Matrix expression of thermal radiative characteristics for an open complex

Abstract

The directionality of thermal radiance of a homogeneous isothermal non-black plane surface is totally decided by its directional emissivity, which depends on the complex dielectric constant and roughness of surface. It can be expressed by $\bar L_\lambda (\theta _k ,T) = \bar \varepsilon _\lambda (\theta _\lambda )L_{b\lambda } (T)$. This paper proves that it is necessary to express emissivity by a matrix when a target becomes an inhomogeneous non-isothermal open complex with complicated inner geometric structure. The matrix describes the inner radiative interaction among components accurately and also expresses its thermal radiative directionality and structural characteristics completely. Advantages of matrix expression are as follows: first, the physical mechanics of effective emissivity of an open complex is described in a simple and perfect way; second, it becomes easy to understand the principle and method to retrieve components temperature from multi-angle thermal remotely sensed data; and third, the differences of directionalities between an open complex and a homogeneous isothermal non-black plane body are expressed by just using an effective emissivity matrix instead of an emissivity vector. Formula $\bar L_\lambda (\theta _k ,T) = \varepsilon _\lambda (\theta _\lambda )L_{b\lambda } (T)$ in classic physics is only the special case of matrix expression; therefore, the matrix is a universal unconditional expression to describe the directionality of thermal radiance.