[mmaimcal]Instrumental Delay offsets

Fri May 28 17:59:36 EDT 2004

Hello John,

At the moment we only have instrumental phase stability specs on 10 sec
and 300 sec time scales, and, as you point out, this is not adequate for
defining what is needed to derive baseline constants.

So maybe we need a spec for 5 x 15 = 75 minute time scale.  But how
tight should that spec be?  This in turn asks how accurately do we need
to determine (and maintain) baseline constants.

In addition to the signal path, this 75 minute spec will impact the LO 
system path length stability (plus the stability of the LO cables as 
they bend over large angles), plus the stability of the antenna structure.

It's not too late to insert a new spec on long term phase stability.  We 
may not get what we want, but we should at least understand what we need.

The antenna requirements specify that the az/el axis offset must not 
change by more than 30 micron (100 fs) in 9 months.

There is no plan at the moment to insert a phase coherent comb into the 
FE signal path.

In addition to 3 (or 6) baseline parameters, you probably will need to 
solve for a few instrumental phase drift parameters per antenna (e.g., 
phase offset plus first and maybe second derivatives with time).

One approach is that our baseline determination should be limited by the 
atmosphere and not by instrumental drift. In general, our criteria has 
been that the instrumental phase stability be better than the atmosphere 
under 95 percentile conditions.  We have a lot of data on atmospheric 
phase variations with time at the ALMA site, looking in a single 
direction, but this may not tell us a lot about phase stability as we 
swing over a few radians in the sky, where large scale gradients and 
model inaccuracies become more important.

Has anyone done a study on the limits the atmosphere will place on the 
ability to determine baseline parameters?  This limit will be a function 
of baseline length.  This would be a useful number in specifying the 
required instrumental stability.

Another approach is to decide what level of baseline errors are 
acceptable so as not to impact astronomical observations.  Then limit 
instrumental phase variations, on some relevant time scale, to permit 
this accuracy in baseline determination (this does not guarantee that 
the atmosphere will permit us to achieve this accuracy of baseline 
determination).

For imaging, where we phase calibrate on a nearby point source, phase
errors in the visibility data due to baseline errors will be of order 
the error in the baseline reduced by the angular separation between 
target and calibrator, a factor of ~0.04.  Assuming a calibrator-target 
separation of 2.5d and single frequency fast switching at 20 sec 
(effective baseline 140m), the 95 percentile atmosphere would introduce 
a phase error of about 70 fs (rms) per baseline.  A baseline error of 
70/.04 = 1750 fs would introduce the same, but constant (very slowly 
changing) error.

Position measurements would be more demanding.  For position 
measurements, I assume ALMA will not be doing fundamental
astrometry, i.e., establishing an astrometric grid.  Rather ALMA will
measure accurate positions relative to a previously established
astrometric grid.  In that case, if the grid spacing is ~10d, the errors
in the phase of the target source will be the baseline errors reduced by
~0.20.  Assuming a calibrator-target separation of 10d and single 
frequency fast switching at 20 sec (effective baseline 200m), the 95 
percentile atmosphere would introduce a phase error of about 90 fs (rms) 
per baseline.  A baseline error of 90/.2 = 450 fs would introduce the 
same, but constant (very slowly changing) error.

The Science Req is currently 65 microns (217 fs) which I assume to be 
rms of the vector magnitude on the longest baseline.  I don't know if 
this accuracy is achievable under realistic atmospheric conditions.  I 
guess the 65 microns is desired for accurate position measurements.

..DS..

John Conway wrote:
> Hi,
> 
>  Actually for the antenna location problem and required
> delay stability there are two critical timescales. One is the
> timescale and size of delay variations over a cycle around 9
> sources. One such cycle wil take 15 minutes, and 4 or 5 such
> cycles would be done  in each calibration run. The second
> timescale would be of order weeks, the interval between
> antenna position observations on a given antenna.
> 
> My main question is whether my simulations of antenna position
> location should solve for a  constant electronic delay or not
> or whether this was stable/or measured so I did not have
> to solve for it from the astro obs. I have been
> assuming that I will have to solve for this term
> but that that it was stable relative
> to the atmosphere in the hour or so it took to
> do the measurements. Is this a correct working assumption?
> I should of course as part of memo specify what is needed
> in terms of delay stability for the antenna location problem.
> 
> As I mentioned earlier whether one solves for the instrumental
> delay or not makes a significant difference in the rms of
> the antenna z component. For this reason in geodectic VLBI some lengths
> are gone to to estimate the analogue delay prior to the digitisation. A
> phase cohherent comb of 1MHz tones is injected at the front end
> and the phase detected after digitisation. The detection can be done
> both at the antenna or at  the correlator. I assume ALMA will
> not have such a capability, or will it?
> 
>   John
> 
> On Wed, 26 May 2004, John Conway wrote:
> 
> 
>>>>In an earlier version of the cal plan I have
>>>>(Butler et 2003-08-07) there is in section 2.3
>>>>a specification  of systematic and random offsets of 11.9 fs(?)
>>>>and 54.5 fs(?). I assume the units are fs not microns
>>>>(although its not clear). Its also not clear what the
>>>>stability times are meant to be for the systemtic and
>>>>random components.
>>>
>>>From Mark Holdaway
>>>
>>>These numbers are from the fast switching work (LAMA Memo 803),
>>>and are in fs.  The systematic component has a 300 s time scale
>>>(time between cross-frequency calibrations if we are calibrating
>>>at 90 GHz and obsering at say 650 GHz).  Consider the 54.5 fs to be
>>>on timescales of ~2-20 seconds.
>>>
>>
>>Hi,
>>
>> In LAMA Memo 803 section 7.1 'Requirments on Instrumental stability'
>>I believe you specify...
>>
>>78fs per antenna random jitter on timescales of a few seconds
>>
>>and a drift in the fre scaled delay difference over 300sec to be
>>32fs or  better
>>
>>These are not exactly the numbers we discuss above, which are
>>somewhat less. Maybe there is another specification in LAMA memo
>>803 which I missed (its quite a long memo).
>>
>>Your memo deals with stabilties on timescales up to  300sec,
>>- because of long slews, cable unwrapping etc,  a cycle around say nine
>>sources for antenna position determionatio will take
>>somewhat  longer than  that (say 15min) so that it the
>>relevant timescale, and the spec  needed
>>in  on the drift in delay at a single freq (probably 90GHz).
>>
>>Are we still at the stage where specifications can still be made?
>>or is hardware being designed and build already on the existing
>>specs. If new Specs for instrucmnetal stability are possible I should
>>carefully consider if a new spec is needed for basleine determination
>>and what it should be.
>>
>>  John
>>
>>
>>
> 
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