Optical interferometry for astronomy was conceived as early as 1868, succeeded in measuring a stellar diameter in 1920 and was only reborn in 1974. Soon after, several remarkable prototype instruments were built, demonstrating the potential power of this technique for stellar studies at visible and near infrared wavelengths. Meanwhile, the physics of the Earth atmosphere, which seriously impacts image quality on ground-based observatories, progressed with the emergence of adaptive optics systems. Then, during the years 1990–2005, ambitious interferometric observatories entered into service, in Europe (VLTI) and in United States (Keck, NPOI, LBT). Today, their results and promises deeply impact stellar studies by providing images of the surface and immediate surrounding of stars, stellar objects and even galactic nuclei.

This paper serves as an introduction to the current book. It provides the basic notions of long-baseline optical/infrared interferometry prior to reading all the subsequent chapters, and is not an extended introduction to the field.

We present in this chapter a description of optical interferometry combining instruments. For that purpose we describe the role of different key functions and give examples of the choice made in current and future instruments in particular at VLTI.

This chapter describes the methods used to extract closure phase from CLIMB data and visibility amplitude from both the CLASSIC and CLIMB beam combiners. It also includes a rather exhaustive description of the theory behind these methods. This high degree of detail is partly because previous publications of this theory contain errors, and partly because having done all this work it*s nice to have it written up in full somewhere, and being slightly beyond the thesis writing stage, this is only possible for me in a chapter like this.

This is one of two chapters that describe the methods used to extract closure phase from CLIMB data and visibility amplitude from both the CLASSIC and CLIMB beam combiners. In this, the second chapter, I describe the pipeline software.

This tutorial paper describes the problem of image reconstruction from interferometric data with a particular focus on the specific problems encountered at optical (visible/IR) wavelengths. The challenging issues in image reconstruction from interferometric data are introduced in the context of a general inverse problem approach. This framework is then used to describe state-of-the-art image reconstruction algorithms specifically developed for optical interferometry.

Stars are not smooth. Their photosphere is covered by a granulation pattern associated with the heat transport by convection. The convection-related surface structures have different size, depth, and temporal variations with respect to the stellar type. The related activity (in addition to other phenomena such as magnetic spots, rotation, dust, etc.) potentially causes bias in stellar parameters determination, radial velocity, chemical abundances determinations, and exoplanet transit detections.

The role of long-baseline interferometric observations in this astrophysical context is crucial to characterize the stellar surface dynamics and correct the potential biases. In this Chapter, we present how the granulation pattern is expected for different kind of stellar types ranging from main sequence to extremely evolved stars of different masses and how interferometric techniques help to study their photospheric dynamics.

We discuss and illustrate contributions that optical interferometry has made on our current understanding of cool evolved stars. We include red giant branch (RGB) stars, asymptotic giant branch (AGB) stars, and red supergiants (RSGs). Studies using optical interferometry from visual to mid-infrared wavelengths have greatly increased our knowledge of their atmospheres, extended molecular shells, dust formation, and winds. These processes and the morphology of the circumstellar environment are important for the further evolution of these stars toward planetary nebulae (PNe) and core-collapse supernovae (SNe), and for the return of material to the interstellar medium.

In this paper, we summarize the basic properties of radiative stellar winds from the theoretical and observational point of views. We illustrate two examples of a radiative code applied to stellar physics: the SIMECA code successfully used to constrain the physics of the circumstellar environment of the Be star α Arae constrained by VLTI-AMBER spectrally resolved measurements and the CMFGEN code applied to the BA supergiants Deneb and Rigel constrained by CHARA-VEGA measurements.

Disks are very common structures found around stars of different masses and evolutionary status. In this chapter we will discuss the basic properties of disks and how interferometric observations can put constraints on their structure. The chapter is organized in three sections: geometry of disks, physical conditions and chemical composition, and kinematics.

Asteroseismology is a powerful technique that can be employed to determine precise fundamental parameters of stars, such as the radius, mass and age. The data are sensitive to the density structure of the star, so if we combine these with an independently measured radius from interferometry, we can determine the mass with high precision. This is one of the only methods for determining masses of single field stars and with high precision – an otherwise unobservable property. Knowing masses of stars has consequences for exoplanetary characterisation, Galactic population studies and for stars themselves, it allows us to constrain stellar model parameters, yields more precise determinations of ages which thus allows us to calibrate age-rotation relations as well as setting stellar constraints on the age of our own Galaxy.

The very high spatial resolution provided by current interferometers (VLTI, CHARA, …) makes it possible to measure directly the change in angular diameter of more than thirty Cepheids over their pulsation cycle. When combined with radial velocity measurements, this allows us to measure precisely their distances in a quasi-geometrical way. This is an essential information to calibrate the Cepheid's Period-Luminosity law. On the other hand, a careful analysis of the dynamical structure of their atmosphere is required to avoid biases in their distance determination.

Surface inhomogeneities are found in many stars. In active sun-like stars and cool giants temperature spots similar to that found in the Sun are recovered from the inversion of spectroscopic data. M-dwarfs also show highly inhomogeneous surface structures in polarized light and photometric variability that are believed to be connected with cool regions on their surface, too. Supergiants have highly inhomogeneous atmospheres because large convective cells, and therefore bright and dark regions, have sizes comparable to the size of stars themselves. Hot luminous stars can have dense clamps in their atmospheres caused by an interaction of fast stellar wind, rotation, and the magnetic fields. Finally, a special class of main-sequence B-F stars, called chemically peculiar stars, have spots of abundance origin. Spots in these stars can look bright or dark depending on wavelength of observation. Modern interferometry is capable of reaching a very high angular resolution that will make it possible to study starspots in very detail. In this review we will focus on starspots in general and abundance spots in chemically peculiar stars in particular, as well as possible application of interferometry to study them.

The signature of activity in general, and of stellar magnetic spots in particular, is present in every measurements, including interferometric ones. Indeed, stellar spots can be found on many stellar surfaces, their size and number varying according to their host's magnetic field and rotational velocity. To correctly determine stellar parameters, it is thus necessary to determine and extract stellar activity's signals. Interferometric observables are disturbed by activity, and this observing technique thus constitutes a good way of probing stellar surface. However, magnetic spots sometimes mimic other phenomenon, like a transiting exoplanet. In that case, the combination of several observing techniques, like photometry and interferometry, is mandatory to extract the planetary signal from the spot's one, and then characterize the exoplanet.

Stellar magnetism and activity are often studied thanks to various spectro-polarimetric techniques but generally the poor angular resolution drastically limits detection and/or diagnosis since the polarized signals are averaged over the stellar surface and thus can be cancelled because of symmetry degrees. Taking benefit of the unprecedent resolving power of optical long-baseline interferometry will be a significant gain, allowing the local polarized features to be studied. In this review we briefly describe the various methods that are classically used to detect and/or map magnetic fields, and then explain how optical interferometry can bring new and complementary observational information.

Rotation has a strong influence in the structure of stars. The centrifugal force caused by rotation produces a deformation of the star that also affects the profile of brightness at its surface, this is known as gravity darkening. In this chapter we will construct a simple model to predict the shape and surface brightness of a rotating star.

We present here two examples of the use of interferometric observations to study stellar rotation effects (flattening and gravity darkening) and spots on the stellar photospheres. From the fit of simple geometrical models to two sets of VLTI data (VINCI and AMBER) using the LITpro tool from JMMC we can estimate stellar physical parameters and have insights on the photospheric intensity distribution.

This chapter discusses the use and possibilities of optical and infrared interferometry to study star formation. It starts with a brief overview of the star formation process and highlights the open questions from an observational point of view. These are found at the smallest scales, as this is, inevitably, where all the action such as accretion and outflows, occurs. We then use basic astrophysical concepts to assess which scales and conditions can be probed with existing interferometric set-ups for which we use the ESO/VLTI instrument suite as example. We will concentrate on the more massive stars observed at high resolution with continuum interferometry. Throughout, some of the most recent interferometric results are used as examples of the various processes discussed.

This paper serves as a reference on how to estimate the parameters of binary stars and how to combine multiple techniques, namely astrometry, interferometry and radial velocities.