The quantities used to describe incoming radiation are presented in this chapter. These quantities should describe the rate of energy flow (power), its variation with time, its variation with frequency of the electromagnetic wave, and the direction(s) from which it flows. Note that "frequency" can also refer to oscillations of intensity as seen in pulsars.

The most general description of the radiation would allow for every point on the sky to have an arbitrary brightness and polarization that varies arbitrarily in time at every frequency of the radiation. The real sky brightness is significantly simpler; the flux from many sources of radiation does not vary substantially in time, and many of the sources are point-like objects. Nevertheless the sky does exhibit a wide range of objects, from point-like stars to diffuse or extended nebulae (e.g., H II regions, supernova remnants, and galaxies), and finally variable-intensity objects (e.g., variable stars, pulsars, supernovae, gamma and x-ray bursts, and quasars).

It is convenient to divide celestial sources into two major groups, point-like and diffuse. A celestial object at a great distance from the earth can be consideredpoint-like if its angular size measured from the earth is much less than the beam width or angular resolution of the antenna or telescope in question. Point-like sources are often called unresolved objects because the telescope can not resolve their small angular sizes. If the source is comparable to, or larger than, the beam in angular extent, the telescope can detect the finite size. In this case, the object is called a diffuse or resolved source.

The beam width (Ch. 5) is due to the intrinsic parameters of the telescope/detector system such as diffraction and also, in the case of optical light, the earth's atmosphere. An optical object of angular size much less than 1" may be considered to be point-like for ordinary (non-interferometric) observations with ground-based optical telescopes because of the atmosphere. A sun-like star of size ~109 m at the relatively close distance of 1017 m (10 LY) subtends an angle of only 10-8 radians, or 0.002", and easily qualifies as a point-like object for ground-based observers. The human eye has a resolving power of only about 1'; anything smaller in angular size appears as a point-like object even though it might appear quite large in angular size when viewed through binoculars or a telescope.

In this chapter, we present quantities used for the measurement of point sources, including the spectral flux density S (W m-2 Hz-1) and the astronomical unit of (logarithmic) flux density called the magnitude. We then address diffuse sources and introduce the quantity that gives their brightness per unit solid angle on the sky (e.g., per steradian or per square arcsecond), namely the specific intensity I (W m-2 Hz-1 sr-1). This latter quantity is amazing. It is independent of the distance to the source and, remarkably, is equal to the intensity emitted from the surface of the celestial object, the brightness B (W m-2 Hz-1 sr-1).

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