Remote sensing of layered random media using the radiative transfer theory

Abstract

[1] The radiative transfer (RT) approach is widely used in remote sensing applications. Although this approach involves approximations, they are often not explicitly stated or explained. The RT approach for random media with nonscattering boundaries has been well studied, and the underlying assumptions are clearly documented. In contrast, our problem has scattering boundaries which are randomly rough. In order to better understand the RT approach to our problem, we adopt a statistical wave approach for modeling multiple scattering in the combined problem of random media and rough surfaces. The geometry of our problem consists of a multilayer discrete random medium with rough boundaries which are planar on the average. The statistical characteristics of the random medium in each layer are independent of each other and independent of the statistics describing the rough interfaces. Using the Green's functions of the problem without the volumetric fluctuations, we represent our problem as a system of integral equations. Employing the T-matrix description, we first average with respect to volumetric fluctuations to obtain a system of integral equations. We next average with respect to surface fluctuations, apply the weak surface correlation approximation, and arrive at a closed system of integral equations for the first and second moments of the electric fields. We use the Wigner transforms to relate the coherence functions to radiant intensities. On applying the quasi-uniform field approximation, we hence arrive at a system of equations identical to those used in the RT approach. In this process, we find that there are more conditions involved in the RT approach to our problem than widely believed to be sufficient. The important additional conditions are the following: (a) the thickness of layers are larger than the mean free path of the layer medium, and (b) the character of interface roughness is such that weak surface correlation approximation is applicable.Citation: Mudaliar, S. (2013), Remote sensing of layered random media using the radiative transfer theory, Radio Sci., 48,[535][536][537][538][539][540][541][542][543][544][545][546]

An overview of methods for deriving the radiative transfer theory from the Maxwell equations. III: Effects of random rough boundaries and packing density

“…Following Ref. [16] as a template, we summarize below the assumptions under which the radiative transfer equation (159) has been derived.…”

“…, we exclude all cross terms. In fact, taking into account that between two scattering events on the rough surface the wave interacts with the particles, we assume that the scattering events on the rough surface are uncorrelated [14,16] . Thus, using (cf.…”

“…A similar approach based on surface scattering operators and Wigner transform was used by Mudaliar [16] . However, in this case, (i) the starting point is the Bethe-Salpeter equation for the dyadic correlation function E (r ) E (r ) V S , (ii) the effective wavenumber and the intensity operator are computed in the framework of the effective field approximation, and (iii) the radiative transfer equation is formulated for the Wigner transform of E (r ) E (r ) V S .…”

“…According to this approximation, the coherent field in a discrete random medium behaves as a wave in a homogeneous medium with an effective propagation constant. In this paper, we revisit the approach used by Mudaliar [16] for analyzing radiative transfer in a layer of discrete random medium with rough boundaries and a sparse concentration of particles. Our goal is to clarify the underlying assumptions and to discuss the meaning of the effective field approximation.…”

Field correlations for off‐axis Gaussian laser beams in atmospheric turbulence

“…The results obtained in these studies indicate that the incident field profiles can appreciably change the characteristics of the received beams when they propagate in the turbulent atmosphere. The second order results also play an important role in modeling of the atmosphere [Moraes et al, 2014] and in remote sensing of layered random media [Mudaliar, 2013].…”