Scattering of a narrow optical beam by a randomly rough, locally Lambert surface in a scattering medium

Abstract

We consider scattering of a narrow optical beam in a scattering medium by a randomly rough surface with Lambert indicatrix of local scattering. Expression for the average power of a signal recorded by the receiver is found for the Gaussian distribution of heights and rough-surface tilts. The obtained formala makes it possible to correctly describe the received-signal power both in a transparent and optically dense atmosphere. It is shown that in the bistatic sounding scheme, the received-signal power significantly depends on the surface heights variance.The power of a signal recorded by the receiver during scattering of a narrow optical beam by a randomly rough surface with Lambert indicatrix of local scattering has been studied in many papers (see, e.g., [1][2][3][4][5]).However, all published papers considered only the case of a transparent atmosphere where the multiple scattering effects in the medium do not distort the structure of the optical beam (on both the source-surface and surface-receiver paths). In what follows, using the general scheme of bistatic sounding, where the source and receiver are separated in space, we study the power of a scattered signal, recorded by the receiver, in the case where a randomly rough, locally Lambert surface is irradiated by a narrow optical beam in a scattering medium for which the multiple scattering effects can be significant. The bistatic scheme is characteristic of semi-active sounding systems (e.g., guidance systems) in which the source and receiver are located in different devices (see, e.g., [6]).Let a rough surface S be irradiated by a narrow laser beam (see Fig. 1). The shadings of one surface element by another will be neglected. Then, in the case of continuous irradiation of the surface, using the reciprocity theorem for the Green's function in a scattering [7] and introducing the notion of a "reciprocal source," i.e., "virtual source with the receiver parameters" [8-10], we obtain an integral expression for the power P of a signal recorded by the receiver in the general case of bistatic sounding in a scattering medium. For this, we use the results given in [11] and the small-angle approximation for the source and receiver and assume for simplicity that the source, the receiver, and their optical axes lie in one plane xz (see Fig. 1). The result is [5]whereA is the reflection coefficient (albedo) of an elementary surface area, E s (R, z s ) and E r (R, z r ) are the illuminances on the surface S from the actual source and the virtual source with the receiver parameters,