LOFAR, the LOw-Frequency ARray, is a new-generation radio interferometer constructed in the north of the Netherlands and across europe. Utilizing a novel phased-array design, LOFAR covers the largely unexplored low-frequency range from 10-240 MHz and provides a number of unique observing capabilities. Spreading out from a core located near the village of Exloo in the northeast of the Netherlands, a total of 40 LOFAR stations are nearing completion. A further five stations have been deployed throughout Germany, and one station has been built in each of France, Sweden, and the UK. Digital beam-forming techniques make the LOFAR system agile and allow for rapid repointing of the telescope as well as the potential for multiple simultaneous observations. With its dense core array and long interferometric baselines, LOFAR achieves unparalleled sensitivity and angular resolution in the low-frequency radio regime. The LOFAR facilities are jointly operated by the International LOFAR Telescope (ILT) foundation, as an observatory open to the global astronomical community. LOFAR is one of the first radio observatories to feature automated processing pipelines to deliver fully calibrated science products to its user community. LOFAR's new capabilities, techniques and modus operandi make it an important pathfinder for the Square Kilometre Array (SKA). We give an overview of the LOFAR instrument, its major hardware and software components, and the core science objectives that have driven its design. In addition, we present a selection of new results from the commissioning phase of this new radio observatory.

Abstract. -The measurement of polarized radiation uses entirely different methods at optical and radio wavelengths. As a result, the algebraic analysis of polarimeter performance differs and, in the case of radio interferometry, is unnecessarily complicated. We demonstrate that the mathematical operation of outer matrix multiplication provides the missing link between the two approaches. Within one coherent framework, we then unite the concepts of Stokes parameters and Wolf coherency matrix, the Jones and Mueller calculi from optics, and the techniques of radio interferometry based on multiplying correlators. We relate the polarization performance of a complete radio interferometer to the (matrix) polarization properties of its successive signal processing stages, providing a clear view of how a radio polarimeter works. Our treatment also clarifies the nature of and the relations between the various types of transformations used in optical polarimetry. We develop the analysis from the radio interferometrist's point of view, but include enough background for a wider audience. In a companion paper, we discuss in more detail the application to the calibration of radio interferometer systems; in a third paper we investigate the IAU (1973) radio definition of the Stokes parameters and its precise translation into mathematical form.

The low frequency array (LOFAR), is the first radio telescope designed with the capability to measure radio emission from cosmic-ray induced air showers in parallel with interferometric observations. In the first ∼2 years of observing, 405 cosmic-ray events in the energy range of 10 16 −10 18 eV have been detected in the band from 30−80 MHz. Each of these air showers is registered with up to ∼1000 independent antennas resulting in measurements of the radio emission with unprecedented detail. This article describes the dataset, as well as the analysis pipeline, and serves as a reference for future papers based on these data. All steps necessary to achieve a full reconstruction of the electric field at every antenna position are explained, including removal of radio frequency interference, correcting for the antenna response and identification of the pulsed signal.

Low frequency radio waves, while challenging to observe, are a rich source of information about pulsars. The LOw Frequency ARray (LOFAR) is a new radio interferometer operating in the lowest 4 octaves of the ionospheric "radio window": 10-240 MHz, that will greatly facilitate observing pulsars at low radio frequencies. Through the huge collecting area, long baselines, and flexible digital hardware, it is expected that LOFAR will revolutionize radio astronomy at the lowest frequencies visible from Earth. LOFAR is a next-generation radio telescope and a pathfinder to the Square Kilometre Array (SKA), in that it incorporates advanced multi-beaming techniques between thousands of individual elements. We discuss the motivation for low-frequency pulsar observations in general and the potential of LOFAR in addressing these science goals. We present LOFAR as it is designed to perform high-time-resolution observations of pulsars and other fast transients, and outline the various relevant observing modes and data reduction pipelines that are already or will soon be implemented to facilitate these observations. A number of results obtained from commissioning observations are presented to demonstrate the exciting potential of the telescope. This paper outlines the case for low frequency pulsar observations and is also intended to serve as a reference for upcoming pulsar/fast transient science papers with LOFAR.

Abstract. -In a companion paper, a mathematical formalism to describe the polarimetric response of a radio interferometer was presented. Some of the instrumental parameters, however, are either unknown or poorly known. Here we consider the determination of these parameters both by a traditional radio-interferometry instrumental approach as well as by using optical polarimetry principles. In doing so, we establish links between the two fields. We show that some degrees of freedom cannot be solved for with various calibration or self-calibration schemes. These degrees of freedom are identified with instrumental parameters and physical source properties. The number of unsolvable degrees of freedom is reduced for a long synthesis with alt-az antennas. We also consider the effect of errors in the assumed instrumental parameters on the resultant calibrated data. The polarimetric calibration procedure for some telescopes is reviewed in the context of this analysis.