[Paper Review] Electromagnetic wave scattering from a random layer with rough interfaces II: Diffusive intensity

Antoine Soubret, Gérard Berginc|ArXiv.org|Dec 22, 2003

Atmospheric aerosols and clouds57 references4 citations

TL;DR

This paper develops a rigorous Green's function-based formalism to derive the vectorial radiative transfer equation for electromagnetic waves scattered by a random medium with rough boundaries, incorporating boundary scattering operators and enhanced backscattering effects. The approach unifies wave and radiative transfer theories by deriving the incoherent intensity from Maxwell's equations, with boundary conditions explicitly expressed via scattering operators and polarization-dependent transmission coefficients recovered via reciprocity and normalization factors.

ABSTRACT

A general approach for the calculation of the incoherent intensity scattered by a random medium with rough boundaries has been developed using a Green function formalism. The random medium consists of spherical particles whose physical repartition is described by a pair-distribution function. The boundary contribution is included in the Green functions with the help of scattering operators which can represent any existing theory of scattering by rough surfaces. By using a standard procedure, we derive the integral Bethe-Salpeter equation under the ladder approximation and, by differentiation, the vectorial radiative transfer equation. Furthermore, with the help of our formalism, the boundary conditions necessary to solve the radiative transfer equation are expressed in terms of the scattering operators of the rough surfaces. Finally, using the reciprocity properties of the Green functions, we are able to include the enhanced backscattering contributions to take into account every state of polarization of the incident and the scattered waves.

Motivation & Objective

• To establish a rigorous link between electromagnetic wave theory and radiative transfer by deriving the incoherent intensity from Maxwell's equations.
• To incorporate rough boundary effects into the radiative transfer equation using scattering operators that generalize existing surface scattering theories.
• To ensure consistency with phenomenological radiative transfer by recovering standard transmission coefficients through normalization factors.
• To include enhanced backscattering and polarization-dependent effects via reciprocity of Green's functions.
• To provide a unified formalism that connects the Wigner function of the electric field to the specific intensity in radiative transfer.

Proposed method

• Uses a Green's function formalism with two types: one for volume scattering and one for rough boundaries, both incorporating scattering operators.
• Applies the Wigner transform to the integral equation derived from Maxwell's equations to obtain the radiative transfer equation.
• Derives the vectorial radiative transfer equation under the ladder approximation by differentiating the Bethe-Salpeter equation.
• Expresses boundary conditions in terms of scattering operators, enabling generalization to arbitrary rough surface models.
• Introduces normalization factors (e.g., √(ε₀/ε′ₑ)) to recover standard transmission coefficients in the limit of plane boundaries.
• Utilizes reciprocity of Green's functions to include enhanced backscattering and full polarization state dependence.

Experimental results

Research questions

• RQ1 How can the incoherent intensity scattered by a random medium with rough boundaries be rigorously derived from Maxwell's equations?
• RQ2 What is the role of boundary scattering operators in defining the boundary conditions for the radiative transfer equation?
• RQ3 How can enhanced backscattering and polarization effects be consistently included in a wave-theoretic derivation of radiative transfer?
• RQ4 How do normalization factors in the scattering operators ensure consistency with classical radiometric transmission coefficients?
• RQ5 In what way does the Wigner function formalism bridge electromagnetic field theory and radiative transfer theory?

Key findings

• The vectorial radiative transfer equation is derived from first principles using the Green's function and Wigner transform formalism, ensuring consistency with wave theory.
• Boundary conditions for the radiative transfer equation are expressed directly in terms of scattering operators, enabling application to arbitrary rough surface models.
• The formalism recovers standard transmission coefficients for plane boundaries when the scattering operators reduce to Fresnel coefficients, validated by normalization factors.
• Enhanced backscattering is naturally included through the reciprocity properties of the Green's functions, accounting for all polarization states.
• The incoherent intensity is shown to be expressible as a Wigner function of the electric field, with the specific intensity identified in the geometrical limit.
• The approach unifies wave and radiative transfer theories, resolving inconsistencies in the electromagnetic definition of intensity by accounting for interference and coherence effects.