[mmaimcal] draft results of holography sensitivity calculations

[Bryan Butler]

hmmm, i thought i had once calculated that the line sources win.  i must 
have miscalculated or used different numbers.  planets don't help much - 
uranus is only around 8 Jy.  mars might be OK if the baseline is short 
enough and the geometry is right (so that it's bigger than a few asec, 
but not at opposition [20 asec-ish]).  if you thought you could do 
holography at 1mm, then uranus would start to be a good option, though 
it starts to get resolved unless the baseline is short...

	-bryan


On 12/6/04 10:27, Mark Holdaway wrote:
>> >>> > 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
>> 
>