This Chapter is for potential MERLIN users who are not familiar with aperture synthesis observations and its jargon. §3.3-3.7 give a qualitative overview of the features of aperture synthesis which are relevant for planning observations. Together with the quantitative information on MERLIN system parameters given in Chapter 4, they should allow you to decide whether your ideas for observations are feasible, and if so to pick an appropriate observational strategy. In §3.2 we sketch how these features arise out of the theory of synthesis imaging. §3.8 describes the purpose and principles behind calibration of synthesis data, while §3.9 describes the mapping process. A few more specialised topics are discussed in §3.10.
The laws of physics dictate that the best angular resolution of a telescope (its diffraction limit) is proportional to lambda/D, where lambda is the observing wavelength and D is the telescope diameter. To achieve similar resolution to, say, a 1-m optical telescope, a single radio dish would therefore have to be many hundreds of kilometres across. An interferometer, such as MERLIN, is an instrument that alleviates this problem and allows high-resolution radio images to be produced with a combination of smaller antennae.
If a radio source is small enough, or distant enough, the electromagnetic waves arriving at the Earth can be considered as parallel planes. A radio receiver will produce a sinusoidal response to such a point source. In a simple two-element interferometer, the sinusoidal signals from two separate antennae are multiplied and accumulated (or cross-correlated) and the resulting signal (which consists of an amplitude and phase) depends only on the geometry of the antenna pair in relation to the source (ignoring atmospheric distortions). For example, if the difference in reception time of a wavefront across the two antennae is the same as the time for the radiation to travel an integral number of wavelengths, the two signals will be in phase and the product will be a maximum.
If this interferomter pair were permanently stationary with respect to the sky it would only ever measure one bit of information about a radio source; its brightness at a certain angular scale and orientation. Fortunately, as the Earth rotates, the position of the object relative to the two antennae changes and so alters the geometry. A series of measurements then gives information about the object over several different angular scales and orientations. We can get even more information simply by adding further antennae to the instrument, each making several new pairs (known as baselines) which act as separate interferometers. This process can be thought of as forming a large-diameter radio dish by allowing the Earth's rotation to move antennae around each other and making measurements at each configuration. If we could sample the output of the interferometer with the antennae in every conceivable configuration we would produce an image equivalent to that which would be obtained with a completely filled-in dish. The result, however, is never that good because there are always gaps in the synthesized dish, but it is possible to interpolate data into the gaps.
Now suppose that the object under study has structure, rather than being a point source. Each antenna will receive radiation from each part of the object and the resulting combined signal will be much more complex. The interferometer produces a signal (amplitude and phase) which is then dependent not only on the array geometry (in projection), but the source structure as well. Fortunately the geometry is well-determined, so the structure of the object can be deduced.
To simplify matters we can regard a complex source to be merely a collection of point sources of different positions, sizes and brightnesses, and deduce the set of point sources that would best match the output of the interferometer. This is the principle behind the reconstruction of the image of the object. It turns out that the brightness distribution of the object (i.e. the radio image) is actually the Fourier Transform of the set of phase and amplitude measurements from the interferometer (known as visibilities). The process of producing a MERLIN map therefore starts with editing the visibility data for corrupted measurements, calibrating and correcting it against data taken for objects for which we have a good idea of the instrumental response. The next step is to Fourier transform the data (accompanied by re-weighting and other measures to attempt to compensate for the missing spacings), and to deconvolve the instrumental response from the resulting image (a process known as CLEANing). This leads to a final image that best represents the actual measurements.
The following sections describe in more detail the principles of the two-element interferometer and synthesis imaging. They are not intended to explain in detail how aperture synthesis works, although you will certainly need to have a good idea about this to get the best from your data if the target is very bright or extended. The best way to find out more is to read one of the text on aperture synthesis listed in Section §3.12.