[mmaimcal] draft results of holography sensitivity calculations

[Jeff Mangum]

Hi Guys,

This stuff really belongs on the CSV wiki.  I have put the relevant
exchanges (including this one) at:

https://wikio.nrao.edu/bin/view/ALMA/HoloGraphy

Please post further discussion there.

--- Jeff


"Mark" == Mark Holdaway <mholdawa at tuc.nrao.edu> writes:

>> 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...
>> 
>> 


Mark> Bryan,

Mark> I think for the VLBA case, with the restricted bandwidth, SiO masers must 
Mark> come out ahead, but for the ALMA case with super-duper 8 GHz bandwidth,
Mark> 3C273 comes out ahead.

Mark> BTW:  I went around the block a few times with Darrel, and we agree that
Mark> the RESOLUTION will be about TWO PIXELS -- I quoted the pixel size in my
Mark> earlier e-mail, but not the resolution.  SO, we can get plenty good
Mark> SNR on the surface (5.8 microns at the edge) with 32x32 pointings, just
Mark> Nyquist sampling, and 0.4 m pixels, or 0.8 m resolution, which means
Mark> that surface setting is not really possible.  THOUGH, as Jeff Mangum
Mark> points out, that is not their goal.  This should be fine for verifying
Mark> that the surface is OK.

Mark> BTW:  Bryan's above expression,    e_{rms} ~ l N / (5 pi SNR), for
Mark> the 32x32 case, SNR = 1300, l = 3333 microns (90 GHz), yields

Mark> e_{rms} = 5.22 microns.   

Mark> In my simulation for Nyquist-sampled 32x32 holography, I get 5.8 microns 
Mark> at the EDGE of the dish, as low as 2.3 microns near the center.  OK, I'm 
Mark> willing to call it a day on this topic.


Mark> Note that in Bryan's expression, there is a hidden N dependence in the 
Mark> SNR; assuming the setup time is neglible (which will not really be the
Mark> case) and that we have the same total integration time, the SNR ~ 1/N,
Mark> and then the error will be proportional to N^2.


Mark> Take care,

Mark>    -Mark