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].

Geometrical optics provides an accurate description of electromagnetic phase fluctuations under a wide range of conditions. The phase variance computed in this way is a benchmark parameter for describing propagation in random media. One can calculate this quantity for most situations of practical interest. We shall find that it is proportional to the first moment of the spectrum of irregularities and is therefore sensitive to the small-wavenumber portion of the spectrum. This is the region where energy is fed into the turbulent cascade process. We have no universal physical model for the spectrum in this wavenumber range and phase measurements provide an important way of exploring that region.

In analyzing these situations, we must recognize the anisotropic nature of irregularities in the troposphere and ionosphere. Large structures are highly elongated in both regions and exert a strong influence on phase. These measurements are also sensitive to trends in the data that are caused by nonstationary processes in the atmosphere. Sample length, filtering and other data-processing procedures thus have an important influence on the measured quantities. By contrast, aperture smoothing has a negligible effect.

Single-path phase measurements have been made primarily at microwave frequencies because phase-stable transmitters and receivers were available in these bands. Early experiments were performed on horizontal paths using signals in the frequency range 1–10 GHz. At least one experiment has measured the single-path phase variance at optical wavelengths. Phase-stable signals from navigation satellites and other spacecraft are beginning to provide information about the upper atmosphere.

The first step in studying electromagnetic scintillation is to establish a firm physical foundation. This chapter attempts to do so for the entire work and it will not be repeated in subsequent volumes. We proceed cautiously because the issues are complex and the measured effects are often quite subtle. Section 2.1 explores the way in which Maxwell's equations for the electromagnetic field are modified when the dielectric constant experiences small changes. Because atmospheric fluctuations are much slower than the electromagnetic frequencies employed, their influence can be condensed into a single relationship: the wave equation for random media. This equation is the starting point for all developments in this field.

To proceed further one must characterize the dielectric fluctuations. We want to do so in ways that accurately reflect atmospheric conditions. Because we are dealing with a random medium, we must use statistical methods to describe them and their influence on electromagnetic signals. For instance, we want to know how dielectric fluctuations measured at a single point vary with time. Even more important, we need to describe the way in which fluctuations at separated points in the medium are correlated. There are several ways to do so and they are developed in Section 2.2. These descriptions assume that the random medium is isotropic and homogeneous. Those convenient assumptions are seldom realized in nature and we show how to remove them at the end of this section. Turbulence theory now gives an important but incomplete physical description of these fluctuations.

History

Quivering of stellar images can be observed with the naked eye and was noted by ancient peoples. Aristotle tried but failed to explain it. A related phenomenon noted by early civilizations was the appearance of shadow bands on white walls just before solar eclipses. When telescopes were introduced, scintillation was observed for stars but not for large planets. Newton correctly identified these effects with atmospheric phenomena and recommended that observatories be located on the highest mountains practicable. Despite these occasional observations, the problem did not receive serious attention until modern times.

How it began

Electromagnetic scintillation emerged as an important branch of applied physics after the Second World War. This interest developed in response to the needs of astronomy, communication systems, military applications and atmospheric forecasting. The last fifty years have witnessed a growing and widespread interest in this field, with considerable resources being made available for measurement programs and theoretical research.

Radio signals coming from distant galaxies were detected as this era began, thereby creating the new field of radio astronomy. Microwave receivers developed by the military radar program were used with large apertures to detect these faint signals. Their amplitude varied randomly with time and it was initially suggested that the galactic sources themselves might be changing. Comparison of signals measured at widely separated receivers showed that the scintillation was uncorrelated, indicating that the random modulation was imposed by ionized layers high in the earth's atmosphere.