optical (and near-infrared) interferometers typically have resolutions designed to resolve stellar and circumstellar features. Therefore gaging the point-source response of the interferometer in its operating environment is critical to the scientific interpretation of data from these devices. This is typically performed with observations of calibration sources that are modeled to be simple and quasi-unresolved by the interferometer. Herein I will discuss the goals and strategies for and issues with the selection of objects to serve as calibration sources for optical interferometry visibility measurements.

The objective of this exercise is to find suitable calibration stars for an interferometric array like the VLTI.

Optical interferometers are instruments that combine the light coming from separated optical telescopes in order to get information with the spatial resolution of the telescope array. One of the major interferometer is the Very Large Telescope Interferometer (VLTI). To observe an astronomical target with the VLTI, like with any other interferometers, one needs to carefully prepare the observations because of the numerous parameters to be fixed. In addition, the VLTI is being developed in the framework of the data flow system created for the Very Large telescopes (VLT) at the European Southern Observatory (ESO). I recall the philosophy of the ESO/VLT data flow system and its adaptation to the VLTI data and then I describe the various steps required to prepare a VLTI observation. Finally, I illustrate the various steps of this preparation with an example focused in the observations of the young binary system Z CMa.

This exercise is aimed at building a complete observing program for the VLTI. It consists in defining the scientific rationale and immediate objectives, ensure that the target are observable, define the VLTI configuration, model the astrophyiscal source and estimate the expected signal-to-noise ratio. At the end one should be able to define the total time requested and the final configuration. This exercise is a simulation of the work required to eventually request time on the VLTI.

This is the manuscript of an "interactive seminar" from the programme of the EuroWinter School. These seminars were designed to illustrate areas of science that will be accessible to the VLTI and its first-generation instruments. This paper discusses the use of optical/IR interferometers to investigate the limb-darkening of stars, with particular emphasis on models with a one or two free parameters i.e. the kind of models that will be constrained by data from the first-generation VLTI. For this reason the paper is not a comprehensive treatment of limb-darkening measurement. Ideas from the introductory lectures of the School are illustrated here, using real data on a Mira variable star from the COAST interferometer.

The observation of protoplanetary disks at the astronomical unit scale is one of the most exciting key programs for long baseline interferometers. Existing observations have questioned the models of circumstellar environments of young stars; but this is just the beginning. Here, to provide the reader with a sense of what can be done today in this field, actual observations of the pre-main sequence star FU Orionis with near-infrared interferometers IOTA and PTI are presented. Every step, from raw data reduction to final interpretation, is described. The limits of current observations and the promise of future contributions from the VLTI are discussed.

Interferometric observations of stars in late stages of stellar evolution and the impact of VLTI observations are discussed. Special attention is paid to the spectral information that can be derived from these observations and on the corresponding astrophysical interpretation of the data by radiative transfer modelling. It is emphasized that for the robust and non-ambiguous construction of dust-shell models it is essential to take diverse and independent observational constraints into account. Apart from matching the spectral energy distribution, the use of spatially resolved information plays a crucial role for obtaining reliable models. The combination of long-baseline interferometry data with high-resolution single-dish data (short baselines), as obtained, for example, by bispectrum speckle interferometry, provide complementary information and will improve modelling and interpretation.

After a brief introduction, this contribution will discuss practical strategies to exploit the unique science potential of closure phases in optical interferometry, especially in the case of only three telescopes when direct imaging is near-impossible. Prototype source morphologies will be investigated in detail (binary and "dust shell + star"), and will illustrate how closure phase measurements can be used both for "Precision Interferometry" as well as qualitatively new probes of circumstellar environments. During this meeting, the notion of a "Closure Differential Phase" came to light, and some interesting properties of this quantity are here introduced.