A monostatic illumination function with surface reflections from one-dimensional rough surfaces

When solving scattering or emissivity problems for rough surfaces, the shadowing effect is often taken into account. Furthermore, for rough surfaces with large root mean square slope, surface reflections of the incidence or emission ray should not be neglected, especially at large observation angles. In this paper, a model of the monostatic statistical illumination function for one-dimensional rough surfaces with single surface reflection is developed, which is based on the Smith illumination function. A Monte Carlo ray-tracing algorithm is used to evaluate the accuracy of the present model. It is shown that, when neglecting the correlation between heights and slopes of the surface, the present model agrees quite well with the Monte Carlo result. Moreover, the result is improved if the correlation between heights and slopes is taken into account. For practical purposes, an empirical factor is introduced to improve the performance of the uncorrelated first-order illumination function to avoid computing the correlated one, which takes a long computation time. Besides, the first-order illumination function is significant at large observation angles, which could be promising to overcome problems in models of surface infrared emissivity where underestimation occurs compared with experimental measurements.