# INFORMATION TECHNOLOGIES

**CALCULATION OF THE INTRINSIC THERMAL RADIATION OF PLANE-PARALLEL QUASI-ANISOTROPIC MULTILAYER PLATES WITH SMOOTH BOUNDARIES**

Mikhail G. Evtikhov, Galina V. Arzamastseva
Kotelnikov Institute of Radioengineering and Electronics of RAS, Fryazino Branch, http://fire.relarn.ru/

1,Vvedensky area, Fryazino 141190, Moscow region, Russian Federation

E-mail: emg20022002@mail.ru, arzamastseva@mail.ru

*Received October 10, 2020; peer reviewed October 19, 2020; accepted October 26, 2020*

**Abstract.** The physical meaning of new algorithms for calculating the intensity of a plane homogeneous monochromatic wave of electromagnetic radiation after passing through a multilayer quasi-anisotropic plane-parallel plate is discussed, taking into account the thermal radiation of the layers. The formula connecting the brightness temperature obtained by a microwave radiometer and the effective temperature of the observed surface is used in remote sensing of the earth's surface [16].In this paper, we develop a mathematical apparatus that allows one to construct algorithms that generalize this formula to an arbitrary number of homogeneous quasi-anisotropic layers of a plane-parallel plate. The solution of the problem is complicated by the need to take into account coherent and incoherent effects in a multilayer plate, as well as by the need to construct an adequate method for identifying the waves and energy fluxes under consideration, by the need to clarify the concept of an ideal radiometer that records the observed microwave radiation. In order to test new algorithms and obtain the first results, the facts obtained earlier [19] by calculating the reflection and transmission coefficients for free ice sheets are reproduced using new algorithms for calculating intensities. For an isotropic ice plate 50 cm thick in the L-range, there is a "transparency window" in the area of observation angles of 30 degrees for both polarizations simultaneously. The influence of ice anisotropy on the effects of bleaching and anti-bleaching and related to the Brewster angle is considered. Additionally, the contribution of the ice's own radiation to the observed brightness temperature was estimated by new methods. The case of an anisotropic ice plate with the same parameters but floating in water is considered. It is shown that a change in the conditions of reflection at the ice-substrate interface can be partially compensated by a change in the ice thickness. To control and evaluate the theoretically possible accumulation of errors in calculations, physical quantities are discussed that are analogous to the components of the Poyting vector and remain constant at the boundaries of the layers. For the considered cases of ice, these values are conserved with high accuracy.

*Keywords*: remote sensing, microwave, anisotropy, fresnel equations, multi-layer interference, transparency, translucency, ice, water, brightness temperature

UDC 0535.391.4, 53.082.53, 53.083.2

*RENSIT*, 2020, 12(3):379-398.

**DOI: 10.17725/rensit.2020.12.379. **

*Full-text electronic version of this article - web site http://en.rensit.ru/vypuski/article/348/12(3)379-398e.pdf*