## 2 Observations  
### The LOFAR Telescope  
The LOFAR system was described in detail [27; 28]. They showed basics on design, configuration, and the signal processing methods. Hereafter we describe only the most important specification of the telescope and its functions.  
The LOFAR interferometer consists of over 100,000 dipole antennas with omnidirectional characteristics. All antennas are grouped into stations. 52 individual stations across Europe were created to this day. The significant number of stations are located in the Netherlands [28], mainly in the region called LOFAR Core, with the Superterp as the central part.  
The stations located outside the Netherlands are a part of the International LOFAR Telescope (ILT). Six stations are located in Germany and one station each in UK, France, Sweden Ireland and Latvia. The three Polish stations built by the Polish LOFAR Consortium (POLFAR) Consortium are fully operational from the beginning of 2016 (see details in [29; 30]. The LOFAR stations are also planned in Medicina (Italy) and in Rozhen (Bulgaria).  
The LOFAR receivers' bandwidth ranges from 10 MHz to 240 MHz (with a gap in the frequency range from 88 to 108 MHz due to strong Earth-bound interference). Each of the 52 stations is built to be a part of ILT system and interferometric observation mode and consists of two antenna fields. The Low Band Antennas (LBAs) and the High Band Antennas (HBAs). Both antenna fields forming the LOFAR station are described in detail by [31].  
Signals from individual dipoles forming a phase system allow for beam formation (see Figure 4) through digital time delay operations. In this way, a single element of the radio telescope is virtually created, which can be controlled fully electronically. This technique allows to point the telescope at any object in the sky and track its daily movement, and with a suitable computer system it is able to track more than one point on the celestial sphere. The field of view, i.e., the beam width (for HBA parts of single station) is about 2 angular degrees. The ILT instrument (the maximum baseline is currently almost 2000 km) gives an angular resolution close to < 0.1 arcsec at 240 MHz and about 2.5 arcsec at 10 MHz. Resolution of LOFAR is given by \(\alpha\lambda/\text{L}\), where L denotes baseline, \(\alpha=0.8\) and \(\lambda\) is wavelength in meters [27].  
Beamforming is an extremely important process during observation with an instrument such as LOFAR, i.e., a phase antenna. This process is also the basis of the main motivation of our research, which is the study of the pulsar signal distorted by the Earth's ionosphere. As already mentioned, the basic sensors of the LOFAR system are pairs of dipole antennas. Each of the dipoles in the HBA part has an omnidirectional pattern. 16 pairs of dipoles make a system closed in a single tile, which can create a beam, but it is still wide (see Figure 4, right). In case of observation with HBA system in ILT configuration, for observations around the frequency of 130 MHz, the beam is about 2 degrees wide on the sky. However, the characteristic of the beam (Figure 4, left) makes the sensitivity greatest in the center of the bundle and drops towards its edges. Even slight deviations in the direction in which the position of the source is calculated (and beam is formed) and the real one, changed by refraction in the ionosphere, reduces the sensitivity of system.