4.2 Optical versus millimeter radio interferometry

Optical and millimeter radio interferometry are essentially the same technique used in two different wavelength domains. Although they share the same fundamentals and the same objectives (see Sect. 4.2.1), their implementations can exhibit some significative differences (see Sect. 4.2.2). More details are given in Chap. 21.

4.2.1 Common issues

Both optical and millimeter interferometers study the coherence of the electric field by the mean of separated apertures, called telescopes, siderostats or antennas. The principle of these two techniques is based on the Zernike-Van Cittert theorem, i.e. the degree of coherence of the light is directly related to the Fourier transform of the spatial distribution of the intensity of the observed object [Goodman 1985].

By using separated apertures, both techniques achieve high angular resolution observation, with a resolution tens to hundreds of time larger than single aperture in the same wavelength domain. They therefore face similar difficulties, since they both used diluted arrays and have to find the best array configurations to reach their respective objectives. Similarly to millimeter radio interferometry, optical interferometry has also to calibrate the measured complex visibilities.

When optical interferometry will become as mature as millimeter interferometry, one will probably use very similar algorithm to reconstruct images from the calibrated visibilities.

4.2.2 Main differences

The differences come mainly from the wavelength domains: the typical optical wavelength is $1 \ensuremath{\mbox{ $\mu$m}}$, which corresponds to a frequency of 300 THz to be compared with the typical millimeter radio wavelength of 1 mm and the corresponding 300 GHz frequency.

The first consequence is the actual angular resolution that can be achieved, defined by the fringe spacing $\lambda/\cal B$. The typical resolution reached in the optical domain is about 1 milli-arcsecond whereas in the millimeter domain, the Plateau de Bure Interferometer (PdBI) reaches about 1 arcsecond. ALMA with its extended baselines will be able to get 0.03 arcsecond but the information will still be 100 times less resolved than with optical interferometers.

A second difference comes from the type of detection and beam combination. In millimeter interferometry, the signal detection occurs at the antenna level thanks to the heterodyne technique. The signal is coupled with a reference signal of high coherence and therefore one records the amplitude and the phase of the coming electric field. The signals from each antenna are then digitized and the combination takes place in the correlator (see first chapters of this book). An electronic phase delay is applied to take into account the difference in path length between two arms. In the optical domain, the heterodyne technique has been successful at $10\ensuremath{\mbox{ $\mu$m}}$ [Gay & Journet 1973,Johnson et al. 1974]. This technique however happens to be not sensitive. That is why optical interferometry is usually achieved by direct detection of interferences. The light beams are propagated to a central lab, where the optical path is equalized and are combined to form interferences before being detected. Since the detection techniques measure only the power of the electric field, one has to code the fringes either temporally or spatially (see Sect. 4.4.2). Finally the two techniques give different types of interferences: respectively multiplicative and additive. The heterodyne technique directly gives access to the electric field $\psi_k$ for each aperture and therefore the interference signal is multiplicative (see also Chapter 2 and 21).

The quadratic detection in the direct technique gives additive interferences:

$$I_{kl} = <(\psi_k+\psi_l)(\psi_k+\psi_l)^*> = I_k + I_l + 2\sqrt{I_kI_l} \; v_{kl} \; \cos \phi_{kl},$$ (4.1)

where $<...>$ stands for a temporal average over a time long compared to the inverse frequency of the signal, $I_k$ is the intensity of the $k$-th beam, and $v_{kl}$ and $\phi_{kl}$ are respectively the amplitude and phase of the normalized visibility. One of the consequences is a different type of calibration process, another is that visibility unit is Jansky in the millimeter domain, whereas in the optical domain it is dimension-less, i.e. flux normalized.

A third and important difference is the influence of the atmosphere. In the optical domain the dominant effect is the corrugation of the wavefront. The spatial Fried's parameter, $r_0$, which corresponds to the spatial scale of the turbulence is smaller than the telescope size. Typical numbers are $0.1-0.2$ m in the visible and $0.5-1$ m in the near infrared. That is a reason why many interferometers have aperture diameters below $1$ m (see Table 4.1). In the millimeter, $r_0$ is larger than the antenna sizes. The temporal Fried's parameter, $t_0$, which corresponds to the temporal scale of the turbulence is of the order of 10-100 ms in the optical versus several minutes in the millimeter. That is why it is possible to use phase referencing (phase calibration on a source with known phase) with radio interferometers by off-pointing the interferometer, when it is almost impossible to calibrate the phase in the optical. The only way to retrieve the phase is to measure closure phases with more than 3 apertures or to use a dual-beam interferometer and an accurate metrology like for narrow-angle astrometry (see Sect. 4.3.2). The fact that the phase is almost impossible to get in the optical makes therefore a large difference in the way the data are processed to obtain images.

A last difference is the type of noise encountered. The main source of noise in millimeter interferometry is the thermal noise. In optical interferometry, the three type of noises are the photon noise, the read-out noise of the detectors and the background noise, coming either from thermal emission or from the sky brightness. In addition, noise from the atmosphere turbulence, either photometric fluctuations or speckles, must be taken into account.