[evlatests] Sensitivity Equation

[Bob Sault]

Rick,

There are some extra caveats to watch with this.

- The equation that you give is right for a baseline. For an array,
  because the self-noise for a point source is not independent on
  different baselines, it does not average down in the way it does
  for a source that is completely resolved out. So you have to be
  careful in determining the sensitivity of the array [this is
  Barry's point about thinking about the SEFD of the (phased) array,
  not a baseline]

- Selfcal can hide much ... amplitude selfcal on a point source
  with self noise can selfcal out the self noise! You cannot
  distinguish between a gain fluctuation and self noise.

Best regards
Bob
  

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Phone:    +61-2-98721028
Email:    rsault at nrao.edu
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-----Original Message-----
From: evlatests-bounces at nrao.edu [mailto:evlatests-bounces at nrao.edu] On
Behalf Of Rick Perley
Sent: Thursday, 24 November 2011 2:53 AM
To: evlatests at aoc.nrao.edu
Subject: [evlatests] Sensitivity Equation

    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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