Laser Interaction with Heterogeneous Biological Tissue by Kirill Kulikov & Tatiana Koshlan

Author:Kirill Kulikov & Tatiana Koshlan
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

5.2 Scattering of a Plane Wave from the Rough Surface

The surfaces of real bodies (in particular, in biology) are not perfectly smooth to a certain extent. For this reason, reflection and refraction of the waves at these surfaces are accompanied by the effects which are not observed for smooth surfaces. Rigorous methods for solving the problem in the case of a rough surface do not exist. The problem can be solved only approximately under certain constraints imposed on the size and shape of roughness. For calculating the scattered field, the small-perturbation method and the Kirchhoff (tangential plane) method are used. In this work, we will use the Kirchhoff method for calculating the scattered field. To solve the formulated problem, we will use the Kirchhoff approximation. To apply the Kirchhoff method correctly, we make the assumption concerning the smoothness of inhomogeneities. At each point, the wave field can be represented as the sum of incident field () and reflected field ().

Let us write the expressions for the field scattered by a certain smooth rough surface in the Kirchhoff approximation. We select a certain region S of this surface, whose linear size is much larger than the mean size of the roughness, which in turn is much larger than the wavelength. We assume that there are no elements of the surface shadowed from the incident wave or scattered wave.

Let us suppose that a plane s- or p- monochromatic wave is incident on a rough surface; the unit wave amplitude has the form

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