Reviews for ALMA Memo 503

ALMA Memo 503: Antenna Position Determination: Observational Methods and Atmospheric Limits: Conway; September 3, 2004

Review from Stephane Guilloteau

Review from Robert Lucas

This mostly reproduces my previous comments. Points 2-3 are aknowledged by John, and also noted by Craig Walker. The last two I've just added.
  1. This is a very good memo with in-depth discussion of many issues.
  2. 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.
  3. 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
  4. 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
      • On this point I do not understand John's reply. Anyway the instrumental delay can be measured on any strong source.
      • By the way, I think (5) and (6) should be fully compatible with current software plans.
  5. 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? [see John's reply]
  6. I'm concerned about the need to spend 30-60 minutes with the whole array during the night after each antenna move (which occur quite often, a few times a week...). This is a lot of observing time and I believe this accuracy is not needed for most projects (especially at low frequencies). Operationally we just need to make sure this is done before each antenna is moved again (up to once a month might be enough).
  7. I'm still not really convinced that there is a need to do the precision measurement with the full array, especially for compact configurations, after each move. I see the need to do the full array calibration typically once a month to avoid error propagation. But after a full measurement, for the next move there is no loss in using only the closest unmoved antenna as a reference for each moved antenna. For the second next move, the precisely measured antennas are a little further away, and so on... So at some point the distance to the closest precisely measured antenna becomes too large for the required precision, and one does a full measurement. I think the occurence of full array measurements should be at most every other move for the extended configurations, and less for compact configurations.

JohnConway - 09 Nov 2004

Point 3) My point is this, if one measures the delay to a bright source this of course incorporates the instrumental delay, but the measured delay also contains a contribution due to the position uncertaintly of the antenna. One can remove this estimated 'Instrumental delay' measured on the bright calibrator from the delay for sources at different elevations and azimuths but if you do this your remaining delay signal depends on the -difference- between the antenna position induced delay toward your two sources.For estimating z coordinates and having minimum elevation of say 30 deg, the difference in delay between a calibrator at the zenith and such an elevation 30 deg source is Delta z/2c. Now in a perfect world where all instrumental delays were zero we would not need to difference data between any two observations, the delay signal for a calibrator observation at the zenith would depend only on the Delta z and be proportional to Delta z/c. This was my thought process when I wrote the memo. I now recognize that even in geodectic VLBI with pulse-cal monitoring (see C.Walkers comments) it is always neccessary to estimate an instrumental delay as part of the data fitting process. Given this the whole argument is moot, absolute delays are not measurable and either one can think of taking the delays to all sources and solve for instrumental delays or one can think of working with difference delays between one bright calibrator and the rest to elliminate instrumental delays. The two processes are of course exactly equivalent from a linear algebra point of view.

Points 6 and 7) What you suggest above is my 'style 3' in section 1 of the memo. I went with doing a full calibration of the array every move day because it was simple and is needed for the largest configurations in order to accumulate 8hrs of solutions to beat down the errors, but looking at Table 2 in the memo it is clear that much less than this is required to reach the specification in the more compact arrays. You are probably right, the time requirement can probably be significantly relaxed for the smaller configurations, the truth is that what was presented was based on what could be analysed easily by the software I had developed in the memo. Knowing the expected rms errors the next stage would be to write a simulation of how errors propogate and accumulate with more complicated calibration strategies.

Review from Craig Walker

ALMA Memo 503 "Antenna position determination: Observational methods and atmospheric limits", John Conway

Review by Craig Walker

Overall the memo is a good discussion of the issues facing the calibration of antenna positions for ALMA. I have comments below on various aspects of the memo, but none are especially serious. At the end of the review, I note some typos.

There is no discussion of changes in instrumental delay when antennas are slewed. Such changes are usually due to the cable wrap. This is a significant concern in geodetic VLBI. Such changes are systematic and can mimic position shifts. Perhaps such changes are either expected to be very small or are measured and removed by the ALMA system, but at least some mention should be made of how they are handled.

JohnConway - 09 Nov 2004. This is a serious omission in the memo and has been partially discussed outside of this wiki by email with Darrell Emerson and others. A specification of instrumental antenna pointing dependent delays is required.

There seems to be a reluctance on the part of the author to use traditional terminology from VLBI for some of the recommended procedures. For example, fitting for phase slopes is part of "fringe fitting" and has a long history. Since the author is a VLBI scientist, I found this somewhat curious. It might be worth relating somewhat more carefully the determination of ALMA baselines to VLBI geodesy, a closely related activity with a significant community of practitioners and a long research history. That community will likely provide the source positions used for the ALMA calibrators and perhaps the delay model.

JohnConway - 09 Nov 2004 I will mention the standard terms to make a clearer interface with the geodetic VLBI world. I guess I did it this way this because I thought 'estimating phase gradients' is more directly understandable to a wider audience (and not much longer to write) than 'fringe-fitting'.

The discussion of dealing with combined bandpass and antenna position uncertainty in Section 2 seems to me to be overly complicated. There seems to be a desire to have an absolute phase and so having both unknown bandpass and unknown geometry (antenna position) is a problem. When doing a geometry solution, one generally has an unknown "clock" offset - which in this case is the instrumental delay. So you don't need to know an absolute delay. Any constant, or slowly changing, offset can be absorbed into the instrumental delay in a fit. So, if you determine a "bandpass", which includes arbitrarily flattening the phases with frequency, for a single scan, then use that to calibrate the rest of the data, you have all that you need. I assume that the relative phases of the different IFs, and the phase shapes within each IF, don't vary (if that is wrong, you need something like a pulse cal system to calibrate it). After the above calibration, a linear phase slope fit should give you a phase and delay for each scan relative to the one used for the bandpass calibration. That can be used to solve for the antenna locations.

JohnConway - 09 Nov 2004 The same point was made by R.Lucas and is acknowleged by me. If one could build a system with zero instrumental delays there would be advantages in the accuracy of position determination. However in practice no system, even geodetic VLBI with pulse cals achieves this, so there is no point even discussing this theorectical possibility (besides such a system even if it could be built would also have disadvantages, such as the need for bandpass stability/accurate bandpass calibration as discussed in the memo, which would outweigh the advantages). So the idea of achieving zero instrumental delays or somehow estimating absolutely the instrumental delay by some measuring device I will consign to a black hole somewhere

Similarly, I suspect it is not really necessary to explicitly resolve the number of residual turn ambiguities for each scan. If you use the residual delays, measured from phase slopes, to do a preliminary delay-based fit, then redo the apriori model with those fit results, I suspect that the residual phases will then be sufficiently constant to not have to worry about ambiguities. This is a bit like using an image to resolve the phase ambiguities when fitting for a source position. Combining the suggestion above about using a scan to determine a bandpass with this scheme for fitting should remove any sensitivity to the quality of the inital antenna positions and bandpasses. The delay fit does not have ambiguities (at least for the nearly complete frequency sampling that ALMA will have across the spanned bandwidth) so the errors can be very large (assuming sufficiently small frequency preaveraging). As noted at the end of section 2, there can be a coherence loss if the apriori geometry is poor enough that the delay changes enough during a calibrator observation to cause a change of phase of a significant fraction of a turn. But in fact, this can be handled by fitting for the phase slope too as is typically done in VLBI fringe fitting.

JohnConway - 09 Nov 2004 This one I will have to think about. In the case of a single baseline with one moved and one unmoved antenna, getting the delay from fringe fitting, correcting the a priori position based on this and computing the phase, is surely exactly equivalent to the process of turn ambiguity resolution I describe??? Again I have to think about this comment more

Page 6. The phase change across a fixed bandwidth due to an antenna position error is actually independent of observing frequency. It only depends on the bandwidth - contrary to what I think is being said here. But if you wish to use a slope measurement to extrapolate to zero frequency (required for resolving turn ambiguities), that requires a more accurate slope measurement at higher frequencies because you have to extrapolate farther. Another way to look at it is that the position accuracy required from a delay-only position fit (as suggested above) has to be better at high frequencies to allow phase ambiguities to be resolved.

JohnConway - 09 Nov 2004 Right I am aware of this. the problem was my bad English I guess what I meant to say on page 6 was ' On the other hand the phase offset introduced at all frequencies within the band due to a given antenna position offset (Table 2 column 3) increases with observing frequency'.I wrote 'the mean phase change across the band' which was ambiguous, I meant by this that the mean of all the phase changes at all frequencies in the band due to a given position offset was proportional to the observiving frequency of the band centre. not that the phase difference across the band was dependant on observing frequency which of course it is not.

One thing to be cautious about; it is not clear that the tropospheric mapping functions used at low elevation, flat sites are very good at high mountain locations. The raw phases, and phase referencing phases, in data from the VLBA site on Mauna Kea are are not nearly as good as might be expected from the nominally good observing conditions. A likely culprit is that the elevation and/or azimuth dependence of tropospheric delay is poorly modeled.

Good point

End of section 5.1. A pulse cal system (which is what is being described here) does not preclude the need to solve for an instrumental delay, especially in VLBI where the independent clocks have unknown and time variable offsets. What that system does do is calibrate any variations in the instrumental delay that are that result from the antenna electronics and cables and that might be a function of pointing direction. Note also that when pulse cal tones are detected at the antenna it is still done after digitization. This is partly because the sampler clock can affect the instrumental delay and partly because it is easier.

John Conway- Since we do not have independant clocks on ALMA one could I guess at least imagine that theoretically that such a pulse cal system would be built to measure absolute instrumental delay - but since it is not part of the ALMA plan to have any such system we do not need to discuss it further

Note that at 90 GHz, the ionosphere can be on the order of 20 ps or 6mm of path length (scaled from a fairly typical 30 ns at 2.3 GHz). One cannot forget it. But that is a daytime total path. It will be much lower at night and ALMA will be dealing with a differential path so it is probably still low enough to ignore. For daytime astronomical observing someone should think through the implications.

Good points

Some typos:

  • Abstract line 11: "there" instead of "their"
  • page 3, paragraph 5, line 7. "isected" instead of "is expected"
  • page 9 just before eqn 5. The \Delta \tau subscript (211j) looks wrong.
  • page 11, line before eqn 19. "we each point" missing something.
  • page 14, sec 4.2 line 6 "positions while the rest" something missing
  • page 18, paragraphs 3 and 5.. There is lots of talk of bolometers when I believe he means barometers.
  • page 19, line 1. "none " should probably be "non-"
  • page 19, line 3. "is" should be "in"
  • page 22, line 4. extra "too", I think.
  • page 22, paragraph 5 line 7 "spend" should be "spent"

-- JeffMangum - 08 Nov 2004
Topic revision: r7 - 2004-11-09, JohnConway
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