Context. Phase-referencing is a standard calibration technique in radio interferometry, particularly suited for the detection of weak sources close to the sensitivity limits of the interferometers. However, effects from a changing atmosphere and inaccuracies in the correlator model may affect the phase-referenced images, and lead to wrong estimates of source flux densities and positions. A systematic observational study of signal decoherence in phase-referencing and its effects in the image plane has not been performed yet. Aims. We systematically studied how the signal coherence in Very-Long-Baseline-Interferometry (VLBI) observations is affected by a phase-reference calibration at different frequencies and for different calibrator-to-target separations. The results obtained should be of interest for a correct interpretation of many phase-referenced observations with VLBI. Methods. We observed a set of 13 strong sources (the S5 polar cap sample) at 8.4 and 15 GHz in phase-reference mode with 32 different calibrator/target combinations spanning angular separations between 1.5 and 20.5 degrees. We obtained phase-referenced images and studied how the dynamic range and peak flux-density depend on observing frequency and source separation. Results. We obtained dynamic ranges and peak flux densities of the phase-referenced images as a function of frequency and separation from the calibrator. We compared our results with models and phenomenological equations previously reported. Conclusions. The dynamic range of the phase-referenced images is strongly limited by the atmosphere at all frequencies and for all source separations. The limiting dynamic range is inversely proportional to the sine of the calibrator-to-target separation. Not surpriseingly, we also find that the peak flux densities decrease with source separation, relative to those obtained from the selfcalibrated images.

Phase referencing is a standard calibration procedure in radio interferometry. It allows us to detect weak sources by using quasisimultaneous observations of closeby sources acting as calibrators. However, atmospheric turbulence may introduce strong differences in the optical paths of the signals of the target and calibrator and affect, or even waste, phase referencing in cases of relatively large calibrator-to-target separations and/or bad weather. The situation is similar in wide-field interferometric observations. We present the results of a Monte Carlo study of the astrometric precision and sensitivity of an interferometric array (a realization of the Square Kilometre Array, SKA) in phase-referenced and wide-field observations. These simulations can be extrapolated to other arrays by applying the corresponding corrections. We consider several effects from the turbulent atmosphere (i.e., ionosphere and wet component of the troposphere) and also from the antenna receivers. We study the changes in dynamic range and astrometric precision as a function of observing frequency, source separation, and strength of the turbulence. We find that, for frequencies between 1 and 10 GHz, it is possible to obtain images with high fidelity, although the atmosphere strongly limits the sensitivity of the instrument compared to the case with no atmosphere. Outside this frequency window, the dynamic range of the images and the accuracy of the source positions decrease. We also find that, even if a good model of the atmospheric turbulence (with an accuracy of 99%) is used in the imaging, residual effects from the turbulence can still limit the dynamic ranges of deep, high-contrast (10 5 −10 6 ), images.

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