Sensitivity

When preparing your observing proposal, it is important that you estimate the expected brightness of your source, required brightness sensitivity and choose a reasonable synthesised beam size given the sensitivity of the ATCA. Increased angular resolution (resulting from either longer baselines or higher frequencies) decreases brightness sensitivity in proportion to the beam area while point source sensitivity remains constant. General expressions for the sensitivity of the ATCA can be found in the ATNF document AT/01.17/025 -- which is available from

http://www.narrabri.atnf.csiro.au/observing/AT-01.17-025.pdf

-- (these expressions have been used in the previous table and the table below).

Table 3.1: Observing Parameters for the 6km Compact Array.

BAND WAVELENGTH[h]	20 cm	13 cm	6 cm	3 cm	1.2cm	3mm
(NAME)	(L)	(S)	(C)	(X)	(K)	(W)
Nominal frequency range (GHz)[a]	1.25-1.78	2.20-2.50	4.40-6.86	8.00-9.20	16.0-25.0	83.5-106.0
Fractional frequency range	35%	13%	44%	14%	44%	24%
Number of antennas	6	6	6	6	6	5
Number of baselines	15	15	15	15	15	10
Primary beam (arcmin)[b]	33'	22'	10'	5'	2'	30"
Synthesised beam (arcsec)[c]	6"	4"	2"	1"	0.5"	2"
System sensitivity S $_{\mathrm sys}$ (Jy)[d]	350	440	420	390	670	8400
Strongest confusing source (mJy)[e]	140	24	2.3	0.4	-	-
10min Flux sensitivity (mJy/beam)[f]	0.19	0.24	0.22	0.21	0.37	5.6
(128MHz, 2-bit)
10min Brightness sensitivity (K)[g]	2.1	2.6	2.1	2.0	3.2	0.2
(128MHz, 2-bit, Dec -45°)
12hr Flux sensitivity (mJy/beam)[f]	0.022	0.029	0.027	0.025	0.043	0.66
(128MHz, 2-bit)
12hr Brightness sensitivity (K)[g]	0.26	0.31	0.24	0.23	0.37	0.02
(128MHz, 2-bit, Dec -45°)

¹ It is possible to observe outside the ranges specified here. For further information contact narrabri@atnf.csiro.au.

² HPBW in RA for 6km array, no taper. Resolution in Dec is $\Delta\alpha/\sin(\delta$).

³ The signal which doubles the system temperature at elevation 40°, adapted from AT/39.2/022 using the revised PKS B1934$-$638 flux-density scale (AT/39.3/040 -- see Appendix F). Nominal frequencies are: 1472, 2368, 4800 and 8640MHz.

⁴ Theoretical rms noise; one frequency; dual orthogonal polarisation; natural weighting. The effect of confusing sources can substantially degrade this number.

⁵ For the 6km array; see Table 3.2 for shorter arrays.

Notes:
(a) It is possible to observe outside the ranges specified here. For further information contact narrabri@atnf.csiro.au.
(b) Full width at half power.
(c) HPBW in RA for 6km array, no taper. Resolution in Dec is $\Delta\alpha/\sin(\delta)$.
(d) The signal which doubles the system temperature at elevation 40°, adapted from AT/39.2/022 using the revised PKS B1934$-$638 flux-density scale (AT/39.3/040 - see Appendix F). Nominal frequencies are: 1472, 2368, 4800 and 8640MHz.
(e) Within FWHM primary beam - see Perley et al. (1989)
(f) Theoretical rms noise; one frequency; dual orthogonal polarisation; natural weighting. The effect of confusing sources can substantially degrade this number.
(g) For the 6km array; see the next table for shorter arrays.
(h) For details of 3mm receivers (W band), see http://www.atnf.csiro.au/observers/docs/3mm/.
You have control over the integration time, bandwidth, wavelength and synthesised beam size. The sensitivity expressions in terms of these variables and the system sensitivity (S $_{\mathrm sys}$: see the table below) reduce approximately to:

$${\Delta~\mathrm{S_{rms}} = 0.0195~\mathrm{S_{sys}}~/\sqrt{\mathrm{t\,B}}~~\mathrm{mJy}}$$ (6)

and

$${\Delta~\mathrm{T_{b}} = 1.36~\frac{\Delta\mathrm{S_{rms}}\lambda^{2}}{\theta_{maj} \theta_{min}}~~\mathrm{K}}$$ (7)

where               
where 		 $\Delta\mathrm{S_{rms}}$ is the rms flux sensitivity


		 $\Delta\mathrm{T_{b}}$ is the rms brightness sensitivity


		 $\mathrm{S_{sys}}$ is the system sensitivity (Jy)


		 $\lambda$ is the observing wavelength (cm)


		 $\theta_{maj}, \theta_{min}$ are the half-power widths of an elliptical beam (arcsec)


		 $\mathrm{t}$ is the integration time (minutes)


		 $\mathrm{B}$ is the bandwidth (MHz)

Table 3.2: Brightness temperature sensitivity (12h, 128MHz, 2-bit, dual orthogonal polarisations).

	ARRAY LENGTH
Wavelength	6 km	3 km	1.5 km	750 m	350 m	214 m	75 m
20 cm	0.26 K	0.080 K	0.020 K	0.0050 K	0.0012 K	0.0006 K	0.00013 K
13 cm	0.31 K	0.093 K	0.023 K	0.0058 K	0.0015 K	0.0008 K	0.00016 K
6 cm	0.24 K	0.075 K	0.019 K	0.0047 K	0.0011 K	0.0006 K	0.00012 K
3 cm	0.23 K	0.071 K	0.018 K	0.0045 K	0.0011 K	0.0006 K	0.00012 K
1cm	0.37 K	0.120 k	0.029 K	0.0072 K	0.0018 K	0.0009 K	0.00020 K
3mm						0.02 K	0.003 K

For a total of $I$ two-element interferometers ( $I\,=\,N(N\,-\,1)/2$ for $N$ antenna elements) using two IF chains, the sensitivity is improved by $\sqrt{2I}$. The ATCA sensitivity values for some standard observing scenarios are presented in this table. The actual image noise for continuum observations is often limited by dynamic range, and therefore greater than the theoretical noise, especially at low frequency. Dynamic ranges of 100:1 are typical for non-self-calibrated data.

Increasing the integration time of the correlated signals decreases the intensity of image features (time smearing). This effect gets worse further away from the phase centre. The choice of integration time is necessarily a compromise. You need a short time so as to minimise the effect of atmospheric/ionospheric instabilities and so that you can image as wide a field as possible. Too short an integration time, however, produces an inconvenient volume of data. Experience has shown that 20s is a suitable integration time for most experiments, but up to 30s is possible. The minimum integration time, dependent on how the correlator is configured, is usually 10s. Integration time can be increased using the averagingoption in ATCASCHED . For more information refer to AT document AT/20.1/008 -- which is available from

http://www.atnf.csiro.au/observers/memos/

-- and the correlator configuration book in the ATCA Control Room.

The webpage http://www.atnf.csiro.au/observers/docs/at_sens/ enables the characteristics (including sensitivity) of an ATCA observation to be calculated.