Requirements

The first question to be decided is whether we wish to correct just the phase error in the interferometric signal or whether we should also plan to take out the tilts in the wavefront across the individual dishes which cause pointing errors. (The latter effect is sometimes called anomalous refraction, although it is only anomalous in the sense that it would not occur if the atmosphere were uniform.) Correcting such pointing errors with radiometers was discussed by James Lamb and Dave Woody in MMA Memo 224. In each case we then need to set detailed requirements. We need to decide the path length error allowed as a function of integration time, weather conditions, zenith angle (z) and change in z. For pointing corrections, we need to set the required accuracy (which should be a term in pointing error budget) again presumably as a function of weather and z. The rms path error given as the goal in existing documents is 38.5 fs which is 11.5 micrometers of path. Note that, at this level, the loss of correlation from this cause is only 5% at 950 GHz and 0.7% at 350 GHz, so this is setting the goal very high. (Compare these to the transmission losses of about 70% and 20% for these same frequencies with 1 mm of water vapour.) No reference is made to whether this figure degrades in less than ideal conditions, but is clear that it can be allowed to without seriously affecting the data. A more realistic goal would be to multiply the above figure by (1 + w_v) where w_v is the amount of water in the path in millimetres. The time allowed for achieving this accuracy is also not presently specified. We have generally been assuming that this refers to a one-second timescale, but we really need to look more closely at the data to see if we are justified in going as fast as this. (Note that the question of whether the correction is applied to the phase in real time or the data taken with short dump-times and stored for later processing has only a small effect on the radiometer requirements but quite large implications for the software.) A ``systematic (avg)'' error of 8.4 fs is also quoted in Larry D'Addario's Phase Stability Specification Note. We believe this is not relevant because any systematic or slowly varying errors in the atmospheric phase correction will be taken out by the observations of calibration sources. For the same reason, it seems to us that the longest timescale that we need to worry about for the radiometers are a few minutes. (We will presumably observe calibration sources much less often than we would if we were using only them to remove atmospheric phase fluctuations, but there seems to be no reason to do it less often than say once every 5 minutes. Note that this implies that the phase stability of the rest of the system must be maintained for at least this length of time. We can, if necessary, move further and use brighter sources than is planned for fast-switching phase calibration. Presumably the same observations will generally be used to check the pointing and/or the amplitude calibration.) It is however essential that we can measure the atmospheric term accurately as we move from source to calibrator. This is certainly more difficult if there are large changes in the total water in the path and/or ground spillover (although it is only the dish-to-dish differences in these effects that are important). At low elevations it would be beneficial to look for calibration sources that are closer to the target in zenith angle than in azimuth, i.e. to search in an elliptical patch of sky. The key sensitivity number is that at the optimum frequency the change in brightness temperature is $\sim 15/w_v$ mK per micrometer of added path. This suggests that a radiometric precision of order 150 mK (corresponding to  10 microns of path) would be sufficient in good conditions. Given bandwidths of >100 MHz and an integration time of 1 second, this looks reasonable, even for a room temperature mixer, for which Tsys of 1500K should be possible. For antenna pointing corrections a suitable budget allocation is 0.3 arcsec rms (in dry conditions). This is a wavefront slope of 1.5 microns per metre, which leads to a figure of 9 microns when taken between two points 6 metres apart on the dish. The measurement is however now a difference between two numbers and it probably has to be measured in shorter times than the interferometric phase. This looks marginal with a single uncooled mixer. Studies of the existing site data (e.g. MMA Memo 223 and references therein) show that much of the observing time will be seriously affected by single dish pointing errors: the overall median seeing is about 1 arcsec compared to the specification for the antennas of 0.6 arc seconds. More study is needed of how fast the pointing fluctuates and how the bad seeing correlates with the other conditions. The obvious conclusion at this stage is that we do need to correct the pointing and that we should assume that this needs to be updated once per second. (With a wind speed of several metres per second and a 12-metre aperture, we can obviously expect some pointing changes on timescales as short as this, but the bulk of the power will normally be a periods of more like 10 seconds.) Note that this has to be done in real time and that we will therefore need to use an algorithm that anticipates the error for a time about one second ahead of the most recent reading. Other requirements: Compatibility of interfaces (CANbus, etc.) Minimum interference with other systems. A special problem is leakage of the LO and its harmonics into other systems via various paths e.g. out of the feed and by reflection off the subreflector. It is unlikely that we can suppress these completely. The LO's should therefore be locked to system clock so any interference is at an accurately defined frequency. The design should use the fixed reference frequencies already provided at each antenna. We might add a requirement that the LO can be shifted by a small amount so that any interference can be moved away from a critical line. Suggested baseline spec: 10(1 + w_v) microns of path and 0.3(1 + w_v) arc sec of pointing over a 5 minutes of time and 1 degree in z, with 1 sec time resolution.