[mmaimcal]Re: Phase Repeatability of the Attenuators

[Mark Holdaway]

> Next, I wonder where the 20d accuracy spec comes from.  We have been
> working with the far tighter goal set forth in the Project Book
> (section 7.0.6) of visibility calibration to 0.1 radian at 950 GHz.

15-20d is what we can get from fast switching.
We can get smaller phase fluctuations, but then you loose
excessive time in the fast switching calibration process and your
noise increases.  Similarly, you can loose much less time calibrating
but then your residual phase errors are much larger.  You also need to
fold in the atmosphere -- ie, you can get 5 deg rms residual phase
errors if you observe during the best atmospheric conditions at a low
frequency.  If you reserve the best conditions for the highest freq
observations, you end up getting 15-20 at all bands.

> Allocating 1/sqrt2 of this to each antenna, and allocating this among
> antenna structure, electronics, and atmosphere, we are left with only
> 2.4d (6.9 fsec) of systematic phase error for one antenna's
> electronics, and 2.9d (8.4 fsec) for the "atmosphere."  The latter is
> intended to be achieved using all available correction techniques,
> including fast switching, and it must include the two items you
> mention: thermal noise in the calibrator observation and the
> difference in atmospheric delay between calibrator and target.
> Perhaps the goal is grossly unrealistic, but it is what ALMA has
> officially adopted.  You have suggested a much looser goal, but you
> have allocated a far smaller fraction of the total to electronics;
> nevertheless, your result for electronics (6.4d) is looser than the
> official goal (2.4d).  The designers would be happy to accept such a
> change!

I agree that the spec is very tight.  It looks forward to the day
when radiometric schemes work better than they do.  Fast switching
will likely not be able to utilize that spec.  On the other hand,
at 15-20 deg from atmosphere and thermal noise, we'd like to add
NOTHING from electronics.

> Third, I want to point out that fast phase switching (with a frequency
> change) provides *no* information about the instrumental phase at the
> target's observing frequency, so it is not a complete phase
> calibration scheme.  An additional calibration observation must be
> made with exactly the same instrumental setup as was used on the
> target source.  Presumably this can be done less frequently, and with
> longer integrating time.  But its error must also be part of the phase
> calibration error budget.  Any instrumental phase variation over this
> longer time interval is part of that error.

Yes, understood.

> You make a good point about the scaling from 90 GHz to 950 GHz.  The
> official goal is written only for 950 GHz, on the assumption that
> performance will be somewhat better at lower frequencies, but with no
> requirement on how much better.  You point out that it ought to be
> *proportionally* better if it is used to calibrate higher frequency
> measurements.  While the errors in some elements of the 1st LO system
> will scale in this way, other parts of the system will scale
> differently and some will have systematic phase errors that are
> independent of the observing frequency.  You are correct to assume
> that variable attenuators are in the latter category.  The overall
> situation is rather complicated.  In some areas, it could imply a
> tightening of requirements relative to our current specs, in spite of
> the fact that you are suggesting a loosening of the overall
> high-frequency accuracy goal.  Variable attenuators are one example
> of this, but there are many others.

It is complicated but feasible in the case of a non-dispersive atmosphere.
Dispersion makes things more difficult, as we then have three different
ways that the phases scale with freq rather than two.

 -Mark