The Theory of Scintillation with Applications in Remote Sensing was published in 2011. This website was established as a forum for discussing the book and its applications, anticipating new insights and refinements of computational procedures. The book has served its original purpose well. However, computational resources have improved considerably, and the implied completeness of the theory needs elaboration.
Developing a theory of scintillation starts with Maxwell’s equations, which characterize the interaction of electromagnetic (EM) fields with material media. In free space Maxwell’s equations can be reduced to a single vector equation that predicts the propagation of EM waves at the speed of light. In a transparent homogeneous medium Maxwell’s equations predict propagating vector waves comprised of two orthogonal circularly polarized characteristic modes.
Exploiting the predictions of Maxwell’s equations started with Marconi’s demonstration of long-range communication with transmissions in the kilohertz (HF) range. Unknown to Marconi, the fields he was detecting were refracted by the earth’s ionosphere, which is an inhomogeneous propagation medium. Manipulating Maxwell’s equations to characterize propagation in an inhomogeneous medium remains a challenging task to this day.
The textbook Waves and Fields in Inhomogeneous Media treats a class of media comprised of homogeneous subregions isolated by discontinuous boundaries. A region defined by a closed boundary is formally a scatterer. Scattering theory treats the interaction of EM waves with collections of scatterers. Boundary integral equations reconcile fields intercepting each scatterer. The complexity of the problem is manifested by the fact that every scatterer potentially interacts with every other scatterer. Discretizing the interactions leads to solving a very large system of coupled linear equations.
Scintillation theory addresses one of the most challenging applications of Maxwell’s equations, namely propagation in a transparent inhomogeneous medium. Forward propagation assumes that in a plane slicing the medium a two-dimensional spatial Fourier decomposition can isolate a set of propagating plane waves constrained to the forward hemisphere, which excludes the source field. No additional constraint is imposed on the propagation directions of the propagating waves. The forward propagation equation (FPE) developed in Chapter 2 of The Theory of Scintillation… is based on a forward propagation equation (FPE). The parabolic wave equation (PWE) is structurally similar to the FPE. However, the square root propagation operator is replaced by a quadratic approximation, which constrains the angular extent and introduces the Fresnel scale. Free-space PWE propagation is unchanged if the propagation distance and the frequency are varied while keeping the Fresnel scale constant.
The fact that the FPE imposes no constraint on the range of propagation angles suggested that it was more general than the PWE. However, when the FPE was applied to the HF propagation of a beam systematic differences between the trajectory of a refracted narrow beam and ray-theory predictions were found. The approximations made in developing the geometric ray equations are not constrained by propagation angles. Agreement with ray theory predictions is a necessary condition. Consequently, solutions to the FPE are no more accurate than their PWE counterparts.
The development in The Theory of Scintillation… is constrained to near line-of-sight propagation. As a general rule propagation calculations that separate free propagation and the media interaction, which allows efficient discrete Fourier transformation implementation are similarly constrained. Severe scintillation may develop but the angular extend of the propagating field cannot exceed more than a few degrees. A review with demonstrations of more accurate but computationally demanding FPE calculations are presented in Scintillation Theory Revisited.
