[mmaimcal] draft results of holography sensitivity calculations

[Mark Holdaway]

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

Hey!  The calculation:

Quoting from some great past unknown E-mail god
(probably Rick Perley:)
> 
>       For a line source, it is
> 
>               Smean x sqrt(Linewidth).  
> 
>       where Smean is the mean flux density in the line over the
> Linewidth.  
> 
>       Wright et al. (AJ, Vol 99, p1299, 1990) give calibrated profiles
> of SiO transitions from numerous sources.  The beefiest of these is 
> W Hya, although Orion-IRc2 is close.  For both, the mean intensity 
> is about 500 Jy, and the equivalent linewidth is 10 km/sec = 2.9 MHz.  
>       Thus, in 'astronomers' units', the equivalent SNR in a line
> is    750 Jy.sqrt(MHz).  
> 

3C273:   15 Jy * sqrt(8000MHz) = 1340 Jy.sqrt(MHz)

ie, 3C273 WINS


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

Sounds like I reinvented your wheel.

>  >>> > 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 
> to within
>  >>> > a factor of 2-4, depending on how we slice it.
> 
> you don't have to hand wave (and i'm sure darrel can calculate this 
> properly, he's an expert in these things...).  the errors look like:
>     e_{max} ~ l N / (pi SNR)
>     e_{rms} ~ l N / (5 pi SNR)
> for wavelength l, and raster size N.  again, see the above two VLBA 
> memos for the derivation, theoretically, and the simulations...
> 
> 	-bryan
>