1.1 Introduction

We can define a radio antenna as an instrument which collects, and detects, electromagnetic radiation from a certain area and direction of the sky, allowing to build up an image from individual observations. In radio astronomy we are interested in the detection and analysis of radiation emitted from celestial objects, i.e. solar system bodies, stars, interstellar gas, galaxies, and the universe. The electromagnetic radiation observed in radio astronomy covers the wavelength range from several meters, say 10m (= 30MHz), to a fraction of a millimeter, say 0.3mm ( $\approx 1000$GHz). Since the antenna must be many wavelengths in diameter in order to collect a large amount of energy and to provide a reasonable directivity (angular resolution), it is evident that antennas for meter wavelengths may have dimensions of many 10 meters to several 100 meters, while antennas for millimeter wavelengths have dimensions of several meters to several 10 meters ($\approx$ 10000 to 50000 $\lambda$'s). The technique of mechanical contruction is therefore different for meter and millimeter wavelength antennas: antennas for m-wavelengths can be constructed, for instance, as mesh-wire networks and plate arrays, mm-wavelength antennas are full-aperture solid surface parabolic reflector antennas. Typical examples are the obsolete Mills-Cross antenna, the Effelsberg and GBT 100-m antennas, and the IRAM 30-m (Pico Veleta) and 15-m (Plateau de Bure) antennas. However, despite the variety of mechanical constructions, all antennas can be understood from basic principles of eletromagnetic radiation, optics, and diffraction.

Here we discuss full-aperture parabolic antennas, like the IRAM antennas, which are used for observations at $\sim$ 3 - 0.8mm wavelength (100 - 350GHz). These antennas are very similar to optical reflector telescopes and use in particular the Cassegrain configuration of a parabolic main reflector and a hyperbolic subreflector (Figure 1.3), with an image formed at the secondary focus near the vertex of the main reflector where the receiver, or a receiver-array, is installed. These antennas are steerable and can observe in any direction of the visible hemisphere, with the facility of tracking, scanning, and mapping of a source.

The collected radiation is concentrated in the secondary focus and is (coherently) detected by a receiver at a certain frequency $\nu$ (or wavelength $\lambda$) and within a certain bandwidth $\Delta\nu$ (or $\Delta\lambda$). Heterodyne mm-wavelength receivers, which preserve the phase of the incident radiation, have small bandwidths of the order of $\Delta\nu = 0.5 - 2$ GHz so that $\Delta\nu/\nu = \Delta\lambda/\lambda \approx 0.5$GHz/100GHz $\approx$ 1/200. From the point of view of antenna optics, these receivers detect ``monochromatic'' radiation, and the antenna characteristics can be calculated for a monochromatic wave (as will be done below). Bolometer receivers, on the other hand, detect power in a broad bandwidth of the order of $\Delta\nu \approx 50$GHz so that $\Delta \nu = 50$GHz/250GHz $\approx 1/5$. These detectors are no longer monochromatic, and the chromatism of the antenna must be considered in their application.

The construction and operation of a radio antenna is based on exact physical theories, like Maxwell's theory of electromagnetic radiation, the pointing theory of an astronomical instrument, the transformation (mixing, down-conversion, amplification) and detection of electromagnetic radiation, etc. The theory of a radio antenna presented here is, however, only the very tip of an iceberg (of several 100000 published pages), but may provide sufficient information for the user astronomer to understand the basic principle of a telescope, either a perfect one, which nobody has but which can be described with high precision, or a real one, with small defects and aberrations, which can be described with sufficient detail to apply corrections.

The theory, construction, and use of radio antennas is contained in many textbooks and journals such as IEEE Transactions Antennas and Propagation, Radio Science, Applied Optics. A biased selection is mentioned here: [Born and Wolf 1975] [Reynolds et al, 1989] [Love 1978] [Lo and Lee] [Kraus 1982] [Goldsmith 1988]