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The Faint Images of the Radio Sky at Twenty-cm (FIRST) is presently the most sensitive large-area, wide-field survey at radio wavelengths. It provides a factor of 50.FIRST is a radio snapshot survey performed at the NRAO Very Large Array (VLA) facility. FIRST covers approximately 10 000°2 of the North and South Galactic Caps with a resolution of approximately 5 arc-seconds. FIRST produces 3-minute snapshots covering a hexagonal grid of the sky, using 2×7 3-MHz frequency channels centred at 1365 and 1435 MHz The survey catalogue contains around one million sources, and it is estimated that nearly 15% of these sources have optical counterparts. The FIRST survey area has been selected to correspond with that of the SDSS. (Sky Survey). FIRST provides a database that is uniform in angular resolution and flux density sensitivity and it offers the opportunity to produce the largest unbiased survey for statistical analysis. FIRST’s design enables the search for radio variability of sources on timescales of minutes to years. (http://iopscience.iop.org/0004-637X/742/1/49/pdf/apj_742_1_49.pdf)  \subsection{Faint \subsubsection{Faint  Images of the Radio Sky (FIRST)}   Figure 1. Histogram of peak flux densities for sources in the FIRST survey. (http://iopscience.iop.org/0004-637X/742/1/49/pdf/apj_742_1_49.pdf)  The Faint Images of the Radio Sky at Twenty-cm (FIRST) is presently the most sensitive large-area, wide-field survey at radio wavelengths. It provides a factor of 50.FIRST is a radio snapshot survey performed at the NRAO Very Large Array (VLA) facility. FIRST covers approximately 10 000°2 of the North and South Galactic Caps with a resolution of approximately 5 arc-seconds. FIRST produces 3-minute snapshots covering a hexagonal grid of the sky, using 2×7 3-MHz frequency channels centred at 1365 and 1435 MHz The survey catalogue contains around one million sources, and it is estimated that nearly 15% of these sources have optical counterparts. The FIRST survey area has been selected to correspond with that of the SDSS. (Sky Survey). FIRST provides a database that is uniform in angular resolution and flux density sensitivity and it offers the opportunity to produce the largest unbiased survey for statistical analysis. FIRST’s design enables the search for radio variability of sources on timescales of minutes to years. (http://iopscience.iop.org/0004-637X/742/1/49/pdf/apj_742_1_49.pdf)  \subsection{Trade-off \subsubsection{Trade-off  between area and depth in FIRST survey - this section is incomplete} Figure 2 : the components of a two-dish interferometer observing in a narrow frequency range. The correlator multiplies and averages the voltage outputs V1 and V2 of the two dishes. 
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FIRST’s high angular resolution and faint flux density threshold (the flux density limit of FIRST is ~ 1 mJ) come at a price. Some of the flux from extended sources is resolved out. This leads to a systematic underestimation of extended source flux density and a survey threshold that is a function of source size  Table 1. FIRST-like VLASS Survey parameters (https://science.nrao.edu/science/surveys/vlass/Richards_WP_r0.pdf)  Table 1 depicts the trade-off between area and depth similar to that which is observed in the FIRST survey. It shows possible scenarios with area between 10 0000 and 20 0000 squared, and depth between 15 and 50 µJy (where Jy is a unit of spectral flux density). To obtain the depth of 10,000°2 at 15 µJy for example, the area needs to be reduce to approximately 2 200 as shown in table 1.   \subsubsection{FIRST and synchrotron radiation - this section is incomplete}  Only in the late 1940s the connection between cosmic radio waves and synchrotron emission could be established. Synchrotron emissions of AGN is due to the presence of magnetic fields. This emission is observable as polarized emission. Cosmic objects emit intense radio waves through the synchrotron emission. It is widely held that radio sources in the cosmic universe emit by the synchrotron process, especially at the lower radio frequencies in the metre and cm wavelength range. This range is detected by the FIRST survey. (http://www.ugr.es/~battaner/escritos/granada_paper.pdf)   
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