## Antenna Location Calibration Discussion

Last Update: JeffMangum - 11 Jul 2006

### Specification

• Antenna Location = = 217 fs

NOTE: path(micron) = c * delta(t)(sec), and that 1 micron ~= 3.348 fs.

### Derivation of the Axis-Nonintersection ("K") Term

Jeff Mangum:

One quantity that I can't be certain that I am visualizing correctly is how we derive the K-term (axis non-intersection). I am assuming that this is not the "axis non-perpendicularity" term in the pointing model, but actually the antenna axis term that is traditionally (though not necessarily) derived by doing interferometry while going over-the-top. Is this correct?

Robert Lucas:

Yes. It's the distance between the az and elev axes. We plan to measure it by fitting a cos(el) dependence to the delays in an antenna position measurement (see ALMA Memo 503: Antenna Position Determination: Observational Methods and Atmospheric Limits, Section 5.3). It's distinct from the Z antenna position error which is seen as a sin(el) dependence of the delays.

As it is independent of anetnna location, it is preferably measured on compact configuration as atmosphere is less of a problem.

-- JeffMangum - 03 Jun 2005

### Baseline Solutions Using Frequency Synthesis

Email exchange regarding SMA experience with baseline solution determination and the use of "frequency synthesis".

Mark Gurwell:

For the SMA we are getting down to somewhere between 50-100 microns positional accuracy (though on much shorter baselines to be sure), and I would argue we have a much tougher environment in which to do so (smaller antennas, poorer receivers, worse atmosphere, etc), so that the ALMA spec should be readily achieved.

(MarkHoldaway comments: ALMA's phase stability will not be much better than yours. And also, we have configurations which have antenna elevations differing by about 500m, so I would actually say that SMA and ALMA just have different difficulties. We do not plan to have local weather at each antenna, though in the more extended configurations, it would be a good thing if we did.

One of the more difficult aspects for us is in compensating correctly for the atmosphere when the vertical height of the antennas varies as much as they do, for example in our 'extended' configuration (which is only 500 m) we have as much as 36 m elevation difference, and modeling the extra path has been problematic, especially as we do not currently have local weather information at each antenna. Thus, changes in local conditions (especially pwv) can deleritously affect the delay model for the array, complicating phase referencing (and antenna location finding). Overall, we've beaten things down, but in the not so efficient manner of obtaining lots of baseline data.

There is one interesting technique we use to get our initial locations once the antennas have been moved, especially useful when utilizing a new, never-been-used pad. The techniqe we employ is to difference the phase between the USB and LSB, effectively creating an observation at the IF separation frequency of 10 GHz (3cm).

This is particularly effective because all sorts of problems that affect the straightforward phase in each sideband (atmospheric phase variability, instrumental phase drift, etc) are nearly canceled out in this differencing, providing a very strong high SNR measure of the antenna-position errors, albeit at the much coarser wavelength of 3cm. Using this technique, though, we can usually get a pretty good baseline determination, down to the 1-2mm range in error, which is extremely helpful as our baseline data is taken at 1.3 mm (230 GHz).

It occurs to me that ALMA might be able to something very similar, even though the data will be SSB only (I think that is right...you won't have both sidebands, correct?). Assuming that is correct, with the 8 GHz bandwidth one could envision using 1 GHz 'chunks' of that bandwidth, say from 0-1 GHz and 7-8 GHz and differencing the 'continuum' phase that could be generated by integrating over those in-sideband frequency ranges. For the large ALMA antennas, excellent site, and good receiver performances that are expected, I would imagine that 1 GHz of bandwidth should give very good SNR on even modest calibration sources of a few hundred mJy in a few seconds. Thus, even if the atmospheric phase stability is really pretty horrific, as long as you can get reasonable detection of the calibration source over a timescale short enough, in the difference the phase variability will nearly cancel out, allowing a pretty precise measure of the antenna position errors, again with the effective frequency equal to the difference in band frequencies. In my straw example here, that would be 7 GHz (4.3 cm). Assuming again really good SNR in the data, I think this should still allow for initial positions to be found within 1 mm, perhaps even better. This would still require an additional data gathering in better phase stability weather to reach the 71 micron/antenna goal, but gives you a good start.

In addition, while getting the delays right is always helpful, with this technique the delays would just have to be close enough to not decorrelate over the 1 GHz 'chunks'. Also, this technique reduces complications from the linear instrumental drifts. Finally, since the effective wavelength is 4.3 cm, initial position errors of several cm can be tolerated, though your goal of 1 cm would be great.

I realize you probably know all this (since you mention use of the phase gradient across the band), but thought an explicit description might be good to add.

David Woody:

Mark G. makes a very good point about using the IF bandwidth to help in solving for the baseline. For the SZA at OVRO we have 8GHz of SSB bandwidth and a correlated noise source to calibrate out most of the downconverter and digitizer phase errors. By looking at the phase slope across a single 500MHz wide band you get degrees_phase/Hz which can be turned directly into delay or distance error with an ambiguity of 1/channel_width. This can be many meters or even kilometers depending upon your spectral resolution (limited by source brightness or correlator capability). Getting around the 1/lambda ambiguity greatly helps in finding baseline solutions. If your whole bandwidth of 8GHz is phase calibrated then you can further improve you baseline accuracy to remove the 1/lambda ambiguities before actually trying the normal baseline solution techniques using phase at the sky frequency. This is basically using frequency synthesis for baseline solutions.

Mel Wright:

Phase acoss band and difference phase between sidebands also used at Hat Creek for initial estimate of long, >1km, BIMA baselines, but beware LO2 phase is opposite in USB and LSB. Some details in ALMA memo 427.

Robert Lucas:

That's more or less what we expect to do:
• First measure the frequency dependent phases on a strong calibrator and then subtract these from all calibrators in the baseline measurement.
• Then use the phases slopes to get delays.
• Then solve for the dependence of delays on direction.
Getting an accurate delay model for the differences in elevation will be a difficulty, I agree. I assume that if our zenith delay model is bad, then we will see our antennas apparently move up and down, in proportion to their actual relative heights, if we do repeated antenna position measurements under vaious weather conditions.

-- JeffMangum - 03 Oct 2005

### Calibration Plan Section

NOTE: This text has been included in the current version of the Calibration Plan

-- JeffMangum - 08 Oct 2004

Dear John and Melvyn

How are you doing?
I am writing to you, because Ryohei Kawabe (ALMA-J Project Scientist)
asked me to be a volumteer of "Antenna Location Calibration"
section in the calibration plan.

At the moment, I have only a few comments on this section.

(1)
I recommend to use subsections for easy understanding.
I think the pointing section is a good example.

(2)
From our experience at Nobeyama, diffential measurements are
very useful to remove the systematic phase drift or long time
scale atmospheric phase drift.  We usually use a few strong
quasars (3C273, 3C454.3 etc) as a reference calibrator.
ALMA 12 m antenna has a good fast motion capability, so
I believe the differential measurement is quite effective
especially for the largest configurations.

(3)
I agree that SNR is not an issue for 65 micron rms, although
this specification would be a bit lax for the ACA.
So, after antenna reconfiguration, it would be OK to use
4 moved antenna + 1 or 2 other antenna for the measurement.
In my simple calculation, we will get enough accuracy by using
100 sources for total 1 hour observing time.  So, I think
we do not need to think seriously about the "tradeoff" in the
first paragraph of p.43.

Cheers,
Koh-Ichiro


-- JeffMangum - 12 Aug 2004

John Conway note regarding immenent ALMA Memo on position calibration...

Hi,

I have been writing an ALMA memo for quite a while on ALMA position
calibration, it now even has a reserved memo number (503).

http://www.oso.chalmers.se/~jconway/ALMA/SIMULATIONS/antposclal.pdf

The conclusions need to be finalised and the main test is somewhat
verbose and needs to be reduced in length before submission.

I realy hope (I really, really really hope) to finish it in the
next few days.

Any comments on this draft are welcome


...and then the promised update on 2004/09/03...

 On Friday I submitted memo 503 on antenna position cal. The submitted
version can  be found at

http://www.oso.chalmers.se/~jconway/ALMA/SIMULATIONS/SIM25/antposclal.pdf

Compared to earlier draft versions I have posted, quite a number of typos
have been corrected, and Sect 2 and the conclusions sections are both
greatly modified.

My main concern in the memo was to ensure that there is nothing in the
hardware specifications which prevent us from doing, in a relatively short
time, the position calibration of 4 antennas moved every 2.5 days on
average, as required by the zoom array concept. The conclusions section in
the memo gives a number of specifications for hardware, software and
operations. Look there, in the abstract and in Table 2 for the 'bottom
line' of the memo.

In section 2 I assumed that we use the phase together with bandpass delay
to resolve turn ambiguities. This method puts a specification of the
stability of the phase of the bandpass phases, ***MY MAJOR REMAINING
INSTRUMENTAL WORRY** - is whether these stability requirement is
achieveable and controlled within the project.  I CC Dick Sramek who may
want to  comment on this.

I do not disscuss fully in Section 2 the possibility of only using the
bandpass delay to get the delay observables (i.e. excluding using the
phase). Although these measurements are noiser they do not involve the
same degree of stability requirement on the bandpass phases (any bandpass
uncertainties are absorbed into the instrumental delay per antenna
-which must be solved for in any case) . This approach could be
investigated further, perhaps in a revised memo version.

Finally the approach I adopted in the memo gives good estimates of the
errors in each cal measurement, however this approach is not so easy to
adapt to calculating the exact propagation of errors in a continually
evolving array. The numbers for median and maximum position errors in
Table 2 are therefore estimates. I think I know how to do a better
calculation; but this will have to be another memo.

John


-- JeffMangum - 07 Sep 2004

### Discussion of ALMA Memo 503

-- RobertLucas - 20 Sep 2004:

I have a few comments on John's memo (503) discussed above:
• It is a very good memo with in-depth discussion of many issues.
• John assumes one needs to perform a very precise bandpass calibration calibration, to resolve the 2 pi ambiguities in the delay determination. Using a previous bandpass calibration will very likely introduce phase offsets (while the bandpass shape will be removed if the bandpass is stable enough). These phase offsets will make resolving the 2 pi ambiguities hasardous (none of the straight lines in Figure 1, page 5, will go through the origin). Actually it is better to subtract the phases observed on a very strong calibrator (e.g. the strongest available at the time of the antenna position measurement) to all the sources. This is what is proposed higher on this page by K.Y. Morita.
• This can be done independently for every (about 30 min.) cycle, thus removing:
• some part of the atmospheric delay variations (wet and dry)
• the instrumental constant delays
• most of the instrumental delay time variations
• This would relax the hardware specs on page 31:
• the 3-day passband shape spec (1) is not needed in this case
• continuously monitoring the instrumental delay (3) is not required
• By the way, I think (5) and (6) should be fully compatible with current software plans.
• Also I believe that, while the z coordinate has more uncertainty than the others, an error in z is affecting the target observations less than in x or y, as it always project on the line of sight with the same sign. So actually the requirement on z precision should be less stringent than on x and y (unless we are interested in geodesy). Can this be quantified?

--Main.JohnConway - 20 Sep 2004

1) I believe that ---once one has removed the turn ambiguities (see below)-- then using differential delays or phases has no advantage over simply using non-differenced delays and solving for an extra instrumental term. In Section 5.1, at the top of page 16 I note that

'One can visualise dealing with instrumental delays by differencing all delays to a reference calibrator, and then fitting these difference delays. Alternatively one can think of explicitly fitting for instrumental delays at each antenna using a solution matrix F incorporating the inverse of matrix B. The solution in both cases is the same'

I think this is a true statement. Working with differential quantititiese, rather than the raw delays means just doing a manipulation on the B matrix where two rows or columns are cancelled, and in turn one solves for one less variable.

2) However - specifically on the question of whether working with differential measurements reduces the specification on bandpass stability to remove turn ambiguities I think you make a very important point. The bandpass phase errors in Fig 1 are additive not multiplicative, hence if I form the difference phase between two calibrator obs at each frequency and then estimate the phase-delay on this difference using group delays to resolve turn ambiguities the effect of bandpass errors goes out - THANKS FOR POINTING THIS OUT.

3) However on the point you make that using differential measurements removes any advantage to monitoring instrumental delay, i.e. my conclusion 3, I disagree. I partly discuss this at the top of page 23 in the memo. One can look at it like this, if there was perfect monitoring of instrumental delays so they could be removed, the undifferenced delay to the zenith calibrator could be used to get the z component. However if I have an instrumental component which I must eliminate I must difference the delay between the zenith source and the ones at 30 deg above the horizon in which case the effect of a given z delay is only half as big on this difference delay as it would be on the total delay to the zenith source if that was useable. The lower accuracy is explained by the shorter 'lever arm' in the presence of atmospheric delay noise. Note using horizon sources at very low elevations is not an option because the delay noise from the atmosphere increases dramatically at low elevations.

This point was at first counterintuative to me, until I understood it in the above terms. Finally I understood why in geodectic VLBI so much effort is put into measuring time constant instrumental delays, when one might think these are just easiy eliminated by differencing delays between calibrators.

4) Your point about z coordinate accuracy being less important is also a good one. I was aware of this when I wrote the memo but I guess just wanted desperately to get a version of the memo out, and my unconcious mind told my concious mind not to analsye it. The problem is that its a little hard to estimate given we don't know the elevation distribution of our sources. For fast switching obs the phase error introduced by a baseline vecor error Delta B is proportional to \Delta B ( s - s_c) where s and s_c are the unit vectors to target and calibrator, if we mainly observe sources near the zenith then s-s_c is in the x,y plane and z errors on \Delta B are less important, but if elevations are 45 deg there is no difference. I can try to bring this up and estimate its effect in the revised version of the memo I am writing and in the cal plan document section on ant position cal.

5) I hope to incorporate all your comments into a revised memo, also Richard Hills comments about using WVR data (email, not in this Wiki). I will revise in particular section 2. I will also de-emphasise the whole turn ambiguity resolution issue. I think in most cases the raw group delays will be sufficent. For the night time cal will be using all 64 antennas and although noiser than phase the thermal noise on the bandpass delays will average over all baselines to be much less than the atmopshere error or our target position accuracy. Again like geodectic VLBI using phase rather than delay would reduce random noise errors but there is little point because in the end its the atmosphere delay variations that dominate the error budget not the thermal noise.

John

### Cal Signal Injection

Email discussion between Darrel Emerson and JohnConway regarding the possibility of using an injected signal to measure instrumental phase stability.

Hi John,

About injecting cal signals:  I think I've missed most of the discussion
on this, so I'm just displaying my ignorance.

What's the main parameter that we'd hope to measure by injecting tones?
Is it the variation of instrumental phase response with frequency,
the linear component of which is a simple delay term?  Or is it
a measurement of any change wrt time in absolute phase shift through the
frontend and backend?  Or polarization parameters? Or the change in
phase offset from one receiver to another at a given antenna?

The LO distribution stability is probably technically the most
challenging thing of the whole ALMA project, and will almost
certainly dominate the total phase error budget by a large factor.
There would also be serious issues in ensuring that injected
cal tones are sufficiently phase-stable, even if they are
tied (as I presume they would have to be) somehow to the
phase of the received LO reference at each antenna.

Cheers,
Darrel.

Al Wootten wrote:

> Hi John
>
> Thanks for the report.  I think this will be good for the Science IPT
> telecon next Tuesday also so I took the liberty of posting it to the agenda
> lightly edited.  You will see Jeff's minutes posted.  Please do check with Bill.
>
> Injection of tones has beend discussed but never endorsed strongly enough
> that it became part of the Plan.  The rebaselining over the next few months
> isn't expected to add many new features to ALMA, but it does offer a chance
> to debate adding features which we think may be necessary (like the weather
> instruments).  I'll cc: Darrel on this reply for his information.
>
> Clear skies (heavy cold rain here),
> Al
>
> John Conway writes:
>  > Hi,
>  >
>  >  Unfortunatley I won't be able to attend the
>  > calibration telecon today.
>  >
>  > News on baseline calibration, I am trying to finish
>  > a revised verion of memo 503 before Christmas. Changea
>  > are mostly minor; the one that is critical to the project
>  > concerns discussion and specification of the instrumental
>  > delay versus large angle (e.g 180 deg) slews. In memo
>  > 503 I had assumed that this would not be a problem, the
>  > technical spec I was working to implied that it would be only slightly
>  > larger  than the variation in instrumental delay over 2 deg,
>  > but I guess publication of my memo made people aware that
>  > instrumental delay error stability over large angles was
>  > an issue (i.e. emails to me from D. Emerson at the start of
>  > November).
>  >
>  >  I wrote to Bill Shillue  a few weeks ago go to suggest that
>  > we start negotiating a joint change request, but got no reply.
>  > I guess he is very busy, I will try again.
>  >
>  > Obviously its important to get to the bottom of this, if we
>  > can't calibrate antenna positions quickly the concept of
>  > continuous reconfiguation may be untenable, and if its really bad
>  > we may not be able to find our antennas at all to high accuracy
>  > even in conventional burst reconfiguration.
>  >
>  > Looking a Craig Walkers excellent comments on my memo, its
>  > clear that in geodetic VLBI active measuremnt of instrumental delay
>  > by injection of phase cal tones at the front end and detection of
>  > phase vs freq is vital to achieve millimeter accuracies. We are
>  > of course trying to achieve 10 times that accuracy without such
>  > a system. If there  are
>  > doubts about whether the instrumental delay stability we require for
>  > antenna position determination are posible, such a scheme might have
>  > to be considered, and worked on as a backup. (and would also be useful
>  > for removing instrumental contribution in conventional fast switching
>  > over 2 deg).
>  >
>  > I understand that the LO distribution stability is one of the critical
>  > items for development in the whole project, I guess my worries on
>  > this issue have been increased after some informal discussions
>  > last week with Ralph Spencer and others at Jodrell Bank, where they
>  > pointed  out  the difficulties being faced in the LO distribution
>  > development.
>  >
>  >   John


-- JeffMangum - 10 Dec 2004

"Darrel" == Darrel Emerson <demerson@nrao.edu> writes:

Darrel> Hi John,
Darrel> About injecting cal signals:  I think I've missed most of the discussion
Darrel> on this, so I'm just displaying my ignorance.

Darrel>   What's the main parameter that we'd hope to measure by injecting tones?
Darrel> Is it the variation of instrumental phase response with frequency,
Darrel> the linear component of which is a simple delay term?  Or is it
Darrel> a measurement of any change wrt time in absolute phase shift through the
Darrel> frontend and backend?  Or polarization parameters? Or the change in
Darrel> phase offset from one receiver to another at a given antenna?

Darrel>    The LO distribution stability is probably technically the most
Darrel> challenging thing of the whole ALMA project, and will almost
Darrel> certainly dominate the total phase error budget by a large factor.
Darrel> There would also be serious issues in ensuring that injected
Darrel> cal tones are sufficiently phase-stable, even if they are
Darrel> tied (as I presume they would have to be) somehow to the
Darrel> phase of the received LO reference at each antenna.

Darrel>         Cheers,
Darrel>                 Darrel.

Hi Darrel,

My suggestion at looking at a phase cal tone injection system was motivated by
the systems on geodetic VLBI antennas to measured pointing position dependant group
delays. A set of tones 1MHz apart and locked to the LO are inseted into the front end,
and their phase can be detected at various points downstream. From phase versus frequency
the antenna position dependent group delay added by cables can be found and then removed later at the correlator or in analysis. To obtain good antenna positions in geodectic VLBI it
is important to remove any such pointing dependant instrumental delays, and this means of doing
it was also mentioned by Craig Walker in his review of my memo 503.

Thinking about this a bit more I now see that the situation may be somewhat different for
ALMA. I am sending these comments also to Craig Walker to check the facts of what I say
below in connection with geodetic VLBI.

In geodetic VLBI at the front end there is a mix down with an LO locked to the
H-maser, the resulting IF is transitted down coaxial cables and then the sampling and time stamping of data is done
in the observing room (with a timer unit also locked to the H-maser). I believe
here the main problem with main antenna pointing dependant instrumental effect is due to variations in the delay of the analog
signal in the cables coming down from the antenna. The delays introduced are all
in the  data transmission path. These delays can be monitored and detected by adding and
detecting the phase cal tones. I guess there may also be small position dependant changes in
the uplinked LO phase (it to must have a cable that wraps or twists)  but these are not important because in geodetic VLBI  only the group delay is used to get
antenna positions. The phase is not used, because errors are dominated by the
atmosphere and not improved by reducing noise error by going from delay to phase.

In the ALMA case I guess the LO mix, sampling and time stamping of digital data all
done at the front end. There are no antenna position dependant delays in the data
transmission path, which is good. All we have to worry about then are phase
changes in the LO delivered to the front end as a function  of antenna pointing. It is
the stability of this  LO over long slews and large cable wraps that we were discussing
writing a change  request for (i.e I think we suggested a delay variatons corresponding to
less than say 30  microns, for azimuth slews of 180deg). I don't know how that kind of stability  is achieved, I guess some type of round trip method is used, but since the LO is a
monochromatic signal it cannot be stabilised by any type of multi-tone injection as
I suggested.

All I should be doing is clearly specifying what needs to be measured and to what
accuracy to achieve the position determination spec, not suggesting how this is achieved,
which is not my area. At the front end there are LO mixes, and I should
suggest required stabilities for these, and then there must be samplers with some form
of timer unit which generates a time stamp or frame giving the time of the digital data.
(perhap you could point me to a simple schematic).
Ultimately  I guess the time signals are locked to the LO, and so they they will not be
more stable than the time delay stability on the LO (except for very short timescales when
perhaps phase locked to crystals or other osscilators).

For position determination we can use either just the group delays of the correlated signal, or group delays to resolve turn ambiguities plus phases. In both cases the relevant parameter
I need to specify is that time stability of the  LO delivered to the front end, versus
antenna pointing. The technical  means (round trip delays, cal signals etc) by which this spec is achived is for for others to decide.

John


-- JohnConway - 13 Dec 2004

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Topic attachments
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png 4aa022eb80898a9f99d936a0a3662d52.png manage 414 bytes 2006-08-06 - 19:06 UnknownUser
pdf antposclal.pdf manage 401 K 2004-09-07 - 10:58 UnknownUser
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