[mmaimcal] Re: WVR memo

[Larry D'Addario]

Richard Hills writes:
 > If you are suggesting that the figure for the drift should be
 > 8.4 femtoseconds of delay, which corresponds to only 2.5 microns
 > of path, then I would be interested to hear the origin of that
 > requirement.  This is after all only 1 degree of phase at 345
 > GHz.  As best I can understand it the equivalent value in the
 > antenna specification is 15 microns.

The reasoning, taken from my 'phaseSpecs.txt' is:

    Absolute visibility calibration to 0.1 radian at 950 GHz (16.8
  fsec).

  Assuming that phase errors are independent among antennas, allocate
  half of the *squared* error budget to each.  Of this, allocate half
  to the atmosphere, one-third to electronics, and the balance to the
  antenna structure.  This gives:

		      Atmosphere  Electronics  Structure  Total/antenna

    systematic (avg)      8.4         6.9         4.8	  11.9 fsec
    random (rms)	 38.5	     31.4	 22.2	  54.5 fsec

So it comes from an overall goal of 0.1 radian (5.7d) at 950 GHz (2d
at 345 GHz), budgeted out as shown.  I realize that this is rather
tight.  For the antenna, you are right that the spec on "non
repeatable residual delay" is 15 um (50 fsec), 10x worse than what I
say here.  Furthermore, the antenna spec applies only to a
doubly-differenced residual:  between points 2d apart on the sky and
3min different in time.  If we were to scale everything by 10x, the
overall error becomes 1.0 radian, which I do not think is good enough
for reasonable imaging.  Maybe the use of phaseless imaging techniques
(retaining closure information only, as in VLBI) will be necessary at
the highest frequencies.  

It is entirely possible that the spec I've suggested is not
achievable.  All three components are difficult.  I think we must hope
that the antenna is considerably more stable than the spec requires.
We must also strive to make the electronics and the atmosphere (after
all available corrections) extremely stable.

...

 > I hope you appreciate that my underlying approach is in sympathy
 > with yours:  we need to get the specifications fixed and the
 > concepts defined.
 > Unfortunately this area is lagging behind others.

Yes, thanks.  As you can tell, I'm feeling some pressure as time
marches on to close off some options.  But I also recognize that it
would be a shame to forego the use of an advanced technique if it
really would provide substantial benefits.


Cheers,
Larry