[mmaimcal]Re: [Almasci] Re: WVR treatement in System Design Description

[Richard Hills]

Dear Larry,

Thanks for your detailed response to my points.  In general I agree with you
about what we are trying to achieve in setting these specifications and am
content to accept the approach you have chosen in order to fix the values. (As
indicated  previously, I would have preferred a rather different approach, but
that is of no real consequence.)  I also agree that there are several steps in
going from the instrumental performance to the final estimate of the errors
and that these need to be evaluated by a combination of experiment and
simulations.  I'll return to that topic later.

The main thing we differ on is the USE of the figure of 25microns as the best
result so far demonstrated for WVR correction.  As I have pointed out in
previous messages, that was done with a radiometer which had no cooled load
(and so had a large imbalance in the switching), rather narrow IF channels,
and various other technical limitations.  It was also done on a interferometer
with relatively poor sensitivity and under atmospheric conditions which were
a lot worse than the 5th percentile on Chajnantor that we are considering 
here.  I believe (that the 25 microns achieved was consistent with the known 
sensitivity and stability of the radiometer and the interferometer.  There is 
therefore every reason to expect that, with the much more sensitive
radiometers we are building for ALMA and under the good conditions we are 
discussing here, we will indeed "routinely" do better.

You say that you would be willing to drop the use of this figure if you had
something else to put in its place.  Let me suggest that you remove it and,
picking up the points that you yourself made, substitute an estimate for the
atmospheric residuals containing three terms:
1) the contribution from noise and short term instability in the radiometers;
2) a term proportional to the uncorrected path fluctuation, to allow for the
uncertainties in the atmospheric conditions and modelling and the errors in
the calibration of the radiometers;
3) a term to allow for atmospheric path fluctuations which are not measured by
the radiometer at all (as discussed, the principle item here is the "dry"
component due to temperature - or more precisely density - fluctuations).

For the first term I suggest you take the specification, which is
10(1+wv/1mm)microns and equals 19.6microns (65.3fs) for the 5th percentile
conditions you have adopted.  This is a long established figure and I think it
is best to stick with it, even though, as I shall describe below, it is quite
conservative.  (Remember that this is a limitation on sensitivity, i.e. it
corresponds to an error that would be there even if there were no fluctuations
at all in the water along the paths through the atmosphere.  There is no
reason to increase it because of uncertainties in the modelling, etc.;  those
go in the next term.)

For the second term I again think that you should take the value of 2% that we
have accepted as a specification.  This is a good deal less conservative
because, as indicated above, it is intended to include all the uncertainties
in the conversion from changes in measured brightness temperatures to the
changes in path due to water molecules.  We think however that this is a
reasonable figure for the "good" conditions that we are considering here and
assuming that some effort gets put into optimizing the phase correction when
we have some real experience on Chajnantor.  This term is in any case not
significant here: 2% of the 143fs of uncorrected phase fluctuation is only
2.9fs.  Adding this in quadrature to the 65.3fs above gives just 65.4fs.

It is difficult to give an estimate for the third term - the atmospheric path
fluctuations due to things other than water.  As we have discussed previously,
these may get quite large when there is strong convection driven by the Sun
heating the ground in the afternoons.  Alison Stirling has started some work
on this problem from the theoretical end, but it will be a while before we can
draw any conclusions.  What we are trying to establish here, however, is a
value for the "best" conditions, which will certainly be much lower and for
which the physical causes are much less clear.  I suspect that the only way to
get real numbers will be to fly balloons or kites on the ALMA site and
measure the temperature fluctuations directly.  We can get some guidance from
optical seeing measurements, but the problem there is the extrapolation of
these from the scale sizes of ~1m that they involved up to those relevant for
ALMA, together with the vexed question of whether or not there is an "outer
scale" on the density fluctuations.  Better information should soon be
available from the optical interferometers (especially the VLTI on Paranal,
which has ~100m baselines and is at least in the same general area even though
it is 2500m lower down).  I will try to find out if they have any values yet.
Meanwhile I suggest you take a value of 10microns (33fs), which I freely admit
is no more than an educated guess, but again, I do not think we can take
speculation that it may be worse than this even under good conditions as a
reason for setting a softer spec on the electronic stability.

This should again be added in quadrature (it will not be correlated with the
radiometer noise) giving a total of 73.3fs.  Applying your methodology then
gives 37fs for the structure and 64fs for the electronics.

On your specific points:

 >> We need
 >> experimental demonstrations, or at least *convincing* simulations.
 >> Perhaps there is data that I have not seen.

I am not sure what you would regard as "convincing simulations".  In about
September '03 I sent you a spread sheet that gives the estimates of the
contribution to the uncertainty due to the noise and instability in the
radiometer, i.e. the first of the terms discussed above.  This shows that,
with reasonably conservative values for noise temperature and stability and
(more importantly) good conditions so that we can use the 4 channels in the
way that gives the best sensitivity rather than trying to optimize the
accuracy, the error should be about 3 times lower than the specification.
e.g. ~6.3microns for 1mm of water compared to 20.  I believe that this basic
calculation is all one needs to do to estimate the sensitivity - the
uncertainties in things like line strengths should be no more than a few
percent.

The evidence on whether or not the radiometers achieve the performance
assumed is starting to emerge from our tests.  For preliminary results, see
http://almaedm.tuc.nrao.edu/forums/alma/dispatch.cgi/iptfemeet/showFile/100152/d20031217084308/No/WVR%20performance%20Dicke%20KO%2020031209.pdf

 >> When you say "come down" I do not know what you are comparing against.

I was comparing the December version of you System Description document to the
previous one (circa Sept), that's all.

 >> We really don't know enough about how to separate differential from common
 >> mode errors, so I've arbitrarily decided to interpret the requirement as
 >> applying to *all* of the fluctuation from *each* band separately.  That
 >> is, I'm assuming that these two things roughly cancel.  When we
 >> understand things better, this can perhaps be refined.

I agree this is reasonable.  (Obviously it would be best to spell it out, so
it doesn't have to argued over again at some point in the future, but I 
realise that you can't cover everything here.  Fortunately, if I have 
understood the abstract on your new memo with Mark rightly, we may be able to 
avoid this two-frequency scheme most of the time so the problem would not arise.

 >> It was my understanding that the 2% error applies at constant air mass,
 >> since the scaling factor can vary with air mass.  Thus, if you want to
 >> measure the difference in water vapor for two sources at different
 >> elevations, then you can expect the error to be greater than 2%.  I also
 >> understood that the spec applies only to the *fluctuations* about the
 >> average value in an interval of ~5 min, so the average value as an
 >> *absolute* delay or column density of water vapor could be in error by
 >> far more than 2%.  If I misunderstood any of this, then I'm ready to be
 >> corrected.

I don't think that the limitation to constant air-mass has appeared before.
ALMA memo 352 suggests that the spec should apply for 1 degree changes in
zenith angle but remarks that this should be refined to be in terms of air
mass.  (The issue was also discussed in memo 303.)  I can't think of a reason
for the multiplicative errors to be very different for the different
circumstances that you describe.  It is of course true that we are generally
only concerned about differences in the path, not the absolute delay, but I
have always assumed that this includes switching to nearby sources.  In that 
case however the error one would be talking about would be 2% of the change in 
the path due to water which occurs due to the change in air-mass.

Note also that the total column density of water vapour is likely to be an 
important measurement for the amplitude calibration.  I agree however that 
these aspects of the use of the radiometer need to be worked through more 
thoroughly and written up.  If it were decided that additional specifications 
on the radiometers were required then that would have to be done through the 
proper procedures.

 >> This sequence, where we use an astronomical method to calibrate the
 >> attenuator's phase variation, is not what I have in mind.  It might be
 >> applied as a last resort, if we get in trouble.  Instead, the
 >> attenuators should just be left fixed for long periods of time.  In
 >> practice, I expect that we will have enough dynamic range that
 >> attenuator changes are not needed except when some other major change of
 >> setup occurs (e.g., change of band or a large frequency change within a
 >> band) or a substantial change in weather conditions occurs.

I am slightly surprised by this.  How much dynamic range do you expect to have
in the digitization?  At some frequencies we expect the atmospheric noise to
be a large part of the system temperature.  This can obviously change a lot
when you track a source from ~40 degrees elevation down to say 25 degrees.
That sort of thing is done quite often with single dishes - e.g. to get a
reasonable amount of integration on a source at high declination, but perhaps 
it would be rare with ALMA.

Best Richard