LOFAR is among the first radio telescopes for which RFI mitigation forms an integral part of the system design. This is needed, as LOFAR will operate in a hostile RFI environment. Unlike the majority of present-day radio telescopes, the signals in most of the frequency bands at the input of the LOFAR A/D converters can no longer be characterized predominantly as white noise. RFI mitigation in radio astronomy is a relative new field, and many RFI mitigation methods are not yet "fully proven". However, many techniques have been extensively demonstrated on prototype systems.
The overall LOFAR approach towards RFI mitigation is to rely in the first place on such well-proven techniques, but to provide also options to study new and promising approaches. Their application will offer enhanced performance in contaminated bands, and ensures that LOFAR can handle the challenges imposed by future changes in the use of the radio spectrum. It is therefore vital to ensure that the LOFAR system is designed in such a way that future, more complex RFI mitigation algorithms can be applied without redesigning parts of LOFAR. LOFAR also offers a unique opportunity to develop and demonstrate new techniques for application in future instruments, in particular the Square Kilometre Array.
The strategy consists of creating several "lines of defence" with increasing complexity, and therefore increasing risk. Simple and proven techniques are expected to be sufficient in the majority of environmental conditions. When necessary, more complex techniques can be applied. While these techniques may require more experimentation in the early phases of operation, they will lead to increased system performance as they become more mature. The adopted strategy assumes that (a) the analog subsystems and digital filters are sufficiently linear and (b) low level semi-stationary RFI sources can be removed from visibility data and images through self-calibration and other post-correlation techniques. Results from prototype antenna and receiver systems indicate that the first assumption can be met. The second assumption has not yet been
sufficiently validated. The generalized self-calibration process is in principle capable of handling low-level RFI, but no definite proof through simulations or processing of realistic data has been provided yet. It should be noted though that many post-correlation RFI mitigation approaches have been tested at existing synthesis telescopes. Post-correlation mitigation has the major advantage that information from all stations is available. This leads to a natural spatial suppression of localized RFI (also through spectral dilution). It often also allows for a better parameterisation (and suppression) of RFI than possible for stations separately because of the spatial properties mentioned above, but also because of the relatively long integration times at post correlation level.
The development of a robust calibration system for LOFAR is among the most challenging and high-risk tasks within the project. The calibration will take place in two main stages: first in each station, referred to as the station calibration and second in the central systems. The goal of the station calibration is to calibrate individual antenna signals for gain and phase differences. These differences are
caused mainly by temperature variations in the electronics. In the central systems the differences between stations will be calibrated using an approach that resembles conventional self-calibration in synthesis arrays. Depending on the scientific application this will be done in (almost) real time or off-line at the central processing site within about a week.
Fundamentally, LOFAR calibration is position-dependent. The station beams change strongly with time as earth-rotation alters the projected geometry of the fixed dipole antenna arrays. Each station will be laid out differently. The ionospheric delay as viewed from a given station is strongly variable as a function of position within the field of view. The low-frequency sky is sufficiently well filled that position-dependence of the gains cannot be ignored. A more sophisticated approach than conventional self-calibration is therefore mandated.
A key point is that it is not possible to take an uncalibrated LOFAR dataset, apply station-based multiplicative corrections, and arrive at a fully calibrated dataset suitable for high fidelity imaging. Such corrections can be valid only for a single point on the sky, implying that the resulting dataset is miscalibrated for all other positions on the sky. The resulting sidelobe responses will result in unacceptable imaging performance. Instead, to get a dataset that can be imaged with high fidelity, one must evaluate the complex gain that applies to each source, subtract the contributions to the visibility for each source, then add them all back in with unit gain. Therefore, we take the dataset with the sky model subtracted source-by-source, and complex gain by complex gain, then image the residuals. Such residual imaging must be performed by "tiling" the field of view with many small patches. For each patch, the residual data are corrected for a single sky location using the calibration parameters, and the rest of the sky can be considered to be empty to an acceptable level. To the resulting residual map, we can then simply add the sky model to arrive at a high fidelity sky image.
Ideally, a generalized self-calibration system would produce an independent complex gain for each point on the sky, for each station, and for each time interval. This set of complex gain estimates would be used to subtract out the sky model, point by point, yielding visibility residuals which can be analyzed to refine estimates of the complex gains. Errors in the sky model would be estimated by imaging of the residual data set. Conceptually, this is closely analogous to conventional self-calibration, except that the number of complex gain parameters to be solved for is larger by a factor corresponding to the number of independent
locations in the field of view. There are, however, two major practical difficulties:
The LOFAR calibration system, and indeed the whole LOFAR instrument, is being designed with these two problems firmly in mind.