Form of switching

For an uncooled system, there seems little chance of obtaining  0.1 K stability with a total power system given a system temperature of at least 1000 K. (Note that we can get some relief because we are observing a line and are to a considerable extent only concerned with the differences between frequencies. We believe that some form of comparison with a load of known temperature will however be necessary.) We should therefore plan to use either a Dicke switch or a continuous-comparison radiometer which takes the difference between the sky temperature and a temperature-controlled load. For the pointing correction we also need to take the differences between different parts of the aperture. Many options are available but we clearly wish to select the simplest, cheapest and most reliable that can do the job. The most basic option is a single mixer with a Dicke switch operating between the sky and a fixed-temperature load. Ideally this load should be at a temperature close to that of the sky brightness at which one obtains the best sensitivity (around 170 K). A modulated calibration signal would also be injected via a coupler on the input. An alternative to injecting a cal signal is to switch between the sky and two loads at different temperatures. This gives more flexibility in the choice of temperatures: something like 100 K and 250 K (spanning the sky brightness range of interest) would be best, but combinations like 200 K and 370 K would also be good. The existing MRAO design uses two loads and an optical switching scheme (a flip-mirror). This works quite well, but for ALMA it would probably be worth developing an all-electronic switching scheme, using ferrites or diode switches, for both reliability and stability reasons. With a single mixer the system would normally run in double-sideband mode and, provided the gain stability was adequate, the sensitivity would be given by the normal radiometer equation:

$$\Delta T = 2 T_{sys} (DSB) / \sqrt{Bt}.$$

The next level of sophistication is to use two mixers. With a hybrid before the mixers and a correlating backend one can then arrange that the output is the difference between the sky temperature and the load. The sensitivity improves by root 2 and with appropriate switching we can presumably separate the sidebands as well, although the advantages of doing this do not seem very great. (It would perhaps give better information about any contribution from clouds.) To obtain the gradient in the emission, which gives us the pointing correction, we need to arrange the optics so that the radiometer illuminates a patch on the subreflector, covering about half of it. For a switching scheme the beam then has to be moved around (most naturally as a circular scan about half way out) and the signal put through a pair of synchronous detectors to generate the required error signal. Lamb and Woody suggested a rotating prism to do this but a rotating mirror with its normal slightly tilted with respect to the axis of rotation would also do the job. An alternative is to again use correlation (i.e. continuous differencing) receivers. The most obvious arrangement would be to have 4 horns in a square, which are optically reimaged onto the secondary. The two diagonal pairs are connected to 4 mixers via hybrids in such a way that the outputs are the differences in the sky brightnesses required. A mechanism for switching against loads would still be needed to give the interferometric phase correction. Although these schemes sound complicated, the technology does probably now exist to build such combinations of splitters, hybrids and mixers in a stripline form at these frequencies. More discussion of these schemes seems appropriate before a choice is made here.