On the solution of the diffuse reflection problem from a semi-infinite medium by the method of decomposition of the resulting field (DRF) of radiation

**Authors:** H. V. Pikichyan **Affiliations:** NAS RA V. Ambartsumian Byurakan Astrophysical Observatory (BAO) Byurakan 0213, Aragatzotn Province, Armenia With the help of the author's recently developed method, the classical diffuse reflection problem (DRP) of radiation from a scattering-absorbing semi-infinite medium in the case of isotropic scattering under the general redistribution law r(x,x^' ) of radiation by frequencies is solved. The proposed method decomposition of the resulting field (DRF) compares favorably with the traditionally used method of decomposition of a single act (DSA) in that in order to obtain a solution of the DRP, there is no need for preliminary decomposition of the characteristic of the single scattering act - the general law of radiation redistribution by frequencies, and the resulting field of multiply scattered radiation is sought directly in the decomposed form. As a result, the solution of the DRF, which depends on four independent variables, is expressed in terms of two auxiliary functions of one variable. Explicit analytical expressions of the two-way relationship between the desired functions of the traditional and the methods proposed by the author are also obtained.