1.6. Interferometric problems
Despite the many advantages in using interferometric techniques there are numerous complications. Some, like confusion, are of similar type to those affecting single-dish observations, but there are also new problems related to bandwidth, integration time and temperature sensitivity.
Radio source and MBR confusion are difficulties for interferometers just as for single dishes, but interferometric data implicitly contain the possibility of filtering out the confusion from small angular scale radio sources. Short interferometer baselines are sensitive to the SZ effects and to large angular-scale structures in the MBR (Fig. 6) as well as to all nearby radio sources. However features with large angular scale are resolved out on long baselines, and only radio emission from small angular scales produces detectable signal. Thus the confusing radio sources of small angular size can be identified using the longest interferometer baselines, which are insensitive to the SZ effects or MBR structures. The effects of these sources can then be removed on the short baselines by a simple subtraction, allowing SZ effects and other MBR structures to be mapped with much reduced radio source confusion. This is particularly valuable since the simultaneous observations of SZ effects and radio sources allows the effects of variable sources to be removed.
Figure 6. Predicted VLA efficiency as a function of baseline for a 5-GHz observation of Abell 665. The shortest baseline available on the VLA is 800, so that most of the SZ effect signal is resolved out by this long-baseline instrument. Since there is no SZ signal on the longest baselines, data on these baselines can be used to obtain accurate flux densities of contaminating radio sources. These flux densities can then be subtracted from the short-baseline data to improve the detectability of the SZ effects.
This procedure relies on a strong separation between the angular scales of emission from radio sources and the SZ effects, and therefore fails for clusters containing bright extended radio emission (such as radio halo sources). In these cases, the radio emission can be reduced in importance by working at high frequencies (since it is generally of steep spectrum), or by using multi-frequency observations to effect a spectral separation.
Calibration issues for interferometers are effectively the same as those for single dishes, with two caveats. First, interferometers present the additional issue of phase calibration. The electrical length of each baseline will vary slightly from day to day due to instrumental instability (e.g. with ambient temperature), and it is essential to calibrate this in order to retain spatial information in the data. This can be implemented by observation of a bright radio source, and comparison of the fringe rate observed with that calculated from a model situation. Phase corrections can then be applied to the data.
Second, it is simplest to calibrate using radio sources that are unresolved on even the longest baselines, thus reducing the number of suitable calibrators compared to those available for single dish work. MBR interferometers have relatively short baselines, but an additional problem is that their collecting areas are often relatively small, and consequently their flux sensitivity relatively low. For example, the VSA (see Sec. 1.7) partially resolves the supernova remnants Cas A and Tau A (angular sizes ~ 5 arcmin, flux densities 180 and 350 mJy at 33 GHz) on its longest baselines, yet the powerful radio galaxy Cyg-A (~ 35 mJy at 33 GHz) is not quite bright enough for accurate phase calibration.
In practice an interferometer does not observe at a single frequency , but rather over a range about some central frequency 0. This means that the values of (u, v, w), which are measured in wavelengths, change across the passband, reducing the peak signal by a factor
This limits the field size, resolution or bandwidth , which directly affects the sensitivity. To avoid this problem, an interferometer may split the band into several sub-bands, and deal with each sub-band separately.
1.6.4. Time constant
Typically, an interferometer will integrate over a few seconds per measurement. This causes off-axis sources to be smeared in arcs in the image plane, again reducing the peak signal. In order to avoid loss of precision, the integration time
This time-constant smearing is only a small effect for CMB interferometers, as their short baselines produce relatively large synthesized beams.
1.6.4. Temperature sensitivity
The temperature sensitivity of an interferometer is given by
(compare eq. 9) where Ncorr is the number of antenna-antenna correlations used in making the synthesized beam of solid angle synth. This equation shows that sensitivity increases with increased bandwidth and observing time in the same manner as for single-dish observing (tint is made up of many measurements, to eliminate time constant smearing), and also increases with the collecting area of the telescope, as described by the number of antennas. However, for an extended source of angular size s, only antennas separated by baselines less than / s contribute to the sensitivity. Longer baselines resolve out the signal, as shown in Fig. 6. The region of high efficiency on this normalized visibility function becomes narrower for sources of greater angular extent. As most interferometers are designed for high point source sensitivity, they tend to contain few short baselines. This severely limits sensitivity to the SZ effects, which subtend large (arcmin or greater) angular scales on the sky. One way to reduce this problem is to to observe at longer wavelengths, however confusion from radio sources soon becomes a limiting factor.
Most SZ observations to date have been made using "normal" interferometers, i.e., those designed to achieve high resolution rather than for this purpose. For example, the Berkeley-Illinois-Maryland Array (BIMA), which operates primarily at mm wavelengths, has been used to good effect in its most compact configuration and at cm wavelengths. Since few BIMA baselines were short enough to detect the SZ signal, long integration times were required to achieve appropriate sensitivity.
A problem that arises in using compact interferometer configurations is that of antenna-antenna cross-talk, since microwave signals radiated from one antenna can leak into adjacent antennas. Such cross-talk signals can easily dominate the signals expected from SZ effects on the sky. A reduction of this cross-talk is often possible by using the different rates of modulation of the cross-talk and sky signals, at the cost of some loss of data and increased noise.