Sensitivity of the LOFAR array

Major Observing modes

Signal Path

Antennas Description

Station Description and Configuration

Array Configuration

Imaging Capability and Sensitivity

Frequency and Subband Selection

Beam Definition 

Transient Buffer Boards

Data Management

Data quality inspection

CEP facilities  

System notes

 

 

Caution: The numbers quoted here are projected for the full array and assume ideal performance of the instrument. The Lofar Image Noise Calculator, which is based on these numbers, can be used to compute the thermal noise of your data. 

 

For more practical information on the actual sensitivity of the current configuration, readers should consult the corresponding "Interferometric Mode", "Beam Formed Mode" and "Direct Storage Mode"  pages.

 

1 System Equivalent Flux Density

 

The System Equivalent Flux Density (SEFD or system sensitivity) is defined as

where k denotes Boltzmann's constant, η denotes the system efficiency factor (~ 1.0) , Aeff denotes the total collecting area, and Tsys denotes the system noise temperature. The latter consists of a sky brightness component and an instrumental component:

For all LOFAR frequencies the sky brightness temperature is dominated by the Galactic radiation, which depends strongly on the wavelength:

where Ts0= 60 ± 20 K for Galactic latitudes between 10 and 90 degrees. The instrumental noise temperature follows from measurements or simulations.

 

Table 1 provides a lower limit for the effective area of the different LBA array selections. The upper limit is given by the number of dipoles times λ2/ 3, and it is given in the last column (for 48 dipoles). Note that the inner array consists of only 46 dipoles. The effective area of each dipole in the array is determined by its distance to the nearest dipole (d) within the full array:

This value is a lower limit of the actual effective area. 

Freq (MHz)
λ (m)
Aeff
inner (46)
Aeff
outer (48)
Aeff
sparse (48)
48*Aeff,dipole
15
20.0
419.77
1973.4
1148.6
6400.0 *
30
10.0
419.77
1343.5
869.14
1600.0
45
6.67
415.37
693.61
558.64
711.11
60
5.00
347.37
398.18
371.19
400.00
75
4.00
239.67
256.00
247.43
256.00
Table 1 Effective area (m2) for the different LBA array selections as function of frequency (MHz) or wavelength (m). (*) An 81.34 m station has an area of 5196.3 m2.

 

For an HBA dipole, the effective area is limited by the available area in a tile. There are 16 dipole antennas within one 5 m by 5 m tile, hence, the dipole effective area is given by

 

The resulting HBA station effective area is given in Table 2: 

Freq (MHz)
λ (m)
Core(*)
Remote
European
120
2.50
600
1200
2400
150
2.00
512
1024
2048
180
1.67
356
711
1422
200
1.50
288
576
1152
210
1.43
261
522
1045
240
1.25
200
400
800

Table 2 Effective area (m2) for the HBA array as function of frequency (MHz) or wavelength (m). At 120 MHz the effective area is limited by the tile size. (*) There are two HBA fields per core station.

 

Empirical SEFD values for the Dutch stations have been derived by utilizing a 2-minute imaging-mode observation of 3C295 in LBA and in HBA, taken near transit.The results are plotted in Figure 1. The visibilities were flagged to remove RFI, and the contributions of Cygnus A and Cassiopeia A were modeled and removed (in the case of the LBA). From these preprocessed data, the S/N ratio of the visibilities was determined for each baseline between similar stations (i.e., core-core and remote-remote baselines for the HBA). The S/N was defined as the mean of the parallel-hand (XX,YY) visibilities, divided by the standard deviation of the cross-hand (XY,YX) visibilities. These S/N values were then combined with the spectral model of 3C295 from Scaife & Heald (2012), and taking the bandwidth and integration time of the individual visibilities into account, an estimate of the SEFD for the type of station comprising this baseline selection was obtained. The most distant remote stations are excluded from this analysis as 3C295 is resolved on all baselines to those stations. For the same reason, we have not attempted to determine empirical SEFDs for international stations using this procedure.

 

 

 

 

 

Figure 1: Plots of the SEFD as a function of frequency for the various LOFAR operating bands and station configurations. The grayed regions are excluded from plotting due to strong post-flagging RFI contamination. In the case of HBA, the circles are for core stations and squares are for remote stations. In the LBA, the circles are LBA INNER core stations and the squares are LBA OUTER core stations.

2 Sensitivities

 

Caution: The numbers quoted here are projected for the full array and assume ideal performance of the instrument

The Lofar Image Noise Calculator, which is based on these numbers, can be used to compute the thermal noise of your data. 

 

For more practical information on the actual sensitivity of the current configuration, readers should consult the "Examples of deliverable LOFAR products" page.

The sensitivity ΔS (in Jy) of a single dipole (or half an ``antenna'') is defined as follows: 

where δν denotes the bandwidth (in Hz) and δ t (in s) denotes the total integration time. An antenna that consists of two (equal) dipoles placed perpendicular to each other has a sensitivity of

For one station, the overlap in effective area from different dipoles has to be taken into account. Using the SEFD of a station (see previous section) for a single polarization, we can calculate its sensitivity:

These sensitivities are somewhat theoretical, since they are usually not measured. However, the noise level on a baseline (i,j) correlation can be derived from it:

In the case of an image, the signals from different baselines and two polarizations are combined. For LOFAR this includes signals from stations with different effective areas. Therefore, the noise level in a LOFAR image is given by

where W denotes a factor for increase of noise due to the weighting scheme (which depends on the type of weighting: natural, uniform, robust, ...), Nc and Nr denote the number of core and remote stations respectively, Score and Sremote denote the SEFDs for the core and the remote stations respectively. This expression can easily be extended to include European stations.

In case of an array having N equal stations (or dishes) the following familiar result is retrieved

Table 4 provides the expected noise levels in LOFAR images. The quoted sensitivities are for image noise calculated assuming 8 hours of integration and an e ffective bandwidth of 3.66 MHz (20 subbands). The sensitivities are based on the zenith SEFD’s derived from 3C295 in the Galactic halo as presented in Fig. 1. These values assume a factor of 1.3 loss in sensitivity due to time-variable station projection losses for a declination of 30 degrees, as well as a factor 1.5 to take into account losses for “robust” weighting of the visibilities, as compared to natural weighting. Values for 15 MHz have not yet been determined awaiting a good station calibration. Similarly values at 200, 210, and 240 MHz should be viewed as preliminary and are expected to improve as the station calibration is improved.

Table 4: LOFAR sensitivities. The different columns refer to the case of a 6-station Superterp, a 24-station core array, a 40-station Dutch array, and a 48-station full array. 

 

The values quoted for the HBA in Table 4 agree with empirical values derived from recent observations on 3C196 and the North Celestial Pole (NCP) where all NL remote stations were tapered to match 24-tile core stations. With improved station calibration, these estimates can likely be improved in the future by a factor of about 1.2. For the more compact LOFAR configurations, confusion noise will exceed the quoted values. The quoted sensitivities for the lower LBA frequencies have not yet been achieved in practice

3 Bandpass

There are several contributions to the frequency dependent sensitivity of LOFAR to incoming radiation (the bandpass). At the correlator, a digital correction is applied within each 0.2 MHz subband to remove the frequency-dependent effects of the conversion to the frequency domain. The station beam is also strongly frequency dependent, except at the beam-pointing centre. Finally, the physical structure of the individual receiving elements causes a strongly peaked contribution to the bandpass near the resonance frequency of the dipole. In the case of the LBA dipoles, the nominal resonance frequency is at 52 MHz. However, as can already be seen in Figure 2, the actual peak of the dipole response is closer to 60 MHz.

Determining the combined bandpass (referred to as the “global bandpass”), which includes all frequency dependent effects in the system that are not yet corrected post-correlation, can be achieved during calibration. To illustrate this, the bright quasar 3C196 has been observed using the core and remote stations in the LBA and in the three HBA bands (see Figure 1).

 

Figure 2: The bright quasar 3C196 has been observed using the core and remote stations. Observations of 3C196 between 15–78 MHz were obtained in two observing sessions (15–30 MHz in one session, and 30–78 MHz in the other). For each subband, a system gain was determined, and the gain amplitude was taken as the value of the global bandpass at the frequency of the particular subband. These figures show the normalized global bandpass for several of the LOFAR bands. The global bandpass is defined as the total system gain converting measured voltage units to flux on the sky. These bandpass measurements were determined using short observations of the bright source 3C196 and calculating the mean gain for all stations in each sub-band. The values have been corrected for the intrinsic spectrum of 3C196 assuming a spectral index of -0.70 (Scaife & Heald 2012). Curves are shown for (upper left ) LBA from 10-90 MHz with 200 MHz clock sampling, (upper right) HBA low from 110-190 MHz with 200 MHz clock sampling, (lower left)HBA mid from 170-230 MHz with 160 MHz clock sampling, and (lower right) HBA high from 210-250 MHz with 200 MHz clock sampling.

 

 

Design: Kuenst.    Development: Dripl.    © 2014 ASTRON