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Chapter 15:
Propagation Through Random Phase Screens
Overview: The notion of a thin turbulent layer along a propagation path has been used for many years to model radio wave propagation through the ionosphere, scattering from a rough sea surface, or propagation of an optical wave between a satellite and the Earth's surface, among other settings. Such a turbulent layer is widely known as a phase screen, although this term generally refers to only a “very thin” turbulent layer. In this chapter we develop a general model for a layer of optical turbulence between a transmitter and receiver along a horizontal propagation path. If the layer is fairly thick,€ it is treated much like an extended medium. However, when the ratio of the turbulent layer thickness to the propagation distance from the turbulent layer to a receiver is sufficiently small, we classify the turbulent layer as a thin phase screen. Basically, this means that only the phase of the optical wave is disrupted as it passes through the turbulent layer - €”not it's amplitude. Consequently, it is not necessary to integrate over the thickness of the layer, thus simplifying some of the expressions for various statistical quantities concerning a laser beam propagating over a path in which only a thin phase screen exists. In our analysis we neglect the presence of extended optical turbulence and concentrate on the effects generated by the phase screen itself, taking into account the placement of the screen with respect to the transmitter and receiver. It is a straightforward extension of our model to embed the phase screen directly in an extended turbulence medium, although we don't do so here. Statistical quantities, like the mutual coherence function and scintillation index developed in Chaps. 6 and 8 for optical turbulence everywhere along the propagation path, are calculated here for the case of a single phase screen. In particular, we show how proper placement of the phase screen between the input and output planes can lead to essentially the same numerical results as that obtained from an extended turbulence model. In addition, we briefly treat the case of multiple thin phase screens that can be arbitrarily located along the propagation path. All results in this chapter, however, are limited to weak irradiance fluctuations for which the Rytov approximation is valid.
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