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This chapter is concerned with techniques of processing that are largely nonlinear and include deconvolution, that is removing, to the extent possible, the limitations of the visibility measurements. There are two principal deficiencies in the visibility data that limit the accuracy of synthesis images. These are (1) the limited distribution of spatial frequencies in and and (2) errors in the visibility measurements. The limited spatial frequency coverage can be improved by deconvolution processes such as CLEAN that allow the unmeasured visibility to take nonzero values within some general constraints on the image. Calibration can be improved by adaptive techniques in which the antenna gains, as well as the required image, are derived from the visibility data. Wide-field imaging, multifrequency imaging, and compressed sensing are also discussed.

This chapter is concerned with the techniques by which angular positions of radio sources can be measured with the greatest possible accuracy, and with the design of interferometers for optimum determination of source-position, baseline, and geodetic parameters.

The neutral gas in the atmosphere has a significant effect on signals passing through it.We are concernedwith three types of effects.

Three distinct ionized media, or plasmas, affect the propagation of radio signals passing through them: the Earth’s ionosphere; the interplanetary medium, also known as the solar wind; and the interstellar medium of our Galaxy. The effects of scattering in other galaxies or in the media between galaxies are not usually important. There are several essential differences between neutral and ionized media with regard to propagation. For neutral media, the index of refraction is greater than unity and is unaffected by magnetic fields. In ionized media, the index of refraction is less than unity and is strongly affected by magnetic fields. Most plasma phenomena scale as , and their effects can be avoided or mitigated, if desired, by observations at high frequency. Absorption plays an important role in neutral media but very little in ionized media since most radio astronomical observations occur at frequencies far above the plasma frequency. Descriptions of scattering phenomena in both types of media are based on Kolmogorov theory. However, the situation in the neutral troposphere is greatly simplified because the turbulent layer lies close to the observer, and only phase fluctuations develop. The ionized media lie far from the observer, and both phase and amplitude fluctuations are often present in the wavefront when it reaches the observer.

This chapter is concerned with the van Cittert–Zernike theorem, including an examination of the assumptions involved in its derivation, the requirement of spatial incoherence of a source, and the interferometer response to a coherent source. Some optical terminology is used, for example, , which includes complex visibility. There is also a brief discussion of some aspects of scattering by irregularities in the propagation medium. Much of the development of the theory of coherence and similar concepts of electromagnetic radiation is to be found in the literature of optics. The terminology is sometimes different from that which has evolved in radio interferometry, but many of the physical situations are similar or identical. However, in spite of the similarity, the literature shows that in the early development of radio astronomy, the optical experience was hardly ever mentioned, an exception being the reference by Bracewell () to Zernike () for the concept of the complex degree of coherence. The van Cittert–Zernike theorem contains a simple formalism that includes the basic principles of correlation in electromagnetic fields.

A basic requirement of radio astronomy is access to a spectrum in which observations can be made without detrimental interference from transmissions by other services. In the early years of radio astronomy, when most of the radio astronomy bands below a few GHz were allocated, bandwidths of radio astronomy systems were generally no greater than a few MHz, and the comparable allocated bandwidths largely sufficed. Some allocations were made for radio lines, most importantly the hydrogen (H1) line, for which 1420–1427 MHz was reserved. In the following decades, as radio astronomy at frequencies in the range of tens of GHz developed, bandwidths of order 1 GHz were allocated, and later, a substantial fraction of the spectrum above ∼ 100 GHz was allocated to radio astronomy. However, spillover of radiation from transmitting services into radio astronomy bands occurs, and generally it has been necessary to choose observatory sites in radio-quiet areas of low population density and to take advantage of terrain shielding where possible. These considerations have led to the choice of sites in South Africa and Western Australia for international development of several of the largest arrays. Also, with the increase in computing capacity at observatories, detection and removal of interfering signals in astronomical observations have become important parts of data analysis. In particular, digital analysis allows the received bandwidths to be divided into as many as 10 spectral channels, which allows those containing interference to be identified and removed. A general discussion of interference in radio astronomy is given by Baan ().

Concepts and techniques similar to those used in radio interferometry and synthesis imaging occur in various areas of astronomy, Earth remote sensing, and space science. Here we introduce a few of them, including optical techniques, to leave the reader with a broader view. All of these subjects are described in detail elsewhere, so here the aim is mainly to outline the principles involved and to make connections between them and the material developed in earlier chapters.