3.1 Introduction

Throughout the universe, the common astronomical objects - stars, stellar clusters, molecular clouds, galaxies, AGNs, QSOs, clusters of galaxies - have typical linear dimensions, and only seldom span a factor of 10 to 100 in scale. The more distant the objects, the smaller therefore their apparent angular size, and hence a higher angular resolution and larger collecting area of a telescope is required to distinguish significant structural detail at a significant level of detection. According to a fundamental optics principle, the angular resolution $\Theta$ of a full aperture telescope (optical or radio) of diameter $\cal D$, or of an interferometer consisting of several connected or disconnected telescopes of longest baseline separation $\cal B$, observing at the wavelength $\lambda$, is

$$\Theta \propto \lambda/ {\cal D} {\rm or} \Theta \propto \lambda /{\cal B} [{\rm rad}]$$ (3.1)

If, therefore, the telescope or the baseline has a diameter/length of $\cal D = B$ = n$\lambda$, the resolution is

$$\Theta \propto \lambda /{\cal D} \propto \lambda/{\cal B} \propto 1/{\rm n}$$ (3.2)

In words, the larger the number (n) of wavelengths spanned by the diameter/baseline the higher is the angular resolution. From these relations it is evident that a high angular resolution is obtained by using short wavelengths (for instance millimeters instead of centimeters), and/or large telescopes, and/or long baselines ([inter]continental distances instead of kilometers). In order to obtain a resolution of $\Theta$ = 1$''$ [the seeing limit at optical wavelengths set by the turbulence of the Earth's atmosphere], the size of the telescope or interferometer baseline must be

$${\cal D}[1'']= {\cal B}[1''] \approx 2 \times 10^ 5, \lambda$$ (3.3)

which is $\cal D$[1$''$] = $\cal B$[1$''$] = 600m at $\lambda$ = 3mm (100GHz). To be comparable in resolution with the HST of $\Theta \approx 10 ^{-2} \times 1 '' = 0.01 ''$, a telescope/baseline of $\cal D = B$ = 60km at $\lambda$ = 3mm is required. To obtain however a resolution of $\Theta$ = 10$^{-2}$$\times$10$^{-2}$$\times$1$''$ = 0.0001$''$ = 0.1 mas at mm-wavelengths it is evident that the telescope must have Earth dimensions. Such a 'telescope' can only be an interferometer of some sort, of which the telescopes are disconnected and located across a continent, or on different continents, or on different continents and in Space. cm The image quality of a mm-VLBI array depends on the available uv-coverage. However, mm-VLBI telescopes cannot be displaced, they are arranged in the given configuration of the observatory sites (see Fig. 3.1), and uv-coverage is only obtained by Earth rotation. The sensitivity of a mm-VLBI array depends on the collecting area and the precision (aperture efficiency) of the participating telescopes. cm Very long baseline interferometry, on baseline dimensions of the Earth's diameter and satellite orbits, requires special techniques to record in-phase the different segments of a wavefront emitted by a source and being received by the individual telescopes of the array. This in-phase recording is achieved by locking the oscillators of the receiver and tape recorder unit to a very precise observatory time standard (Hydrogen-maser), which in turn is synchronized to an 'outside clock', available at all stations. This outside clock is provided by time signals of the Global Positioning System (GPS).