3.6 From observations to correlations, step by step

3.6.1 Observing Techniques

Figure 3.4: Disconnected two-telescope VLBI array; one telescope is located in Europe, the other one is located in the USA. At both observatories, the local oscillators (LO$_{1}$, LO$_{2}$), the sampler, and the tape unit are locked to the observatory H-maser, synchronized to the satellite GPS time signal. The observations are correlated either at Haystack or Bonn; here the delays and Doppler shifts are introduced.

Figure 3.5: Allan standard deviation vs. integrated time for several frequency standards. The phase fluctuations of mm-VLBI are usually dominated by atmospheric phase fluctuations. From [Thompson et al. 1986]. Copyright: @1986 Wiley-Interscience Publications. Reprinted by permission of John Wiley & Sons, Inc.

$\parbox{150mm}{ \caption{Figure 3.6: Ty... ...l H-maser drift measured at Pico Veleta (by courtesy of J. Penalver, IRAM). }}$

A 2-telescope disconnected mm-VLBI array and the (far away) correlator station are shown in Figure 3.4. mm-VLBI observations are made with telescopes separated by several hundreds or thousands of kilometers not sharing a common time/frequency reference as used in connected interferometry. At each VLBI-telescope therefore the receivers, frequency down-up converters, tape recorders, phase-calibration systems etc. are locked to a Hydrogen-maser which has a typical short-term stability of $\sim$10$^{-15}$ and a typical drift of a few 10 nano-seconds per day, or smaller, as shown in Figures 3.5 & 3.6. The VLBI time/frequency systems of the individual telescopes are locked to the GPS system which gives an absolute time reference at the participating telescopes of a few hundred nano-seconds, or better. This time difference must be retrieved a posteriori in the data correlation. cm mm-VLBI observations are made at a fixed frequency, preferably at Single-Side-Band tuning in order to reduce noise from the non-used sideband. Fringe rotation and Doppler shifts are introduced a posteriori at the correlator.

3.6.2 Data Recording

In VLBI observations, the telescopes are disconnected and real-time correlation of the signals from the individual telescopes is not possible. At each telescope, the signals are recorded on tape synchronous with the time signal provided by the Hydrogen-maser. In MkIII mode observations, the data are available as 28 channels of 4MHz bandwidth each; the bandwidth of the recording is $\Delta$$\nu$ = 28$\times$4MHz = 112MHz. The 28 tracks are recorded simultaneously on magnetic tape. The required bitrate of the recording is

$$bits/s = 2 n_c \Delta \nu$$ (3.6)

For $\Delta$$\nu$ = 112MHz and a sampling efficiency n$_{c}$ $\approx$ 1-1.6, the bitrate recorded on tape is $\sim$224Megabites/s. mm-VLBI is being upgraded to 256MHz bandwidth, and more (MkIV).

3.6.3 Correlation Time

The short-term frequency stability (up to a few 1000s, see Figure 3.5) of a Hydrogen-maser is $\sim$10$^{-15}$. There are long-term drifts which can be checked against GPS signals (see Figure 3.6) and adjusted so that they are below, say, ten nano-seconds per day. The maximum possible integration time ($\tau$) of an observation is set by the requirement that the relative frequency drift $\Delta$$\nu$ must not exceed, say, $\Delta$$\nu$ $\approx$0.2 radians. The integration time then is ([Kellerman & Thompson 1985])

$$\Delta \nu /(2 \pi \nu \tau ) \approx 0.2/(2 \pi \nu \tau) \approx 10^{-15}$$ (3.7)

This relation gives $\tau$(86GHz) $\approx$ 350s $\approx$ 5minutes and $\tau$(230GHz) $\approx$ 150s $\approx$ 2minutes.

$\parbox{150mm}{ \caption{Figure 3.7: VL... ... for 3C 279 at 215 GHz (upper panel) and 2145+067 at 86 GHz (lower panel).}}$

3.6.4 Phase Correction

Because of phase variations introduced by atmospheric water vapour fluctuations, the correlation time $\tau$ derived above can be significantly shorter, $\tau$ $\approx$ 10-30s, especially when observing at high frequencies. Because of the scarcity of strong mm-wavelength VLBI sources at sufficiently close distances in the sky, phase referencing as used in connected mm-wavelength interferometry (for instance used on PdB) has not yet generally been applied in mm-VLBI. Efforts are however undertaken to apply phase corrections from local line-of-sight water vapour measurements (sky emission measurements). As an example, the phase stability of a 86GHz and 215GHz measurement between Pico Veleta and Plateau de Bure is shown in Fig.3.7. A typical atmosphere-induced phase variation and phase correction applied to 86GHz VLBI measurements made at Pico Veleta is shown in Figure 3.8.

3.6.5 Correlation

The recorded mm-wavelength VLBI data are correlated at Haystack (USA) or at Bonn (Germany). The end-product of the correlation are calibrated visibility values (uv-tables) which can be used in the same way as data, for instance, obtained with the PdB interferometer.