Introduction

This document gives a description of the CLIC software, developed to calibrate the data taken with the IRAM millimeter-wave interferometer on Plateau de Bure. CLIC stands for ``Continuum and Line Interferometer Calibration''. The way the data must be calibrated is very much dependent on the acquisition procedures and the backend hardware. For that reason it was felt easier to develop a dedicated program that to try to use an existing package such as AIPS. The situation is different for mapping software, for which our needs are certainly covered by the capabilities of AIPS. Thus a gateway from CLIC calibrated visibility files into the AIPS world is provided.

We outline now the different steps in data calibration. The (complex) visibility W measured on the baseline from antenna $i$ to antenna $j$ at frequency channel $k$ is related to the true object visibility $V_{ij}$ by

$$W_{ijk} = g_i(t) g_j^*(t) b_{ijk}(t) V_{ij}(u_k(t),v_k(t)) + noise term$$ (1)

where $u_k(t)$ and $v_k(t)$ are the spatial frequencies corresponding to baseline $ij$ at time $t$ and frequency $k$, and we assume the object has a flat spectrum. Calibrating the data is computing the complex ``calibration curves'' $g_i(t)$ and $b_{ijk}(t)$. For the relatively narrow bandpass of millimeter astronomy, $u_k(t)$ and $v_k(t)$ are almost independent of the frequency channel $k$ (even the sideband separation is only 3 % of the observing frequency).

$b_{ijk}(t)$ is the bandpass of the detection system, and is usually almost constant with time. It can be formally decomposed in a product of RF bandpass, caused by receivers and cables and usually with weak dependence on frequency, and IF bandpass, caused by the backend (spectral and continuum correlators at Bure).

For the $g_i(t)$, we must separate the calibration of amplitude and phases since amplitude and phase errors have very different origins. The amplitude corrections is related to several effects: atmospheric absorption, receiver gain, antenna gain (affected by pointing errors, defocussing, surface status and systematic elevation effects), and correlation losses due to phase noise. Phase errors may come from delay errors, baseline errors, or a slow drift in atmospheric or receiver phases.

• Amplitude calibration: Atmospheric absorption and receiver gain are derived in the same way as for single dish data, the correction factors being determined from ``chopper wheel calibrations'' being performed at regular intervals (typically 10-15 minutes). This in the same time corrects for the amplitude passband (except for antenna chromatism effects). The atmospheric model calculations are done on-line to help monitoring data quality, and applied to the data. However, the calibration parameters are stored in the headers as well as the overall amplitude factor applied. In this way, the model calculations can always be repeated at any stage in the data reduction process, with the possibility of correcting wrong atmospheric parameters.
• IF Passband Calibration: Phase errors introduced in the backend are measured by connecting all correlator inputs to the same source of white noise (a noise generator in the IF). Ideally all outputs should give $100\%$ correlated signals. The phases then are the channel-to-channel phase errors. Normally this operation should be done every time the spectral correlator setup is changed. It is actually done as often as the amplitude calibration, since it can be done during antenna motion from one source to the next, and since it provides a good means to trace down hardware problems in the backend.
• Phase Calibration is necessary to correct the raw visibilities for instrumental and atmospheric short-term phase fluctuations. This is done by repeatedly observing a nearby point source for which the measured phases should be zero if delays are correctly tracked. The phase closure relations may also be used. If the calibrator is very close to the source, this will also correct to first order baseline errors.

  The visibilities amplitudes measured on the calibration source, if strong enough, give an estimate of the additional amplitude corrections introduced by pointing and focussing inaccuracies and atmospheric phase jitter. They are commonly used to calibrate the source amplitude relatively to the flux of the phase calibrator, thus eliminating to first order the decorrelation effect due to the atmospheric phase fluctuations.

• RF Passband Calibration: Ideally the phase calibration should be done separately for each receiver channel (but calibrators are not strong enough). However if one assumes that phase fluctuations are not frequency-dependent one may calibrate the relative phases of the channels on a strong source, before or after the observations. Actually only the RF passband needs observing a source in the sky for this, since the passband of the correlators may be calibrated in autocorrelation mode on a noise source (see above). RF passband calibration may be necessary only for broad band spectra or objects where a high channel to channel dynamic range is needed.

Amplitude calibration and IF passband calibration have now been moved into the acquisition software. They are however described in section 4.1. Instrumental phase and RF passband calibrations might need more user intervention, depending on the data quality, and are described later, after a section dedicated to the data display capabilities of CLIC. Finally some specific operations, such as baseline calibration, are explained.