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.

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.

LOFAR is the LOw‐Frequency Radio interferometer ARray located at midlatitude (52°53′N). Here we present results on ionospheric structures derived from 29 LOFAR nighttime observations during the winters of 2012/2013 and 2013/2014. We show that LOFAR is able to determine differential ionospheric total electron content values with an accuracy better than 0.001 total electron content unit = 1016m−2 over distances ranging between 1 and 100 km. For all observations the power law behavior of the phase structure function is confirmed over a long range of baseline lengths, between 1 and 80 km, with a slope that is, in general, larger than the 5/3 expected for pure Kolmogorov turbulence. The measured average slope is 1.89 with a one standard deviation spread of 0.1. The diffractive scale, i.e., the length scale where the phase variance is 1rad2, is shown to be an easily obtained single number that represents the ionospheric quality of a radio interferometric observation. A small diffractive scale is equivalent to high phase variability over the field of view as well as a short time coherence of the signal, which limits calibration and imaging quality. For the studied observations the diffractive scales at 150 MHz vary between 3.5 and 30 km. A diffractive scale above 5 km, pertinent to about 90% of the observations, is considered sufficient for the high dynamic range imaging needed for the LOFAR epoch of reionization project. For most nights the ionospheric irregularities were anisotropic, with the structures being aligned with the Earth magnetic field in about 60% of the observations.