[mmaimcal] draft results of holography sensitivity calculations

[Mark Holdaway]

>     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,

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

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

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

e_{rms} = 5.22 microns.   

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


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


Take care,

   -Mark