ANALYTICAL CALCULATION OF THE LAMBERTIAN PART OF THE SPECTRUM OF OPTICAL RADIATION REFLECTED FROM A SEMIINFINITE DISORDERED MEDIUM

In this paper, we propose a new approach to the calculation of spectra of backscattered optical radiation in the case when a plane scatterer is irradiated with a broad light beam. The proposed approach is based on the Ambartsumyan equation for the reflection function (RF), which provides a detailed description of the angular spectrum of reflected r adiation for arbitrary angles of incidence and reflection and arbitrar y optical characteristics of the medium. Using the principle of partia l fluxes developed earlier, we separate the fraction of photons in the RF that emerge from a medium, having changed the sign of their veloci ty projection on the normal to the surface of the medium only once (th e first partial RF). These photons are responsible for the anisotropy in the spectrum of reflected radiation for an arbitrary relation betwe en the wavelength of the light beam and characteristic sizes of scatte ring centers. The intensity of the remaining reflected radiation flux, which consists of photons that change the sign of their velocity proj ection three and more times before they emerge from a medium, is a muc h smoother function of angular variables, which Follows the Lambertian law with high accuracy. In this paper, we develop and implement a reg ular method for the calculation of the Lambertian part of reflected ra diation that can be applied for an arbitrary law of single scattering of photons from chaotically distributed scattering centers in a medium . We provide a comprehensive analysis of isotropic scattering and deri ve a simple expression Ear the Lambertian part of reflected radiation in this case. The results of our calculation are compared with predict ions of Ambartsumyan-Chandrasekhar theory.