We turn now to the task of describing the variance of amplitude and intensity fluctuations. We avoided this problem in Volume 1 and it is important to recall why we did so. That development was based entirely on solutions for Maxwell's equations generated by the geometrical-optics approximation. The electromagnetic wavelength is completely absent from the eikonal and transport equations that define those solutions. On the other hand, astronomical observations and terrestrial experiments show that the level of scintillation does depend on wavelength. The fundamental problem is that geometrical optics completely ignores diffraction. Yet we know that amplitude fluctuations are caused primarily by small atmospheric irregularities. Diffraction by these small eddies is the principal cause of the amplitude fluctuations that characterize atmospheric scintillation.

Our task in this chapter is to estimate the level of scintillation for optical and microwave propagation. To do so we will depend on the Rytov approximation developed in Chapter 2 that includes diffraction in a rigorous way. It is limited to weak-scattering situations but that covers a broad range of applications. The Rytov approximation gives a complete description for terrestrial microwave links and can often describe millimeter-wave propagation. The same approach characterizes the scintillation experienced by optical and infrared signals that travel near the surface on relatively short paths. By contrast, astronomical observations are characterized by weak scattering unless the source is close to the horizon.