[mmaimcal]Instrumental Delay offsets

[John Conway]

Hi

 Thanks for your email. After some off-line interchange
with Mark I now realise that the long term instrumental
delay stability requirement from the antenna position determination
is not as severe as I first thought. The present fast switching
spec over  300sec might even  be sufficent, but I still
need to  think a little more  about it.

On Fri, 28 May 2004, Dick Sramek wrote:

> 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.
>

see above

> 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.
>

The time to cycle through say 9 cal sources, if one does it in the optimum
order, is less than my original claim of 15 minutes, its  closer to 5-7
minutes. Still one want many cycles to beat down the noise. A long period
is needed for the largest arrays, to start to get any statistical
reduction at all.  If the atmopshere outer scale can sometimes be very
large  in the extreme case of  10km baselines and 10m/s winds
one needs to integrate for >1000sec to start to get a statistical
reduction. Unfortuantly we don't know anything really about the outer
scale at  Chajnantor execpt that it significantly larger than 300m.
Fortunately I think  the dominant  timescale  for linear changes of instrumental delay is
the  cycle  time of 5-7 min. Say if one does a sequence for 5 cal sources
ZNESW-ZNESW... where Z is a zenith source and N,E,S,W are sources above
the North, East etc horizons, instrumental delay drift will effect the
NS and EW delay difference and hence y and x positions, but the relevant
number is the instrumental delay change over a cycle not the whole period
of the cal expt. Eveything is linear algebra so one can solve for the
geometrical parameters in each cal sequence and average the results.
In fact given this linearity,  using  a more optimum order like
ZNESW-WSENZ..  will largely  remove the bias of any linear instrumental
drifts. What is left is a spec of the quadratic or Allen variance of the
instrumental  delay drift over of order 300sec. This may already be
contained within the present specs for fast switching.


> 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.

Right so I will assume that I will always have to solve (at least) for
a time constant instrumental delay offset. This as I have noted has
an impact on the z coordinate positions. Since we are not building an
array for geodectic measurements I  see that instrumental delay
calibration is not such a priority as it is for geodetic VLBI.

>
> 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).
>

As noted above I think the linear drift may not be so much a problem.
I can perhaps do tests of solving for the second derivative wrt time.
compared to simply setting a spec so I don't have to solve for a second
derivative.

> 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.
>

Right any spec on the stochastic component of the instrumental delay
variation need only be less than the atmosphere, still there needs to a
spec on systematic effects like time gradients and second derivatives.

> 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.
>

Thats essentially what my memo is trying to do (some first results
in a very rough draft are in the link
http://www.oso.chalmers.se/~jconway/ALMA/SIMULATIONS/SIM25)

> 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.
>

The present spec of 65micron (190fs) comes from having less than 10 deg
phase error due to antenna pos error at 950GHz with a 10 deg target-cal sep.
It is a challenging spec (and may well be over ambitious). I intend to do
some imaging simulations-
remember that in the continuous reconfiguration scheme the residual
position errors will been very different for each antenna because it
will depend how long it was since the antenna was moved, and therefore
on how many 'full array' calibrations it has been involved in. A few
antennas with relatively large postion errors will not effect the dynamic
range much.


> 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.
>

I think the spec is certainly achiveable for the smaller arrays (<3km) ,
When  one goes to the largest Y+ array its an open question (it depends
a lot on the unknown atmospher outer scale).  In addition
to the long timescales of the dominant variations in phase vs time
preventing statistical reduction, there are worries about
modelling/solving for the hydrostatic delay, when we consider that the
antenna elevations above sea level are different by several 100m. At
least 6 barometers widely scattered across the array to measure spatial
gradients in pressure and lapse rate are desirable.

What I find is that for the largest  arrays the antenna z coordinate is
the  hardest to determine. However  this is one number
per antenna, for imaging if you are looking at  a bright enough source
that inaccurate  z positions effects your dynamic range I calculate that
you certainaly have enough juice to  self-cal  it.  Of course this doesn't help for
source  relative  position determination, as might the case in the largest
arrays looking for stellar reflex motions due to planetary
companions- and I gues this kind of expt is what ultimatley should set
the spec on position determination accuracy for the Y+ arrays.

    John


P.S As noted at the last Sci IPT telecon my memo does not consider using
the WVRs to remove atmospheric delay contributions and so improve
position determination. I was assuming the WVR's were primarily designed
for short term stability. At Onsala for VLBI we have the opposite problem
we have WVRs with good long term stability for geodetic VLBI, but
on  short timescales their SNR is lousy and so cannot be used to extend
the coherence time of mm-VLBI obs.

If the WVR  instrumental delays were stable over
long periods (60 mins) I am sure they could usefully be used in antenna
position detemination, my goal was to see if astronomical cal by itself
could do the job. I doubt that excellent long term stability of the WVRs
is an important part of their spec, but of it can be built in that would
be good  of course.





> ..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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