Mathematical Model of Diffuse Reflection Light of Materials Used In Agriculture

Abstract

There has been developed and obtained theoretical dependence of the diffuse reflection coefficient $\rho$ from the angle of incidence of the light beam $\alpha$. To test the adequacy of the mathematical model there has been developed a computer programme admitting realization of the diffuse reflection of the light thus based on the Monte Carlo method. The results of computer calculations of the diffuse reflection coefficient, with an error not exceeding 0.03%, are consistent with the proposed theoretical dependence $\rho(\alpha)$. With the values of the angle $\alpha$ in the range 0°-12°, values of the diffuse reflection coefficient are designated within the range 0$.395\lt\rho\lt0.405$. The area of consistency for a mathematical model and experimental results is specified. The region of the spectrum where reference values of the reflection coefficient of materials and objects are consistent with the value of 0.4 is principally in the visible part. The area of agreement in the ultraviolet part of the spectrum has been determined by the measurement results made in the Institute of Atmospheric Optics after V. E. Zuev SB RAS, at $\alpha=8^{\circ}$. Conducted researches had been followed by the conclusions formulated as follows: the obtained function $\rho(\alpha)$ admits to theoretically estimate the diffuse reflection coefficient for the acknowledged angle of incidence of the beam light; and the developed computer program allows to calculate the diffuse reflection coefficient due to averaging at random directions of the reflected beam; values of the theoretical and of the calculated diffuse reflection coefficient are well consistent at small light angles with the experimental values $\rho=0.4$ for the materials used in the agriculture.