1.2. Single-dish techniques
A single-dish telescope provides an adaptable platform on which to mount a receiver system. While other arrangements are possible, receivers and receiver arrays are generally located at either prime or secondary focus, with the choice of focus depending on the physical size of the receiver, the size of the focal plane that is to be occupied by a receiver array, the gain of the telescope, and the amount of scattered radio power that can be tolerated.
It is useful to begin our analysis of single-dish radiometry by considering the simplest case, of a single beam of solid angle aligned with the telescope boresight. A receiver behind such a system will record a power, P, which is not only related to the brightness temperature of the sky within the beam, Tsky, but also to any other signals that may appear at the receiver. These inevitably include some emission from the atmosphere and a parasitic ground signal, Tgnd, so that
and no measure of the incoming power, however carefully calibrated, will be a good measure of the temperature of the sky because of the unknown contributions of Tatm and Tgnd to P.
The sensitivity of this radiometer system is
where Tsys is the system noise temperature, is the bandwidth of the receiver, and t is the integration time used. For systems operating at ~ 30 GHz, values of Tsys ~ 30 K and ~ 1 GHz are readily obtained, so that the antenna temperature noise after about 1 hour of integration should be TA ~ 11 µK, and the correponding sky noise (for an antenna with efficiency 0.6) would be Tsky ~ 19 µK. While this estimate suggests that sky temperatures can be measured to high accuracy in a relatively short time, it is hopelessly optimistic. The sensitivity does not improve as t-1/2 over long timescales in measurements with a single radiometer because of the varying ground and atmosphere contributions, and because the receiver noise cannot be made "white" over such a long period. Furthermore, the interesting astronomical signal cannot be extracted from the contaminating atmospheric and ground signals. Thus a different observing technique must be used.
The simplest improvement is to move the observing direction between the point of interest (the target, T) and a reference background region (R) every few seconds. Subtracting the resulting powers should provide a measure of the sky temperature difference between the target and reference region since most of the atmospheric and ground signals should be slow functions of time and position. This technique of position switching can provide a good measurement of the temperature difference Tsky, T - Tsky, R. The angular separation of the target and reference regions must be sufficiently small that the atmosphere and ground signals are similar at the two locations. However, the differencing scheme then means that only sky structures which differ at the target and reference region can be detected. Since half the observing time is spent on either the target or reference region, and then two noisy measurements have to be subtracted, the maximum sensitivity of the system is a factor 2 worse than the estimate in eq. (9).
A difficulty with this type of observation is that it relies on conditions being stable during the interval between observing the target and reference regions. Since large telescopes tend to move slowly, large changes in the contaminating signals are likely under any but the best conditions, and smaller changes are expected under all conditions because of the varying position of the telescope as it tracks the target across the sky. This problem can be alleviated by moving the beam's position using an oscillating mirror, or a nutating subreflector, rather than by moving the entire telescope. Although this can reduce the position-switching time to a second or less, the moving optics almost inevitably induce systematic differences in the parasitic signals entering the receiver, and there is a mechanical limit to the rate of position-switching.
An alternative strategy is therefore to observe with two beams, provided by two separate feeds. The two feeds are placed symmetrically about the boresight of the telescope, so that the beams have the same shape on the sky, and the target region is placed in one beam (the main beam, beam A) while the reference region lies in the other beam (beam B). The signals from these two directions are constantly measured and compared by the receiver system, whose internal switching between the beams can occur on millisecond timescales -- sufficiently fast to freeze out atmosphere, ground, and receiver fluctuations. The resulting measurement of
is averaged over the desired integration time. This beam-switching method of observing is faster than position-switching, and reduces the dead time when no data are being taken. Beam-switching can be highly effective because of its superior removal of parasitic signals. A problem that remains is that the target and reference region are being observed with different feeds, and so different systematic errors on the two sides of the receiver can lead to systematic errors in the measurement.
A further improvement is then to combine beam-switching and position-switching. Now an observing cycle of duration tcy is broken into three segments
and then the best estimate of the sky brightness difference between the target and the average brightness of two reference regions offset to either side of the target is proportional to
This symmetrical switching pattern is relatively efficient at reducing the levels of noise induced by time-varying atmosphere and ground signals, and changing receiver characteristics, since it takes out linear drifts in the behaviour of the system. Typically the integration time, tint, is (80 - 90)% of the time taken for the complete observing cycle, tcy, with the lost time being taken up by moving the telescope.
It is still necessary to design the equipment to reduce non-ideal behaviour to the maximum extent possible. The receiver should be designed to have similar gains on the two sides with the minimum possible signal losses, and maximum symmetry of illumination of the telescope. The switching scheme should place beams A and B through similar columns of atmosphere, so that switching is generally performed in azimuth. The ground signal can be equalized if the terrain near the telescope is flat and unstructured, or carefully screened, and should be reduced further by designing the feeds to under-illuminate the antenna.
Since the observation of an SZ effect may take a number of hours, spread over a number of days, the positions of the reference beams rotate on the sky about the target to populate reference arcs which may extend into a full circle for a circumpolar source (Fig. 1).
Figure 1. Target position, and the development of reference arcs, for OVRO 40-m observations of a point near the centre of Abell 665. The current target and reference positions are shown as solid circles on a line of constant azimuth. As the sky rotates during the observation the reference beams sweep out arcs about the target position. For some parallactic angles, p, these arcs lie near contaminating radio sources: in the configuration shown, the NW reference beam lies near sources s7 and s8.
As with all astronomical measurements, the observation of an SZ effect will be subject to confusion from foreground and background sources. Beam- and position-switched observing has a higher level of confusion than simple single-beam observing since sources may lie near both the target and reference beam positions. Fortunately, switching in azimuth modulates the confusing signal according to the parallactic angle, p. Contaminated data can then be filtered according to the value of p and removed. With sufficient instantaneous sensitivity, binning by parallactic angle can be used to find and remove even variable sources, which tend to be a large fraction of the source population at the high radio frequencies favoured for SZ effect work.
The discussion above has concentrated on two-beam systems, and a simple position-switching strategy, but this concept can be extended to receiver arrays and more complicated switching schemes designed to remove higher-order systematic effects. Additional levels of switching can also be added: for example, identical observations may be made on fields leading and trailing the target field, and the observations can be timed so that the fields are observed over the same range of hour angle. This can remove a residual level of environmental systematic error. The receiver can be rotated, so that the main and reference beams exchange identities, to remove a level of asymmetry in the data caused by imprecise balance in the receiver system. Observations can be conducted at different times of year, so that the position of the Sun and the associated heating of the telescope and ground change, allowing checks for the major spillover signals to be performed.