having seen no response to this, let me make a proposal, and see if it generates any discussion. first, let's define the total delay D thusly: D = Dg + Da + Ds + De + Df where Dg is the geometric delay; Da is the atmospheric delay; Ds is the structural delay; De is the electronics delay; and Df is everything left over. of course, parts of this that are common to both antennas cancel out - the atmospheric term is only the differential atmosphere, e.g... Dg is composed of at least: source position; baseline vector (or separate antenna locations); earth orbital and orientation state, including precession, nutation, etc...; wavefront curvature correction; gravitational bending (due to the sun); plate motion; tides; ocean and atmospheric loading. sometimes some parts of antenna structure are included in the geometric delay calculation (the axis non-intersection, for instance). Da is composed of the differential bulk neutral and ionospheric delay and the fluctuating atmosphere (wet, dry, and ionospheric). Ds is composed of predictable structure related terms: axis non-intersection (if not included in Dg); focus change (if different for different antennas); temperature related changes; etc..., and random errors (e.g., due to wind). De is measured by the round-trip phase system, and includes all parts of instrumental delay between the measurement points. Df is all the rest, and is essentially what we measure when we do a delay calibration. if we calibrate Df only infrequently, then we have to require that the systematic errors in the other terms are small - smaller than the fluctuating terms. this is, e.g., the case at the VLA - what is called the "peculiar delay" is measured relatively infrequently (of order months, or when something changes on an antenna). if we calibrate it often (every few minutes, say), then the allowable systematic errors can be larger because they are effectively swept up in the Df term. i think we are in this situation with ALMA, but it is a bit tricky if you assume that the calibration is done at 90 GHz and you are observing at a different frequency. so maybe we're in a situation where the delay is calibrated on 10's of minutes timescales. given those parts of delay, i propose: 1 - that we spec the system to 650 GHz; 2 - that the allowable phase "error" on a visibility at 650 GHz is 30 deg total. this allows for 90% coherence. this implies a path length error of 38 um, or a delay of 130 fs, or, for each antenna, 90 fs; 3 - that we recognize that we will not observe at 650 GHz when conditions are poor (see PWV modification of allowable atmospheric random delay below); 4 - that we split this delay error into systematic and random components for the above delay terms: Dg, Da, Ds, and De. 5 - that the allowable antenna delay error Da is as specified in the RFP: 67 fs (20 um of path) for the repeatable (systematic), 50 fs (15 um of path) for the nonrepeatable (random); 6 - that the allowable electronics delay error De is as specified in chapter 7 of the PB: 7 fs for systematic, 31 fs for the random; 7 - that the allowable random atmospheric delay error is given by: Da = 38 * (1.25 + PWV) fs, where PWV is the precipitable water vapor column in mm. this adds an additional 10 fs on top of the error that the WVR folks have adopted, for dry + ionospheric fluctuations; 8 - that the allowable systematic atmospheric delay error is 10 fs; 9 - that the allowable systematic geometric delay calculation error is 20 fs, with no associated random part; 10 - that the timescales are 1 s to 10000 s (copied from PB chapter 7). so, taking the RSS of the terms (all entries in fs): Dg Da De Ds total per antenna systematic 20 10 7 50 55 random 0 38*(1.25+PWV) 31 67 sqrt(7700+2170*PWV+1440*PWV^2) for 0.5mm of PWV (good conditions), the total random part is 95 fs; for 1.0mm of PWV (median), it's 106 fs, and for 4mm of PWV (poor conditions), it's 200 fs (which is still less than 10 deg of phase at 3mm). note that our ability to calibrate the Df term has to be a small fraction of this total error. note that the systematic error is dominated by the antenna. i don't see how we can avoid this, given that's the value in the RFP. part of my problem with the atmospheric spec is that it depends only on the PWV. we know there are times when the PWV is high but the phase fluctuations are small, so we might still want to observe at high frequency. maybe we just have to hope that fast switching works well enough in those conditions. but in that case, we have a spec that doesn't fit our idea of what is going to be done, which is not a good thing. -bryan On 2003.05.11 14:20 Bryan Butler wrote: > > all, > > i would like to initiate some discussion on exactly what the > top level allowable delay (phase, if you like, but i prefer > calling it delay) error should be. > > some history. > > 1 - in the dim reaches of time (1995), the "MMA phase calibration > working group" met and decided on some top-level phase stability > specs for the MMA, which were written down in MMA memo 144. > they are as follows (from the table in that memo): > > conditions net gain atmosphere antenna electronics > best 98% 6deg=17um 5deg=14um 3deg=7um > median 90% 14deg=38um 11deg=31um 6deg=16um > 80th% 50% 36deg=100um 28deg=79um 14deg=40um > > note that they were considering conditions at 300 GHz. these > had essentially been carried along in chapter 3 of the project > book, despite being badly outdated. > > 2 - larry d'addario, in his chapter 7 of the Project Book (which > is the LO chapter - admittedly perhaps an odd place for the > top level delay stability spec to be written, but there it > is), broke it down in a more sensible way, distinguishing > between systematic and fluctuating (or random, or rms) errors, > thusly (in table 7.4): > atmosphere electronics structure total per antenna > systematic (avg) in fsec 8.4 6.9 4.8 11.9 > random (rms) in fsec 38.5 31.4 22.2 54.5 > > where the total allowable error was set so that there was > at least 90% coherence at 950 GHz. > > 3 - the WVR folks have been working to a spec of allowable path > length error of: 11.5 * (1 + PWV) in microns, where PWV is > the precipitable water vapor column in mm. see memos 352 > and 303. this is essentially a spec for the allowable random > atmospheric delay, but, really, this is not the *total* > value, since there will be additional terms from the dry > fluctuations, ionospheric fluctuations, and other unmodelled > sources of path length fluctuation. > > there is more history than this, of course, but i think these are > the three most important items. > > so, where does that leave us? confused, and with no clear coherent > (pardon the pun :) top-level spec on allowable delay for ALMA, at > least as far as i see it. > > i propose that we adopt larry's way of breaking down the allowable > delay errors - into separate systematic and random parts, and that > we come up with acceptable values for the separate parts (splitting > it into atmosphere, electronics, and antenna makes sense, although > you might add a software component, since, for example, the precision > with which you calculate geometric delay will fold in at some level > [you might just specify that it has to be smaller (by some fraction) > than any of the other terms and leave it at that as well though]. > > can we start some discussion on what the values should be? > > as i see it, the first two things to decide are: > > 1 - what is the highest frequency we work to? in the current baseline > plan this is 650 GHz (roughly). if we allow for either the > japanese participation, or a future "upgrade" to include band 10, > then we need to work to 950 GHz (roughly). which is it? > > 2 - what is the largest allowable phase error at that frequency? > from this, we determine the total allowable delay, which must then > be broken down into its constituent parts. > > after that, we can argue/agree on values for the separate components. > > > > -bryan > > _______________________________________________ > Almacal mailing list > Almacal@listmgr.cv.nrao.edu > http://listmgr.cv.nrao.edu/mailman/listinfo/almacal > _______________________________________________ Almacal mailing list Almacal@listmgr.cv.nrao.edu http://listmgr.cv.nrao.edu/mailman/listinfo/almacal