[mmaimcal]Re: [Almasci] New System Design Description

[Richard Hills]

Dear Al and Larry,

You asked for comments on this.  First of all let me repeat what I said 
last time - that it is really excellent to have this all laid out so 
clearly and completely - and I should add that most of it seems to be 
converging well.  

Secondly, I am afraid that I have to make again my objections to the way 
in which the WVR residuals are brought into the discussion about 
instrumental phase stability.  I think I have made all these points 
before, but it doesn't seem to have had any effect, so I will try once more.

In the second full paragraph of page 12 (part of section 3.1.1.2) it 
states that the WVR correction goal under 5th percentile conditions at 
45 degrees elevation is 68 fs.  (This is fact the value derived from the 
present WVR *specification*, not the *goal*.  Our goals, and the 
presently predicted performance, correspond to a considerably lower 
figure.)  The paragraph then goes on to disregard this firgure on the 
grounds that it is unrealistic to expect ALMA to do better than has 
already been demonstrated on existing telescopes.  Instead the figure of 
83 fs is taken, and this is then adopted as the specification for the 
"instrument" - telescopes plus electronics.  I am not aware of this sort 
of defeatist policy being adopted anywhere else in the project.  I think 
that it is inappropriate and that this whole section should simply be 
removed.  

I do understand the principle of what you are trying to do here, which 
is to distribute the error budget in a reasonable way so that we do not 
have tight targets, which will be very difficult or expensive to meet, 
in one area if the losses involved are negligable compared to those in 
other areas.  I feel, however, that putting the atmosphere, the 
structure and the electronics together is not helpful because they 
behave in such diffierent ways with respect to conditions.  As you 
explain, the atmospheric term is highly dependent on the state of the 
atmosphere, the baseline and the techniques used to correct for it.  In 
table 4B you have focussed on the numbers for very good atmospheric 
conditions.  The figures given for the telescope structure are, by 
contrast, close to the maximum allowed.  On these short timescales,  
these residuals are likely to be dominated by winds, and the figure of 
50 fs  (15 microns), which is still the one in given in the latest 
version of the antenna specification that I have seen, is required to be 
met for winds of 6m/s in the daytime or 9m/s at night (with an 
appropriate spectrum of gusts).  It was not clear to me whether you were 
proposing that this 50fs figure be replaced by your new one of 42 fs 
and, if so, for what environmental conditions it would apply.  In any 
case the point is that the structural contribution to the error should 
be less than this value for much of the time.  (I have just noticed that 
in this document you define the coherence error as being the deviation 
within a 1 second time interval.  The errors on that short a time should 
indeed be very small for the antennas, so 42fs seems much too large an 
allocation.)

This whole section, 3.1.1, is in fact dealing with the specification of 
the LO.  By constrast to the atmospheric and antenna contributions, I 
think it is likely that the loss due to lack of coherence in the LO 
signals will be largely independent of conditons,  i.e. it will be there 
all the time.  It seems to me much simpler therefore just to look at the 
actual value of the loss as a function of frequency and decide whether 
or not this is acceptable.  For the proposed value of 72fs, for all the 
electronics, I get that the efficiencies are:   83.1% at 950GHz,  91.5% 
at 660GHz and 97.6% at 345GHz.  These seem to me to be pretty reasonable 
figures.  One can see that one is getting into diminishing returns here 
- reducing this error by root 2 to 51fs would only improve the signal to 
noise by 9.7% at 950GHz, and 1.2% at 345GHz.

As an alternative way of putting these values in context, one can look 
at the antenna losses due to surface errors (which scale in the same way 
with frequency).  To get the same improvement in signal to noise as the 
above (the reduction from 72 to 51fs ) one would have to remove (in 
quadrature) a component of 7.65 microns, which corresponds to reducing 
the overall surface error from 25 to 23.8 microns (or from 20, if that 
were to be adopted, to 18.5).  Does this seem like an equitable sharing 
of the difficulty?  If people agree that it is, then we should simply 
adopt the 72fs figure for the electronics and get rid of the discussion 
about the structure and how well the atmospheric correction will work.

I have one final point about the electronics coherence number:  it is 
given in terms of a delay, and we generally assume that this is an error 
at the RF frequency so that it causes a loss which scales with RF 
frequency squared.  There will however be some contributions for which 
this is not true - e.g. phase noise on the second LO.  These losses 
would still be present at 30 or 100GHz when the other effects are much 
lower.  Now I am sure that in practice we can ensure that these 
frequency independent losses small - e.g. less than say 0.1% for all 
such contributions, but  do we have a spec that actually pins this down?

Turning now to the accuracy figures, it is interesting to see that these 
have come down from 50fs for each of the structure and the electronics 
to 14 and 24fs.  As I understand it this is a result of taking the 
figure of 28fs from the simulations of the fast-switching and 
distributing it in the same way as the coherence.  Again, this section 
on the LO spec does not seem to be place for setting the requirement on 
the antenna, but I note that the figure of 14fs seems very small 
compared with the 50fs in the current antenna spec.  I note that the 
50fs already assumes that most terms are subtracted out by going to a 
reference source - the spec refers to a 2 degree distance on the sky and 
timescales of up to 3 minutes.  At the very least, it seems to me that 
we have some problems with consistency here.  (I find the antenna spec 
hard to follow on this point - does anyone know if it has it gone out 
with that section in the form it was in that Al circulated in early 
December?)

Focussing on the electronics number, I see that you have taken the 
timescale for the accuracy requirement to be from 1 second to 1000 
seconds.  I assume that this is because it is assumed that 1000s is the 
maximum time between observations of bright broad-band point sources to 
tie together the phase of the ~100GHz system used for the fast switching 
and that of the band being used for the astronomy.  Is that right?   If 
so, then shouldn't we really separate the contributions that are common 
between the two systems from those that are not?   The common errors on 
timescales longer than the fast-swtiching cycle are presumably not 
important, where those that are independent between frequency bands will 
contribute on both the source and the calibrator.  This last point 
suggests that the imdependent errors need to be a factor of root 2 lower 
if the intention is to limit the errors on the final data to these values.

Moving on to section 3.3.4, page 19, para 4, which again concerns the WVR.  

1) The contributions due to noise in the radiometer and the scaling 
error are independent so the requirements, should be given separately as 
0.02deltaL and 0.01w + 10microns. These should be added in quadrature. 
 This also needs to be fixed in the appendix.  This was my fault for 
writing the expression down incorrectly on a slide shown at ALMA week 
last year, although I thought I sent round an e-mail correction.  In the 
examples,  for deltaL = 500microns and w = 1.8mm the (rounded) value 
should be 30microns and for 100 and 1.6 it is 16.

I think the comments starting "but there is no assurance that this can 
be achieved..." up to "...more precise" should be removed:  there is no 
equivalent discussion on other subjects.  If you want to put in a 
warning, then it is worth pointing out that fluctuations in the dry 
component obviously cannot be corrected in this way and that performance 
is likely to deterioratate in the presence of clouds.  As regards the 
next sentence, it was certainly my understanding that the 2% 
proportional error includes the errors in atmospheric modelling and also 
that it applies to changes in the total water vapour path due to e.g. 
switching to a reference source, if one wanted to use it in that way.

Turning to different points:

Section 2.3 para 4.  The point is made that the attenuators should not 
be changed over a phase calibration cycle.  In practice this presumably 
means a cycle beginning and ending on the source which ties together the 
phase of the astronomical receiver and the 100GHz Rx.  This suggests to 
me that the software would need to be monitoring the IF level e.g. as a 
source was setting and the atmospheric noise rising, and deciding 
whether a change in attenuator was needed  The sequence would then be:  
go to the reference source and check the phase;  then switch the 
attenuator and measure the phase again;  then go back to the source. 
 Are the software people aware of this - i.e. is it in the software 
requirements?  A similar point presumably applies to adjustment of the 
LO power.

Section 3.3.3.  You say that no special instrumentation is "planned" for 
rmeasuring atmospheric extinction.  In fact a good deal of work has gone 
into discussing what equipment would be helpful (and indeed required) in 
meeting the amplitude calibration accuracy requirements and a set of 
outline specifications for these ahve been drawn up.  It is an 
interesting question as to whether any budget for these has been 
assigned.  More generally it seems to me that more work is needed in 
relating the technical specs you are giving here to the scientific 
requirements, especially on calibration.

Finally some pedantic corrections of typos, etc:

Page 3.  Band three is given as 84-116GHz in the table and 86-116GHz in 
the text immediately below.

Page 8. the section labelled 6.1.3.4 should be 2.6.1.4 ?

Page 8.  Last paragraph but one.  I thought that given that we have a 
limited number of bits, there is an improvement in signal to noise from 
over-sampling.  If so the statement that there is no loss of sensitivity 
is not strictly correct.

Top of page 9.  K is introduced without, I think, any definition.

Lower on page 9 - 4th bullet - "filteR bank"

Page 11. Table 4A  Band 3  range given as 96-204GHz  - should be 104 ?

That's all I have at the moment.

Best Richard