6.3.1 Array calibration

The astronomical setup of the interferometer involves a number of steps that are done under the joint responsibility of the array operator and of the astronomer on duty (AoD). The goal of the setup is to maximize the interferometer performance in view of sensitivity and positional precision.

6.3.1.1 Change of array configuration

A change of configuration is the responsibility of the operators and of the technical staff. Since most projects, as mapping, mosaicing and snapshot observations, require more uv-coverage than a single configuration can provide, the antennas are moved typically every three weeks or so, to a new configuration. Every additional configuration increases the mapping sensitivity and the uniformity of the uv-coverage by adding N(N-1)/2 baselines to the sampling function (these are 10 baselines during the winter period, 6 baselines during the summer period when the array is operated with only 4 antennas). Configurations are usually selected among six types according to several criteria: antenna availability, project type, atmospheric seeing, uv-coverage, pressure in local sidereal time, sun avoidance and other factors.

Six primary configurations are needed to cover the desired range of angular resolution at the two operating frequencies with 5 antennas:

Configuration	Stations
D	W05 W00 E03 N05 N09
C1	W05 W01 E10 N07 N13
C2	W12 W09 E10 N05 N15
B1	W12 E18 E23 N13 N20
B2	W23 W12 E12 N17 N29
A	W27 W23 E16 E24 N29

Set	Configurations	Purpose
D	D	detection / lowest resolution
CD	D, C2 or C1	3.5'' at 100GHz
CC	C1, C2	higher resolution than CD
BC	B1, C2	2.0'' at 100GHz
BB	B1, B2, C2	higher resolution and sensitivity
AB	A, B1, B2	1.0'' at 100GHz

Special configurations and sets of configurations are used during the annual antenna maintenance period which is usually between May and October. During this period observations at 1mm are for most of the time not feasible, specially in the two extended B configurations. Observations in the A configuration whether at 3mm or 1mm will in general only be scheduled during the winter period. Requested non-standard configurations are considered only in exceptional cases.

6.3.1.2 Antenna focus

Sensitivity is one of the most important concerns. As a rule of thumb, an axial displacement of the secondary by $\sim \lambda/3$ results in a 20% loss of sensitivity. To avoid losses larger than 3%, the position of the secondary needs to be measured to much better than $\lambda/10$ on regular time intervals. The positional precision, however, depends on the source strength, the operating wavelength, the sampling of secondary positions and, finally, on atmosphere stability. In general, the focus is measured at 3mm on a strong quasar by displacing the secondary in steps of 1mm (in steps of 0.45mm if done at 1mm). This is systematically done by the operators at the beginning of every project and is automatically verified by the system every hour during project execution.

6.3.1.3 Antenna pointing

A high pointing accuracy is demanded in view of sensitivity and mapping quality. Antenna pointing errors affect the global sensitivity of the interferometer and may lead to severe errors in the image restoration process. As a rule, a pointing precision of $\Delta\theta\sim \theta_{\rm FHWP}/20$ is desirable at the highest frequency. The good pointing accuracy results from an optimized structural design: a good knowledge of the gravitational load, a good positional stability of the receivers (a good alignment is needed for dual-frequency observations), a precise control of the secondary, high precision bearings and position encoders, a good servo system, $\ldots$ and a good software control for repeatable antenna pointing errors. The quality of a pointing model is generally limited by wind and thermal load effects. The absolute pointing accuracy achievable with the IRAM antennas is in general below the 2-3'' rms at each axis with a slightly higher uncertainty in elevation. Such a pointing accuracy leads to very small intensity variations, most of the time with negligible effects on the image reconstruction. Higher accuracy is obtained by regular relative pointing measurements every hour.

Each antenna is characterized by a fixed set of pointing parameters. These are measured only in certain circumstances: when an antenna is going to see first light, when modifications are made which may affect the pointing of an antenna, or more generally in cases of suspected pointing problems. In these cases a precise interferometric pointing session, eventually with a preceding less sensitive full-sky single-dish session, is required to derive the full set of antenna pointing parameters. Such pointing sessions are reduced with a dedicated non-linear fitting program in use at Plateau de Bure.

The pointing model is actually based on 5 parameters only, all others being negligibly small. These parameters are: IAZ and IEL (the azimuth and elevation encoder zero point correction), COH (the antenna horizontal collimation), and IVE and IVN (the antenna East-West and North-South inclination). IAZ, IEL, IVE and IVN are in station dependent, while COH is in principle an antenna constant. IAZ, IEL and COH are measured in interferometric mode by pointing on a few low elevation and high elevation sources. In general, three strong quasars at 3mm are fully sufficient. The remaining two parameters, IVE and IVN are measured on every project start with an inclinometer by making an antenna turn through 360 $^\circ$ .

6.3.1.4 Delay measurements

Delay measurements aim at the correction of cable length (electric path) differences between two antennas after compensation of the geometrical path length. An improper knowledge of the difference in cable length is visible as a frequency dependent phase slope in the intermediate frequency bands (IF1 and IF2), and, depending on the amplitude of the slope, may result in a more or less important loss of sensitivity. The delay is measured by a cross-correlation on a strong radio source at the beginning of every project.

6.3.1.5 Baseline lengths measurements

The goal is to measure the position of each antenna i relative to a common reference point (distances X_ij,Y_ij,Z_ij between antennas i and j or distances dX_i,dY_i,dZ_i with respect to the theoretical station position) in order to subtract the phase term $2\pi w$ (see lecture 2 by S.Guilloteau) at any hour angle and declination from the observed phase. The absence of a good baseline solution is equivalent to having large uncertainties in the baseline separation between different antennas. As a consequence, the geometrical delay might improperly be compensated and large time-variable phase errors might affect observations.

Though the quality of a baseline solution is easily found out - the calibrator's visibility phase shouldn't vary with reference to the phase tracking center as function of hour angle and declination - a good baseline solution is truly indispensable for the purpose of phase calibration. Phase errors can often be more deleterious on compact configurations where source visibilities are stronger than on extended configurations. As a reference, winter conditions allow baselines in the D configuration to be measured at 3mm with a $5^\circ-8^\circ$ phase accuracy and with $5^\circ-20^\circ$ in the A configuration. In summer conditions the accuracy is often 2-3 times lower.

Though no high accuracy is needed for antenna positioning (offset position from the target location is routinely within a wavelength), the actual antenna position has to be known with high precision: within a small fraction of a wavelength (70-300 $\mu$ m). The precision is limited essentially by the atmosphere and by thermal effects.

The baseline parameters can be obtained to high accuracy from observations of a number k of relatively strong point sources, well-distributed in hour-angle and declination, for which accurate positions are available. The analysis of these observations is usually carried out with CLIC, the calibration program, using a least-square-fit analysis on the geometric phase difference for antenna pairs (i,j):

$\begin{displaymath}\phi_{ij}^g=\phi_{ij}^s+\phi_{ij}^a=2\pi\,w = \end{displaymath}$

$\begin{displaymath}=\frac{2\pi}{\lambda}\,\underbrace{(X_{ij},Y_{ij},Z_{ij})}_{b... ...ta \\ sin \delta \\ \end{array} \right) }_{s}+\phi_{ij}^a \end{displaymath}$

$\begin{displaymath}\longrightarrow\,\,\,\,\, \Delta\phi_{ijk}^g = \frac{2\pi}{\... ...derbrace{b_{ij}\cdot \Delta s_k)}_{\simeq 0}+\Delta\phi_{ijk}^a\end{displaymath}$

In theory, three sources are sufficient to measure the actual baseline lengths, in practice 10-12 sources are necessary to obtain an accurate measurement. Since a displacement by 1'' at 100GHz on a baseline of 100m translates already to a phase offset of $\sim 58.2^\circ$ ( $\sim 1$ rad), the positions of the radio sources used for baseline measurements need to be known with an accuracy $\Delta s_k$ better than 0.02''.

The baseline equation implies that positional errors are equivalent to phase errors. Since baseline length errors scale with the angular separation between calibrator and source, the aim is to have calibrators as close as possible to minimize the phase errors.

Sometimes, accurate baselines are not required as in the case of self-calibration projects. Sometimes, however, even if good baselines are required, they simply cannot be determined precisely enough after a change of configuration. Projects observed in the meantime will then need to wait for a better baseline model. Such projects will in general not be phase-calibrated by the astronomer on duty, but phase-calibration has to be done later on by the proposers of the observations.

6.3.1.6 Gain measurements

Gain measurements (GAIN scans) are cross-correlations on strong radio sources which are essentially used to measure the image to signal sideband ratios for both the 3mm and 1.3mm receivers. The required sideband ratio depends on the project, the achievable sideband ratio depends on the receiver and the frequency. An accurate measurement of the receiver gain is necessary for a good estimate of the atmospheric opacity and of the associated thermal noise with which the atmosphere contributes during the observations. Therefore, results of a gain measurement are followed by an atmospheric calibration (scan CALI).

6.3.1.7 Receiver stability

As a rule, a high receiver stability $\le 3.10^{-4}$ is never required. Sometimes, however, depending on atmospheric conditions, array configuration and observing frequency, a higher stability may be desirable in view of a very promising radiometric phase correction. Though such a high stability is not always achievable on all the receivers, it makes possible an improvement in data quality when the atmospheric phase correction technique becomes practical (see lecture 9 by M.Bremer). Experience at Bure from the last three years shows that the radiometric phase correction is quite efficient under clear sky conditions: from spring to autumn essentially during the evening and morning hours, in winter almost always when the weather allows to observe.

Since observations on more compact baselines suffer less from the effects of the atmospheric phase noise - for reference, an rms of less than 10 $^\circ$ rms at 3mm is routinely obtained on the shortest baselines - a high receiver stability in compact configurations is only exceptionally required. Typically, under average observing conditions with a receiver stability of 3.10^-4 we may already correct atmospheric phase fluctuations with a precision of 10 $^\circ$ at 115GHz.