The laws of geometrical optics were known from experiments long before the electromagnetic theory of light was established [1]. Today we recognize that they constitute an approximate solution for Maxwell's field equations. This solution describes the propagation of light and radio waves in media that change gradually with position [2]. The wavelength is taken to be zero in this approximation and diffraction effects are completely ignored. The field is represented by signals that travel along ray paths connecting the transmitter and receiver. In most applications these rays can be approximated by straight lines. These trajectories are uniquely determined by the dielectric constant of the medium and by the antenna pattern of the transmitter. In this approach energy flows along these ray paths and the signal acts locally like a plane wave. Geometrical optics provides a convenient description for a wide class of propagation problems when certain conditions are met.

The assumption that the medium changes gradually means that geometrical optics cannot describe the scattering by objects of dimensions comparable to a wavelength. Similarly, it cannot describe the boundary region of the shadows cast by sharp edges. A further condition is that rays launched by the transmitter must not converge too sharply – as they do for focused beams. These conditions must be refined when ray theory is used to describe propagation in random media.

Geometrical optics is widely used to describe electromagnetic propagation in the nominal atmosphere of the earth, other planets and the interstellar medium.

Degradation of stellar images is the most familiar example of propagation through random media and is visible to the naked eye. When a star is viewed through a telescope this degradation manifests itself in three ways: (a) as a variation of the image intensity, (b) as image broadening and (c) as wandering of the centroid of the image. This chapter is devoted to the third effect, which has also been called quivering, dancing and jitter. Image wandering is influenced primarily by large irregularities in the lower atmosphere for which ray theory is a good description. Image motion and angle-of-arrival fluctuations are different manifestations of the same random ray bending by atmospheric irregularities.

Image motion is readily observed in photographic plates placed at the focal plane of a stationary telescope. If there were no atmosphere, the stellar source would trace a smooth star trail on the plate as the earth and telescope turn together. Actual star trails exhibit random angular fluctuations about this nominal trajectory of 1 or 2 arc seconds as indicated in Figure 7.1. This random motion is observed in all astronomical measurements, although the magnitude varies with time, altitude and location. The error ranges from 0.5 to 2.0 arc seconds at sea level. It decreases with altitude and is usually 0.5 arc seconds on Mauna Kea (14 000 ft) but is sometimes as small as 0.25 arc seconds. Geometrical optics provides a valid description for astronomical quivering over a wide range of applications [1][2][3][4].