OTF Mapping

The prospects for doing OTF mapping at the Chajnantor site have been discussed in detail by Holdaway, Owen, and Emerson (1995, MMA #137) (HOE). The basic idea is that a raster scan of the object under study will be made with a very rapid turn-around of the scan at the end of each row in a region that is off the source. During the scan across the source, the receiver power is read out at a rate which corresponds to at least the Nyquist sampling of the source structure. That is, at least as often as twice per beam width. Thus, there are many ``on" observations across the source with an ``off" observation at the end of each row. The ``off" observations last about one second during the turn-around at the end of each row. The time on each ``on" observation is much smaller. HOE used the path length fluctuations as measured by the site testing interferometer at Chajnantor to infer the expected atmospheric brightness fluctuations. They were able to work out the magnitude of the fluctuations as functions of both the time and pointing angle with respect to the source. Under the assumptions that (1) the antenna could slew as rapidly as 1^o/second, (2) the antenna could accelerate and decelerate between normal tracking and full slew in one or two seconds, and (3) the correlator could dump the spectral data every .003s, they concluded that OTF mapping should work well at the Chajnantor site. Their Figure 2 shows that the expected receiver noise and atmospheric noise contributions will be about equal at 230 GHz 80% of the time for a scan that is a large as 1^o. For smaller scans the situation is even better. At the time of the HOE memo, is was not clear whether their assumptions about the antenna and correlator would be met. We now have more information about the array components. The present NRAO design for the correlator will allow correlator read-out at the rate of once every .001 second, which is fast enough to permit OTF mapping of both continuum and line observations (J. Weber, private communication). The planning for the antenna prototype has included studies of the capability of the antenna to carry out the OTF observing. It appears that if feed forward is used in the drive servo design, it will be possible to turn the antenna around at the end of an OTF scan in about one second as assumed by HOE. The maximum smooth scan rate will be at least about 0.5^o/sec, comparable to the 1^o/sec rate assumed by HOE. One further point that needs to be considered is the required receiver gain stability for the OTF scheme to work. The planned continuum bandwidth of 8 GHz calls for unusually good gain stability. The time between any of the ``ons" and the off at the end of the scan is about one second. The gain must be stable over that time interval. The fractional total power noise for one of the ``on" measurements is: $\Delta T/T=2/SQRT(B t_s)$. B is the bandwidth, and t_s is the time on each source. The 2 is the usual factor due to switching. Here the long ``off" time reduces the noise in the subtraction, but it is also about twice as long as the total ``on" source observing time. The fractional total power fluctuation due to gain variations is: $\Delta T/T=\Delta G/G$. If we take the scan time to be always one second, then t_s depends on the scan length and the beam width. For scan lengths between 5' and 60' and beam widths between 25'' (220 GHz) and 6'' (800 GHz) the time on source varies between .08 sec and .002 sec. For B=8 GHz, and equating the receiver noise fluctuation to that due to the gain fluctuation, we find a necessary gain stability in the range of 0.8 x 10^-4 to 5 x 10^-4. Thus, a receiver gain stability of about 1 x 10^-4 over a time scale of about 1 second is required for the receiver. This level of stability can certainly be achieved, but it requires careful attention to the construction of the receiver. The above argument leading to a gain stability requirement of 1 x 10^-4 depends on the relative time on each ``on'' during the scan being small compared with the total scan time of about 1 second. Thus, the OTF method works best for large scans (M. Wright, private communication). Even for short scans, it will still work reasonably well, requiring a little more gain stability. It will be important to keep the total scan time to be about the same time as the turnaround time, in order that the overall observing be efficient. Another question concerns the number of antennas that must be used to achieve the necessary sensitivity in the single antenna measurements to equal the corresponding array sensitivity. The answer here depends on the amount of redundancy in the short interferometer spacings. If there is no redundancy in the short interferometer spacings, then, for approximately equal sensitivity in the OTF measurements, the same amount of time must be spent on the single dish map as on any of the array baselines. That means about the same amount of time in the single dish mode as in the array mode. The only difference is in the factor of 2 in the OTF (switched) mode. This implies that a measurement with 4 antennas for the same duration as the array observation would suffice. However, with the likely large redundancy in the short interferometer spacings, much more time in the single dish mode will be required. Exactly how much time will depend on the details of the compact interferometer array. Probably most of the antennas will be required to operate in the single antenna mode simultaneously to produce the uv plane sensitivity comparable to the of the array. The requirement that all the antennas have the good gain stability makes the most sense. It is not a difficult requirement, and it will benefit the interferometer operation as well.