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

[Larry D'Addario]

Richard,

I won't be able to respond in detail to all your points right now, but
the bottom line seems to be very little change from my numbers.  I am
happy to drop the language in the System Design Document about the
best reported WVR residual, using instead your estimate of the
performance.  You are merely suggesting that

a.  The 2% scaling error should be added in quadrature to the
radiometer noise error; and

b.  We allow an additional 10 microns for non-water-vapor
fluctuations, also in quadrature to the other terms.

I do think that the last value may be optimistic; it implies that the
fluctuations are only ~5 ppm compared with the total dry air delay at
Chajnantor.  I also think that the 2% scaling error is optimistic; I
have never seen a basis for it, and you seem to agree when you say
that it is "less conservative."  Nevertheless, I'll accept these
numbers because I don't have any better ones.  

This gives, as you say, 73.3 fsec total under the adopted conditions
for the 5th percentile, compared to the 68 fsec that I got without the
last term, and compared with 83 fsec as the best-reported WVR residual. 
This range is not significant.

What I would appreciate is some document (other than an email!) in
which this is written up and to which I can refer.  IMHO, a set of
powerpoint slides doesn't count.  When can we have this?  If it needs
to be written, can you provide a title, author(s), and document
location (either an ALMA document number, or the name of a memo series
or journal to which it will be submitted) so that I can reference it
as "in preparation"?

I'll mention a couple of details from your message.

Richard Hills writes:
 > ...  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.

Not quite.  We are interested in specifically defined conditions, not
somebody's idea of "best" conditions.  The latter depends on how
many things you want to take into account, and how much of the time
you insist on observing.  We've chosen the 5th percentile of opacity
and phase for this purpose.  If, for example, you also insist upon low
wind, either you move down from the 5th percentile to get the same
opacity/phase, or you accept worse opacity/phase to stay at the 5th
percentile.

Flying balloons to measure temperature would be interesting for
studying the atmospheric physics, but for determining the accuracy of
interferometric phase corrections it is enough to have both the
interferometers and the WVRs in operation.

...
 > 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.

I thought we want to optimize the accuracy, so I don't quite see
what you are getting at here.  Perhaps the spec is conservative if it
really is limited by radiometer noise.  But it also needs to include
the conversion from detector output voltage to absolute sky brightness
temperature.  So I don't think we should be less "conservative" in
estimating this term.

...

 > How much dynamic range do you expect to have in the digitization?

The signal levels to the digitizers can vary +-3 dB with very little
effect on sensitivity, so I would not be re-adjusting the attenuators
even if the system temperature becomes twice its initial value.  If I
can anticipate that this will happen, I would start off with the gain
somewhat lower than optimum.

With ideal passband shapes, the quantization loss at the ideal signal
level is 0.881 (4 level quantization).  At very low or very high
levels, the result is equivalent to 2-level quantization, where the
loss is 0.637.  Thus, the worst-case effect for variation of signal
level is 0.627/0.881 = 0.757.  In practice, due to non-ideal
passbands, this ratio will be closer to unity.  For almost all
observations, accuracy will be more important than raw sensitivity,
and we get better accuracy if we don't mess with anything -- including
attenuators -- during the observing cycle.

 > At some frequencies we expect the atmospheric noise to be a large
 > part of the system temperature.

But not more than half, right?

 > 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.

I think that tracking below an air mass of 2 will be very rare,
except perhaps at the lowest frequency bands where many things become
easier.

--Larry