[mmaimcal] draft results of holography sensitivity calculations

[Jeff Mangum]

Hi Bryan,

"Bryan" == Bryan Butler <bbutler at nrao.edu> writes:

Bryan> OK, more comments, since i just skimmed more deeply into the email...



>> 
>> "Mark" == Mark Holdaway <mholdawa at tuc.nrao.edu> writes:
>> 
>>>> > Furthermore, I use my canonical ``quiescent'' 3C273
>>>> > spectrum, which pegs the non-flaring 90~GHz flux of 3C273 at 15 Jy.
>>>> > Planets cannot be used for interferometric holography, and 3C273 will
>>>> > be among the brightest of compact sources that could be used at 90
>>>> > GHz.

Bryan> the SiO masers (mostly from the envelopes of stars) will be better. 
Bryan> couple of hundred Jy, if memory serves.  very compact (for the purposes 
Bryan> of doing two-element interferometry, where you want the dishes close 
Bryan> together).  variable (factor of 2 or so), but so what, since you're just 
Bryan> doing holography.

Right, this was where Robert and I ended-up when we last discussed
this issue.  This would have to be done at 3mm.  I point this out
because OOF beam maps would have to be done at 1mm (for several
reasons, most notably the limited focus translation stage range,
unless my CRE is adopted).

>>>> > I've made a simple holography simulation package in AIPS++/glish
>>>> > (this software package is really great for things like this, I must
>>>> > say;  it is such a pity that AIPS++/glish is so underappreciated
>>>> > and underutilized).  

Bryan> i made a similar simulation package in IDL, which i am happy to send to 
Bryan> anybody if they want it.  it is described in VLBA test memos 57 (the 
Bryan> theory) and 62 (describing the simulations).  i also implemented it in 
Bryan> good old FORTRAN, which is significantly faster and doesn't need an IDL 
Bryan> license, but doesn't give you a nice graphical display...  it allows for 
Bryan> investigations of sensitivity to raster size, oversampling factor, SNR, 
Bryan> phase rms, amplitude rms (gain fluctuations), pointing errors (both 
Bryan> fixed offset and rms for both the fixed and rastering antennas), and 
Bryan> type of transform...

Oooo!  Please send both to me!  Especially interested in the IDL
version (but am aware of the drawbacks for the reasons you describe).

>>>> > The problem is now: what does the
>>>> > peak SNR mean?  Darrel Emerson made a hand-waving argument that
>>>> > translates the peak SNR in the image plane to the sensitivity to
>>>> > surface errors in the aperture plane, and it is probably correct 
Bryan> to within
>>>> > a factor of 2-4, depending on how we slice it.

Bryan> you don't have to hand wave (and i'm sure darrel can calculate this 
Bryan> properly, he's an expert in these things...).  the errors look like:
Bryan>     e_{max} ~ l N / (pi SNR)
Bryan>     e_{rms} ~ l N / (5 pi SNR)
Bryan> for wavelength l, and raster size N.  again, see the above two VLBA 
Bryan> memos for the derivation, theoretically, and the simulations...

--- Jeff