4.3 Description of optical interferometers

This section is dedicated to the overview of interferometric systems. We first go through the functional description of a typical optical interferometer, then describe the different types of interferometers with specific objectives.

4.3.1 Functional description

Optical interferometry aims at measuring the complex degree of coherence of the observed object. To achieve such a goal, optical interferometers require the following functionalities:

• Interferometric array. Several types of array configurations have been designed in order to give access to the different spatial frequencies (see Fig. 4.2). The three criteria are the number of telescopes, but also the length and the orientation angle of their associated baselines. One can choose to have either fixed telescopes (PTI, KI, VLTI/VIMA) or movable telescopes (GI2T, IOTA, VLTI/VISA). Like in radio interferometry, Earth rotation allows to sample the $uv$ tracks. If the object displays a wavelength-independant structure like a binary, the coverage of the $uv$ plane can be performed with spatial frequencies at different wavelengths.

  Figure 4.2: Four examples of optical interferometers. The array can be linear and continuous (GI2T), L-shaped with several stations (IOTA), Y-shaped with fixed telescopes (CHARA) or the filling of an equivalent 200-m aperture (VLTI).

  

• Apertures. They ensure the light collection. Either siderostats (IOTA, PTI, SUSI) with diameter less than $50$ cm or more or less traditional telescopes (GI2T, CHARA, KI, VLTI) for larger diameters can be used. In case of large siderostats, a fixed beam compressor is used to compress the beam diameter for propagation toward the central lab.
• Beam transportation. Once the object light has been captured by the apertures, one carries out the individual beams toward the combination laboratory. Usually the optical path is designed so that a complete symmetry of the mirrors in each arms minimizes the differential polarization effects. The optical train contains typically of the order of 20 mirrors. [Froehly 1981] suggested to use optical fibers to carry the light from the apertures to the lab. This technology has been tested by [Coudé Du Foresto, Mazé, & Ridgway 1993] and is the key of the coming O'HANA project which will gather the light from the 8-m class telescopes on the Maunea Kea in Hawaii [Perrin et al. 2000]. Some interferometers use vacuum optics (PTI, IOTA, NPOI,...) to decrease the dispersion due to the propagation in the air of the delayed beam (see Sect. 4.5.2).
• Wavefront correction. The incoming light travels through the atmospheric turbulence (see Sect. 4.5.1). The wavefront is then corrugated and the images of the object move due the seeing. Almost all interferometers have therefore at least a 2-actuator adaptive optics system that corrects from the tip and the tilt (IOTA, NPOI, PTI). Large interferometers with aperture diameter larger than $1$ m have plans for higher correction of the wavefront (VLTI/VIMA, KI-main, GI2T, LBT, CHARA). The goal is to stabilize the light and to increase the Strehl ratio of individual beams, i.e. the quality of the central peak. One should note that GI2T currently works in multi-speckle mode and therefore does not formally require AO systems to properly work, even if it would increase its sensitivity performance.
• Delay lines. When the object observed is traveling across the sky, the external optical path difference (OPD) between two arms is equal to ${\cal B}\sin z$, where $\cal B$ is the baseline length and $z$ is the zenith angle. To achieve the fringe detection, the two arms should be equal at the level of the micrometer. In the first experiment by [Labeyrie 1975], the stabilization of the OPD was performed by moving the beam combination table. Nowadays, most interferometers prefer to use optical delay lines (DL) using cat's eyes located on movable chart. Moving a DL either in one arm or another compensates the sidereal motion of the star, exactly like telescope mounts follow the stars displacements. For very long delays, one often has to design and build long DLs that offer only optical delays by steps of a few meters coupled with DLs with shorter strokes (KI, CHARA).

  Figure 4.3: Some examples of delay lines

  

• Optical path difference stabilization. The atmospheric turbulence produces not only wavefront corrugation at the level of individual apertures but also at the level of the interferometer called atmospheric piston. The consequence is that the OPD is fluctuating and the fringes move back and forth. Using a fringe sensor (a simple beam combiner that measures the OPD at a frequency higher than the typical atmosphere timescale), one is able to send corrective commands to the DLs. This feature is the zero-degree of adaptive optics for an interferometer. A fringe sensor coupled with a DL is called a fringe tracker and allows to stabilize the signal for longer integration.
• Beam combination.

  Figure 4.4: Beam combiners. Left: beam combiners in bulk optics. Right: beam combiners using the integrated optics technology.

  
  The interferences between the various beams can be achieved in many ways (see Sect. 4.4). One usually distinguishes the so called co-axial beam combiners (BCs) that combine the light coming from the same optical axis (like with a beam splitter in the laboratory Michelson interferometer) and the multi-axial ones that produce interferences between beams coming from different directions (like in the Young's experiment). The beam combination is usually made with lenses, mirrors and/or beam splitters. However, the optical functions used by the telecommunication industry has given birth to fibered BCs (e.g. FLUOR [Coudé Du Foresto, Mazé, & Ridgway 1993]) and integrated optics ones (see IONIC experiment [Malbet et al. 1999]) using single mode waveguides.
• Detection. This fundamental step makes use of photon detector either with photo-counting capability in the visible range or CCD with low read-out noise in the infrared. The dispersion of the light can be done just before the detection and the instrument looks similar to a spectrograph.

The schematic layout of the VLTI is displayed on Fig. 4.5. It is typical of most of interferometers. A difference is that the focal plane hosts several instruments: VINCI the commissioning BC based on known technology, AMBER the near infrared spectrograph and MIDI the thermal infrared camera. Smaller interferometers have usually only one dedicated instrument optimized for their astrophysical targets (binaries, stellar diameters, envelopes,...).

Figure 4.5: VLTI optical layout

4.3.2 Specific applications

I see 5 types of scientific usages of the interferometric light combination.

Interferometry in the past has been most often used with only two apertures. Therefore since the atmospheric piston prevents any absolute phase calibration, the astronomers can only measure the amplitude of the complex visibility and a phase difference between two spectral channels when the instrument has some spectroscopic capability. The goal is then to measure the visibility amplitude or a differential phase, also called two-color phase, and to interpret the variations of these measurements with time, with baseline length, or with baseline angle. An important field of application is the measure of stellar diameters and binary orbits, but recently it has been extended to circumstellar envelopes and accretion disks.

The dream of most interferometrists is to perform actual imaging like in the radio domain using aperture synthesis. The interferometer COAST has been built with this goal in mind. That is why it is composed of 4 telescopes in order to increase the efficiency of the $uv$ plane coverage, but also to use the technique of closure phases. This closure phase technique, used to be of high importance in radio interferometry, allows to self-calibrate the sum of the phases measured simultaneously by three baselines. This method is very similar also to the bispectrum one in speckle interferometry. However for technical reasons, the beam combination of $N\geq3$ beams appears to be difficult and only few reconstructed images have been obtained so far. The outcome of integrated optics might change the situation in the future [Malbet et al. 1999].

The group working on NPOI has been focusing on the wide-angle astrometry for a long time (previously at the Mark III interferometer, ancestor of PTI and NPOI). The idea is simple and once again similar to what is being done in radio: when the interferometer detects fringes, the two paths of the interferometer are equal to a fraction of a micrometer. Since the delay due to the sidereal motion of the stars is given by

$$\delta = {\cal B} \cos \theta + C,$$ (4.2)

where $\cal B$ is the length of the baseline, $\theta$ is the altitude of the star in the sky and $C$ an internal constant, then the knowledge of $\cal B$ and $C$ together with the measure of the stroke given to the DL give access to $\cos \theta$. The objective consists in measuring the group delay of several tens of stars at different moments of the night and to fit the curves with cosine of the same amplitude $\cal B$. The internal metrology measures the internal constant $C$. After post-processing, both the position of the stars and the baseline are deduced with a precision of the order of the fringe spacing $\lambda/\cal B$, i.e. about 1 mas.

Recently, following the work on Mark III, [Shao & Colavita 1992] proposed the narrow-angle astrometry technique. The idea is to observe two objects sufficiently close so that the atmospheric perturbations affecting the stellar path on each telescope is almost the same for the two objects. The correlations in the perturbations is used to increase the accuracy of astrometric measurements down to $10$    $\mu$as opening the search for the reflex motion of stars due to the presence of planets. To achieve such an objective, one has to separate the field at each aperture in two sub-apertures and to propagate in parallel the light from the two stars in two different interferometric systems. A differential metrology allows to link the two interferometers. When the fringes are detected on the two detectors, the differential metrology gives the differential delay between the two stars:

$$\Delta\delta = {\cal B} \Delta \theta + d,$$ (4.3)

Where $\Delta\theta$ and $d$ are respectively the differential angle between the two stars and the internal constant. One interesting application of such a dual interferometer is phase referencing like in radio: if a close-by reference star has a zero-phase then the measure $\Delta\delta$ leads to the actual phase of the science target. In radio, the atmosphere is quiet enough to measure the phase reference by depointing the interferometer whereas in the optical domain, the two measurements must be made at the same time. The PTI is the interferometer that hosts this technique.

Finally, many groups are working on the concept of nulling interferometers. The idea [Bracewell 1978] is to use the coherence of the light to interferometrically cancel the light arriving in the interferometer boresight. An object located off-axis has translated fringes. In certain directions, the bright peaks of the object fringes are located over the dark zones of the central star fringes. If the nulling in the dark fringes is high enough, the dynamic range of this technique can reach high values (see Fig. 4.6).

Figure 4.6: Principle of a nulling interferometer (see text for details).

This application is extremely interesting in the case of the study of extra-solar planets. Those planets are expected to be between $10^4$ and $10^9$ fainter than their parent stars. Nulling the light of the central star is the only way to detect photons from these worlds. To achieve such performances, the instruments like DARWIN pill up several stages of such nulling interferometers to reach high rejection rate.