[evlatests] Sensitivity Equation
Rick Perley
rperley at nrao.edu
Wed Nov 23 10:52:56 EST 2011
In yesterday's 'Stokes V' discussion, I mentioned the sensitivity
equation, which includes the effects of 'self-noise'.
The nicest form of the equation is in the article by Joan and Craig
in the 'Synthesis Imaging' book, Eq. 10 in Chapter 9. It can be
written, for a single correlator (real or imaginary part of a single
complex correlator), and a point source as:
sigma = sqrt(A)/(eta.sqrt(B))
where:
A = 2.S_t^2 + 2.S_t.S_e + S_e^2
B = 2.BW.T
eta = system (correlator, electronics) efficiency.
and
S_t = source flux density (Jy)
S_e = antenna SEFD (Jy)
BW = bandwidth (Hz)
T = visibility integration time (sec)
If the source is resolved, then a modification is needed to the
first term in A:
Replace
2.S_t^2
with
S_c^2 + S_t^2,
where S_c is the correlated flux on the baseline of interest. Keep
in mind that S_c and S_t will be different between the real an imaginary
parts, depending on where the source is. For a properly phased array,
and a point source, these terms will only apply to the real part.
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